FORMATION DAMAGE BY ORGANIC DEPOSITION

C

H

A

P

T

E

R

14

FORMATION DAMAGE BY ORGANIC DEPOSITION

Summary Paraffins, asphaltenes, and resins are the primary sources of organic deposition in wells, pipelines, and reservoir formation during petroleum production. As a generic term, “wax” refers to deposits of paraffins, asphaltenes, and resins, mixed with some inorganic matter, such as clays, sand, and other debris. Organic deposition can occur both on the surfaces of well tubing and reservoir formation pores to reduce the flow efficiency and eventually to clog the flow paths completely. This chapter presents a review of the thermodynamic and physicochemical foundations of organic precipitation and scale formation as well as the governing phase behavior and rate equations. The criteria for precipitation are derived. The single-phase and multiphase formation damage models are modified to accommodate organic precipitation at below and above bubble point conditions. The outstanding models available for prediction of formation damage by organic deposition are reviewed. Applications are presented for the formation damage in petroleum reservoirs by organic deposition.

14.1 INTRODUCTION Organic scaling can be classified in two groups: (1) natural and (2) induced (Houchin and Hudson, 1986; Amaefule et al., 1988). Invasion of the near-wellbore formation by high pH filtrates, and injecting low surface tension fluids, such as light paraffins including pentane, hexane, 468

Formation Damage by Organic Deposition

469

diesel, gasoline, and naphta, and gas condensates into asphaltenic oil reservoirs can cause asphaltene precipitation (Amaefule et al., 1988). Asphaltenic/parafinic sludges can be formed with the spent acid at low pH conditions that can be created during acidizing (Amaefule et al., 1988). In contrast, paraffins deposit primarily by cooling. Generally, the organic deposits encountered along the production string and surface facilities contain larger proportions of paraffins, some asphaltenes and resins co-precipitated with the paraffins, some oil trapped within the deposits, and various inorganic substances, including clays, sand, and other materials (Khalil et al., 1997). The paraffin deposition primarily occurs by temperature decrease, whereas asphaltene and resin deposition occur because of a number of complicated phenomena, including the polydispersivity, steric colloid formation, aggregation, and electrokinetic deposition processes (Mansoori, 1997). Leontaritis et al. (1992) state, “Probable causes of asphaltene flocculation are: (1) Drop in the reservoir pressure below the pressure at which asphaltenes flocculate and begin to drop out; (2) Mixing of solvents, CH4  CO2 with reservoir oil during EOR.    After flocculation asphaltenes exhibit an intrinsic change, which is usually positive. As a result, they show a strong tendency to attach to negatively charged surface, such as clays and sand.” As soon as the wells in asphaltenic reservoirs begin to produce, the organic deposition begins within the upper section of the wells over which the pressure drops to below the asphaltene flocculation pressure, and then the organic deposition zone gradually progresses toward the bottomhole and eventually enters the near wellbore formation (Minssieux, 1997). Especially, the reservoir formations containing clays of large specific surfaces, such as Kaolinite, can initially adsorb and retain the polar asphaltenes and resins rapidly (Minssieux, 1997). As a result, multilayer molecular deposits are formed over the pore surface (Acevedo et al., 1995). However, as the asphaltene precipitates suspended in the oil phase combine and form sufficiently large aggregates, these particles cannot pass through and are captured at the pore throats (Minssieux, 1997). The pore throat plugging causes the severest permeability loss because the gates connecting the pores are closed and/or an in situ cake is formed by pore filling if the plugged pore throat still allows some flow through the jammed particles. Simultaneously, the flow is diverted toward larger flow paths (Wojtanowicz et al., 1987, 1988; Civan, 1995a; Chang and Civan, 1997; Minssieux, 1997). “Organic deposits usually seal the flow constrictions because they are sticky and deformable. Therefore, the

470

Formation Damage by Organic Deposition

conductivityof a flow path may diminish without filling the pore space completely” (Civan, 1994a, 1995a). Leontaritis (1998) stresses that the organic damage in oil reservoirs is primarily caused by asphaltene deposition and the region of asphaltene deposition may actually extend over large distances from the wellbore, especially during miscible recovery. Wang and Civan (2005a,b,c) have confirmed that asphaltene deposition is not only limited to the near-wellbore region, but it can occur throughout the reservoir formation, whereas the wax deposition is rather limited to a short distance (less than 1 feet) from the wellbore, because wax deposition in the near wellbore region usually occurs by the cooling of the oil caused either by high perforation pressure losses during oil production or by invasion and cooling of the hot oil saturated with the wax dissolved from the well walls as a result of the overbalanced, hot oiling treatments of the wells. The decline of productivity of wells in asphaltenic reservoirs is usually attributed to the reduction of the effective mobility of oil by various factors (Amaefule et al., 1988; Leontaritis et al., 1992; Leontaritis, 1998). The effective mobility of oil is a convenient measure of oil flow capability because it combines the three relevant properties in one group as 0 =

Kkr0 0

(14-1)

where K is the permeability of the reservoir formation, and kr0 and 0 are the relative permeability and viscosity of the oil, respectively. Hence, Leontaritis (1998) states that the asphaltene-induced damage can be explained by three mechanisms. The first is the increase of the reservoir fluid viscosity by formation of a water-in-oil emulsion if the well is producing oil and water simultaneously. The oil viscosity may also increase by the increase of the asphaltene particle concentration in the near-wellbore region as the oil converges radially toward the wellbore. But, experimental measurements indicate that the viscosity increase by asphaltene flocculation is negligible. The second mechanism is the change of the wettability of the reservoir formation from water-wet to oil-wet by the adsorption of asphaltene over the pore surface in the reservoir formation. However, this phenomenon is less likely because, usually, the asphaltenic reservoir formations are already mixed-wet or oil-wet, due to the fact that asphaltenes have already been adsorbed over the pore surface during the long periods of geological times prior to opening the wells for production. The third and most probable mechanism is the impairment of

Formation Damage by Organic Deposition

471

the reservoir formation permeability by the plugging of the pore throats by asphaltene particles. The problems associated with organic deposition from the crude oil can be avoided or minimized by choosing operating conditions such that the reservoir oil follows a thermodynamic path outside the deposition envelope and, therefore, the deposition envelope concept can provide some guidance in this respect (Leontaritis et al., 1992). For example, Wang and Civan (2005a,b,c) accomplished this condition by an early water injection process. However, mathematical models implementing the deposition phase charts are also necessary in developing optimal strategies for optimal mitigation of the deposition problems during the exploitation of the petroleum reservoirs. In the following sections, the characteristics, adsorption and phase behavior, and deposition and formation damage modeling of organic precipitates are presented.

14.2 CHARACTERISTICS OF ASPHALTENIC OILS As indicated by Figure 14-1 by Philp et al. (1995), the boiling and melting points of hydrocarbons increase by the carbon number. Heavy crude oils contain large quantities of higher boiling components, which create problems during oil production (Speight, 1996). Speight and Long (1996) point out that chemical and physical alteration of oils may affect the dispersibility and compatibility of their higher molecular weight fractions and create various problems such as phase separation, precipitation, and sludge formation during the various phases of petroleum production, transportation, and processing. Speight (1996) classified the constituents of the crude oil into four hydrocarbon groups: (1) volatile saturates (paraffins) and aromatics, (2) nonvolatile saturates (waxes) and aromatics, (3) resins, and (4) asphaltenes. The determination of saturates, aromatics, resins, and asphaltenes present in oil is referred to as the “SARA analysis.” Speight (1996) explains that the nomenclature of the petroleum fractions, such as given in Figure 14-2, is based on the techniques of separation of the crude oil into its fractions. Figure 14-3 by Leontaritis (1997) describes the various steps and techniques involved in the analysis of the crude oil, including cryoscopic distillation (CD), solvent extraction (SE), gas chromatography (GC), high performance liquid chromatography (HPLC), and gel permeation chromatography (GPC). Table 14-1 by Srivastava and

472

Formation Damage by Organic Deposition

600 500

Temperature - °C

400 300 200 100 0 Boiling point –100

Melting point

–200 0

10

20

30 40 Carbon number

50

60

70

Figure 14-1. Effect of n-alkane carbon number on boiling and melting points (after Philp, R. P., Bishop, A. N., Del Rio, J.-C., and Allen, J., Cubitt, J. M., and England, W. A. (eds), Geological Society Special Publication, No. 86, pp. 71–85, ©1995; reprinted by permission of R. P. Philp and the Geological Society Publishing House).

Feedstock n-Heptane

Deasphaltened oil

Insoluble Benzene or Toluene

Silica or Alumina

Insolubles

Asphaltenes

Carbon disulfide or Pyridine

Carboids (insolubles)

3. BenzeneMethanol

Carbenes (solubles)

Resins (polars)

2. Benzene or 1. Heptane Toluene

Aromatics

Saturates

Figure 14-2. Classification of petroleum constituents based on laboratory fractionation (reprinted from Journal of Petroleum Science and Engineering, Vol. 22, Speight, J. G., “The Chemical and Physical Structure of Petroleum: Effects on Recovery Operations”, pp. 3–15, ©1999, with permission from Elsevier Science).

473

Formation Damage by Organic Deposition Live sample

Cryoscopic distillation C7+ fraction

C6– fraction

nC6 Aspaltene separation

nC6 Resins

nC6 Asphaltenes

Insoluble fraction nC6 Asphaltenes

GPC

Soluble fraction nC6 Maltenes

HPLC

GC, GPC

Heterocyclics

Aromatics

Paraffins-Wax

Heterocyclics

Aromatics

Paraffins-Wax

GC Analysis

Pure components

Pseudo-components

Figure 14-3. Steps of oil analysis and characterization for paraffin, aromatic, resin, and asphaltene (after Leontaritis, ©1997 SPE; reprinted by permission of the Society of Petroleum Engineers).

Huang (1997) presents data on the chemical and physical properties of typical oil samples taken from Weyburn wells. Leontaritis (1996)∗ described the heavy fractions of petroleum as the following: Asphaltenes These are highly condensed polyaromatic structures or molecules, containing heteroatoms (i.e., S, O, N) and metals (e.g., Va, Ni), that exist in petroleum in an aggregated state in the form of suspension and are surrounded and stabilized by resins (i.e., peptizing agents). They are known to carry an electrical charge, and thought to be polydisperse. Asphaltenes ∗

Reprinted from Leontaritis ©1996, p. 14, by courtesy of Marcel Dekker, Inc.

474

Formation Damage by Organic Deposition Table 14-1 Chemical and Physical Properties of Weyburn Dead-Oils∗ Oil W1a

Temperature 

C

Density kg/m3

15 20 59 61 63

8789 8759 8461

Pressure MPa

Density @59 Cd

0.1 3.54 6.99 10.44 17.33

8461 8492 8524 8580 8609

Oil W2b

Viscosity mPa•s

Oil W3c

Density kg/m3

Viscosity mPa•s

Density kg/m3

Viscosity mPa•s

8549 8424 – 8131 –

– 460 – 235 –

8692 8644 – – 8394

1176 940 – – 315

Viscosity @59 Cd

Density @61 Cd

Viscosity @61 Cd

Density @63 Cd

Viscosity @63 Cd

42 – – – –

8131 8164 8196 8229 8293

235 249 262 276 304

8394 8424 8452 8484 8547

315 326 337 349 371

– 128 42 – –

BS&W, vol%

01

0.2

0.5%

Molecular Weight, g/g-mol

230

203

215

Component

wt.%

wt.%

wt.%

Saturates Aromatics Resins Asphaltenes

48.5 33.5 13.2 4.8

55.3 31.1 9.6 4.0

48.4 33.5 13.2 4.9

a b c d ∗

Collected from Weyburn well 14-17-6-13 W2M. Collected from Weyburn well 3-11-7-13 W2M. Collected from Weyburn well Hz 12-18-6-13 W2M. Reservoir temperature for the oil samples. After Srivastava and Huang, ©1997 SPE; reprinted by permission of the Society of Petroleum Engineers.

are a solubility class; hence, they are not pure, identical molecules. Pentane and Heptane are the two most frequently used solvents for separating asphaltenes from crude oil. The prefix n-Pentane or n-Heptane in asphaltenes refers to the solvent used for their separation. The composition of n-Pentane asphaltenes is different from that of n-Heptane asphaltenes. Resins These are aromatic and polar molecules, also often containing heteroatoms and metals, that surround the asphaltene structures and are dissolved in the

Formation Damage by Organic Deposition

475

oil and help keep the asphaltenes in suspension. They are surface active and, at some thermodynamic states, form their own reversible micelles. They are polydisperse and have a range of polarity and aromaticity. Resins are considered to be precursors to asphaltenes. Paraffin Waxes These are primarily aliphatic hydrocarbons (both straight and branched chain) that change state from liquid to solid during conventional oil production and processing operations. In addition to aliphatics, field deposits usually contain aromatic, naphthenic, resin, and asphaltenic molecules as well. The combined mass is called wax. Paraffin waxes usually melt at about 110–160 F. Field waxes contain molecules that can have melting points in excess of 200 F. Asphalt This is the residual (nondistillable) fraction of crude oil that contains suspended asphaltenes, resins, and the heaviest aromatic and paraffinic components of oils. Although propane has been traditionally a very efficient and convenient solvent for separating asphalt from petroleum, the latest commercial processes use other more efficient solvents for asphalt separation.

Leontaritis (1997) describes that “Since waxes, asphaltenes, and most resins are solid in their pure form and the other oil molecules are in liquid form, the overall crude oil mixture is a liquid solution of waxes, asphaltenes, and resins in the remaining liquid oil.    In general, the waxes and resins are dissolved in the overall crude oil. Whereas the asphaltenes are mostly undissolved in colloidal state.” Andersen et al. (1997) state, “Petroleum asphaltenes are defined as the solids precipitating from a crude oil upon addition of an excess of a light hydrocarbon solvent, in general n-heptane or n-pentane.” Therefore, for practical purposes, the crude oil is considered in two parts. The first part consists of the high-boiling-point and polar asphaltic components. This fraction of the crude oil creates various deposition problems during the exploitation of petroleum reservoirs. The second part is the rest of the crude oil, referred to as the deasphaltened oil or the maltenes. This fraction of the crude oil acts as a solvent and maintains a suspension of the asphaltenes in oil as illustrated in Figure 14-4 by Leontaritis (1996). However, ordinarily, the asphaltenes do not actually disperse in the maltene unless some resins are also present in the crude oil. The resins help asphaltenes to disperse in oil as a suspension by means of the hydrogen-bonding process and the irreversible acid-base reactions of

476

Formation Damage by Organic Deposition

Liquid phase

Asphaltene phase

Figure 14-4. A proposed model for asphaltenic oils (after Leontaritis, ©1996; reprinted by courtesy of Marcel Dekker, Inc.).

the asphaltene and resin molecules (Speight, 1996; Chang and Fogler, 1994, 1996; Speight and Long, 1996). Therefore, Leontaritis et al. (1992) point out that: “An oil that contains asphaltenes will not necessarily cause asphaltene problems during recovery and processing.” Leontaritis et al. (1992) draw attention to the fact that the Boscan crude of Venezuela has not created any asphaltene problems, although it has a large fraction (over 17% by weight) of asphaltenes (Lichaa, 1977). Whereas, the HassiMessaoud oil of Algeria has created severe asphaltene problems, although it has only a small fraction (0.1% by weight) of asphaltenes (Haskett and Tartera, 1965). In fact, de Boer et al. (1995) have concluded that light to medium crudes containing small amounts of asphaltenes may create more asphaltene precipitation problems during primary production. Nghiem and Coombe (1997) explain: “Heavier crudes that contain a larger amount of

Formation Damage by Organic Deposition

477

asphaltene have very little asphaltene precipitation problems as they can dissolve more asphaltene.” Leontaritis et al. (1992) state that: “Asphaltene flocculation can be prevented by addition of resins and aromatics.” The investigations of Chang and Fogler (1994, 1996) using model chemicals for resins have verified this statement. Leontaritis (1996) describes that “   asphaltene particles or micelles aggregate or flocculate into larger aggregates or flocs.    Asphaltene flocculation can be both reversible and irreversible.    Paraffin waxes, on the other the hand,    exhibit the phenomenon of crystallization.    Wax crystallization is generally a reversible process. However, paraffin waxes more than often precipitate together with resins and asphaltenes (which are said to be responsible for the observed irreversible thermodynamic phenomena). Hence, some wax precipitation is occasionally reported as irreversible.” Leontaritis (1996) points out that temperature and composition have a large effect and pressure has a small effect on the solubility of wax in oil. Leontaritis (1996) explains that the behavior of wax in oils can be determined by means of the cloud and pour points. Ring et al. (1994) defined the cloud point as “the equilibrium temperature and pressure at which solid paraffin crystals begin to form in the liquid phase.” Leontaritis (1996) states that the flow or “pour point is defined as the lowest temperature at which the fuel will pour and is a function of the composition of the fuel.”

