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Mathematical modeling and field application of heavy oil recovery by Radio-Frequency Electromagnetic stimulation
Journal of Petroleum Science and Engineering 78 (2011) 646–653
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Journal of Petroleum Science and Engineering j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / p e t r o l
Mathematical modeling and field application of heavy oil recovery by Radio-Frequency Electromagnetic stimulation Alfred Davletbaev a, Liana Kovaleva b, Tayfun Babadagli c,⁎ a b c
RN-UfaNIPIneft, Rosneft, Russian Federation Bashkir State University, Russian Federation University of Alberta, Canada
a r t i c l e
i n f o
Article history: Received 14 February 2011 Accepted 29 July 2011 Available online 6 August 2011 Keywords: electromagnetic heating heavy-oil recovery field results mathematical modeling
a b s t r a c t A multi-layer, two-dimensional mathematical model of reservoir heating by Radio-Frequency (RF) Electromagnetic (EM) radiation for heavy oil recovery is presented. The model takes into account the heat loss in the wellbore and into the surrounding formations. The validity of the mathematical model is tested on a real field case application. A sensitivity analysis on the damping coefficient of EM waves is also performed. It is shown that the occurrence of volumetric heat sources at the bottom hole caused by EM field action yields an intensive deep heating of the reservoir with a small temperature gradient. Numerical calculations show that the bottom-hole pressure and the EM generator power are essential factors in determining the heat transfer processes and heavy oil production. The method of RF-EM radiation is also compared to “cold” production (without any influence of heating). © 2011 Elsevier B.V. All rights reserved.
1. Introduction Heavy-oil and bitumen recovery from difficult geological media such as deep, heterogeneous and high shale content sands and carbonates, and water repellent oilshale reservoirs requires techniques other than conventional thermal and miscible injection methods. Materials in oil reservoirs (formation water, crude oil, oil–water emulsions, bitumen and their components like resins, asphaltenes, and paraffin) are nonmagnetic dielectric materials with low electrical conductivity. If an electromagnetic field can be created to change these properties, electrothermo controlled hydrodynamics could improve the displacement and recovery of heavy-oil/bitumen. This paper deals with the recovery improvement of heavy-oil by Radio-Frequency (RF) Electromagnetic (EM) radiation. The RF-EM fields in the form of waves can penetrate deeply enough – from fractions of a meter to several hundred meters – into oil and gas containing reservoirs to generate heat and eventually improve recovery mainly due to the reduction of oil viscosity. Results of RF-EM treatment experiments were well documented in numerous studies (Chakma and Jha, 1992; Kasevich et al., 1994; Nigmatulin et al., 2001; Ovalles et al., 2002). Theoretical aspects of heavy-oil production were covered by Abernethy (1976), Islam et al. (1991), Sahni et al. (2000), Sayakhov et al. (2002), and Carrizales et al. ⁎ Corresponding author at: Department of Civil and Environmental Engineering, School of Mining and Petroleum Eng., 3-112 Markin CNRL-NREF, Edmonton, AB, Canada T6G 2W2. E-mail address: [email protected] (T. Babadagli). 0920-4105/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2011.07.006
(2008). Several other studies investigated the heat and mass transfer processes in heavy oil reservoirs stimulated by EM radiation (Davletbaev et al., 2008, 2009; Kovaleva and Khaydar, 2004; Kovaleva et al., 2004; Sayakhov et al., 1998). A number of other investigations proposed analytical models of lab experiments (Nigmatulin et al., 2001; Ovalles et al., 2002). Various methods of EM treatment of hydrocarbon deposits were reported over more than five decades (Bridges, 1979; Dyblenko et al., 1981; Haagensen, 1965, 1986; Jeambey, 1989, 1990; Ritchey, 1956; Sayakhov, 1992, 1996, 2003; Sresty et al., 1984). Field tests of bottomhole heating by RF-EM radiation were carried out in a number of oil fields in Russia, the USA, and Canada (e.g., Kasevich et al., 1994; Sayakhov et al., 1980; Spencer, 1987, 1989). Abernethy (1976), in one of the pioneering works, solved the problem of heat transmission within the production well under the RF-EM field influence. The following expression for the oil flow rate, taking into account the effect of temperature on the oil viscosity, and the one-dimensional expression for the density of heat sources, was adapted in that paper: q = 2αd Jb
rd expð−2αd ðr−rd ÞÞ; r
ð1Þ
where αd is the damping factor of the EM-wave, Jb is the intensity of radiation at the well bottom, and rd is the radius of EM-wave radiator. The use of two horizontal wells for bitumen recovery by EM heating in Alaska was simulated by Islam et al. (1991). According to the model presented, one of the wells is intended for water or gas injection and
