Evaluation of formation damage in heterogeneous reservoirs

Evaluation of formation damage in heterogeneous reservoirs* John S. Archer and A n d r e w Hurst ¢ Imperial College of Science and Technology, Petroleum Engineering Section, Royal School of Mines, Prince Consort Road, London SW7 2BP, UK

Received 3 May 1986 The interpretation of formation damage by analysis of well tests is presented. This type of interpretation is limited by assumptions of reservoir heterogeneity in the damaged and unaltered regions. An example is provided of the application of modern radial flow reservoir simulators in representing the distribution of formation damage and any subsequent permeability improvement. The success of the reservoir simulation approach is strongly coupled to the development of detailed geological models and the conduct of formation damage experiments on core samples from all sections of the perforated well. The technique provides the basis for an integrated approach to formation damage assessment and the recommendation of remedial action. Keywords: Formation damage; Reservoir characterization; Zonation; Reservoir modelling

Representation of formation damage

depends on the mobility (X) of the particular fluid:

The term formation damage suggests carelessness yet gives a hint that repair may be possible. A logical approach in the analysis of formation damage might perhaps be to assess the scale and magnitude of damage, to understand the nature of damage, to determine ways of repair, and to propose a course of remedial action. This route of course presupposes that the nature of the undamaged reservoir is known. The purpose of this paper is to present some of the factors on which knowledge of the damaged and undamaged reservoir is based and to show how quantitative assessment of repair potential can be deduced.

--* dq~' V=-X-dL

(1)

Linear flow. The flow velocity can be equivalenced to a reservoir condition volumetric flow rate (q) divided by the effective cross sectional area (A) over which flow is occurring. The fluid mobility can be defined as effective fluid permeability (ke) divided by fluid viscosity (la). The effective permeability for a particular fluid in the presence of other fluids in the pore space is defined as the product of the absolute permeability (k) and the relative permeability (kr) of the fluid at the prevailing saturation. The general transport equation thus becomes:

Transport of fluids in reservoirs The start point for observation of reservoir damage and for information about reservoir characteristics is a well. In order to design recovery methods for hydrocarbons from petroleum reservoirs it is necessary to understand the distribution of hydrocarbons in the reservoir porosity and the distribution of permeability. In this way the numbers and types of well required, and well locations may be selected. Since wells only occupy an extremely low volume of a petroleum reservoir an understanding of bulk reservoir characteristics must be developed which is guided by inter-well correlation and conceptual geological models (Archer and Wall, 1986). The laminar flow of incompressible fluids in any particular region of a reservoir is governed by transport equations which relate flow velocity in a particular direction ( ~ ) to a potential gradient in that direction ( d ~ ' / d L ) . The constant coefficient in such an equation

q -

k krA d~' la

(2)

dL

The potential gradient can be considered as a datum corrected pressure gradient which accounts for potential changes related to the fluid density (9) and the elevation (z) from the datum at which the pressure P is evaluated. Using g' as the appropriate gravitational constant this means that: • ' = P + g' 9 z

(3)

For horizontal flow (i.e. z = 0) then the transport equation (2) for flow between position 1 and position 2, separated by a distance L becomes the familiar linear flow Darcy relationship:

q =

k k,.A (PI - P2)

(4)

laL *Paper presented at the meeting on 'Sensitivity and Formation Damage in Sandstone Reservoirs', Petroleum Group, Geological Society of London, llth February, 1986. +Present address: Statoil, Forus, PO Box 300, N-4001, Stavanger, Norway. 0264-8172/87/020119-08 $03.00 ©1987 Butterworth & Co. (Publishers) Ltd

Radial flow. For radial flow under steady state conditions (all boundary effects experienced) from some distance re from the well to a wellbore of radius rw

Marine and Petroleum Geology, 1987, Vol 4, May

119

Formation damage in heterogeneous reservoirs: J. S. Archer and A. Hurst in a formation of net thickness h, the relationship between flow rate and the potential difference (O'~-~P'w) is given by the radial Darcy equation:

q

___)

q =

2rt /~ k r h ( q b ' - ~ ' w )