14.3 MECHANISMS OF THE HEAVY ORGANIC DEPOSITION In this section, the mechanisms of the heavy organic deposition according to Mansoori (1997) are described. Mansoori (1997) states that organic deposition during petroleum production and transportation may occur by one or several of the following four mechanisms: 1. Polydispersivity effect: As depicted in Figure 14-5a by Mansoori (1997), a stable state of a polydispersed oil mixture can be attained for a certain proper ratio of the polar to nonpolar and the light to heavy constituents in the crude oil at given temperature and pressure conditions. Thus, when the composition, temperature, or pressure is varied, the system may become unstable and undergo several processes. Figure 14-5b by Mansoori (1997) depicts the formation of micelle-type aggregates of asphaltene when polar miscible compounds

478

Formation Damage by Organic Deposition

(a)

(b)

(c)

(d)

(e)

(f)

Figure 14-5. (a) Heavy organics in petroleum crude (straight/curved line = paraffin molecules, solid ellipse = aromatic molecules, open ellipse = resin molecules, and solid blocky forms = asphaltene molecules). (b) Colloidal phenomenon activated by addition of a polar miscible solvent (solid ellipse = an aromatic hydrocarbon). (c) Flocculation and precipitation of heavy components by addition of a nonpolar miscible solvent (dashed line = a paraffin hydrocarbon). (d) Steric colloidal phenomenon activated by addition of paraffin hydrocarbons. (e) Migration of peptizing molecules (solid arrows) by change of chemical potential balance. (f) Flocculation and deposition (big arrow) of large heavy organic particles (reprinted from Journal of Petroleum Science and Engineering, Vol. 17, Mansoori, G. A., “Modeling of Asphaltene and Other Heavy Organic Depositions”, pp. 101–111, ©1997, with permission from Elsevier Science; after Mansoori ©1994 SPE; reprinted by permission of the Society of Petroleum Engineers).

Formation Damage by Organic Deposition

479

are added into the system. Figure 14-5c by Mansoori (1997) describes the separation of the asphaltenes as a solid aggregate phase when more paraffinic hydrocarbons are added into the system. 2. Steric colloidal effects: At high concentrations, asphaltenes tend to associate in the form of large particles, as depicted in Figure 14-5d by Mansoori (1997). In the presence of some peptizing agents, such as resins, these particles can adsorb the peptizing agents and become suspended in the oil. 3. Aggregation effect: When the concentration of the peptizing agent is low and its adsorbed quantity is not sufficient to occupy the particle surface completely, several particles can combine to form bigger particles as depicted in Figure 14-5e by Mansoori (1997). This phenomenon is called flocculation. When the particles become sufficiently large and heavy, they tend to deposit out of the solution as depicted in Figure 14-5f by Mansoori (1997). 4. Electrokinetic effect: As explained by Mansoori (1997), during the flow of oil through porous media and pipes, a “streaming current” and a potential difference are generated because of the migration of the charged particles of the asphaltene colloids. The asphaltene particles are positively charged but the oil phase is negatively charged, as depicted in Figure 14-6 by Mansoori (1997). Therefore, the negative upstream and positive downstream potentials are generated along the pipe to resist the flow of the colloidal particles, as depicted in Figure 14-7 by Mansoori (1997). This, in turn, induces a back diffusion of the colloidal asphaltene particles. Mansoori (1997) points out that the deposition of the polar asphaltene by the electrokinetic effect and the nonpolar paraffins by the dynamic pour point crystallization effect could occur simultaneously when the oil contains both asphaltenes and paraffins.

14.4 ASPHALTENE AND WAX PHASE BEHAVIOR 14.4.1 14.4.1.1

Deposition Envelopes Description of deposition envelopes

In this section, a brief summary of the review of the asphaltene and wax phase behavior by Leontaritis (1996) is presented.

480

Formation Damage by Organic Deposition Flowing crude oil

Charged heavy organic particles

Conduit

Figure 14-6. Streaming potential generated by oil flow in a pipe (reprinted from Journal of Petroleum Science and Engineering, Vol. 17, Mansoori, G. A., “Modeling of Asphaltene and Other Heavy Organic Depositions”, pp. 101–111, ©1997, with permission from Elsevier Science; after Mansoori ©1994 SPE; reprinted by permission of the Society of Petroleum Engineers).

Figure 14-7. Electrokinetic deposition in a pipeline (reprinted from Journal of Petroleum Science and Engineering, Vol. 17, Mansoori, G. A., “Modeling of Asphaltene and Other Heavy Organic Depositions”, pp. 101–111, ©1997, with permission from Elsevier Science).

481

Formation Damage by Organic Deposition

Accurate measurement of the asphaltene and wax phase behavior is expensive and requires sophisticated techniques for proper handling of the reservoir fluid samples and laboratory testing of the recombined reservoir fluids. Therefore, Leontaritis (1996) suggests that phase diagrams can be more economically and rapidly developed by simulation with a limited number of actual data required for tuning and calibration. Leontaritis (1996) demonstrated this exercise by applying the Thermodynamic– Colloidal model by Leontaritis (1993). Nghiem and Coombe (1997) state, “Above the saturation pressure, the precipitation is solely due to pressure, while below the saturation both pressure and composition affect the precipitation behavior.” Leontaritis (1996) points out that wax crystallization and asphaltene flocculation phenomena occur at low and high temperatures, respectively. Then, he hypothesizes that these two phenomena should, therefore, represent the two extreme cases of the phase behavior and there should be continuously varying intermediate phase behavior in between these two extremes depending on the composition of the heavy fractions of the crude oils, as schematically shown in Figure 14-8 by Leontaritis (1996). The schematic Figures 14-9 and 14-10 by Leontaritis (1996) depict the features of typical asphaltene deposition envelope (ADE) and wax

WDE behavior

Pressure

ADE behavior

Low T

High T

Figure 14-8. Unification of the wax deposition envelope (WDE) and the asphaltene deposition envelope (ADE) (after Leontaritis, ©1996; reprinted by courtesy of Marcel Dekker, Inc.).

482

Formation Damage by Organic Deposition

(Pres, Tres) Liquid phase ADE up

per bou

Bubble-point line

ndary

Pressure

Liquid +Asphaltene phases

Liquid + Vapor + Asphaltene phases Liquid + Vapor phases

E

AD

er low

un

bo

ry da

Temperature

Figure 14-9. Typical asphaltene deposition envelope (after Leontaritis, ©1996; reprinted by courtesy of Marcel Dekker, Inc.).

Bubble-point line

Pressure

Liquid phases Solid + Liquid phases

Liquid + Vapor phases Solid + Liquid + Vapor phases

Temperature

Figure 14-10. Typical wax deposition envelope (after Leontaritis, ©1996; reprinted by courtesy of Marcel Dekker, Inc.).

483

Formation Damage by Organic Deposition

deposition envelope (WDE), respectively. As explained by Leontaritis (1996), the phase diagrams of the asphaltenic fluids typically do not have a critical point, because the asphaltenic fluids can only have bubblepoint lines and no dew-point lines, as they cannot vaporize. Leontaritis (1996, 1998) refers to the locus of the thermodynamic conditions for asphaltene flocculation as the ADE, as shown in Figure 14-9. Typically, the pressure–temperature phase diagrams of the asphaltenic oils are characterized by several phase quality lines and a saturation (bubble-point) line in between the upper and the lower boundaries of the ADE as indicated in Figure 14-11 by Leontaritis (1996) for a South-American oil. Leontaritis (1996) estimated the intersection of the upper ADE with the bubble-point line at around 370 F for this oil. Figures 14-12–14-14 by Leontaritis (1996) are typical simulated charts showing the ADE, the asphaltene phase volume vs. temperature, and the asphaltene phase volume vs. pressure for a North-American oil, respectively. Leontaritis (1996) refers to the locus of the thermodynamic conditions for wax crystallization as WDE. The sketch of a typical WDE is given in Figure 14-10 by Leontaritis (1996). Figures 14-15 and 14-16 by Leontaritis (1996) depict the effect of the light-ends and the

7000

Upper ADE boundary 6000

1.0*

Pressure, psig

2.0 3.0

5000

4.0

ne ration li

3.0

Satu 4000

3000

E r AD owe

ry

nda

bou

L 2000 140

180

220

260

300

Temperature, °F * Mls of asphaltene phase per mole of reservoir fluid.

Figure 14-11. Asphaltene deposition envelope for a South American reservoir oil (after Leontaritis, ©1996; reprinted by courtesy of Marcel Dekker, Inc.).

484

Formation Damage by Organic Deposition

400

No solids

350

Reservoir pressure, 350.0 atm Reservoir temperature, 344.27° K No solids

300

Pressure, atm

Solids

250 200

Lower onset P Bubble P

Solids

150

Upper onset P

100 50 0 280

300

320

340 360 Temperature, °K

380

400

420

Figure 14-12. Asphaltene deposition envelope for Asph Wax Oil Company live-oil (after Leontaritis, ©1996; reprinted by courtesy of Marcel Dekker, Inc.).

400

Temperature, ° K

380

Reservoir pressure, 350.0 atm Reservoir temperature, 344.27° K 360

340

320

300

0

0.5

1

2 2.5 1.5 Asphaltene phase volume, cc

3

3.5

Figure 14-13. Asphaltene phase volume vs. temperature for an Asph Wax Oil Company live-oil at 200 atm pressure (after Leontaritis, ©1996; reprinted by courtesy of Marcel Dekker, Inc.).

pressure–temperature relationship on the onset of wax crystallization (cloud point) of oils. The effect of the pressure on the onset of wax crystallization is demonstrated for three live oils in Figure 14-17 by Leontaritis (1996). The typical WDE of North American recombined live-oil developed by laboratory measurements is given in Figure 14-18 by Leontaritis

485

Formation Damage by Organic Deposition 400 350

Bubble point pressure, 279.16 atm at 340° K

Pressure, atm

300 250

Reservoir pressure, 350.0 atm Reservoir temperature, 344.27° K

200 150 100 50 0 0

1

2

3

4

5

6

7

8

Asphaltene phase volume, cc

Figure 14-14. Asphaltene phase volume vs. pressure for Asph Wax Oil Company live-oil at 340 K temperature (after Leontaritis, ©1996; reprinted by courtesy of Marcel Dekker, Inc.). 130

Onset of wax crystallization, ° F

120

110

100

90

80

70

60 0

1000

2000

3000

4000

5000

Bubble point pressure, psig (at 195° F)

Figure 14-15. Onset of wax crystallization vs. the bubble-point temperature (after Leontaritis, ©1996; reprinted by courtesy of Marcel Dekker, Inc.).

(1996). He also developed the WDE given in Figure 14-19 for North Sea live-oil by using a Wax Model. Using the same Wax Model, Leontaritis (1996) has predicted the effect of temperature on the fraction of the wax crystallized at 200, 50, and 1 atm pressures as shown in Figures 14-20,

486

Formation Damage by Organic Deposition

6000

Onset pressure, psia

5000 4000 3000 2000 1000 0 68

70

72

74

76

78

80

82

84

Onset temperature, °F

Figure 14-16. Pressure–temperature effects on onset of wax crystallization in a synthetic mixture of kerosene and candle wax (after Leontaritis, ©1996; reprinted by courtesy of Marcel Dekker, Inc.). 140

Temperature, ° F

130 120 Oil A

110

Oil B Oil C

100 90 80 70 2000

3000

4000

6000 5000 Pressure, psig

7000

8000

Figure 14-17. Upper wax deposition envelope boundaries for three different reservoir oils (after Leontaritis, ©1996; reprinted by courtesy of Marcel Dekker, Inc.).

14-21, and 14-22, respectively, as well as the effect of the pressure on the fraction of the wax crystallized at 280 K as shown in Figure 14-23. 14.4.1.2

Representing the asphaltene deposition envelope

For convenience, Wang and Civan (2005a,b) described the asphaltene deposition envelope using a truncated bi-variate power series expansion as

487

Formation Damage by Organic Deposition 3000 2500

Pressure, psig

Onset pressure, psig BP pressure, psig

2000 1500 1000 500 0 30

40

50

60

70

80

90

100

Temperature, °F

Figure 14-18. Wax deposition envelope for a North American recombined reservoir oil (after Leontaritis, ©1996; reprinted by courtesy of Marcel Dekker, Inc.). 250

Pressure, atm

200

No solids Solids

Reservoir pressure, 280.0 atm Reservoir temperature, 338.0° K

150

100

50

0 250

Onset pressure

No solids

Bubble point pressure

Solids

260

270

280

290 300 310 Temperature, °K

320

330

340

350

Figure 14-19. Wax deposition envelope for an Asph Wax Oil Company live-oil (after Leontaritis, ©1996; reprinted by courtesy of Marcel Dekker, Inc.).

xA = 1 + 2 p + 3 p2 + 4 p3 + 5 T + 6 pT + 7 p2 T + 8 T 2 + 9 pT 2 + 10 T 3

(14-2)

where xA is the concentration of precipitated asphaltene, i , where i = 1 2     10, denotes fitting coefficients, and T and p denote the temperature and pressure of the oil. Wang and Civan (2005a,b) show that Eq. (14-2) represents the Leontaritis (1996) asphaltene deposition

488

Formation Damage by Organic Deposition 0.100

Wax weight fraction

0.080

0.060

Reservoir pressure, 280.0 atm Reservoir temperature, 338.0° K

0.040

0.020

0.000 240

250

260 270 Temperature, °K

280

290

Figure 14-20. Wax weight fraction vs. temperature for an Asph Wax Oil Company live-oil at 200 atm pressure (after Leontaritis, ©1996; reprinted by courtesy of Marcel Dekker, Inc.). 0.15

Wax weight fraction

0.12

0.09

Reservoir pressure, 280.0 atm Reservoir temperature, 338.0° K

0.06

0.03

0 250

260

270

280 290 300 Temperature, °K

310

320

330

Figure 14-21. Wax weight fraction vs. temperature for an Asph Wax Oil Company live-oil at 50 atm pressure (after Leontaritis, ©1996; reprinted by courtesy of Marcel Dekker, Inc.).

envelope satisfactorily. Wang and Civan (2005c) obtained the polynomial coefficients yielding the best fit of the asphaltene deposition data of Leontaritis (1996) as 1 = −121 × 101 ml/moleoil  2 = 9026 × 10−3 ml/moleoil − psi 3 = −2402 × 10−6 ml/moleoil − psi2  4 = 2574 × 10−10