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another well is intended for fluid recovery. Sahni et al. (2000) analyzed the use of low-frequency electric field (ohmic) heating (ω = 60 Hz) and microwave electromagnetic heating (ω = 0.915 GHz). Application of the EM heating for oil recovery in two oil reservoirs was tested. The heat equation with a heat source in a one-dimensional formulation was solved by Ovalles et al. (2002). The aim of this work was to mathematically model the physical experiments described in the same paper. A satisfactory agreement between the calculated and the laboratory data was obtained. Then, the mathematical model was used for EM simulation in three hypothetical oil fields in Venezuela with different viscosities of heavy oil. EM oil recovery by horizontal oil wells was also considered by Kovalyova (Kovaleva) and Khaydar (2004) and Kovaleva et al. (2004). Later, EM radiation and electrical heating methods were compared by Carrizales et al. (2008). Mathematical models were developed for one-dimensional radial and linear cases. The solvent injection combined with RF electromagnetic radiation in a producing well for extra-heavy oil recovery was presented by Davletbaev et al. (2008, 2009). These models considered the heat losses in the well and surrounding formations. Nigmatulin et al. (2001) studied the effects of RF-EM radiation when applied simultaneously with miscible oil displacement. The high-viscosity oil production method introduced in Dyblenko et al. (1981) and Spencer (1987,1989) defines production stimulation by thermal excitation of the producing wells. In these methods, a hydrocarbon reservoir saturated by heavy-oil or bitumen is exposed to radio-frequency electromagnetic radiation (RF-EM) produced by a surface generator. Due to dielectric losses in the pay zone, the transmitted EM energy is converted into thermal energy that generates volume heat sources in the rock. Due to finite conductivity of the coaxial conductor (the tubing and casing strings), part of the EM energy traveling from the well head to its bottom hole transforms again into thermal energy. The heat released prevents paraffin dropout along the wellbore and provides additional heating of the oil in place, thereby increasing its mobility. The results of field tests in Russia (heavy oil reservoir by Ishimbayneft, Yultimirovskaya and Mordovo_Karmalskaya tar sands) and basic mathematical model of RF-EM application were described by Davletbaev et al. (2010). This paper begins with mathematical modeling of the RF-EM process to determine the optimal application conditions. The model was described and a critical sensitivity analysis using the model was provided as a sample exercise. Field case results (Yultimirovskaya tar sands) were used to test and validate the model. The algorithm of calculation included the refinement of the unknown parameters, in particular, an estimate of the damping factor of EM waves in the reservoir (adaptation of the measured and theoretical data temperature).
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The heating process has a volumetric character and is largely governed by the structure of the electromagnetic wave, the frequency and power of radiation, and the dielectric properties of the medium. The emergence of volume heat sources in the substance serves to heat and ultimately reduce the viscosity of oil.
3. Definition of the model: geometry and basic equations This paper presents a two-dimensional mathematical model and numerical results of the heavy oil recovery by EM radiation from a well, taking into account the convective heat transfer along the well and heat losses into the surrounding rock. The EM radiation effect and usual “cold” recovery of high-viscosity oil were also compared. The heat propagation process and fluid filtration in the layer were assumed as radial. An axial-symmetric coordinate system (r, z) with the axis z, oriented along a well axis from top to bottom was used. The well, pay zone and surrounding rocks were a multilayer system consisting of six layers along the coordinate r, and 3 layers along the coordinate z (Fig. 1). The first layer along the coordinate r is a layer from the well axis to the inner radius of tubing 0 b r b R1, the second layer is the tube itself from its inner to outer radiuses R1 b r b R2, the third layer is the well annulus filled with air R2 b r b R3, the fourth layer is the casing of a well from the inner to the outer radius of R3 b r b R4, the fifth layer is baffle plate R4 b r b R5, and the sixth layer is a surrounding rock from the outer radius of the baffle plate to the boundary of a layer R5 b r b re. Oil flows through the borehole from the well bottom to the wellhead. The first layer along the coordinate z in the model is a nonproductive layer, i.e., the layer from the wellhead to the roof of pay zone 0 b z b Z1; the second layer is the producing layer from the roof to the subface Z1 b z b Z2; the third layer is non-productive layer (surrounding rock) Z2 b z b Z3. It is assumed that in each elementary volume of the porous medium, the heat transfer between the skeleton of the porous medium and fluid occurs instantaneously. The deformation of the skeleton of the porous medium is absent and the filtration of fluid in a porous medium is described by Darcy's law. The general system of equations describing the processes in the system (well-pay zone-rocks surrounding the well and the pay zone), includes the continuity equation for the fluid in a porous medium (diffusion equation), the Darcy law, and the equation of heat. Appendix A presents the mathematical model in detail. The boundary-condition differential equation system was solved by the finite difference method using the implicit scheme.
2. Physics of RF-EM heating of oil The distribution of electromagnetic waves in oil is associated with frequency dispersion of dielectric inductivity (capacitance) caused by orientational polarization of polar components. Under the RF-EM influence, additional heat (besides the Joule heat) is generated owing to electric polarization effects. The dissipation of the EM energy is accompanied by the occurrence of heat sources distributed in the medium. Such distribution is, in the general case, given by the following equation (Landay and Lifshitz, 1984; Ramo and Whinnery, 1944): q=
ωε0 ε′ tgδ 2 E ; 2
ð2Þ
where ω— frequency of EM waves, ε0— electric constants, ε' — relative permittivity of the medium to liquid, tgδ— dielectric loss (dissipation) tangent, and E— electric field intensity.
Fig. 1. Structural model used in the development of mathematical model: (1) well, (2) pay zone, (3) and (4) surrounding rock (matrix).