(5)

iii

B Iog~ (re/r~.) The average formation effective permeability thickness product (keh) can be estimated from steady state flowing well tests by measuring the 'bottom hole' wellbore pressure under flowing conditions (Pwf) and having prior knowledge of the pressure at the external bounday, Pc. The prior knowledge is interpreted from pressure build up analyses when the flowing well is subsequently 'shut-in' or 'closed-in'. At datum /~eh

=

q B logo (rJrw)

re

/

j

j

j

wf

(6)

It is more usual to interpret this 'bulk average' effective permeability thickness product from pressure build-up analysis of closed in well performance in the 'transient' time regions before any reservoir boundary effects are observed. In these circumstances the reservoir behaves as if it were infinitely large and particular solutions to flow equations apply. The analytical solutions assume some idealised properties of the reservoir system, namely that the reservoir is considered homogeneous in all its rock properties and that permeability is constant and does not have different values in different directions (it is an isotropic property). It is further assumed that the well is perforated over the complete formation thickness so that fully radial flow will occur. Under these conditions the relationship between the measured 'bottom hole" pressure of the shut-in well and a time function will lead to an estimate of the original reservoir pr_essure in the virgin formation and an estimate of k~.h using techniques such as Horner plot (Horner, 1951) or Type Curve Analysis (Gringarten, 1985). If the boundaries of a reservoir are reached by the pressure disturbance emanating from production of a well then a semi steady state or steady state condition may be reached. The steady state radial flow equation describes the relationship between pressure (P) and

" re

(keh) b (keh) a ra ---(ke~la • /Oge-(w qpS z~Ps (keh)b c o n s t a n t S

Figure 2 Effect of formation damaged 'skin' zone on steady state radial flow pressure drawdown

radial distance (r) from the well bore (Figure 1) as follows: P

=

Pwf -t-

wellbore

Figure 1 Steady state pressure distribution for radial flow in a homogeneous reservoir. See text for definition of symbols

Marine and Petroleum Geology, 1987, Vol 4, May

qla 2g [¢ch

r log,.-

(7)

rw

'Skin' When the region around a producing well has a different effective permeability thickness product (k~h) from that of the bulk formation there will be a modification to the pressure versus radial distance relationship. For any reduced effective permeability thickness product (formation damage) there will be an additional reduction in the observed bottom hole pressure of the flowing well (P,4) compared with that for the system with homogeneous formation properties (constant 'bulk formation character'). Alternatively there could of course be a region of increased effective permeability thickness product (formation stimulation) in which case the observed well pressure would be higher. The region of altered effective permeability thickness product is known as a region of 'skin', defined with the symbol (S), in terms of the keh products of the bulk (subscript b) formation and the altered (subscript a) regions and the radial distances of the altered region (G) and the wellbore (r~): (/~eh)b- (/~oh)a r,

h

120

or

~ ¸:¸:¸5

2rl (P~ - P,, f)

/

sk,n

z a,torod zone

rw

It can thus be seen, that S takes on a positive value for damaged regions and a negative value for stimulated regions. The additional pressure change compared with the unchanged system (S = 0) under steady state flow can be expressed as APs and is illustrated in Figure 2. The skin factor S can be more easily incorporated into well inflow equations by defining an 'effective' wellbore radius (r'w) which includes the skin region:

rw' = rwe-"

(9)

Thus the steady state radial flow equation which

Formation damage in heterogeneous reservoirs." J. S. Archer and A. Hurst 30

includes skin can then be written by combining equations (6) and (9) in terms of the bulk average formation properties as: q =

2rl/~c h (P - Pwf)

1ANN

(10)

25

la logo (r/r'w) Evaluation of formation damage thus depends on evaluation of the magnitude of the term S when using traditional analytical solutions. For the early flowing time during a well test when transient flow conditions are occurring there is a linear relationship between the flowing bottom hole pressure (Pwf) and the logarithm of time (logmt). The straight line can be used to estimate a value of pressure (Pwf (1 hour)) after a steady state flow rate (q) has commenced. For units of pressure in psia, time (t) in hours, porosity (q)) as a fraction, total compressibility (e) in psia -L, radial distances (r) in feet, effective permeability (ke) in millidarcies and the slope of the Pwf vs. t line (m) in psi/log cycle, the skin (S) can be determined as: S = 1.151 (P