489

Formation Damage by Organic Deposition 0.3

Wax weight fraction

0.25 Reservoir pressure, 280.0 atm Reservoir temperature, 338.0° K

0.2 0.15 0.1 0.05 0 250

260

270

280 290 300 Temperature, °K

310

320

330

Figure 14-22. Wax weight fraction vs. temperature for an Asph Wax Oil Company stock-tank-oil at 1 atm pressure (after Leontaritis, ©1996; reprinted by courtesy of Marcel Dekker, Inc.). 0.200

Wax weight fraction

0.160

0.120

Reservoir pressure, 280.0 atm Reservoir temperature, 338.0 °K

0.080

0.040

0.000 0

50

100 Pressure, atm

150

200

Figure 14-23. Wax weight fraction vs. pressure for an Asph Wax Oil Company live-oil at 280 K temperature (after Leontaritis, ©1996; reprinted by courtesy of Marcel Dekker, Inc.).

ml/moleoil − psi3  5 = −5444 × 10−3 ml/moleoil −  F −5 6 = 3786 × 10 ml/moleoil − psi −  F 7 = −1035 × 10−8 ml/moleoil − psi2 −  F 8 = −3402 × 10−4 ml/moleoil −  F2  9 = 1701 × 10−7 ml/moleoil − psi −  F2  and 10 = −9675 × 10−7 ml/moleoil −  F3 

490

Formation Damage by Organic Deposition

14.4.1.3 Pressure–composition phase diagrams for miscible gas injection

Mansoori (1997) mentions that experimental measurement of the pressure–composition phase diagrams involving heavy organic deposition by miscible gas injection, at reservoir temperatures, is very costly. Therefore, he has suggested generating these charts by simulation. Figure 14-24 produced by Mansoori (1997) is an example of a typical chart for asphaltenic oils dissolving carbon dioxide. Figures 14-25 and 14-26 by Mansoori (1997) indicate the electrokinetics affect on asphaltene deposition in pipelines from typical asphaltenic oils dissolving a miscible component at various temperatures. These figures contain two charts. The upper chart shows the static onset of deposition of asphaltene on a pressure vs. composition relationship. The lower chart shows the dynamic, Q (defined below) vs. pressure relationship for asphaltenic oils flowing in wells or pipelines for different miscible component and oil ratio. The Q function is given by (Mansoori, 1997) Q=

U 175 D075

(14-3)

3500

Pressure (psig)

3000 2500 2000

1Φ

1500

3Φ

1000

2Φ

500 0 0

10

20

30

40

50

60

70

80

90

100

CO2 mole%

Figure 14-24. Static pressure vs. composition (P–x) phase diagram of a crude oil mixed with a miscible injectant (MI) at 60 F (reprinted from Journal of Petroleum Science and Engineering, Vol. 17, Mansoori, G. A., “Modeling of Asphaltene and Other Heavy Organic Depositions”, pp. 101–111, ©1997, with permission from Elsevier Science, after Mansoori ©1994 SPE, reprinted by permission of the Society of Petroleum Engineers).

Formation Damage by Organic Deposition

491

T = 120 F

3000

Pressure, psig

L L-A

2000

L-V 1000 P = 1520 psig

L-V

L-V-A

x = 43.46 L-V

0 0

20

40

60

80

100

X, Mole % of miscible injectant

7

x E-6

MI/crude oil T = 120 F MI/Oil mole % 0.0 25.5 40.6 63.1 77.4 87.2 93.2

6

Q 5 4

3 0

1000

2000

3000

Pressure, psig

Figure 14-25. Static pressure vs. composition (P–x) and dynamic (P–Q) phase diagrams of the same crude oil in Figure 14-24, mixed with the same miscible injectant at 120 F (reprinted from Journal of Petroleum Science and Engineering, Vol. 17, Mansoori, G. A., “Modeling of Asphaltene and Other Heavy Organic Depositions”, pp. 101–111, ©1997, with permission from Elsevier Science, after Mansoori ©1994 SPE, reprinted by permission of the Society of Petroleum Engineers).

in which U is the average oil velocity in the pipe, D is the pipe diameter, and is the conductivity of the oil. The regions above and below these curves express the flow conditions leading to deposition and no deposition of asphaltenes, respectively. Hence, these charts help determine the proper operating conditions of pipes to avoid precipitation.

14.4.2

Solubility Theory

The theoretical relationships describing the paraffin and asphaltene solubility in crude oil are presented below.

492

Formation Damage by Organic Deposition T = 160 F 3000 L

Pressure, psig

L-A 2000

L-V

P = 1770 psig

L-V-A

1000 L-V X = 44.0

L-V

0 0

20

40

60

80

100

X, mole % of miscible injectant

xE-6 7

Ml / Crude oil T = 160 F Ml / Oil mole % 0.0 25.5

6

40.6 Q 5

63.1 77.4 87.2 93.2

4

3

0

1000

2000

3000

Pressure, psig

Figure 14-26. Static pressure vs. composition (P–x) and dynamic (P–Q) phase diagrams of the same crude oil in Figure 14-24, mixed with the same miscible injectant (MI) at 160 F (reprinted from Journal of Petroleum Science and Engineering, Vol. 17, Mansoori, G. A., “Modeling of Asphaltene and Other Heavy Organic Depositions, pp. 101–111, ©1997, with permission from Elsevier Science, after Mansoori ©1994 SPE, reprinted by permission of the Society of Petroleum Engineers).

14.4.2.1

Solubility of paraffin in oil

Essentially, the solubility of paraffin in crude oil depends on temperature and less on presseure. The solubility of paraffin in crude oil can be estimated by applying the following real solution model (Chung, 1992):

Formation Damage by Organic Deposition

  V HP 1 1 − P  m − P 2 xPL = xPS exp − − R T TPM RT    VP VP −1+ − ln Vm Vm

493



(14-4)

where, xpL denotes the dissolved paraffin mole fraction in oil, xpS is the paraffin precipitate mole fraction in oil, HP is the latent heat of fusion of the paraffin, R is the universal gas constant, T is temperature, TPM is the melting point or fusion temperature for paraffin, VP and Vm are the molar volumes of paraffin and oil, and P and m are the solubility parameters of paraffin and oil. 14.4.2.2

Solubility of asphaltene in crude oil

The experimental approaches used in an effort to determine the existence state of asphaltene in crude oil can be summarized in four categories (Wang and Civan, 2005a,b): 1) Electron microscope (Prechshot et al., 1943; Katz and Beu, 1945) 2) Electrical effect (Dykstra et al., 1944; Katz and Beu, 1945) 3) Reversibility (Hirschberg et al., 1984; Thawer et al., 1990; Danesh et al., 1987; Danesh et al., 1989) 4) Molecular weight (Ray et al., 1957; Witherspoon and Munir, 1958; Speight and Long, 1996; Speight, 1999). Reviewing the existing literature, Wang and Civan (2005a,b) conclude that “the existence state of asphaltene in crude oil is not very clear. Nevertheless, the following facts can be expressed. Crude oil containing asphaltene is a uniform solution, asphaltene precipitation and dissolution processes are reversible, and molecular weight of asphaltene ranges within 1500–2500 g/mole.” There are two essential theoretical approaches available concerning the physical description of the existence state of asphaltene in crude oil: 1) Colloidal theory. The colloidal theory assumes that asphaltene is suspended as a colloid in crude oil and therefore can better describe the asphaltene peptization/flocculation phenomena (Leontaritis and Mansoori, 1987; Mansoori, 1994a,b, 1997).

494

Formation Damage by Organic Deposition

2) Real-solution theory. The real-solution theory assumes that asphaltene is completely dissolved in crude oil (Hirschberg et al., 1984; Burke et al., 1990; Novosad and Costain, 1990; Kawanaka et al., 1991; Chung, 1992; Thomas et al., 1992; Nghiem et al., 1993; Nor-Azian and Adewumi, 1993; Boer et al., 1995; Cimino et al., 1995; MacMillan et al., 1995; Yarranton and Masliyah, 1996; Zhou et al., 1996; Nghiem and Coombe, 1997; Nghiem et al., 1998; Wang et al., 1999; Wang and Civan, 2001, 2005a,b; Kohse and Nghiem, 2004). The real-solution theory has been implemented as either a regular solution or a polymer solution. However, the polymer solution theory is preferable because the asphaltene molecules are large molecules (Hirschberg et al., 1984; Wang and Civan, 2005a,b). Hirschberg et al. (1984) combined the Flory–Huggins theory with the Hildebrand solubility concept to express the volume fraction of asphaltene dissolved in the crude oil A as   V V

A = exp A − 1 − A  A − L 2 (14-5) VL RT where VA denotes the asphaltene molar volume, VL is the oil molar volume, R is the universal gas constant, and T is the absolute temperature. The symbol A denotes the solubility parameter of asphaltene, calculated by A = 20041 − hT

(14-6)

where h is a characteristic constant value for a given oil. The symbol L denotes the solubility parameter of oil, calculated by (Hildebrand, 1929)  L = Uvaporization /VL (14-7) where Uvaporization represents the change of internal energy per mole of oil by vaporization. Wang and Civan (2005a,b) represented the precipitation and dissolution of asphaltene in crude oil by means of the vapor–oil and asphaltene– oil equilibriums. They first calculated the composition of oil based on the vapor–oil equilibrium using the Peng–Robinson equation and then the solubility of asphaltene in oil using the polymer solution theory for the asphaltene–oil equilibrium. The crude oil is the solvent-rich phase and asphaltene precipitate is the solute-rich phase (Hirschberg et al., 1984).

Formation Damage by Organic Deposition

495

Wang and Civan (2005a,b) assumed that the asphaltene molecules present in the oil are identical so that Eq. (14-5) formulated for monodisperse polymer solutions can be used and that the second equilibrium does not effect the first equilibrium. Wang and Civan (2005a,b) applied the shift parameter concept to improve the predicted value of the molar volume of oil (Jhaverl and Youngren, 1988). They determined the critical properties and eccentric parameter of C7+ to match a characteristic property of the oil, such as the bubble-point pressure, and calculated the vapor–oil equilibrium using the Peng–Robinson equation and the molar volume of oil using the modified Peng–Robinson equation (Jhaverl and Youngren, 1988).

14.4.3 14.4.3.1

Asphaltene Adsorption Bilinear adsorption model

Nonequilibrium adsorption in porous media may be described by a bilinear adsorption model according to Gupta and Greenkorn (1973), given by     = k1 + k2 c + k3  + k4 c = k1 + k2 c 1 + + k3  (14-8) t k2 /k4 subject to the initial condition that  = 0  t = 0 At equilibrium, Eq. (14-8) becomes   k1 k k 1 c− = − 3 − 4c  k2 k2 k2

(14-9)

In Eqs (14-8) and (14-9), t is time,  is the concentration of species adsorbed in porous media, c is the concentration of the species in solution, and k1  k2  k3 , and k4 are some empirical coefficients. Manoranjan and Stauffer (1996) used simplified forms of Eqs (14-8) and (14-9). The first is referred to as the nonequilibrium sorption equation given by  = kf c s −  − kb s t

(14-10)

subject to the initial condition that  = 0 

t=0

(14-11)

496

Formation Damage by Organic Deposition

The second is the Langmuir isoterm, which applies at local equilibrium (/t = 0 in Eq. (14-10)), c c 1 = +  s s K

(14-12)

80 30 28 60

24 20

40

16 Toluene/n-Dodecane (1.75:1.0 w/w)

12

Toluene 8

Nitrobenzene

4

0

20

Chloroform

400

800

1200

1600

2000

2400

0 2800

Weight asphaltene adsorbed/weight kaolin, mg/g

Weight asphaltene adsorbed/weight kaolin, mg/g

where kf and kb denote the rate constants for the forward, sorption, and backward, desorption, rate processes, K = kf /kb denotes the equilibrium constant, s is the saturation concentration of the adsorbed species at complete monolayer coverage of the pore surface. Dubey and Waxman (1991) have shown that the adsorption of asphaltene from anhydrous nonpolar solvents and toluene on common minerals followed the monolayer, Langmuir Type I adsorption mechanism according to Eq. (14-12). However, the adsorption of asphaltene from nitrobenzene solution followed a multilayer, Langmuir Type II adsorption mechanism (Figures 14-27 and 14-28 by Dubey and Waxman (1991)). They have also shown that there is an adsorption/desorption hysteresis for asphaltene as indicated by Figure 14-29. Figures 14-30 and 14-31 reported by Acevedo et al. (1995) also indicate monolayer and multilayer adsorption mechanisms, respectively.

Equilibrium concentration of asphaltenes, ppm

Figure 14-27. Adsorption isotherms for asphaltenes on kaolin from various solvents (after Dubey and Waxman, ©1991 SPE; reprinted by permission of the Society of Petroleum Engineers).

Formation Damage by Organic Deposition

497

40

mg Asphaltenes adsorbed/g substrate

35

30

25

20

15

10

Berea sandstone (>100 mesh) Dickite (Wisconsin) Dolomite (Dolocron) Ottawa sand (Super x, >325 mesh) Calcite (Dover chalk) Kaolin mineral Illite (Beaver’s bend) Alumina

5

0

1000

2000

Equilibrium asphaltene concentration, ppm Figure 14-28. Adsorption isotherms for asphaltenes on clay and mineral surfaces from toluene (after Dubey and Waxman, ©1991 SPE; reprinted by permission of the Society of Petroleum Engineers).

14.4.3.2

Surface excess theory

Ali and Islam (1997, 1998) used the following model for adsorption of asphaltene according to the application of the surface excess theory by Sircar et al. (1972). The asphaltenic oil is considered to have an asphaltene and an oil (maltene) pseudo-species, denoted respectively by the indices i = 1 and i = 2. Let xi and xi denote the mass fractions of

498

Weight asphaltene adsorbed/ Weight kaolin, mg/g

Formation Damage by Organic Deposition

30

20

10

1000 500 1500 2000 Asphaltene equilibrium concentration, ppm

0

2500

Figure 14-29. Hysteresis of adsorption/desorption isotherms for asphaltenes on kaolin from toluene (after Dubey and Waxman, ©1991 SPE; reprinted by permission of the Society of Petroleum Engineers).

Equilibrium concentration in solid (mg/g)

3.5 3 2.5 2 1.5 1 0.5 0

0

300 600 900 1200 3000 Equilibrium concentration of asphaltenes (mg/l)

Figure 14-30. Adsorption isotherm for Cerro Negro asphaltenes on inorganic material surface from toluene at 26 C (reprinted from Journal of Fuel, Vol. 74, Acevedo, S., Ranaudo, M. A., Escobar, G., Gutiérrez, L., and Ortega, P., “Adsorption of Asphaltenes and Resins on Organic and Inorganic Substrates and Their Correlation with Precipitation Problems in Production Well Tubing”, pp. 595–598, ©1995, with permission from Elsevier Science).