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An example calculation was performed using the following hypothetical data for a sensitivity analysis in the next section: Pi = 1 MPa; Pwf = 0; 0:25; 0:5; 0:75 MPa; kr = 0:183 10−12 m2 ; kz = 0; T0 = 8:8˚С; ϕ = 0:25; γo = 0:042 K−1 ; ct = 10−9 Pa−1 ; R1 = 0:03 m; R2 = 0:035 m; R3 = 0:105 m; R4 = 0:11 m; R5 = 0:115 m; re = 60 m; Ng = 0; 10; 20; 30 kW; αd = 0:03267 m−1 ; αo = 1912680 J = m3 ·K ; ρo = 950 kg = m3 ; λo = 0:125 W = ðm·KÞ; αm = 1200000 J = m3 ·K ; λm = 3 W = ðm·KÞ; h = 10 m; f = 13:56 MHz; μat = 3:42·10−6 ; σt = 3:4·106 ; Z1 = 83 m; Z2 = 93 m; Z3 = 96 m; Zc = 376:8 Ohm; λR2;R4 = 45 W = ðm·KÞ; αR2; R4 = 3641900 J = m3 ·K ; λR3 = 0:0315 W = ðm·KÞ; αR3 = 142977 J = m3 ·K ; λR5 = 1:2 W = ðm·KÞ; αR5 = 2500000 J = m3 ·K ; λZ1;Z3 = 3:95 W = ðm·KÞ; αZ1;Z3 = 2926000 J = m3 ·K ; μ0 = 1 Pa·s: The average parameters were chosen in the range typical of highviscosity oil deposits of the Urals region of Russia. Details about the field characteristics can be found in Davletbaev et al. (2010). Note that the electromagnetic radiation we use is of radio frequency range (f =13.56 MHz) and therefore, its absorption is mostly in oil. The water absorbs high frequency waves really high in microwave. In addition, the saturation of water in the collector is small and it can be neglected. 4. Application of the model and analysis of the results The results obtained using the solution of the mathematical model for the RF-EM treatment/continuous oil production process and applying the data given above are presented in Figs. 2–6. Fig. 2 shows reservoir temperature distribution curves at different times for μ0 = 1 Pa·s Pwf = 0.5 MPa, Ng = 10 kW. The temperature of the medium at the bottom can reach sufficiently high values due to enhanced absorption of energy by electromagnetic waves near the radiator (in this case ~100 °C). We can also observe increasing temperature and its gradient in the borehole zone during electromagnetic radiation into the reservoir. Fig. 3 shows reservoir temperature distribution curves for different output performance settings of the RF-EM generator for μ0= 1 Pa·s, Pwf = 0.5 MPa and time t = 3 days. It is apparent that by changing the
Fig. 3. Temperature distribution across the reservoir during simultaneous RF EM heating and production for different RF generator performance settings: Ng = 10, 20, 30 kW for μ0 = 1 Pa·s; t= 3 days, Pwf = 0.5 MPa.
emitting performance of the generator, it is possible to achieve the target bottom-hole temperature and bottom-hole zone heating depth. Fig. 4 illustrates the 3-D distributions (for r-φ coordinates, corresponding to 10 m from the wellhead) of temperature after 3 days of treatment for an RF-EM generator power of 10 kW (Fig. 4-a) and 20 kW (Fig. 4-b), μ0 = 1 Pa·s, Pwf = 0.5 MPa. The generated thermal field in the first case (Fig. 4) is characterized by high temperatures (because of intense absorption of EM energy) in the borehole environment, decreasing monotonically with distance from the borehole. We consider the combined technology, including radiofrequency electromagnetic field impact and injection of solvent into the formation in other studies (Davletbaev et al., 2008, 2009). We noticed that such technology is more effective for extra-heavy crude oil and can increase the processing of well bottom zone in comparison with RF treatment only more than twice. Fig. 5 illustrates wellbore temperature distributions after 3 days of treatment, at different distances from the wellbore central axis: 0.035 m (on the tubing surface); 0.7 m (in the annular space); 0.11 m (on the inner wall surface of the cement casing); 0.5 m (in the surrounding rock). The absolute bottom-hole temperatures correspond to the values of the reservoir temperature distribution curves
a
100
T, °C
100
75
50 0 10
50 25 5
0
5
y, m
10
10
0
5
5
10 0
x, m
b
200
T, °C
100
150
50 0 10
100 50 5
0 y, m
Fig. 2. Temperature distribution across the reservoir during simultaneous RF-EM heating and production at different times: t = 0.1, 0.5, 1.5, 3 days forμ0 = 1 Pa·s; Pwf = 0.5 MPa, Ng = 10 kW.
5
10
10
0
5
5
10 0
x, m
Fig. 4. Temperature distribution across the reservoir during simultaneous RF EM heating and production for different RF generator performance settings: Ng = 10 kW (a) and Ng = 20 kW (b); t = 3 days, μ0 = 1 Pa·s, Pwf = 0.5 MPa.