- _Pwf(l hi_ logm F 3.23 (11) m ¢ la e rw2

The term P* denotes the pressure which would exist if the reservoir were shut-in for an infinitely long time. Before any significant production from the reservoir (before 'pressure depletion') P* is equal to the initial reservoir pressure. The magnitude of the additional skin pressure drop A P~ in the same units as used above is then as follows: A Ps -

141.2 q ItS

- 0.868mS

(12)

Flow efficiency and damage factor The flow efficiency of a well can be defined in terms of the ratio of the actual productivity index (Pl~ctua~ = J) to the productivity index of the well with zero skin (P/ideal = J I ) '

J/Jl -

P*-Pwf-

APs

(13)

P* - Pwf The inverse of the 'flow efficiency' is sometimes known as the 'damage ratio' of a well. Another term sometimes used in this connection is the 'damage factor' which is (1 - - flow efficiency) or, APs

Damage factor -

(14)

P* - Pwf The analysis of well tests is thus seen to lead to an assessment of total formation damage. A comparison with the ideal non-damaged reservoir behaviour leads to an expectation of the magnitude of improvement which might be possible in a homogeneous reservoir.

1ANNA

riO k- 2 0 -

0 < Ii

z__ 1 5 u) 0 D

LLI

10-

O9 el_

5-1

O

m

0

I

I

I

I

I

I

.1

.2

.3

.4

.5

.6

FRACTIONAL

I

.7

I

.8

I

.9 1.0

PENETRATION

Figure 3 Pseudo skin factors in partial well completions (after Brons and Marting, 1961) measured APs will include the contributions of a number of types of 'skin'. In common terminology 'total skin' is considered as the sum of 'mechanical skin', 'multiphase flow skin' (relative permeability effects) and 'non-Darcy skin' (result of high velocity non-laminar flow patterns). The mechanical skin term can result from formation damage caused by drilling and completion fluids, by perforating techniques and by partial penetration. It is particularly important to discount the skin pressure (AP~) contributions from deviated wells and from wells not perforated throughout the full reservoir net thickness interval before contemplating flow efficiency improvement. The contribution to mechanical skin by a well only perforated for production in part of the total formation thickness (partial penetration) has been evaluated (Brons and Marting, 1961) and is known as pseudo skin (Sb). Pseudo skin is correlated with the fraction of the total interval open to flow for various values of a dimensionless flow geometry term 'F'. This latter term involves the ratio of the perforation thickness symmetry element (h) and the wellbore radius (rw) as well as the square root of the ratio of radial direction permeability (k×) to vertical permeability (k,). The relationship is shown in Figure 3. The remaining mechanical skin is the target for treatment and its origin and repair require the acquisition of core samples and the conduct and interpretation of laboratory tests.

Nature of skin damage The skin damage of particular interest is that which can be altered by some remedial action. In practice, the

Real reservoirs and the treatment of scale effects The analytical treatments presented in the previous Marine and Petroleum Geology, 1987, Vol 4, May

121

Formation damage in heterogeneous reservoirs: J. S. Archer and A. Hurst sections have assumed that reservoirs are hydrocarbon propose that because of the complexity of real filled pore volumes with homogeneous properties in the heterogeneous reservoirs that assessment of formation bulk reservoir. It has been further assumed that a damage should be conducted at a scale appropriate to a homogeneous 'skin', or region of formation damage, valid geological model of heterogeneity and thus, reservoir zonation. can exist in the vicinity of the wellbore. Application of such analytical techniques is severely limited for Comparison between the scales of observation and understanding the quantitative distribution of measurement of reservoir characteristics and the scale formation damage in a reservoir as few, if any, of application of reservoir characteristics in reservoir reservoirs are homogeneous. simulation model calculations (Figure 4) shows quite If we make the proposition that real reservoirs are dramatically that experiments conducted on core plugs heterogeneous in the interval intersected by the may not be directly applicable to calculations on a wellbore, implying the presence of different lithologies reservoir engineering scale. Advances in mathematical or sedimentary facies, it is probable that the different methods and computing over the last five years or so zones or sedimentary rock types are subject to different have realised a capability to model individual well kinds of damage or to different degrees of damage. behaviour in quite fine details. Radial coordinate Damage may be produced for example, by chemical or simulation models are now commercially available. In physical alteration of the rock matrix, clay minerals this study, we define near wellbore regions with radii at often being particularly sensitive. Acknowledging the the scale of centimetres from a wellbore and with existence of reservoir heterogeneity makes implicit that thicknesses of a metre. The 'PORES' black oil model a particular treatment will result in different degrees of supplied by ERC Energy Resource Consultants improvement in the damaged zone, or that a variety of Limited to Imperial College was used to demonstrate treatment designs will be required. We therefore the principle of variable damage to reservoir zones. Geological reservoir zonation can be used to produce three-dimensional descriptions of reservoirs and A .~3S0r~ r ~ H E_I Reiative volume reservoir continuity down to the metre scale or less 50 ItOGENE( Well test 10 (Weber, 1982, Johnson and Stewart, 1985). Figure 5 shows examples of fine scale (Figure 5A) and } OClTT] simulation grid cell scale (Figure 5B) descriptions of Reservcir model grid cell 2x10~2 fluvial sandstones typical of many North Sea reservoirs. Fluvial sandbodies have strongly anisotropic properties on both scales shown in Figure 5 and clearly defined I[-~[~ Wireline Log intervai 3x107 heterogeneities with respect to grain size and permeability. In Figure 6 a more homogeneous II Core O]ug 5x102 TM