Equilibrium concentration in solid (mg/g)

Formation Damage by Organic Deposition

499

24 21 18 15 12 9 6 3 0 0

200

400

600

800

1000 1200 1400 1600 1800 2000 2200 2400 2600

Equilibrium concentration of asphaltenes (mg/L)

Figure 14-31. Adsorption isotherm for Ceuta asphaltenes on inorganic material surface from toluene at 26 C (reprinted from Journal of Fuel, Vol. 74, Acevedo, S., Ranaudo, M. A., Escobar, G., Gutiérrez, L., and Ortega, P., “Adsorption of Asphaltenes and Resins on Organic and Inorganic Substrates and Their Correlation with Precipitation Problems in Production Well Tubing”, pp. 595–598, ©1995, with permission from Elsevier Science).

species i dissolved in the oil phase and adsorbed in the porous medium, respectively. ni is the mass of species i adsorbed per unit mass of porous media. n is the total mass of species (oil plus asphaltene) adsorbed per unit mass of porous media given by n =

2 

ni

(14-13)

i=1

Then, assuming that all oil is in contact with the porous media, the surface excess of species i can be expressed as nei = n xi − xi 

i = asphaltene or oil

(14-14)

They assume that the theory is applicable for both monolayer and multilayer adsorption. A balance of the oil and asphaltene adsorbed over the pore surface yields 1 x1 x2 = + n m1 m2

(14-15)

500

Formation Damage by Organic Deposition

In Eq. (14-15), m1 and m2 denote the monolayer coverage of asphaltene and carrier oil, respectively, expressed as mass of species adsorbed per unit mass of porous solid. Then, a selectivity parameter, as defined below, is introduced: S=

x1 /x2 x1 /x2

(14-16)

Therefore, from Eqs (14-15) and (14-16), they obtained the following expression for the amount of asphaltene adsorbed: ne1 = n x1 =

m1 x1 S Sx1 + m1 /m2 x2

(14-17)

Using Eqs (14-14) and (14-16), they derived the following expression for the surface excess amount of the asphaltene: nea 1 =

m1 x1 x2 S − 1 Sx1 + m1 /m2 x2

(14-18)

As a result, the rates of adsorption or desorption are expressed according to nea 1 = kj ne1 − nea 1  t

j = adsorption, desorption

(14-19)

denote the amount of species 1 (asphaltene) where ne1 and nea 1 adsorbed/desorbed and the actual surface excess of species 1 per unit mass of porous formation. The initial condition is given as ea nea 1 = n10 

14.4.4

t=0

(14-20)

Asphaltene Aggregation Kinetics

Asphaltene melocules form miscelles and then the miscelles combine to form aggregates (Yen and Chilingarian, 1994). In this section, the description of the Asphaltene aggregation kinetics according to the approach developed by Burya et al. (2001) is presented. Burya et al. (2001) explain that essentially the asphaltene particle stability in crude oil depends on the aromatics-to-saturates ratio and resins-to-asphaltenes ratio, reduction of which may cause the coalescence

Formation Damage by Organic Deposition

501

of the asphaltene particles in oil to form larger aggregates. Burya et al. (2001) demonstrate that the aggregation kinetics of colloidal asphaltene particles involves the diffusion-limited aggregation (DLA) and reactionlimited aggregation (RLA) mechanisms with a crossover between them. The average number of particles N forming fractal aggregates is given by  N=

R Ro

d f (14-21)

Where Ro and R denote the initial particle radius and the instantaneous mean aggregate radius, respectively, and df is the fractal dimension. Equation (14-21) can be applied for both the diffusion- and the reaction-limited fractal aggregates with different values of the fractal dimension df . Therefore, N denotes the average number of asphaltene molecules forming an aggregate for the DLA. Alternatively, N denotes the average number of miscelles forming an aggregate for the RLA and crossover. Let the subscripts D and R refer to the DLA and RLA mechanisms, respectively. Burya et al. (2001) described the crossover behavior from the RLA to DLA by N dN = D N + R dt

(14-22)

subject to t = to

N = No 

(14-23)

Where  is a constant, given by  =

R Ro

 df (14-24) D

The symbols D and R denote the characteristic times char for the DLA and RLA mechanisms, respectively. Thus, a scaled time can be defined as t∗ =

t char

(14-25)

A scaled radius can be defined as: R∗ =

R Ro

(14-26)

502

Formation Damage by Organic Deposition

Thus, the analytical solution of Eq. (14-22) subject to Eq. (14-23) is given by D  N − No + R ln N/No = t − to

(14-27)

Note that No = 1 to = 0 at the beginning of the aggregation process. Two special solutions of the Smoluchowski equation can be readily generated from Eq. (14-27) in terms of the scaled time and scaled radius defined by Eqs. (14-25) and (14-26). The solutions obtained for these special cases can be expressed in terms of the aggregate radius by substituting Eq. (14-21) for N . These special solutions are given below (Burya et al., 2001): Solution #1: For diffusion-limited aggregation, D >> R and thus the diffusion-controlled aggregation kinetics is described by simplifying Eq. (14-27) by substituting R = 0. N = 1 + t/D 

R = 1 + t/D 1/df Ro

(14-28)

Solution #2: For reaction-limited aggregation, D << R and thus the reaction-controlled aggregation kinetics is described by simplifying Eq. (14-27) by substituting D = 0. N = exp t/R 

R = exp t/R df  Ro

(14-29)

Solution #3: For crossover from RLA to DLA: D /R N − 1 + ln N = t/R  (14-30) D R/Ro D  + R df ln R/Ro R  = t df

Burya et al. (2001) demonstrate the application of these analytic solutions by correlating the experimental data obtained by the light-scattering technique in Figures 14-32 and 14-33.

14.5 PREDICTION OF ASPHALTENE STABILITY AND MEASUREMENT (DETECTION) OF THE ONSET OF ASPHALTENE FLOCCULATION Asphaltene precipitates as a result of composition change by depressurization or mixing. Typical asphaltene precipitants are the flocculants,

503

Formation Damage by Organic Deposition

105 104

N

103 102 101 100 10–1

100

102

101

103

104

t*

Figure 14-32. Scaled mean number of particles in an aggregate plotted as a function of the scaled time t ∗ for the DLA (dashed curve), the RLA (solid curve), and the crossover (dotted curve) in a 5-g/l asphaltene solution (after Burya et al., ©2001; reprinted by permission of the Optical Society of America).

Figure 14-33. Mean radius of the asphaltene aggregates plotted vs. the monitoring time for Unocal’s Swanson River oil with 5% by volume of the precipitant. Two dynamic processes, power-law growth and exponential growth, can clearly be seen in the double-logarithmic scale (after Burya et al., ©2001; reprinted by permission of the Optical Society of America).

such as n-heptane n-C7 and n-pentadecane n-C15 , and solvents, such as toluene, can dissolve the asphaltene aggregates (Wang et al., 2004). Wang et al. (2004) define the onset condition by the smallest amount of flocculant required for asphaltene flocculation in a mixture of a crude oil and a flocculant.

504

14.5.1

Formation Damage by Organic Deposition

Asphaltene Precipitation Detection Techniques

Among the outstanding techniques for detection of the onset of asphaltene precipitation (OAP) or flocculation (OAF) are (Jamaluddin et al., 2002; Wang et al., 2004) a. Gravimetric method (GM) b. Acoustic resonance technique (ART) c. Light-scattering technique (LST) (Fuhr et al., 1991; Jamaluddin et al., 1998) d. Filtration technique (FT) e. Fluorescence spectroscopy technique (FST) (Wehry and Rogers, 1966) f. Conductivity measurement technique (CMT) (Fotland et al., 1993). Only the first four frequently used techniques are described here. 14.5.1.1

Gravimetric method

Jamaluddin et al. (2002) concluded that the gravimetric method is timeconsuming but yields precise results with accuracies comparable to those obtained by the analytical methods. They stated that the gravimetric method enabled the determination of the bubble-point condition and the construction of the upper and lower asphaltene deposition envelopes. The gravimetric method shown in Figure 14-34 by Jamaluddin et al. (2002) P > Poap

P < Poap

Air bath

Figure 14-34. Schematic diagram of gravimetric concept (after Jamaluddin et al., ©2002; being used with the permission of the Petroleum Society of CIM. The author thanks the Petroleum Society for the use of this material with a reminder that copyright remains with the Petroleum Society and that no other copies may be made without the express written consent of the Petroleum Society of CIM).

505

Formation Damage by Organic Deposition

Asphaltene content (%, w/w)

n -Heptane insolubles

n -Pentane insolubles

1.5 Poap (lower) = 13.5 Mpa

Pb – 22 Mpa

1.0

0.5 Poap (upper) – 43 MPa

0.0

0

10

20

30

40

50

60

70

Pressure (MPa)

Figure 14-35. Results of gravimetric method (isothermal depressurization using Oil A) (after Jamaluddin et al., ©2002; being used with the permission of the Petroleum Society of CIM. The author thanks the Petroleum Society for the use of this material with a reminder that copyright remains with the Petroleum Society and that no other copies may be made without the express written consent of the Petroleum Society of CIM).

is based on the measurement of the precipitating asphaltene particles, separating and settling at the bottom of a pressure–volume–temperature (PVT)-cell under the gravity effect when the system is depressurized isothermally to allow the separation of dissolved gas. Figure 14-35 by Jamaluddin et al. (2002) shows the separated asphaltene weight percent as a function of the pressure at a prescribed temperature of 116 C for oil, referred to as Oil A. As can be seen, the upper and lower asphaltene precipitation conditions can be readily identified from the inflection points. The two data sets given in Figure 14-35 are for the n-pentane and n-heptane insolubles. However, Jamaluddin et al. (2002) did not indicate the specific data shown for the n-pentane and n-heptane in this figure. 14.5.1.2

Acoustic resonance technique

Jamaluddin et al. (2002) conclude that the acoustic resonance technique is rapid and can determine the bubble-point and upper asphaltene envelope, requiring only a small amount of oil sample. But, it could not determine the lower asphaltene deposition envelope for the crude oils used in their study. The operation principle of the acoustic resonance technique is as following. As shown in Figure 14-36 by Jamaluddin et al. (2002), an oil sample is placed in between two piezoelectric elements. An electric voltage is applied to the first piezoelectric element (source) causing it to vibrate and apply an acoustic stimulation to the oil sample. Then,

506

Formation Damage by Organic Deposition

the stimulated fluid oscillations cause the second piezoelectric element (receiver) to vibrate and generate a voltage. As shown in Figure 14-37 by Jamaluddin et al. (2002), the normalized measurent of the acoustic response (sonic frequency measured in Hertz) as a function of pressure allows the determination of the bubble-point and upper asphaltene Temperature probe

Acoustic

Acoustic receiver Air bath

Normalized acoustic response

Figure 14-36. Schematic diagram of acoustic resonance technology (after Jamaluddin et al., ©2002; being used with the permission of the Petroleum Society of CIM. The author thanks the Petroleum Society for the use of this material with a reminder that copyright remains with the Petroleum Society and that no other copies may be made without the express written consent of the Petroleum Society of CIM).

1.00

0.75

0.50

0.25 Poap (upper) = 43 MPa

Pb = 23 MPa

0.00

0

10

20

30

40

50

60

70

Pressure (MPa)

Figure 14-37. A typical acoustic response (isothermal depressurization using Oil A) (after Jamaluddin et al., ©2002; being used with the permission of the Petroleum Society of CIM. The author thanks the Petroleum Society for the use of this material with a reminder that copyright remains with the Petroleum Society and that no other copies may be made without the express written consent of the Petroleum Society of CIM).

Formation Damage by Organic Deposition

507

deposition condition during the isothermal depressurization tests. The sudden appearances of gas and asphaltene phases are detected by two sharp variations, respectively, as shown in Figure 14-37. Jamaluddin et al. (2002) explain that the lower asphaltene envelope could not be identified with this technique because resolubilization of asphaltene occurs gradually. 14.5.1.3

Light-scattering technique

Jamaluddin et al. (2002) concluded that the near-infrared (NIR) lightscattering technique enabled the construction of the upper and lower asphaltene deposition envelopes. This technique is implemented using a visual PVT-cell equipped with visual observation glass plates, placed on opposite sides as depicted in Figure 14-38 by Jamaluddin et al. (2002). The transmittance of an optimized laser light through the oil sample undergoing an isothermal depressurization test in the PVT-cell is measured as a function of pressure. Therefore, partial light scattering caused by gas bubbles and asphaltene precipitates reduces the light transmission through the oil sample. The bubble-point, and the upper and lower asphaltene deposition pressures can be conveniently identified as illustrated in Figure 14-39 by Jamaluddin et al. (2002). Measurements of the transmitted light using a solid detection system (SDS) based on the deviation of the transmitted light measurements from the Beer’s law predictions is illustrated in Figure 14-40 by Wang et al. (2004). P > Poap

P < Poap

NIR NIR Light transmittance

Light receiver

Light transmittance

Light receiver

Figure 14-38. Light transmittance principle (after Jamaluddin et al., ©2002; being used with the permission of the Petroleum Society of CIM. The author thanks the Petroleum Society for the use of this material with a reminder that copyright remains with the Petroleum Society and that no other copies may be made without the express written consent of the Petroleum Society of CIM).

508

NIR response

Asphaltene content on filter

Light transmittance power (mW)

1.00

8.0 Poap (upper) = 37 Mpa

0.75

6.0

0.50

4.0 Pb = 29 Mpa

0.25

2.0 Pap (lower) = 26 Mpa

0.00 0

20

40

60

0.0 100

80

Pressure (MPa)

Asphaltene portion on filter from SARA (%, w/w)

Formation Damage by Organic Deposition

Figure 14-39. Light transmittance response test at 82 C using Oil B (after Jamaluddin et al., ©2002; being used with the permission of the Petroleum Society of CIM. The author thanks the Petroleum Society for the use of this material with a reminder that copyright remains with the Petroleum Society and that no other copies may be made without the express written consent of the Petroleum Society of CIM).

35 Beer’s law l = 35800 exp(–11ρoil)

Oil A1

Transmitted light (mW)

30 25 20 15

onset (P ~13000 psi)

10 5

Pb

0 0

10000

5000

15000

P (psia)

Figure 14-40. Asphaltenes in Oil A are predicted to be unstable at all pressures. SDS trace (from DBR) and fit to Beer’s Law equation, in which I = the transmitted light intensity and oil = the live-oil density (g/mL) (after Wang et al., ©2004; reprinted by permission of the Society of Petroleum Engineers).

Formation Damage by Organic Deposition

14.5.1.4

509

Filtration technique

Jamaluddin et al. (2002) concluded that the filtration technique enables the construction of the upper and lower asphaltene deposition envelopes faster than the gravimetric technique but slower than the acoustic resonance and light-scattering techniques. The filtration technique utilizes a visual PVTcell similar to the light-scattering technique. The oil sample placed in the PVT-cell is mixed well using a magnetic mixer, thus preventing gravity settling of the asphaltene precipitates, during the isothermal depressurization tests. Small amounts of oil samples are taken at various pressures and the asphaltene precipitates are filtered at the same pressure and temperature conditions of the PVT-cell. Then, the saturates, aromatics, resins, and asphaltenes present in the materials filtered out of the oil are determined at various pressures by laboratory analytical procedures, referred to as the SARA analyses. Jamaluddin et al. (2002) presents the asphaltene content and resin/asphaltene ratio as a function of pressure for typical oil. Figure 14-39 by Jamaluddin et al. (2002) compares the results obtained by the filtration and light-scattering techniques. The trends of the results obtained by these techniques may differ for a number of reasons. For example, sufficiently small size precipitate particles may pass through the filter used in filtration, part of the filtered materials may resolubilize in dense oil, and increased oil density at below the bubble-point pressure conditions may change the light transmission through the oil (Jamaluddin et al., 2002). 14.5.2 Asphaltene Precipitation and Stability Prediction Methods As stated by Wang and Buckley (2001), the prediction of conditions for the OAF or OAP is essentially based on two approaches: 1. Asphaltene phase behavior (APB) and 2. Comparison of the measured and predicted refractive indices. These are described in the following. 14.5.2.1

Asphaltene phase behavior

This approach is based on investigating the APB thermodynamically with parameters estimated through the representation of the high pressure and high temperature (HTHP) experimental data using an appropriate model

510

Formation Damage by Organic Deposition

(already explained above) (Wang and Buckley, 2001). Jamaluddin et al. (2002) state, “The asphaltene precipitation envelope (APE) is defined as the pressure at which the precipitation of colloidally dispersed asphaltene is detected at a given temperature.” (Figure 14-41 by Jamaluddin et al. (2002)). Figure 14-42 by Jamaluddin et al. (2002) demonstrate that the asphaltene deposition envelope can be generated by modeling using an equation of state, such as the Soave–Redlich–Kwang (SRK) equation of state with volume correction. 14.5.2.2

Refractive index method (RIM)

This approach is based on investigating the mixture solubility by measuring the refractive index (RI) which relates to the square root of the molar volume of the precipitant causing the asphaltene flocculation, leading to the formation of asphaltene precipitate (Wang and Buckley, 2001). Buckley et al. (1998) have shown that the RI of a live-oil can be predicted using the equation given below with the PVT data:     2 1 n2 − 1 n −1 = n2 + 2 live–oillo Bo n2 + 2 stock–tank–oilsto + 752 × 10−6

m Rs  x Bo i=1 i i

(14-31)

Example reservoir conditions

Pressure

L

S-L

Upper asphaltene envelope

V-L Equilibrium S-L-V

Lower asphaltene envelope

Temperature

Figure 14-41. Pressure–temperature (P–T) diagram (after Jamaluddin et al., ©2002; being used with the permission of the Petroleum Society of CIM. The author thanks the Petroleum Society for the use of this material with a reminder that copyright remains with the Petroleum Society and that no other copies may be made without the express written consent of the Petroleum Society of CIM).