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of the wellbore caused by the EM wave absorption by the tubing string and the influx of ‘hot’ oil from the matrix can help prevent paraffin formation and produce heated oil coming to the surface, which is more mobile than the initial oil in place. Fig. 6 shows the flow dynamics for different generator output performance settings (Fig. 6a) for different reservoir/bottom-hole differential pressures (Fig. 6b). At the initial stage of production, the liquid rate falls rapidly; this decreasing trend then slows and turns into a monotonous upward tendency. The initial rate drop is due to the well reaching the stationary flow regime; the succeeding rate increase is the result of reduction in oil viscosity. The greater the duration of stimulation and the power of the emitter of EM waves, the greater is the increased oil production as compared with the production of cold oil. Pressure differential between the borehole and the formation has no significant effect on the dynamics of change in flow rate (in the case considered here the range of pressure difference between wellbore and formation, the duration of oil production and the duration of EM radiation). The greater the pressure differential between the borehole and formation, the greater is the flow of oil from the reservoir. Fig. 5. Temperature distribution along the wellbore during simultaneous RF EM heating and production for different RF generator performance settings: Ng = 10 kW (a), Ng = 20 kW (b); Pwf = 0.5 MPa, μ0 = 1 Pa·s, t = 3 days.
(Figs. 2–5). An abrupt fall in temperature is observed on the border between the pay zone and the reservoir bottom, which can be attributed to the absence of heat sources in this zone. Within the pay zone, the wellbore temperature curves indicate the presence of hightemperature spots. This is due to well/rock interaction effects in the bottom-hole zone — volume heating occurring within the pay zone 83 ≤ z ≤ 93 m is caused by EM energy absorption by the medium and a convective heat transport from the heated oil in the reservoir. Heating
Fig. 6. Production rate dynamics during RF EM treatment for “cold oil” production Ng = 0 kW and for generator performance settings Ng = 10, 20, 30 kW (a); and for different reservoir/bottom-hole differential pressures P0 − Pwf = 0.25, 0.5, 0.75 MPa (b).
5. Model validation using a field case RF-EM tests were conducted in the Yultimirovskoye bitumen field located in Sugushlinskaya Square operated by Tatneft. An experimental section was selected for these tests in the field. The test section included two wells: no. 150 and no. 1. The distance between these wells is 5 m. The pay zone has 25% porosity, 3.6% bitumen saturation and the permeability ranges between 0 and 183 mD. The EM energy was produced by a RF generator and transmitted by a coaxial conductor (well). Initially, water from Well 150 was displaced by air at an injection pressure of 0.4–0.6 MPa. The temperature in both wells was measured by thermocouple elements. One measuring element was lowered through the tubing string into Well 150 and positioned at 87.5 m (the middle part of the radiator), and the other element was lowered into Well 1 at 83.5 m. The EM heating of the bitumen reservoir was performed in several stages for different RF generator operation modes. Initially, the generator was switched to the prolonged heating mode and its output performance was set to approximately 20 kW. Fig. 7 shows the changes in temperature recorded in the bottom-hole zones of the wells during the RF-EM treatment. Fig. 2 indicates that after t1 =1.39 days (33.4 h) of continuous heating in this mode, the temperature at the bottomhole of Well 150 increased from 8.8 °C to 117.9 °C. At the next stage, the generator was readjusted to output 30 kW. As a result, after 6 h (by t2 =1.64 days), the temperature in Well 150 reached 149.8 °C. After that, the generator was
Fig. 7. Temperature distribution in Well 150 during RF-EM heating, with the generator performance set to 20 kW, 30 kW, 60 kW, and 0 kW.
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6. Energy balance calculation
Fig. 8. Temperature distribution across the reservoir during simultaneous RF-EM heating for different stages.
set to its maximum output capacity of 60 kW. As seen in Fig. 2, the heating dynamics soared and within 3.7 h (t3 =1.64–1.80 days) of operation at the maximum-output mode, the temperature at the well bottom hole increased from 149.8 to 191.3 °C. After that, the RF generator was switched out for 1.72 h (t4 =1.80– 1.87 days). Then, the RF-EM system worked at maximum output of the generator with electromagnetic waves of ~60 kW for 32 h (t5 =1.87– 3.21 days). The RF-EM generator was shut for 72 h (t6 =3.21–6.20 days). During the RF-EM treatment of Well 150 the temperature on the bottom of Well 1 which was on distance of 5 m from Well 150 was registered. The increase in temperature to 44.8 °C was detected. Fig. 8 shows the theoretical curves of temperature distribution in the reservoir from borehole 150 in different time periods. The results indicate, after the 5th (t5 = 1.87–3.21 days of generator at 60 kW operating) and 6th stages (t6 = 3.21–6.20 days generator stop), the temperature at 5 m from the well (Well-150) increased to 32 °C. Fig. 9 illustrates the theoretical and measured temperature distributions along the borehole (from the wellhead to bottom). As seen, the measured and theoretical curves are in good agreement. Note that the mathematical model did not take into account the geothermal gradient of temperature, hence, the absolute values of temperature do not coincide. The distribution of temperature along the borehole (Fig. 9) calculated after a few days shows a small loss of heat at the top and bottom of the reservoir. When modeling, the damping factor of the EM waves in the reservoir was used as a parameter to match the measured and theoretical data in Figs. 7 and 9. The best combination of measured and theoretical data was obtained at the value of αd = 0.03267 m − 1. This value of damping coefficient of EM waves in the reservoir was used for mathematical modeling of the RF-EM field and the production of extra-heavy oil.