GeoLogical thin section

A

1

Direction of deposition and K anisotropy

Figure 4 Scales of measurement and application used in reservoir evaluation

A

Meander belt

T'00=

I

°Z > 10m

B 5km

4

Ov'r'1

B

decease ~ ~ m grains,ze, |

C°u~'~er=~ng ~ ............

i2 to .......

°

L ~

~ ~-- ~

-

~-_ :

-

~ -~;

T ~-

•

±10m

2krn

Key High permeability (>5D) r--I 10 to 50m

Figure 5 Heterogeneity in sedimentological models. (A) Meandering fluvial channel facies sandstones. (B) Internal characteristics of a cross-bedded sandstone, arrows indicate direction of permeability anisotropy

122 Marine and Petroleum Geology, 1987, Vol 4, May

Good permeability (250mD 5D)

[i_]

Low permeability /ctay and mica rich <250roD) -" "

Pebbles Micaceous

Figure 6 Heterogeneities in shoreface sandstones, (A) detailed description; (B) field-scale description

F o r m a t i o n d a m a g e in heterogeneous reservoirs. J. S. A r c h e r a n d A. Hurst modification is initially uncertain and can only be validated by the eventual production history match (Archer 1984)). The transmissibility modification factor 'p is used in the x, y, z (three linear dimensions) i e 5000m or r, z (radial dimension and thickness) planes of orientation to provide the required value of transmissibility T'. In some particular direction for linear flow:

qo

Layer 1 hp

lore ( Layer 8 Layer

,

9

! LayerlO

• --

' --

' --

' --

i

i

' I

Oil w a t e r

/~oA

r'=f×

cor,,tsct

T

q la }

=i×

(15)

)

and for radial flow the equivalent relationships are: r!

8

r9

2r~/~oh

rl 0

r' = f x

log e

Figure 7 Grid a r r a n g e m e n t f o r 10 × 10 r - - z (radius thickness) simulation model

shoreface sandstone reservoir is represented in which the grid scale (Figure 6B) description gives a coarse overall impression of homogeneity whereas the fine-scale model (Figure 6A) reveals considerable heterogeneity and anisotropic characteristics. Although Figure 6B may be a suitable model for the purposes of a field-scale reservoir simulation, Figure 6A is probably on a scale more suitable for modelling the effects of formation damage. The incorporation of near well bore and bounding reservoir characteristics in a radial mode reservoir simulation model requires appropriate representation of individual cell properties, particularly permeability, porosity and saturation. The geological data can play a most significant role in determining the character of the model. Typical model dimension might be as represented in Figure 7 for a single well on test in a newly developing reservoir. Each cell defines a 'homogeneous' region and cell size is thus in the combined control of reservoir engineers and geologists involved in setting up the integrated model. In contrast to analytical calculations where pressure and saturations are continuous with distance, a simulator has step changes in pressure and saturation between adjacent cells at the intercell boundary. The value of permeability at the intercell boundary is usually computed from cell average values as a harmonic average. Enhancement or restriction (faults or seals) of flow at the scale of the grid cell can be controlled by deterministic or stochastic transmissibility modification. The magnitude of a particular transmissibility Table 1 Reservoir model properties