511

Formation Damage by Organic Deposition 100 Simulated phase envelope Measured Pb Simulated upper poan Measured upper poan Simulated lower poan Measured lower poan

Pressure (MPa)

80

60

40

20

0

0

100

200

300

400

Temperature (°C)

Figure 14-42. Measured and simulated phase envelopes for Oil A (after Jamaluddin et al., ©2002; being used with the permission of the Petroleum Society of CIM. The author thanks the Petroleum Society for the use of this material with a reminder that copyright remains with the Petroleum Society and that no other copies may be made without the express written consent of the Petroleum Society of CIM.)

Where n = RI (dimensionless), Bo is the oil formation volume factor (rb/stb), Rs is the gas solubility in oil (scf gas/stb oil), xi denotes the mole fraction of species i (dimensionless), and i denotes the molar refraction of species i (ml/mole). The Flory–Huggins regular solution theory expresses the interaction parameter proportionally to the enthalpy of mixing as (Huggins, 1941; Flory, 1942; Hirschberg et al., 1984; Wang and Buckley, 2001) √  = m /RT   a − m 2  or m = a − /RT 1/2 m (14-32) Where  is the Flory–Huggins interaction parameter (dimensionless), vm denotes the molar volume of the mixture excluding the asphaltene (ml/mole), a and m are the solubility parameters of the asphaltene and the mixture excluding the asphaltene MPa1/2  T is the absolute temperature (K), and R is the universal gas constant (8.31441 J/K-mole). m is calculated as the volume-weighted average using m =

m  i=1

i i

(14-33)

512

Formation Damage by Organic Deposition

Where m denotes the total number of species excluding the asphaltene, i is the solubility parameter MPa1/2 , and i is the volume fraction of species i in a mixture (dimensionless). Wang and Buckley (2001) estimate the molar volume of the flocculant (precipitant) p (ml/mole) from the PVT data using p ml/mole = 15890 × 105 Vg /11957Rs

(14-34)

Where Vg (rb) is the actual volume and Rs (scf/stb) is the solubility of the precipitant gas dissolved in crude oil at reservoir oil conditions. Wang et al. (2004) demonstrated that the RI measured at the onset of asphaltene flocculation RIp rendering asphaltenes unstable is related to the solubility parameter (essentially linearly) and hence the square root of the molar volume of the flocculant dissolved in oil as shown in Figure 14-43a by Wang et al. (2004) for a typical oil of 312 API and 232 g/mole average molecular weight, containing 3.7% (wt) n-C7 asphaltene. Comparison of the RI of live-oil predicted using Eq. (14-31) and the onset refractive index RIp measured at 188 F displayed in Figure 14-43b by Wang et al. (2004) indicates that they do not intersect and therefore the oil is stable in the considered pressure range. However, when mixed with a gas, the oil becomes unstable at different pressures at 70, 140, and 210 F temperatures as indicated by the intersection of the predicted onset refractive index curve with the measured refractive index curve, as shown in Figure 14-43c by Wang et al. (2004). In Figure 14-43d the plot of the onset of asphaltene flocculation pressure vs. temperature obtained from Figure 14-43c delineates the regions of stable and unstable asphaltene conditions. Civan (2006b) correlated these data as described below. Civan (2006b) states, The Arrhenius (1889) and Vogel–Tammann–Fulcher Equations (VTF) (Vogel, 1921, Tammann and Hesse, 1926, and Fulcher, 1925) have been widely facilitated for correlation of the temperature dependency of the parameters of various physical and chemical processes. As described by Civan (2004, 2005a), these are asymptotic exponential functions, expressed in a general form, as: ln f = ln fc −

E R T − Tc

(14-35)

where f represents a temperature dependent parameter (unit determined by the type of property), fc a pre-exponential coefficient (unit determined

Formation Damage by Organic Deposition

513

Figure 14-43. Effect of temperature on asphaltene onset pressure for asphaltenes destabilized by addition of lift gas. (a) Oil C onset conditions. (b) Oil C asphaltenes are predicted to be stable at all pressures. (c) Addition of lift gas 149 m3 /m3  destabilizes asphaltenes from Oil C (solid lines: RI of oil+lift gas; dashed lines: PRI at each temperature). (d) Onset pressure increases with increasing temperature for asphaltenes from Oil C + lift gas (after Wang et al., ©2004; reprinted by permission of the Society of Petroleum Engineers).

by the type of property), T and Tc the actual and critical-limit absolute temperatures (K), respectively, E the activation energy (J/kmol), and R the universal gas constant (J/kmol-K). Because Eq. (14-35) is a threeparameter empirical equation, a minimum of three data points are required for determination of its parameters. Whereas, the Arrhenius equation assumes Tc = 0. Therefore, a minimum of two data points are sufficient for estimation of the parameters of the Arrhenius equation.

514

Formation Damage by Organic Deposition 8.00 Arrhenius equation 7.95 Vogel–Tammann– Fulcher equation InP, P in psia

7.90

7.85 Arrhenius equation InP = 8.950 – 647.1/T R 2 = 0.99

7.80

Vogel–Tammann– Fulcher equation InP = 8.281 – 95.37/(T – 360.) R 2 = 1.00

7.75

7.70 0

0.002

0.004

0.006

0.008

1/(T-Tc), T and Tc in R

Figure 14-44. Correlation of the onset pressure of asphaltene flocculation vs. temperature data of Wang et al. (2004) using the Arrhenius and Vogel–Tammann–Fulcher type equations (after Civan, 2006; reprinted by permission of the Society of Petroleum Engineers).

Figure 14-44 by Civan (2006b) presents an accurate correlation of the predicted onset pressure of asphaltene flocculation vs. temperature data of Wang et al. (2004) by means the Arrhenius and Vogel–Tammann– Fulcher (VTF) equations.

14.6 ALGEBRAIC MODEL FOR FORMATION DAMAGE BY ASPHALTENE PRECIPITATION IN SINGLE PHASE Minssieux (1997) has demonstrated that the predominant mechanisms of the asphaltene deposition can be identified by means of the Wojtanowicz et al. (1987, 1988) analytic models. Minssieux also observed that the asphaltene precipitates existing in the injected oil can pass into porous media without forming an external filter cake. The characteristics of the oils used are given in Tables 14-2 and 14-3, and the conditions and results of the coreflood experiments are given

515

Formation Damage by Organic Deposition Table 14-2 Characteristics of Stock-Tank-Oils∗

Field

Reservoir SARA ANALYSIS temperature Res/Asph Viscosity ( C) Sat Ar Resins Asph. ratio (cP 20 )

Weyburn

50

401

461

85

5.3

16

13

Lagrave

80

657

228

75

4

19

7.7

Hassi– Messaoud Boscan (Reference) ∗

119 81

705

255

15

37

33 34

0.15 14



API

29 43 

1580

22

43

24

10

After Minssieux, ©1997 SPE; reprinted by permission of the Society of Petroleum Engineers.

Table 14-3 Characteristics of Crude and Asphaltenes∗ Crude origin % Asphaltene Average MW ( API) (weight) (vpo/toluene)

Asphaltenes analysis H/C

O/C

%S

Tmax ( C) pyrolysis

Weyburn 29

53

6000

100

0025

Lagrave 43

4

“7000–8700”

100

0010

380

416

H. Messaoud 45

015

1120 “well scales”

088

0034

080

420

8000

114

0039

670

406

Boscan (10 ) “as a reference” ∗

107

416

After Minssieux, ©1997 SPE; reprinted by permission of the Society of Petroleum Engineers.

in Tables 14-4 and 14-5 by Minssieux (1997). The analyses of typical data according to Wojtanowicz et al. (1987, 1988) formulae are given in Figures 14-45 and 14-46 by Minssieux (1997). Figure 14-45 shows the results of the analysis of the GF3 test data considering the possibility of the gradual surface deposition, single pore plugging, and in situ cake formation by pore-filling mechanisms in formation damage. As can be  seen, only the K/K0 vs. PV (pore volume) data yields a straightline plot, indicating that the damage mechanism is the gradual surface deposition. In the case of the GV5 data, Figure 14-46 indicates that the damage mechanism is the in situ cake formation by pore filling, because K0 /K vs. PV data yields a straight-line plot for this case (see Table 10-1).

516

Formation Damage by Organic Deposition Table 14-4 Conditions of Core Floods∗ Petrophysical data

Injection rate (cm3 /hour)

Test ref.

Type of rock T( C) Crude used

ø%

GF 1

Fontainebleau sandstone

50

Weyburn

131

GF 2 GF 3

id. id.

id. id.

id. id.

136 137

87 774

50 80 10 10 20 50 80

GF 12

id.

80

H. Messaoud

8

6

10

GVM 5

50

Weyburn

247

29

10

GVM 10

Vosges sandstone id.

50

Weyburn

243

122

GVM 13 GVR 8 GVR 11

id. id. id.

80 50 80

Lagrave Weyburn Lagrave

26 226

73 152

10 5 10 10

GP 9

Palatinat sandstone

80

H. Messaoud

226

11

GP 14

id.

id.

id.

23

2

HMD 11

Res. rock from HMD id.

id.

id.

id.

id.

HMD 26 ∗

71

KH (mD)

107

067

10 5 5

8

After Minssieux, ©1997 SPE; reprinted by permission of the Society of Petroleum Engineers.

14.7 PLUGGING–NONPLUGGING PATHWAYS MODEL FOR ASPHALTENE DEPOSITION IN SINGLE PHASE Ali and Islam (1997, 1998) considered only asphaltene deposition and resorted to a simplified, single-phase formation damage modeling approach according to Gruesbeck and Collins (1982a). Here, their model is presented in a manner consistent with the rest of the presentation of this chapter. Also, a few missing equations are supplied. Note that this model applies for undersaturated oils.

W.

W. Lagrave

W. Lagrave

H.MD

H.MD

H.MD

H.MD

GVM 5

GVM 10 GVM 13

GVR 8 GVR 11

GP 9

GP 14

HMD 11

HMD 26

0.41 (“Resins”)

0.58 (“Resins”)

No plugging

0.33

0.11 <0.10

0.48 –

1.0

0.21 0.34

0.30

Uniform

Uniform

Decreasing

Decreasing Near core inlet accumulation

Decreasing –

Decreasing

Uniform Decreasing

Uniform

Deposition profile inlet→outlet

After Minssieux, ©1997 SPE; reprinted by permission of the Society of Petroleum Engineers.

W. H.MD

GF 3 GF 12

∗

Weyburn W.

Crude used

GF 1 GF 2

Test ref.

Average amount of deposits (mg/g rock)

6 (50 after 700 PV)

–

60

87

89 <10

88

58.5 0 (47 after 150 PV)

20 42.5

K reduction (%) after 50 PV

Table 14-5 Conditions of Core Flood Tests∗

Reservoir-rock core samples from H.MD field

Palatinat sandstone (Kaolinite) Crude injected with additive

Vosges sandstone II Final KH difficult to measure

Additive in flowing crude (750 ppm)

Vosges clayey sandstone (illite)

Model type of porous medium (pure silica)

Observations Formation Damage by Organic Deposition

517

518

Formation Damage by Organic Deposition

4

RUN GF3

3.5 3

Koil variation

K o/K

2.5 2 1.5 1 K /Ko

0.5 0

K /Ko

0

10

20

30

40

50

60

70

80

Crude PV injected

Figure 14-45. Correlation of the experimental permeability reduction data reveals a uniform surface deposition mechanism (after Minssieux, ©1997 SPE; reprinted by permission of the Society of Petroleum Engineers).

6

RUN GV5

5

Koil evolution

K o /K 4 3 2 1 0

K /Ko K /Ko 0

10

20

30 40 Crude PV injected

50

60

70

Figure 14-46. Correlation of the experimental permeability reduction data reveals a pore-blocking deposition mechanism (after Minssieux, ©1997 SPE; reprinted by permission of the Society of Petroleum Engineers).

Formation Damage by Organic Deposition

519

The rate of deposition in the plugging paths is given by

p = kp up p 1 + bp t

(14-36)

where b is an empirical constant. p = 0

t=0

(14-37)

The deposition in the nonplugging paths is expressed by

np = kd wpL − ke np unp − uc t np = 0

(14-38)

t=0

(14-39)

ke = 0

unp ≥ uc

(14-40)

ke = 0

unp < uc

(14-41)

Note

The fluid flux in the plugging pathways is given by   Kp up = u fp Kp + fnp Knp

(14-42)

Note that Ali and Islam (1997, 1998) used the original Gruesbeck and Collins (1982a) equation, which misses the fp and fnp terms in Eq. (14-42), instead of the corrected Eq. (14-42) given independently by Civan (1992) and Schechter (1992). The flow in the nonplugging pathways is given by   Knp (14-43) unp = u fp Kp + fnp Knp Note that fp + fnp = 1

(14-44)

Following Gruesbeck and Collins (1982a), Ali and Islam (1997) assumed fp and fnp as some characteristic values of the porous medium and determined them to match the model predictions to experimental data.