The energy balance calculations were performed for: (1) “cold” oil production at a constant bottomhole pressure in the well (the period of 30 days of oil production), and (2) 5 days — oil production and RFEM radiation and 25 days — oil production stopped RF-EM generator (the total duration of 30 days). These two cases were compared and the additional oil production by high-frequency electromagnetic radiation into the reservoir was calculated. These data were used to estimate the energy balance, i.e. energy equivalent of additional oil production to compare the expenditure of energy of using RF-EM radiation. Power consumption, RF electromagnetic generator, its efficiency, energy losses in transmission lines from the thermal station (where oil production is burned conventionally) to the location of RF-EM generator, and the efficiency of power transmission lines were included in this exercise. RF-EM generator has efficiency ηG = 0.67. Transmission line of EM waves from the wellhead to the bottom is a coaxial system of tubing and casing, the efficiency is ηL = 0.476. It is assumed that the efficiency of the transmission line from the thermoelectric power station to the location of the RF-EM generator is ηTF = 0.563. Efficiency of thermoelectric power station is ηEPS = 0.35. Heat loss EM energy in the borehole that are associated with oxidation and contamination of surface pipe tubing, with the presence of water in the well production is ηLH = 0.75. Total power consumption with all the loss is determined from the following expression:
NPC =
N0 : ηG ηL ηEPS ηTF ηLH
Assessment of energy balance is described by the form factor Kem, which equal to the ratio of produced additional energy, WAP to the consumed energy due to the RF generator WPC:
Kem =
WAP : WPC
Here, the energy consumption is equal to the product consumed by power RF-EM generator NPC on the duration of RF-EM radiation t1: WPC =NPC ⋅t1. In addition the energy obtained is determined by the formula of WAP =M⋅G, where G— calorific value of oil, which is assumed to be 4.61∙107 J/kg, M=ΔQo ⋅ ρo— the mass of additional oil, which is determined from the density of oil ρo and the volume of additional oil ΔQo. In calculating the energy balance was taken 5 days of oil production with RF-EM heating and then 25 days production without RF-EM radiation. The base case is accepted by the “cold” oil production 30 days without RF-EM radiation. The analysis showed that the ratio of the energy balance is 5.29. 7. Conclusions
Fig. 9. Wellbore temperature distribution in Well 150 (from the well head) after RF-EM treatment (measured and calculated curves).
1. We formulated a two-dimensional mathematical model of heavy oil recovery for RF-EM radiation heating. This model allowed us to quantify the degree of heating the reservoir. The mathematical model takes into account the heat losses into the rock surrounding the wellbore and reservoir, and can be used to quantify the magnitude of heat loss. 2. Simulation results were compared with those of a field test. The damping coefficient of EM waves in a reservoir was evaluated to match the measured and calculation data. 3. Numerical simulations suggest that bottom-hole temperature and heat/mass transfer effects in the reservoir can be controlled by setting the output performance of the RF generator and by the difference between the reservoir and bottom-hole pressure.
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4. The RF-EM energy loss along the wellbore (between the generator and the bottom hole) can be considered an advantage as it prevents paraffin deposition and boosts the mobility of the produced oil. Nomenclature ω frequency of EM waves, MHz; ε0 and χ0 electric and magnetic constants, respectively; ε' relative permittivity of the medium to liquid; tgδ dielectric loss (dissipation) tangent; E electric field intensity; λ0 length of the EM wave produced by the generator, m; P pressure, MPa; P0 initial reservoir pressure, MPa; Pwf bottom-hole pressure, MPa; T temperature, °C; ΔT = T − T0, T0 initial temperature of the medium, °C; R1 and R2 inside and outside radius of tubing, respectively, m; R3 and R4 inside and outside radius of casing, respectively, m; R5 outside radius of baffle plate, m; Z1 and Z2 coordinates of the roof and subface of stratum, respectively, m; Z3 maximal observed distance along coordinate z, m; rd radius of EM-wave radiator (rw = R2), m; re pool boundary along coordinate r, m; ρo density of the oil, kg/m 3; ñ specific heat capacity of oil, J/(kg·K); α heat capacity per unit volume, J/(m 3·K); αm heat capacity of the rock skeleton, J/(m 3·K); αo heat capacity of oil, J/(m 3·K); λ thermal conductivity of the medium, W/(m·K); λm thermal conductivity of the rock skeleton, W/(m·K); λo thermal conductivity of oil, W/(m·K); ϕ porosity of the medium; kr and kz permeability of productive stratum along coordinates r and z, respectively, m 2; h stratum thickness, m; ct total compressibility of the system, Pa − 1; cm and co compressibility of the rock skeleton and of oil, Pa − 1; υr and υz rate of filtering in the stratum along and across stratification, m/s; ωw flow in the tubing, m/s; Q flow rate, m 3/c, m 3/day; μ0 value of viscosity at T = T0, Pa·s, mPa·s, cP; γo coefficient allowing for temperature dependence of the viscosity of oil, 1/K; N0 power of EM-wave radiator, kW; Ng power of RF EM generator, kW; Sb area of EM-wave radiator, m 2; Jb = N0/Sb intensity of radiation at the well bottom, kW/m2; αd damping factor of EM-wave, m − 1; αd2 and αd4 damping factor of EM waves in the tubing and casing, respectively, m − 1; Rs active part of surface resistance of tubes; Zc wave resistance of air filling the intertube space, Ohm; f cyclic frequency of EM waves, MHz; μat and σat absolute magnetic permeability and specific electrical conductivity of the tubes, respectively; ηG efficiency of RF-EM generator; ηL efficiency of transmission line of EM waves of a coaxial system of tubing and casing; ηTF efficiency of transmission line from the thermoelectric power station to the location of the RF-EM generator; ηEPS efficiency of thermoelectric power station; ηLH efficiency of heat loss EM energy; Kem energy balance factor; WAP produced additional energy, J; WPC energy due to the RF generator working, J;
NPC t1 G ρo ΔQo
651
total power, J/s; duration of RF-EM radiation; calorific value of oil, J/kg; density of oil, kg/m 3; volume of additional oil, m 3.