Layer n u m b e r Layer thickness (m) 1 2 3 4 5 6 7 8 9 10

5 3 1 1 1 1 3 10 20 50

Radial cell number

Radius f r o m w e l l b o r e (m)

1 2 3 4 5 6 7 8 9 10

0.O6 0.08 0.10 0.50 2.0 10.0 50.0 250.0 1000.0 5000.0

OWC at mid depth o f layer 10 in radial centre of model Initial pressure at 3000 mSS, 350 bar E1 constant at 0.25 Sw~rr constant in oil zone at 0.20 Production rate constant at 10,000 stb/d, Bo~ = 1.48 rb/stb Perforated interval layers 2 - 7

q ta

=fx

r/r,,'

P -

(16)

Pwr

Radial simulation example Figure 7 and Table 1 show a part of the full radial symmetry of a test case (0 = 360°C). The base case model represents a large undersaturated oil reservoir region underlain by an aquifer. In order to demonstrate the pressure gradients in a truly uniform permeability oil reservoir system the properties are as shown in Table 2. The producing well is perforated in a 10 m interval near the top of a 70 m oil zone. The initial reservoir pressure is taken as 5075 psia at 3000 mSS and an uniform initial water saturation of 0.2 is assigned in the oil zone. The vertical permeability in a given cell is one tenth of the radial direction permeability and the porosity is everywhere uniform at 0.25%. The radius at the external boundary of the system is 5 km. A constant production rate of 10,000 stb/day is required and the initial value of the oil formation volume factor is 1.48 rv/sv. The pressure distribution after one day of production is shown in the region bounded by layers 1-7 (top 15 m) and radial cells 1-5 (up to 2 m from the Table 2 Permeability distribution layers (L) 1 - 10 and c o l u m n s (C) 1 - 10 for base case, md

v

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10

750 750 750 750 750 750 750 750 750 7.5

750 750 750 750 750 750 750 750 750 7.5

750 750 750 750 750 750 750 750 750 7.5

750 750 750 750 750 750 750 750 750 7.5

750 750 750 750 750 750 750 750 750 7.5

750 750 750 750 750 750 750 750 750 7.5

750 750 750 750 750 750 750 750 750 7.5

750 750 750 750 750 750 750 750 750 7.6

750 750 750 750 750 750 750 750 750 7.5

750 750 750 750 750 750 750 750 750 7.5

Table 3 Permeability distribution layers (L) 1 - 10 and c o l u m n s (C) 1 - 6 f o r d a m a g e case, md

1 2 3 4 5 6 7 8 9 10

Marine

and

1

2

3

4

5

6

750 7.5 75 7.5 75 7.5 75 750 750 7.5

750 7.5 75 7.5 75 7.5 75 750 750 7.5

750 7.5 75 7.5 75 7.5 75 750 750 7.5

750 10 100 10 100 10 100 750 750 7.5

750 100 500 100 500 100 500 750 750 7.5

750 750 750 750 750 750 750 750 750 7.5

Petroleum

Geology,

1 9 8 7 , V o l 4, M a y

123

Formation damage in heterogeneous reservoirs: J. S. Archer and A. Hurst

oo

~

c:)

o

2

6

7

1

2

3

4

5

Figure 8 Pressure distribution after one day. The base case (case I} f o r a h o m o g e n e o u s reservoir. Units in psi. Radial cell n u m b e r s and layer n u m b e r s as in Table I

wellbore) in Figure 8. The flowing pressure gradients are not excessive and the ideal mechanical skin is initialized as zero. In order to illustrate the possible effect of a variable formation damage in different 'layers' of the reservoir (Table 3) the pressure distribution after one day of production at 10,000 stb/d is shown in Figure 9. A severe skin effect is evident and A P S is about 1090 psia giving a skin factor of +33. If sufficient core is available to conduct selective formation damage tests a remedial scheme might be developed which would result in permeability improvement to most layers. In this example we have assumed some layers have permeability restoration (Table 4) whilst others, for good geological and chemical reasons might not. The 'cleaned up' permeability distribution predicted on the basis of a proposed treatment might then look like the example in Table 4. Again, a flow rate of 10,000 stb/day shows a pressure profile after 1 day as in Figure 10. The effects of variable permeability restoration are easily seen and the A Ps is now only 100 psi giving a skin factor of +3. Although these examples are simplistic they illustrate how particular formation damage treatments can be analysed at a scale appropriate to the geological model of the well and its environment. Such an application requires recognition of reservoir zonation and the distribution of appropriate reservoir properties in the damaged zones. This indicates the essential nature of 124

Marine and Petroleum Geology, 1987, Vol 4, May

valid core samples in all zones and careful correlation with wireline log data. The distinction between formation damage during drilling and completion and diagenetic damage becomes important in characterising reservoir model properties.