520

Formation Damage by Organic Deposition

The permeability impairments in the plugging and nonplugging pathways were represented by the Gruesbeck and Collins (1982a) empirical expressions, given, respectively, by

Kp Kpo exp −4p (14-45) Knp

Knpo 1 + np

(14-46)

where Kpo and Knpo denote the permeabilities of the plugging and nonplugging pathways, respectively, before damage, and  and  are some adjustable constants. Ali and Islam (1997) assumed the same concentrations in the plugging and nonplugging pathways. Thus, the mass balance of the suspended particles of asphaltene in the flowing fluid can be expressed as (Civan, 1995a, 1996a)  

wpL wpL wpL  + L uL =

L DpL ˙ L wpL + m ˙ p −m

L t x x x (14-47) In laboratory core tests, the mass rate of phase L added per unit bulk volume of porous media is zero: m ˙L=0

(14-48)

The mass rate of asphaltene particles added to phase L per unit bulk volume of porous media is given by   p ea p + (14-49) m ˙ p = −p t t where p and ea p denote the asphaltene retention by filtration and adsorption, respectively. The formulation given by Ali and Islam (1997) implies that they expressed the dispersion coefficient as a linear function of the interstitial velocity of the fluid: DpL = L

(14-50)

where  is an empirically determined coefficient and L is the interstitial velocity, given by: u  (14-51) L = L

Formation Damage by Organic Deposition

521

The symbol  denotes the tortuosity of porous media. Assuming a constant rate injection of oil into a core plug and constant oil density, and applying Eqs (14-48)–(14-51), Eq. (14-47) can be written as   wpL wpL 2 wpL p ea p

L + L uL = L uL + (14-52) − p t x x2 t t It can be shown that Eq. (14-52) can be reformulated in the form given by Ali and Islam (1997, 1998). However, the last term in their equation appears to have an error, because  in their equation should be replaced by /t. The initial and boundary conditions for Eq. (14-52) are given by wpL = 0 o wpL = wpL − 

0 ≤ x ≤ L t = 0

(14-53)

wpL  x

(14-54)

wpL = 0 x

x = 0 t > 0

x = L t > 0

(14-55)

Using the input data given in Table 14-6, Ali and Islam (1998) obtained the results presented in Figures 14-47–14-49.

14.8 TWO-PHASE AND DUAL-POROSITY MODEL FOR SIMULTANEOUS ASPHALTENE–PARAFFIN DEPOSITION Here, the formulation of Civan’s (1995a) model is presented.

14.8.1

Considerations of the Model

The reservoir fluid system can be single-phase or multiphase depending on the prevailing reservoir conditions. Above the bubble-point pressure conditions, the oil is undersaturated and single phase. Below the bubblepoint pressure conditions, the oil is saturated and can be two-phase. Civan (1995a) developed a model that is applicable for both conditions. His model also considered the possibility of simultaneous deposition of asphaltenes and paraffins. As stated by Civan (1995a), “Although they are a mixture of different molecular weight components, the paraffins and

522

Formation Damage by Organic Deposition Table 14-6 Model Parameters∗ Experimental Parameters W0 , wt% K, mD n0 , mg/g q, mL/min

1   API r , g/mL Pore volume, cm3 Run 1, mL/min Run 2, mL/min Run 3, mL/min Run 4, mL/min

3 11.3 200 0.5, 1, 2, 3 0.35 29.29 2.71 136 0.5 1 2 3

Adjustable Parameters , cm ma /mo S ma K1  hour −1 K2  hour −1 ke  cm−1 kd  second−1 uc  cm · second−1 kp  cm−1 b cm−1  fp  Kpi , mD Knpi /Kpi

0.1 15 100 0.05 n0 20 0.008 6.3 0.00085 through 0.01 0.032 0.2 50 10 0.82 10 11.3 10

∗ Modified after Ali and Islam, ©1998 SPE; reprinted by permission of the Society of Petroleum Engineers.

asphaltenes are lumped into two groups as the paraffin, p, and the asphaltene, a, pseudo-components. The other components of the oil are grouped as the oil pseudo-component, o, which acts as a solvent. The mixture of the various gases are grouped as the gas pseudo-component, g.” Thus, Civan’s (1995a) model considers four pseudo-components: (a) paraffin, par, (b) asphaltene, asp, (c) oil, o, and (d) gas, g. The system of the fluids and the porous formation is considered in three phases as the vapor, V, liquid, L, and solid, S, following Ring et al. (1994). The solid

Formation Damage by Organic Deposition

523

Figure 14-47. Permeability reduction for injection at 0.5 mL/min rate (after Ali and Islam, ©1998 SPE; reprinted by permission of the Society of Petroleum Engineers).

Figure 14-48. Permeability reduction for injection at 2 mL/min rate (after Ali and Islam, ©1998 SPE; reprinted by permission of the Society of Petroleum Engineers).

phase is considered in two parts: (1) porous matrix (unchanged), and (2) organic deposits (varying). Civan (1995a) considers that the paraffin and asphaltene transport may occur in both dissolved and precipitate forms depending on the state of saturation of the oil phase. This assumption is supported by Mansoori (1997) who points out that “   asphaltenes are partly dissolved and partly in colloidal state (in suspension) in oil peptized (or stabilized) primarily by resin molecules that are adsorbed on asphaltene surface.” The permeability impairment may occur by (a) gradual pore size reduction, and (b) pore throat plugging, obstruction, and sealing. The ratio of the plugging and nonplugging paths vary by organic deposition. Single- or two-phase fluid conditions may exist depending on whether the condition is above or below the bubble-point pressure. The various phases are assumed at thermal equilibrium within the bulk volume. Non-Newtonian fluid behavior is considered for high concentrations

524

Formation Damage by Organic Deposition

Figure 14-49. Permeability reduction for injection at 3 mL/min rate (after Ali and Islam, ©1998 SPE; reprinted by permission of the Society of Petroleum Engineers).

of organic precipitates and solutes. Non-Darcy flow behavior is assumed for flow through passages narrowing due to precipitation. 14.8.2

Porosity and Permeability Relationships

The porosity and permeability alterations are predicted based on a modified version of the plugging and nonplugging pathways concept of Gruesbeck and Collins (1982a). Relatively smooth and large diameter flowpaths are assumed to mainly undergo a surface deposition and are called nonplugging. Highly tortuous and variable diameter flowpaths are called plugging. The retainment of organic deposits in the plugging pathways occurs by jamming and pore throat blocking. Consider that po and npo denote the pore volume fractions and p and np are the fractions of the bulk volume occupied by organic deposits of the plugging and nonplugging pathways of the porous media. Thus, the instantaneous porosities in the plugging and nonplugging flow paths are given, respectively, by

p = po − p

(14-56)

np = npo − np

(14-57)

Although Gruesbeck and Collins (1982a) assume characteristic constant values, it is reasonable to consider that the fractions of the bulk volume

Formation Damage by Organic Deposition

525

containing the plugging and nonplugging pathways vary during deposition and are estimated by, because of the lack of a better theory, fp =

p

(14-58)

fnp =

np

(14-59)

The instantaneous and initial porosities of the porous medium are given, respectively, by

= p + np

(14-60)

o = po + npo

(14-61)

The total organic deposit volume fraction and the instantaneous porosity are given, respectively, by  = p + np

(14-62)

= o − 

(14-63)

The rate of deposition in the plugging pathways can be expressed by p /t = kp up p p

(14-64)

subject to the initial condition  p =  po 

t=0

(14-65)

for which kd = 0

when t ≥ tp

kd = 0

t < tp

(14-66) (14-67)

Here, tp is the time of initiation of the particle bridges and jamming. This is the time at which the ratio of the pore throat to particle diameter drops to below its critical value determined by the following empirical correlation (Civan, 1990, 1996a):     

Dt Dt Dt <  = A 1 − exp −BRep + C (14-68) Dp Dp cr Dp cr

526

Formation Damage by Organic Deposition

in which the particle Reynolds number is given by

Rep = p p uDp p /  p

(14-69)

The symbol p denotes the tortuosity of the plugging paths. The rate of deposition in the nonplugging tubes can be expressed by (Civan, 1994, 1995, 1996a) np = kd unp np 2/3 np − ke np e w − cr t

(14-70)

subject to the initial condition np = npo 

t=0

(14-71)

ke = 0

w ≥ cr

(14-72)

ke = 0

w < cr

(14-73)

Here,

For simplification purposes, Civan (1995a) assumed that organic deposits are sticky and, therefore, once deposited they cannot be removed anymore. Consequently, the second term in Eq. (14-70) can be dropped. Mansoori (1997) tends to support this argument. Although Leontaritis (1998) considered the possibility of erosion of deposits, it is not apparent if he actually implemented this possibility in his calculational steps. kd and ke are the surface deposition and mobilization rate constants, respectively. e is the fraction of the uncovered deposits estimated by e = exp −k

(14-74)

Where k is an empirical coefficient. cr is the minimum shear stress necessary to mobilize the surface deposits. w is the wall shear stress given by the Rabinowitsch–Mooney equation (Metzner and Reed, 1955): w = k 8/D n



(14-75)

in which the interstitial velocity, v, is related to the superficial velocity, u, as follows (Dupuit, 1863): v=

unp

(14-76)

527

Formation Damage by Organic Deposition

Where the symbol np denotes the tortuosity of the nonplugging paths, and the mean pore diameter is given by 

1/2 D ∼ 4 2np Knp / np (14-77) The permeabilities of the plugging and nonplugging pathways are given by the following empirical relationships (Civan, 1994a,c): 

n

Kp = Kpo exp − po − p 1 = Kpo exp −np 1

(14-78)

and

Knp = Knpo

np

npo

n2

= Knpo

np 1−

npo

n 2 (14-79)

Where  n1 , and n2 are empirical constants. Then, the average permeability of the porous medium is given by K = fp Kp + fnp Knp

(14-80)

The superficial flows in the plugging and nonplugging pathways are given respectively, by up =

uKp K

(14-81)

unp =

uKnp K

(14-82)

The total superficial flow is given by (Gruesbeck and Collins, 1982a) u = fp up + fnp unp

(14-83)

Considering the simultaneous deposition of paraffins and asphaltenes, p and np in Eqs (14-56) through (14-62) denote the sum of the paraffins and asphaltenes, that is, p = p par + p asp

(14-84)

np = np par + np asp

(14-85)

528

14.8.3

Formation Damage by Organic Deposition

Description of Fluid and Species Transport

The preceding treatment of the porous media impairment phenomena implies that the suspended particle and dissolved species concentrations may be different in the plugging and nonplugging pathways. Then, separate sets of balance equations are required for the plugging and nonplugging pathways. Consequently, the numerical solution would require a highly intensive computational effort. However, this problem can be conveniently circumvented by assuming that there is hydraulic interaction between these pathways (i.e., they are not isolated from each other). 1. The mass balances are considered for the following four pseudocomponents: a. Gas b. Oil c. Suspended paraffins and asphaltenes d. Dissolved paraffins and asphaltenes 2. Total thermal equilibrium energy balance is considered. 3. Non-Newtonian fluid description using the Rabinowitsch–Mooney equation is resorted. 4. The Forhheimer equation for the non-Darcy flow description is used. 5. The average flow is defined as a volume fraction weighted linear sum of the flow through the plugging and nonplugging paths according to Gruesbeck and Collins (1982a). 6. The average permeability is defined as a volume weighted linear sum of the permeabilities of the plugging and nonplugging paths according to Gruesbeck and Collins (1982a). a. In the plugging paths, a snowball deposition effect is represented by an exponential decay function. b. In the nonplugging paths, a gradual pore size reduction, represented by the power law function, is considered. 7. The precipitation of the asphaltene and paraffin is predicted, applying Chung’s (1992) thermodynamic model, discussed previously, for nonideal solutions to determine the cloud point and the quantity of the precipitates to be formed. The total mass balance of the gas component is given by





 ˙ g L = 0 ˙ g V + m

SV V + SL L wg L + V uV + L uL wg L + m t x (14-86)

Formation Damage by Organic Deposition

529

The first, second, and third terms respectively represent the accumulation, transport, and well production. Assuming that the oil component exists only in the liquid phase and does not vaporize into the gas phase, the oil component mass balance is given by    SL L woL + L uL woL + m ˙ OL = 0 t x

(14-87)

for which Ring et al. (1994) assumed woL 10. Considering that organic precipitates only exist in the liquid phase, because it is the wetting phase for these particles, the suspended paraffin and asphaltene particle mass balances are expressed by



 ˙ p L

SL L wp L + p p + uL L wp L + m t x    wp L 

SL DpL =  p = asphaltene or paraffin x x

(14-88)

Note that L wp L = p L = p p L

(14-89)

If the particle density, p , is assumed constant, and the suspended particle content is expressed by the volume fraction of organic substance (paraffin or asphaltene), pL , according to Eq. (14-89), then Eq. (14-88) can be simplified as  



p m p L ˙ pL  

SL DpL = +  +

SL p L + u  t x L p L x t p x p = asphaltene or paraffin

(14-90)

Note that both Ring et al. (1994) and Civan (1996a) neglected the term on the right, representing the dispersion of particles. The mass balances of the paraffin and asphaltene dissolved in oil is given by       m ˙ iL =  SL L xiL +  u x +

SL DiL L xiL  t x L L iL Mi x x i = asphaltene or paraffin

(14-91)

530

Formation Damage by Organic Deposition

where S is the saturation,  is the density, t is the time, x is distance, u is the volume flux, pL is the volume fraction of the organic precipitates in the liquid phase, wpL denotes the mass fraction, xiL is the mole fraction of organic dissolved in the oil, Mi is the molecular weight and DiL is the dispersion coefficient. p /t represents the volume rate of retention of organic deposits in porous media determined according to Eqs (14-62), (14-63), and (14-70). Assuming that the various phases are at thermal equilibrium at a temperature of TV = TL = TS = T , the total porous media energy balance is given by   SV V UV + SL L UL + par par Upar + asp asp Uasp t

 + 1 − − par − asp S US  + V uV HV + L uL HL + q˙ V + q˙ L x  P  P = uV V + uL L +  SV V + SL L + par par + asp asp x x x 

T + 1 − − par − asp s  (14-92) x where U and H are the internal energy and enthalpy, respectively, q˙ V and q˙ L denote the energy loss, p is pressure, denotes the thermal conductivity, and T is temperature. Ring et al. (1994) simplified Eq. (14-92) as  

SV V UV + SL L UL + Sp p Up + 1 − s Us t    T  + V HV uV + L HL uL + QL + QH + QE =

x x x

(14-93)

The first, second, and last terms represent the accumulation, convection, and conduction heat transfer. The QL  QH and QE terms represent the heat carried away by production at wells, heat losses into formation surrounding the reservoir, and the external heat losses. The deposition of organic precipitates in porous media reduces the flow passages causing the fluids to accelerate. Therefore, Darcy’s law

Formation Damage by Organic Deposition

531

is modified as following, considering the inertial effects and horizontal flow, according to the Forchheimer equation (Civan, 1996a): uJ = −−1 J NndJ KpJ /x 

J = V or L

(14-94)

where K is the permeability, pJ is the fluid pressure, and the non-Darcy number is given by NndJ = 1 + ReJ −1

(14-95)

in which the porous media Reynolds number is given by ReJ =

J uJ K J

(14-96)

where  is the inertial flow coefficient, and J and J denote the density and viscosity of a fluid phase J. Note that the formulations presented here are applicable for multidimensional cases encountered in the field if /x is replaced by · and a vector-tensor notation is applied. 14.8.4

Phase Transition

The source terms appearing on the right of Eqs (14-86)–(14-93) are considered a sum of the internal (rock–fluid and fluid–fluid interactions) and external (wells) sources. When the oil is supersaturated, the internal contribution to the source terms in Eq. (14-88) is determined as the excess quantity of organic content of oil above the organic solubility at saturation conditions determined by Chung’s (1992) thermodynamic model:

s s (14-97) /t xpL > xpL m ˙ pL =  xpL − xpL m ˙ pL = 0 

s xpL < xpL 

p = asphaltene or paraffin

(14-98)

s where xpL represents the mole-fraction of dissolved organic at saturation. Civan (1995a) carried out case studies similar to Ring et al. (1994) using the Sutton and Roberts data (1974). Figure 14-50 shows a comparison of the predicted and the measured permeability impairments by paraffin deposition for cases below and above bubble-point pressure. Note that, above the bubble point pressure, only the liquid phase exists and there is more severe formation damage. Whereas, below the bubble point pressure, both the liquid and the vapor phases exist and there is less severe formation damage.