Acknowledgment This paper is the revised and improved version of SPE 136611 presented at the 2010 SPE Canadian Unconventional Resources and Int. Petr. Conf., Calgary, AB, Canada, 19–21 Oct. Appendix A. Formulation of the problem and basic equations We assumed that the filtration of fluid in the reservoir and the distribution of the thermal field in the radial direction is carried out uniformly, i.e. ∂ T/∂ ϕ = 0 and ∂ P/∂ ϕ = 0. The general system of equations includes the equation of heat transfer, the diffusion equation and Darcy's law. The heat conductivity equation in the system is defined as follows: ∂T 1 ∂ ∂T 1 ∂ ∂T ρ c ∂T = rλ + λ −υr o o α⋅r ∂r α ∂z α ∂r ∂t ∂r ∂z −ωw
ðA 1Þ
∂T q + ; 0 ≤ r ≤ re ; 0 ≤ z ≤ Z3 ; α ∂z
where α— heat capacity per unit volume, λ— thermal conductivity of the medium, υr— rate of filtering in the stratum along stratification, ρo— density of the oil, co— specific heat capacity of oil, ωw— flow in the tubing, q— density of distribution of these heat sources, and Z3— maximal observed distance along coordinate z. The pressure distribution in the reservoir is described by the diffusion equation: ∂P k 1 ∂ r ∂P k ∂ 1 ∂P = r + z ; rw ≤ r ≤ re ; Z1 ≤ z ≤ Z2 ; ϕct r ∂r μ ∂r ϕct ∂z μ ∂z ∂t
ðA 2Þ
where kr and kz— permeability of productive stratum along coordinates r and z, ϕ— porosity of the medium, μ— oil viscosity, ct— total compressibility of the system, rw and re— well radius and pool boundary along coordinate r, Z1 and Z2— coordinates of the roof and subface of stratum, respectively. The rate of fluid flow in a porous medium is determined from Darcy's law: υr = −
kr ∂P ; r ≤ r ≤ re ; Z1 ≤ z ≤ Z2 ; μ ∂r w
ðA 3Þ
It is assumed that the fluid motion along the wellbore from the borehole to the wellhead is defined by ωw =
Q ; 0 ≤ r ≤ R1 ; 0 ≤ z ≤ Z1 ; π⋅R21
ðA 4Þ
where R1— inside radius of tubing, and Q— flow rate. Reservoir oil viscosity is a function of temperature as given by: μ = μ0 expð−γo ⋅ΔT Þ;
ðA 5Þ
where μ0— value of viscosity at T = T0, ΔT = T − T0— change in temperature in the reservoir, and γo— coefficient allowing for temperature dependence of the viscosity of oil.