Integrated approach to formation damage evaluation The application of very fine grid cell radial reservoir simulation models in the analysis of formation damage marks a considerable improvement from the sole use of 'homogeneous' analytical models. There are however pitfalls in their usage, not least of which must be their Table 4 Permeability distribution layers (L) 1 - 10 and c o l u m n s (C) 1 - 6 f o r repaired p e r m e a b i l i t y case

1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

750 750 75 750 75 750 75 750 750 7.5

750 750 75 750 75 750 75 750 750 7.5

750 750 75 750 75 750 75 750 750 7.5

750 750 100 750 100 750 100 750 750 7.5

750 750 500 750 500 750 500 750 750 7.5

750 750 750 750 750 750 750 750 750 7.5

Formationdamagein heterogeneousreservoirs:J. S.ArcherandA.Hurst

~

",3 0

0

2

C)

after one day

a

reservoir (case II). Units in

and layer numbers as

blI 1

1 2 3 4 5 Figure 18 Pressure distribution after one day in a reservoir with repaired damaged (case III). Units in psi. Cell and layer numbers as in

Table1

M a r i n e a n d P e t r o l e u m G e o l o g y , 1987, V o l 4, M a y

125

F o r m a t i o n d a m a g e in h e t e r o g e n e o u s r e s e r v o i r s : J. S. A r c h e r a n d A. H u r s t v a l i d a t i o n by m a t c h i n g o b s e r v e d w e l l test b e h a v i o u r . References

The validation exercise is not unique. Notwithstanding this problem the ability to conduct reservoir engineering calculations at a scale consistent with geological models of heterogeneous reservoirs is particularly tempting. The coordination of core collection and petrophysical interpretation to provide the model data base is vital. The conduct of laboratory tests on samples from all relevant intervals in order to optimize formation damage treatment goes a long way to help predict likely treatment success. The improvement in permeability predicted for each reservoir model zone can then be used in a detailed simulation model to calculate the overall well improvement possible. Such an analysis may result in a firmer economic evaluation of potential formation damage treatments.

Acknowledgement The authors gratefully acknowledge the help of Dr. T. S. Daltaban at Imperial College, London in preparing and executing the 'PORES' reservoir simulation experiments.

126

M a r i n e a n d P e t r o l e u m G e o l o g y , 1987, V o l 4, M a y

Archer, J. S. and Wall, C. G. (1986) Petroleum Engineering - Principles and Practice, Graham and Trotman, London Archer, J. S. (1984) Reservoir definition and characterisation for analysis and simulation, in: Proc. Eleventh World Pet. Cong. Vol 3, PD(6) 1, J. Wiley and Sons, London, pp 65-78 Brons, F. and Matting, V. E. (1961) The effect of restricted fluid entry on well productivity, J. Pet. Tech. Feb, 172-174 Gringarten, A. C. (1985) Interpretation of Transient Well Test Data, in: Developments in Petroleum Engineering I (Ed. Dawe and Wilson), Elsevier App Sci. Pub., London, pp 133-196 Horner, D. R. (1951) Pressure build up in wells, in: Proc. Third World Pet. Cong, Vol II, E. J. Brill, Leiden, pp 503-523 Weber, K. J. (1982)Influence of common sedimentary structures on fluid flow in reservoir models, ,1. Pet. Tech. March, 665-672 Johnson, H. D. and Stewart, D. J. (1985) Role of clastic sedimentology in the exploration and production of oil and gas in the North Sea, in: Sedimentology: recent developments and applied aspects (Eds. P. J. Brenchley and B. P. Williams), The Geol. Soc., Blackwell Scientific Publications, Oxford, p 249-310