532

Formation Damage by Organic Deposition

Figure 14-50. Comparison of the Sutton and Roberts (1974) experimental data and simulation results for permeability reduction by organic deposition below and above bubble point pressure.

14.9 SINGLE-POROSITY AND TWO-PHASE MODEL FOR ORGANIC DEPOSITION Ring et al. (1994) developed a two-phase model considering only the paraffin precipitation. They assumed that (1) oil is always saturated with the paraffin, (2) the solution is ideal, (3) paraffin deposition obeys a firstorder kinetics, (4) pores undergo an irreversible continuous plugging, and (5) permeability reduction obeys a power law: K Ko



o

m (14-99)

Ring et al. (1994) determined that m 8 for paraffin deposition. Wang et al. (1999) and Wang and Civan (2005a,b) developed improved models considering the simultaneous deposition of asphaltenes and paraffins. These models incorporate the essential features of Civan’s (1995a) dual-porosity model for a single-porosity treatment. The formulation of the Wang and Civan (2005a,b) model and its experimental verification are described in the following. However, their formulation is presented in a manner consistent with the material presented in this book.

Formation Damage by Organic Deposition

14.9.1

533

Model Formulation∗

Wang and Civan (2005a,b) state (©2005 ASME, reprinted by permission of the American Society of Mechanical Engineers) The organic deposition during oil production by primary depletion under isothermal conditions is preferentially of the asphaltene types. Prior to the initiation of primary oil recovery, asphaltene is completely dissolved in the reservoir oil. Upon production, the reservoir oil pressure continuously declines. Asphaltene begins to separate and precipitate from the oil when the pressure decreases to the onset of asphaltene precipitation pressure Pp . Asphaltene precipitation attains a maximum value around the bubble-point pressure. When the pressure decreases in the below bubble-point region, then some asphaltene precipitates are redissolved back into oil. However, in some situations encountered in the field involving temperature variation, paraffin and asphaltene may precipitate and deposit together. For example, injection of fluids at temperatures colder than the reservoir oil temperature during hydraulic fracturing or acid stimulation processes may reduce the conditions of the reservoir oil to below the cloud point of paraffin. After the fracturing, the well begins to produce oil and the pressure in the near wellbore region declines. As a result of the simultaneous effect of temperature decrease and pressure depletion, paraffin and asphaltene may deposit in porous rock simultaneously in the near-wellbore region. For such applications, it is necessary to use a model for simultaneous deposition of paraffin and asphaltene in porous media.

Wang and Civan (2005a,b) used the real-solution theory to describe the dissolution/precipitation of paraffin in crude oil, the polymer-solution theory to describe the dissolution/precipitation of asphaltene in oil; an improved one-dimensional, three-phase, and four-pseudo-component model to represent the transport of paraffin and asphaltene precipitates; and a deposition model including the static and dynamic pore surface depositions and pore throat plugging to describe the deposition of paraffin and asphaltene. The model was developed for analysis of the laboratory core flow tests as well as for field-scale impairment by organic deposition. The capillary pressure effects between vapor and liquid phases have been neglected. The oil, gas, and solid phases were assumed at thermal equilibrium. ∗

Reprinted by permission of the Society of Petroleum Engineers from Wang et al., ©1999 SPE, SPE 50746 paper.

534

Formation Damage by Organic Deposition

The oil, gas, paraffin, and asphaltene pseduo-components are denoted by O, G, P, and A, respectively. The vapor and the liquid phases are denoted by V and L, respectively. The paraffin and asphaltene pseudocomponents exist only in the liquid phase (a suspension of the oil, and the paraffin and asphaltene particles) and as organic deposits in porous media. Considering both the free and the dissolved gases, the gas component mass balance equation is given by   SV V + SL L wGL +  · V uV + L uL wGL = 0 t

(14-100)

where represents the porosity of the porous media, Sv  v  uv are the saturation, density, and flux of the vapor phase, respectively, and SL  L  uL are the saturation, density, and flux of the liquid phase, respectively. wGL represents the mass fraction of the dissolved gas in the liquid phase and t denotes the time. The divergence operator is given by  ≡ i/x + j/y + k/z where i, j, and k denote the unit vectors in the x y, and z Cartesian directions. Considering that the oil component exists only in the liquid phase, its mass balance is given by   SL L wOL +  · L uL wOL = 0 t

(14-101)

where wOL is the mass fraction of the oil component in the liquid phase. The volume fraction is resorted to express the concentrations of the paraffin and asphaltene particles suspended in the oil because the permeability impairment in porous media can be expressed conveniently. On the other hand, mass fraction is more convenient to express the concentrations of the paraffin and asphaltene dissolved in the oil. The paraffin mass balance equation is expressed by considering that it may be partly dissolved and/or suspended as particles in the liquid phase and deposited in porous media:   SL L wP + SL P P + P P +  · uL L wP + uL P P = 0 t (14-102) where A is the volume fraction of the suspended paraffin in the liquid phase and P is the density of the paraffin. wPL represents the mass fraction of the dissolved paraffin in the liquid phase. wSPL is the mass ratio of the paraffin precipitates suspended in the liquid phase to the

Formation Damage by Organic Deposition

535

liquid phase. P is the volume fraction of the deposited paraffin in the bulk porous media. The asphaltene mass balance equation is written similarly as   SL L wA + SL A A + A A +  · uL L wA + uL A A = 0 t (14-103) in which A is the volume fraction of the suspended asphaltene in the liquid phase and A is the density of asphaltene. wAL represents the mass fraction of the dissolved asphaltene in the liquid phase. wSAL is the mass ratio of the asphaltene precipitates suspended in the liquid phase to the liquid phase. A is the volume fraction of the deposited asphaltene in the bulk porous media. The vapor- and liquid (suspension)-phase volumetric fluxes are given by Darcy’s equation, respectively, as uV = −

kRV K · PV + V gk V

(14-104)

uL = −

kRL K · PL + L gk L

(14-105)

where K is the absolute permeability tensor of the porous media, and kRV and V are the relative permeability and viscosity of the vapor phase, respectively. kRL and L are the relative permeability and viscosity of the liquid phase, respectively. The capillary pressure between the vapor and liquid phases is neglected. Thus, PV = PL = P represents the pressure of the pore fluids. The total thermal equilibrium energy balance equation is expressed as  

SV V HV + SL L HL + P P HP +A A HA t  + 1 − − P − A F HF +  · V uV HV + L uL HL   

SV V + SL L + P P + A A T =· (14-106) + 1 − − P − A F where HV  HL  HP  HA , and HF are the enthalpies, and V  L  P  A , and F are the thermal conductivities of the vapor and liquid phases, paraffin and asphaltene, and porous media, respectively. T is the equilibrium temperature of the system.

536

Formation Damage by Organic Deposition

The saturations of the flowing vapor and liquid phases add up to 1.0: SV + SL = 10

(14-107)

The paraffin and asphaltene deposition rates are given, respectively, by

P = kdP SL P − keP P L − LcrP + ktP uL SL P t

(14-108)



A = kdA SL A − keA A L − LcrA + ktA uL SL A t

(14-109)

in which the first term represents the pore surface deposition and kd is the pore surface deposition rate coefficient. The second term represents the entrainment of the surface deposits by the flowing fluid and ke is the pore surface entrainment rate coefficient. L is the interstitial velocity of the liquid (oil) phase and Lcr is the critical interstitial velocity of the liquid phase required for mobilization or entrainment of the pore surface deposits. The third term represents the pore throat plugging deposition and kt is the plugging deposition rate coefficient. The pore surface entrainment rate coefficient is assigned as kej = keji  kej = 0

when L > crL  j = P A otherwise

j = P A

(14-110) (14-111)

keji is the value of the entrainment rate coefficient. The pore throat plugging deposition coefficient is considered based on the following criteria: ktj = ktji 1 + j P + A  ktj = 0

Dt ≤ Dtcr  j = P A

otherwise

j = P A

(14-112) (14-113)

ktji is the initial value of the plugging deposition rate constant. j represents empirically determined constants. The instantaneous porosity is given by

= i − P − A

(14-114)

and the instantaneous permeability is estimated by (Civan et al., 1989) K = fp Ki  / i 3

(14-115)

Formation Damage by Organic Deposition

537

where i and Ki are the initial porosity and permeability of the porous media, respectively. fp is a parameter representing the extent of pore connectivity.

14.9.2

Model Assisted Analysis of Laboratory Data

Wang and Civan (2005a,b) solved the model equations using an implicit finite-difference method with a block-centered grid system. They discretized the time derivative by the first-order backward finite-difference approximation and the space derivatives by means of a second-order central finite-difference approximation. They generated stable numerical solutions using uniform time increments and grid sizes. They determined the best estimates of the parameters by history matching of experimental data. The data used in the test cases and the best estimates of the model parameters are presented in Tables 14-7 and 14-8 by Wang and Civan (2005a,b). The typical case studies carried out by Wang and Civan (2005a,b) are briefly described in the following. Case 1 – Simultaneous Paraffin and Asphaltene Deposition

Sutton and Roberts (1974) first heated a Berea sandstone core saturated with a Shannon Sand crude oil to 544 C and then cooled the outlet of the core to 211 C for 2 hours without any flow. The cloud point of the oil used in their experiment was 378 C. The paraffin and asphaltene contents of the crude oil were 4.1 and 0.7 weight percents, respectively. Then, they conducted a flow experiment by injecting the Shannon Sand crude oil at a rate of 0.38 ft/day (Ring et al., 1994). The temperature of the outlet of the core was kept at 211 C. They first simulated the static pore surface deposition during 2 hours of cooling without fluid flow. Then, they simulated the damage during flow. The pore throat plugging and deposit entrainment did not take place as indicated by the estimated values of rate constants given in Table 14-7. Figure 14-51 shows that the simulated results are satisfactory. Case 2 – Simultaneous Paraffin and Asphaltene Deposition

Sutton and Roberts (1974) injected a Muddy formation crude oil into a Berea sandstone core at a rate of 0.30 ft/day (Ring et al., 1994). The outlet temperature of the core was kept at 211 C. The cloud point temperature

538

Formation Damage by Organic Deposition Table 14-7 Parameters for Cases 1 and 2∗

Experiment Experimental Conditions Tin   C Tout   C Bubble-point pressure, psia Flow rate, ft3 /day Back pressure, psia Gas pseudo-component Mg , g/mole gsc  g/cm3 Oil pseudo-component Mo , g/mole osc  g/cm3 Paraffin pseudo-component MP , g/mole wPS % Psc  g/cm3 TPM   C HP , cal/g-mole Asphaltene pseudo-component MA , g/mole wAs (%) Asc  g/cm3

1

2

54.4 21.1 2050 0.38 1900

54.4 21.1 2050 0.30 1900

16.0 0.00083

16.0 0.00083

104.11 0.72

122.51 0.75

522.4 4.1 0.83 75.7 26,000

478.7 6.1 0.98 71.7 23,600

2,500 0.7 1.1

2,500 0.1 1.1

30.5 2.5 0.25 0.405

30.5 2.5 0.25 0.314

Core Properties L, cm D, cm

o , fraction Ko , Darcy Simulation Parameters Grid spacing, x, cm Time increment, t, sec Number of blocks Deposition Parameters Dptcr , cm vcrL , cm/sec kdP = kdA , 1/sec kePi = ketAi , 1/cm ktPi = ktAi , 1/cm P = A , constant

2.54 40 12

2.54 40 12

N/A N/A 0.0241 0.0 0.0 0.0

N/A N/A 0.0182 0.0 0.0 0.0

Deposition mechanism

Surface deposition

Surface deposition

∗

Modified after Wang et al., ©1999 SPE; reprinted by permission of the Society of Petroleum Engineers, and Wang and Civan, ©2005b ASME; reprinted by permission of the American Society of Mechanical Engineers).

29.0 5.3

50 50

0.00048 0.0 0.0017 0.0 0.07 35 0.91

Oil Properties API of Crude Oil Asphaltene Content, wt. %

Experimental Data Flow Rate, cm3 /hour Temperature,  C

Deposition Parameters Dptcr  cm crL  cm/sec kd  1/sec ke  1/cm kt  1/cm , constant fp , constant

∗

Surface deposition, deposit entrainment

0.0145 0.0018 0.69 0.0 0.0 1.0

10 50

29.0 5.3

77.4 13.7 6.0 2.3

GF3

Surface deposition, deposit entrainment

0.01 0.0051 0.003 0.0 0.0 1.0

10 50

29.0 5.3

18.0 24.3 6.0 2.3

GV10

Surface deposition, deposit entrainment

0.01 0.0128 0.012 0.0 0.0 1.0

10 50

29.0 5.3

29.0 24.7 6.0 2.3

GV5

Surface deposition, deposit entrainment

0.000643 0.0275 0.0006 0.0 0.0 1.0

10 80

43.0 0.15

1.1 22.6 6.0 2.3

GP9

After Wang et al., ©1999 SPE, and Wang and Civan, ©2005c SPE; reprinted by permission of the Society of Petroleum Engineers.

Surface deposition, pore throat plugging

107 13.1 6.0 2.3

Core Properties Initial Permeability, Ko  mD Initial Porosity, o , % Length of Core Sample, cm Diameter of Core Sample, cm

Deposition Mechanism

GF1

TESTS

Table 14-8 Parameters for Case 3∗

Surface deposition, pore throat plugging

0.00016 0.0 0.0065 0.0 0.035 0.0 0.96

8 80

43.0 0.15

0.67 7.1 6.0 2.3

HMD26

Formation Damage by Organic Deposition

539

540

Formation Damage by Organic Deposition

Ratio of average permeability to initial permeability (K/Ko, fraction)

1.0 Experiment 1 data 0.8 Simulated data for Experiment 1

0.6 0.4 0.2 0.0 0

2 3 4 1 Injection pore volume of oil (PV)

5

Figure 14-51. Comparison of the simulation results with the Experiment 1 data of Sutton and Roberts (1974) (after Wang and Civan, ©2005 ASME; reprinted by permission of the American Society of Mechanical Engineers).

of the oil sample is 35 C. The paraffin and asphaltene contents of the crude oil were 6.1 and 0.1 weight percents, respectively. The pore surface depositions occurred, but the pore throat plugging and deposit entrainment did not occur as indicated by the values of the rate constants given in Table 14-7. Because the oil and core properties are very close for Cases 1 and 2, the permeability damage is also similar, as shown in Figures 14-51 and 14-52. Figure 14-52 shows the satisfactory simulated results.

Ratio of average permeability to initial permeability (K/Ko, fraction)

1.0 Experiment 2 data 0.8

Simulated data for Experiment 2

0.6 0.4 0.2 0.0 0

2 3 4 1 Injection pore volume of oil (PV)

5

Figure 14-52. Comparison of the simulation results with the Experiment 2 data of Sutton and Roberts (1974) (after Wang and Civan, ©2005 ASME; reprinted by permission of the American Society of Mechanical Engineers).