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λ = ð1−ϕÞλm + ϕλo ;
ðA 6Þ
where R4— outside radius of casing, while in the other layers of the well q = 0. The total flow, Q of the injected agent is given by the filtration velocity at the bottom hole:
α = ð1−ϕÞαm + ϕαo ;
ðA 7Þ
Q = 2π rw hυr ;
αj = cj ⋅ρj ; j = m; o;
ðA 8Þ
Thermal conductivity and volumetric heat capacity of the saturated porous medium (defined in rw ≤ r ≤ re, Z1 ≤ z ≤ Z2) are as follows:
where λm and λo— thermal conductivity of the rock skeleton and of oil, respectively, αm and αo— heat capacity of the rock skeleton and of oil, respectively, cm and co— specific heat capacity of the rock skeleton and of oil, respectively, and ρm and ρo— density of the rock skeleton and of the oil. The energy interaction between the EM waves and the reservoir rock causes the emergence of volumetric heat sources distributed across the reservoir. The density of distribution of these heat sources can be formulated as follows (Abernethy, 1976): q = 2αd Jb
rd expð−2αd ðr−rd ÞÞ; rd ≤ r ≤ re ; Z1 ≤ z ≤ Z2 r
ðA 9Þ
where αd— damping factor of EM-wave, Jb— intensity of radiation at the well bottom, and rd— radius of EM-wave radiator. The output performance (power) of the EM radiator is obtained from the known generator output performance, Ng: N0 = Ng exp½−2ðαd2 + αd4 ÞZ1 ;
ðA 10Þ
where Ng— power of RF EM generator, αd 2 and αd4— damping factor of EM waves in the tubing and casing. The EM wave damping factor for the coax conductor (well tubing and casing) is estimated from: αd2 =
Rs 1 ⋅ ; 2Zc ⋅ lnðR3 = R2 Þ R2
ðA 11Þ
αd4 =
Rs 1 ⋅ ; 2Zc ⋅ lnðR3 = R2 Þ R3
ðA 12Þ
where Rs— active part of surface resistance of tubes: 2
Rs =
πf μat ; σt
ðA 13Þ
and Zc— wave resistance of air filling the intertube space: 2
Zc =
χ0 : ε0
ðA 14Þ
Here, f— cyclic frequency of EM waves, μat and σt— absolute magnetic permeability and specific electrical conductivity of the tubes, respectively, χ0 and ε0— electric and magnetic constants, R2— outside radius of tubing, and R3— inside radius of casing. It is assumed that the EM waves, while traveling along the annual space from the head towards the bottom hole of the well, lose part of their energy, which creates a sort of ‘internal distributed heat sources’ in the tubing and casing walls. These are given by: q=
q=
αd2 N0 expð−2ðαd2 + αd4 ÞzÞ; R1 ≤ r ≤ R2 ; 0 ≤ z ≤ Z2 ; π r 2 lnðR2 = R1 Þ ðA 15Þ αd4 N0 expð−2ðαd2 + αd4 ÞzÞ; R3 ≤ r ≤ R4 ; 0 ≤ z ≤ Z1 ; π r 2 lnðR4 = R3 Þ ðA 16Þ
ðA 17Þ
where h— stratum thickness. The initial and boundary conditions for the equations are determined by matching the well/reservoir/surrounding rock system, and are given as follows: P ðr; z; t = 0Þ = P0 ; rw ≤ r ≤ re ; Z1 ≤ z ≤ Z2 ;
ðA 18Þ
T ðr; z; t = 0Þ = T0 ; 0 ≤ r ≤ re ; 0 ≤ z ≤ Z3 ;
ðA 19Þ
P ðr = rw ; z; t Þ = Pwf ; Z1 ≤ z ≤ Z2 ;
ðA 20Þ
∂T ðr = 0; z; t Þ = 0; 0 ≤ z ≤ Z3 ; ∂r
ðA 21Þ
T ðr = re ; z; t Þ = T0 ; 0 ≤ z ≤ Z3 ;
ðA 22Þ
∂T ðr; z = 0; t Þ = 0; 0 ≤ r ≤ re ; ∂z
ðA 23Þ
∂T ðr; z = Z3 ; t Þ = 0; 0 ≤ r ≤ re ; ∂z
ðA 24Þ
P ðr = re ; z; t Þ = P0 ; Z1 ≤ z ≤ Z2 :
ðA 25Þ
Here P0— initial reservoir pressure, Pwf — bottom-hole pressure. References Abernethy, E.R., 1976. Production increase of heavy oils by electromagnetic heating. J. Can. Petrol. Technol. 15 (3), 91–97. Bridges, J.E. 1979. Method for In-situ Heat Processing of Hydrocarbonaceus Formation. US Patent 4,140,180. Carrizales, M.A., Lake, L.W., Johns, R.T., 2008. Production improvement of heavy-oil recovery by using electromagnetic heating. Paper SPE 115723 presented at the 2008 SPE Annual Technical Conference and Exhibition, Denver, Colorado, USA, 21– 24 September. Chakma, A., Jha, K.N., 1992. Heavy-oil recovery from thin pay zones by electromagnetic heating. Paper SPE 24817 presented at the 67th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Washington D.C., 4–7 October. Davletbaev, A.Ya., Kovaleva, L.A., Nasyrov, N.M., 2008. Numerical simulation of injection of a solvent into a production well under electromagnetic action. Fluid Dyn. 43 (4), 583–589. Davletbaev, A.Ya., Kovaleva, L.A., Nasyrov, N.M., 2009. An investigation of the processes of heat and mass transfer in a multilayer medium under conditions of injection of a miscible agent with simultaneous electromagnetic stimulation. High Temp. 47 (4), 574–579. Davletbaev, A., Kovaleva, L., Babadagli, T., Minnigalimov, R., 2010. Heavy oil and bitumen recovery using radio-frequency electromagnetic irradiation and electrical heating: theoretical analysis and field scale observations. Paper SPE 136611 presented at the 2010 SPE Canadian Unconventional Resources and Int. Petr. Conf., Calgary, AB, Canada, 19–21 Oct. 2010. Dyblenko, V.P., et. al. 1981. Oil Production Deep-Well Pumping Unit. SU Patent 802,527. Haagensen, A.D. 1965. Oil Well Microwave Tools. US Patent 3,170,119. Haagensen, D.B. 1986. Oil Recovery System and Method. US Patent 4,620,593. Islam, M.R., Wadadar, S.S., Banzal, A., 1991. Enhanced oil recovery of Ugnu Tar Sands of alaska using electromagnetic heating with horizontal wells. Paper SPE 22177 presented at the International Arctic Technology Conference, Anchorage, Alaska, 29–31 May. Jeambey, C.G. 1989. Apparatus for Recovery of Petroleum from Petroleum Impregnated Media. US Patent 4,187,711. Jeambey, C.G. 1990. System for Recovery of Petroleum from Petroleum Impregnated Media. US Patent 4,912,971. Kasevich, R.S., Price, S.L., Faust, D.L., Fontaine, M.F., 1994. Pilot testing of a radio frequency heating system for enhanced oil recovery from diatomaceous earth. Paper SPE 28619 presented at the 69 Annual Technicel Conference and Exhibition, New Orleans, USA, 25–28 September. Kovaleva, L.A., Nasyrov, N.M., Khaidar, A.M., 2004. Mathematical modeling of highfrequency electromagnetic heating of the bottom-hole area of horizontal oil wells. J. Eng. Phys. Thermophys. 77 (6), 1184–1191.