541

Formation Damage by Organic Deposition

Case 3 – Asphaltene Deposition

Ratio of average permeability to initial permeability (K/Ko, fraction)

Wang and Civan (2005a) describe that Minssieux (1997) used the dead oils obtained from the Weyburn oil (Canadian oil) containing 5.3% asphaltene and 8.5% resin by weight, and the Hassi–Messaoud crude oil (Algerian oil) containing 0.15% asphaltene. Therefore, the fluid system used in the core tests was single-phase. Because Minssieux (1997) did not report the compositions of these oils, Wang and Civan (2005a,b) approximated the compositions of the Weyburn and Hassi–Messaoud crude oils using the compositions of the dead-oils that Hirschberg et al. (1984) have provided. Wang and Civan (2005a,b) adjusted the shift parameters, eccentric factor, and critical properties of the C7+ fraction to match the present oil asphaltene contents. Minssieux (1997) used the Fontainebleau, Vosges, and Palatinat sandstones (permeability ranging from 0.67 to 107 mD and porosities ranging from 7.1 to 24.7%) and a HMD (Hassi–Messaoud) reservoir rock sample. Minssieux (1997) injected the dead-oils into the horizontal core samples (5.0 to 7.0 cm long and 2.3 cm diameter) at flow rates ranging from 8 to 10 cm3 /hour. Minssieux (1997) conducted the core tests at 50 C and 80 C temperatures by applying a 145 psia backpressure. The simulation results compared well with the measurements of the six Minssieux (1997) experiments, referred to as GF1, GF3, GV5, GV10, GP9, and HMD26 as shown in Figures 14-53–14-58 by Wang and Civan (2005a), respectively. The 1

0.9

0.8

Experiment data

0.7

Simulated results 0.6 0

10

20 30 40 50 60 Injection pore volume of oil (PV)

70

Figure 14-53. Comparison of the simulated results with the Experiment GF1 data of Minssiuex (1997) (after Wang and Civan, ©2005 ASME; reprinted by permission of the American Society of Mechanical Engineers).

542

Formation Damage by Organic Deposition

Ratio of average permeability to initial permeability (K/Ko, fraction)

1.0 Experiment data Simulated results

0.8

0.6

0.4

0.2 0

10

20 30 40 50 60 Injection pore volume of oil (PV)

70

Ratio of average permeability to initial permeability (K/Ko, fraction)

Figure 14-54. Comparison of the simulated results with the Experiment GF3 data of Minssiuex (after Wang and Civan, ©2005 SPE; reprinted by permission of the Society of Petroleum Engineers).

1 0.9

Experiment data

0.8 Simulated results

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

10

20 30 40 50 Injection pore volume of oil (PV)

60

Figure 14-55. Comparison of the simulated results with the Experiment GV5 data of Minssiuex (1997) (after Wang and Civan, ©2005 ASME; reprinted by permission of the American Society of Mechanical Engineers).

mechanisms involved in each cases are identified based on the estimated values of the rate constants given in Table 14-8 by Wang and Civan (2005c).

543

Formation Damage by Organic Deposition

Ratio of average permeability to initial permeability (K/Ko, fraction)

1.0 0.9

Experiment data

0.8 Simulated results

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0

10 20 30 40 Injection pore volume of oil (PV)

50

Ratio of average permeability to initial permeability (K/Ko, fraction)

Figure 14-56. Comparison of the simulated results with the Experiment GV10 data of Minssiuex (after Wang and Civan, ©2005 SPE; reprinted by permission of the Society of Petroleum Engineers).

1.0 Experiment data 0.9

Simulated results

0.8

0.7

0.6

0.5 0

10 20 30 Injection pore volume of oil (PV)

40

Figure 14-57. Comparison of the simulated results with the Experiment GP9 data of Minssiuex (after Wang and Civan, ©2005 SPE; reprinted by permission of the Society of Petroleum Engineers).

544

Formation Damage by Organic Deposition

Ratio of average permeability to initial permeability (K/Ko, fraction)

1.0 0.9 0.8 0.7 Experiment data

0.6

Simulated results 0.5 0

100

200 300 400 500 600 Injection pore volume of oil (PV)

700

Figure 14-58. Comparison of the simulated results with the Experiment HMD26 data of Minssiuex (after Wang and Civan, ©2005 SPE; reprinted by permission of the Society of Petroleum Engineers).

14.9.3 Simulation of Field-Scale Asphaltene Deposition by Pressure Depression in Oil Reservoirs during Primary Recovery For field-scale simulation of asphaltene deposition and its effect on oil productivity, Wang and Civan (2005c) incorporated their model presented in the previous section into the U.S. Department of Energy BOASTVHS three-dimensional and three-phase black-oil simulator (Chang et al., 1992). Then, they simulated a number of production scenarios involving vertical and horizontal wells completed in a horizontal, homogeneous, and isotropic reservoir at isothermal conditions. For illustration purposes, Wang and Civan (2005c) considered a reservoir formation located at 10,000 ft depth and having a 25 mD initial permeability and a 25% initial porosity. Initially the reservoir oil was undersaturated at 5283 psia pressure and 212 F temperature conditions. Its gravity was 19 API at the stock-tank conditions and bubble-point was 2050 psia. This oil contained 16.1% (by weight) asphaltene. According to the asphaltene precipitation chart given in Figure 14-59 by Wang and Civan (2005a,b), the onset of asphaltene precipitation pressure is 5056 psia. The precipitation amount increases by pressure depression below 5056 psia. The maximum asphaltene precipitation occurs at the bubble-point pressure. Thereafter, the precipitation amount decreases if the pressure decreases below the bubble-point. The simulation results

Formation Damage by Organic Deposition

545

Figure 14-59. Asphaltene Precipitation Curve (after Wang and Civan, ©2005 ASME; reprinted by permission of the American Society of Mechanical Engineers).

obtained by implementing four vertical wells and two horizontal wells in this reservoir are described as follows. Case 1 – Four Equally Spaced Vertical Production Wells

Wang and Civan (2005a,b) considered four equally spaced vertical production wells completed in a reservoir having 4200 ft by 4200 ft lateral dimensions and 50 ft thickness as shown in Figure 14-60. The flowing bottom pressure was assumed as 1000 psia, the initial productivity index

Figure 14-60. Reservoir with four vertical wells (Case 1) (after Wang and Civan, ©2005 SPE; reprinted by permission of the Society of Petroleum Engineers).

546

Formation Damage by Organic Deposition

as 1.0 bbl/day-psi, and the wellbore radius as 0.5 ft for the wells completed in this reservoir. Because of the symmetrical positioning of the wells, Wang and Civan (2005c) presented the results for one well only in Figures 14-61–14-65 by taking advantage of the symmetry.

Figure 14-61. Simulated reservoir oil pressure profile at different production times for a vertical well (after Wang and Civan, ©2005 ASME; reprinted by permission of the American Society of Mechanical Engineers).

Figure 14-62. Simulated reservoir oil asphaltene precipitate concentration profile at different production times for a vertical well (after Wang and Civan, ©2005 ASME; reprinted by permission of the American Society of Mechanical Engineers).

Formation Damage by Organic Deposition

547

Figure 14-63. Simulated reservoir rock asphaltene deposit profile in reservoir at different production times for a vertical well (after Wang and Civan, ©2005 ASME; reprinted by permission of the American Society of Mechanical Engineers).

Figure 14-64. Simulated reservoir rock porosity profile at different production times for a vertical well (after Wang and Civan, ©2005 ASME; reprinted by permission of the American Society of Mechanical Engineers).

Their simulation results indicate that the vertical well began producing at a rate of 4000 bbl/day with a rapid decline to 100 bbl/day; the asphaltene deposition problem was not only limited to the near-wellbore region but it propagated the whole reservoir formation. However, the near-wellbore damage was more pronounced. Figure 14-66 shows the rapid productivity

548

Formation Damage by Organic Deposition

Figure 14-65. Simulated reservoir rock permeability profile at different production times for a vertical well (after Wang and Civan, ©2005 ASME; reprinted by permission of the American Society of Mechanical Engineers).

Figure 14-66. Simulated well productivity decline with production time for vertical and horizontal wells (after Wang and Civan, ©2005 SPE; reprinted by permission of the Society of Petroleum Engineers).

index decline trend of the vertical well compared to that of the horizontal well discussed below. Case 2 – Two Equally Spaced Horizontal Production Wells

Wang and Civan (2005c) considered two equally spaced horizontal wells, as shown in Figure 14-67, in a reservoir of the same properties as

Formation Damage by Organic Deposition

549

Figure 14-67. Reservoir with two horizontal wells (Case 2) (after Wang and Civan, ©2005 SPE; reprinted by permission of the Society of Petroleum Engineers).

described in Case 1. However, the lateral dimensions of the reservoir were taken as 4200 ft by 2100 ft. The flowing bottomhole pressure was assumed as 1000 psia, the initial productivity index as 17.5 bbl/day-psi, and the wellbore radius as 0.5 ft for the wells completed in this reservoir. Because of the symmetrical positioning of the wells, Wang and Civan (2005c) presented the results for one well only in Figures 14-68–14-73 by taking advantage of the symmetry. Wang and Civan (2005c) determined

Figure 14-68. Simulated reservoir oil pressure profile at different production times for a horizontal well (after Wang and Civan, ©2005 SPE; reprinted by permission of the Society of Petroleum Engineers).

550

Formation Damage by Organic Deposition

Figure 14-69. Simulated reservoir oil dissolved asphaltene concentration profile at different production times for a horizontal well (after Wang and Civan, ©2005 SPE; reprinted by permission of the Society of Petroleum Engineers).

that the horizontal well began producing at a relatively high rate of 70,000 bbl/day. Consequently, the average reservoir pressure and the production rate decreased rapidly. Initially, the asphaltene deposited more within the wellbore region where the oil pressure became lower than the onset of asphaltene precipitation pressure (Figure 14-68). As emphasized by Wang and Civan (2005c), the maximum asphaltene precipitation and the lowest solubility conditions occur when the bubble-point is reached at various locations throughout the reservoir. Therefore, the maximum precipitation and lowest solubility conditions progress from the wellbore location to the rest of the reservoir as the pressure drops further with continued production (Figures 14-69 and 14-70). The asphaltene solubility increases and precipitation decreases in regions behind the bubble-point pressure front where the pressure is below 2050 psia bubble-point pressure. The highest asphaltene precipitation, and porosity and permeability impairment occurred at about a 100 ft distance from the wellbore (Figures 14-70–14-73). Figure 14-66 depicts that the productivity decline trend of a horizontal well is more favorable compared to that of a vertical well. The above-described simulation case studies carried out by Wang and Civan (2005a,b,c) revealed that the permeability impairment by asphaltene deposition lowered the production rate of a well rapidly towards the lowest economic production rate limit suggesting the abandonment of the

Formation Damage by Organic Deposition

551

Figure 14-70. Simulated reservoir oil asphaltene precipitate concentration profile at different production times for a horizontal well (after Wang and Civan, ©2005 SPE; reprinted by permission of the Society of Petroleum Engineers).

Figure 14-71. Simulated asphaltene deposit profile at different production times for a horizontal well (after Wang and Civan, ©2005 SPE; reprinted by permission of the Society of Petroleum Engineers).

well in a short period of time. For example, the vertical well in Case 1 should be abandoned after 4 years if a 10 bbl/day production is considered as the economic production limit. On the other hand, the horizontal well in Case 2 should be abandoned after 3 years if a 100 bbl/day production is considered as the economic production limit for the horizontal well. Such practices will cause a substantial loss of productivity from the asphaltenic

552

Formation Damage by Organic Deposition

Figure 14-72. Simulated reservoir rock porosity profile at different production times for a horizontal well (after Wang and Civan, ©2005 SPE; reprinted by permission of the Society of Petroleum Engineers).

Figure 14-73. Simulated reservoir rock permeability profile at different production times for a horizontal well (after Wang and Civan, ©2005 SPE; reprinted by permission of the Society of Petroleum Engineers).

oil reservoirs. Wang and Civan (2005c) state that “Although some stimulation treatments can be applied to enhance the production, not much oil can be recovered from the reservoirs because the formation has been damaged throughout the reservoir and the reservoir pressure is rather low. Once the formation has been damaged by asphaltene deposition, it is almost impossible to restore the productivity.”

Formation Damage by Organic Deposition

553

14.9.4 Preventing Asphaltene Deposition in Petroleum Reservoirs by Early Water-Injection Wang and Civan (2005c) emphasized that the maximum asphaltene precipitation and the lowest solubility conditions occur when the bubblepoint is reached and the reverse conditions are observed as the pressure declines to below or increases to above the bubble-point pressure (see Figure 14-59). Haskett and Tartera (1965) observed severe asphaltene deposition occurrence on vertical wellbores as the oil pressure approached the bubble point but deposition could be avoided by reducing the pressure sufficiently below the bubble point. However, such practice may neither be feasible to accomplish throughout a reservoir nor desirable. The same can be accomplished by maintaining a reservoir pressure above the onset of the asphaltene precipitation pressure as long as possible. Therefore, they recommend avoiding formation damage due to asphaltene deposition by applying an early water injection into such reservoirs. They have demonstrated the validity of this application by the following exercises. Case 3 – One Vertical Early Water-Injection Well and Three Vertical Production Wells

Three of the four production wells described in Case 1 were operated at a 5057 psia bottomhole flowing pressure, maintained higher than the onset of the asphaltene precipitation pressure. The remaining well was converted to a water injection well operated at 8000 psia bottomhole injection pressure. All four wells started operation at the same time. The economic limit of the production wells was set higher than Case 1 at a 100 bbl/day in the early-water injection scheme in view of the cost involved in the water injection well. The reservoir fluid pressure and the oil and water production trends are shown in Figure 14-74. Wang and Civan (2005c) determined that the early water-injection scheme yielded over three times the oil production obtained by the primary recovery described in Case 1. Case 4 – One Horizontal Early Water-Injection Well and One Horizontal Production Well

One of the two production wells described in Case 2 was operated at a 5057 psia bottomhole flowing pressure, maintained higher than the onset of the asphaltene precipitation pressure. The remaining well was

554

Formation Damage by Organic Deposition

Figure 14-74. Simulated reservoir performance for Case 3 (after Wang and Civan, ©2005 SPE; reprinted by permission of the Society of Petroleum Engineers).

converted to a water-injection well operated at a 8000 psia bottomhole injection pressure. Both wells started operation at the same time. The economic limit of the production wells was set higher than Case 2 at a 200 bbl/day in the early-water injection scheme because of the high cost involved in the water injection well. Figure 14-75 shows the reservoir fluid pressure and the oil and water production trends. Wang and Civan

Figure 14-75. Simulated reservoir performance for Case 4 (after Wang and Civan, ©2005 SPE; reprinted by permission of the Society of Petroleum Engineers).

Formation Damage by Organic Deposition

555

(2005c) determined that the early water-injection scheme produced more than twice the oil production obtained by the primary recovery described in Case 2.

Exercises 1. Based on the data given in Figure 14-45, determine the value of the empirical constant C5 in Eq. T1-1 given in Chapter 10, Table 10-1. 2. Based on the data given in Figure 14-46, determine the value of the empirical constant C6 in Eq. T1-2 given in Chapter 10, Table 10-1. 3. Apply Eq. (14-4) with the data given in Figures 14-20 and 14-21. Determine the values of various parameters of this equation from a least-squares fit to the linear plot of lnX vs. 1/T. 4. Prepare a three-dimensional plot of Eq. (14-5) showing the variation of the amount of asphaltene adsorbed on pore surface as a function of the amount of adsorbed asphaltene and concentration of asphaltene in oil. 5. Prepare a set of Langmuir isotherms based on Eq. (14-12) for a set of assumed parameter values. 6. Prepare a linear plot of the asphaltene adsorption data given in Figure 14-30 according to Eq. (14-12) and determine the values of the various parameters. 7. Consider Oil A containing 0.3 weight % asphaltenes and 0.1 weight % resins, and Oil B containing 12.5 weight % asphaltenes and 5.0 weight % resins. Which of these two different oils is likely to cause formation damage by asphaltene deposition? Explain the reason. 8. Analyze the data of Burya et al. (2001) given in Figures 14-32 and 14-33 to determine the parameters of their aggregation kinetics model described in this chapter.