A. Davletbaev et al. / Journal of Petroleum Science and Engineering 78 (2011) 646–653 Kovalyova (Kovaleva), L.A., Khaydar, A.M., 2004. Physical and rheological properties of petroleum fluids under the radio-frequency electromagnetic field effect and perspectives of technological solutions. Appl. Surf. Sci. 238 (1–4), 475–479. Landay, L.D., Lifshitz, E.M., 1984. Electrodynamics of Continuous Media. Pergamon Press, Oxford. Nigmatulin, R.I., Sayakhov, F.L., Kovaleva, L.A., 2001. Cross transport phenomena in disperse systems interacting with a high-frequency electromagnetic field. Dokl. Phys. 46 (3), 215–218. Ovalles, C., Fonseca, A., Lara, A., Alvarado, V., Urrecheaga, K., Ranson, A., Mendoza, H., 2002. Opportunities of downhole dielectric heating in venezuela: three case studies involving medium, heavy and extra-heavy crude oil reservoirs. Paper SPE 78980 presented at the International Thermal Operations and Heavy Oil Symposium and International Horizontal Well Technology Conference, Calgary, Alberta, Canada, 4–7 November. Ramo, S., Whinnery, J.R., 1944. Fields and Waves in Modern Radio, 1st ed., General Electric Advanced Engineering Program, New York, NY. J. Wiley and Sons, Inc.; Chapman and Hall, London, England. Ritchey, H.W. 1956. Radiation Heating System. US Patent 2,757,738. Sahni, A., Kumar, M., Knapp, R.B., 2000. Electromagnetic heating for heavy oil reservoir. Paper SPE 62550 presented at SPE/AAPG Western Regional Meeting, Long Beach, California, 19–23 June.
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Sayakhov, F.L., 1992. Method for Thermal Treatment of Hydrocarbon Pool. SU Patent 1,723,314. Sayakhov, F.L., 1996. Method for Mineral Recovery. SU Patent 1,824,983. Sayakhov, F.L., Kovaleva, L.A., Nasyrov, N.M., 1998. Special features of heat and mass exchange in the face zone of boreholes upon injection of a solvent with a simultaneous electromagnetic effect. Inzh.-Fiz. Zh. 71 (1), 161–165. Sayakhov, F.L., et al. 2003. Method of Development of High-Viscosity Oil and Bitumen Pools. RU Patent 2,213,858. Sayakhov, F.L., et al., 1980. RNTS Neftepromysl. Delo (1), 5–8. Sayakhov, F.L., Kovaleva, L.A., Nasyrov, N.M., 2002. Heat and mass transfer in the wellstratum system under the electromagnetic action on massive oil deposits. J. Eng. Phys. Thermophys. 75 (1). Spencer, H.L. 1987. Electromagnetic Oil Recovery Ltd. Calgary. Spencer, H.L., 1989. Electric heat breaks paraffins, boosts production. Enhanced Recovery Week. . (30.10 - P.1-2). Sresty, G.C., Snow, R.H., Bridges, J.E. 1984. Recovery of liquid hydrocarbons from oil shale by electromagnetic heating in situ. US Patent 4,485,869.
Contents lists available at ScienceDirect
Journal of Petroleum Science and Engineering j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / p e t r o l
Mathematical modeling and field application of heavy oil recovery by Radio-Frequency Electromagnetic stimulation Alfred Davletbaev a, Liana Kovaleva b, Tayfun Babadagli c,⁎ a b c
RN-UfaNIPIneft, Rosneft, Russian Federation Bashkir State University, Russian Federation University of Alberta, Canada
a r t i c l e
i n f o
Article history: Received 14 February 2011 Accepted 29 July 2011 Available online 6 August 2011 Keywords: electromagnetic heating heavy-oil recovery field results mathematical modeling
a b s t r a c t A multi-layer, two-dimensional mathematical model of reservoir heating by Radio-Frequency (RF) Electromagnetic (EM) radiation for heavy oil recovery is presented. The model takes into account the heat loss in the wellbore and into the surrounding formations. The validity of the mathematical model is tested on a real field case application. A sensitivity analysis on the damping coefficient of EM waves is also performed. It is shown that the occurrence of volumetric heat sources at the bottom hole caused by EM field action yields an intensive deep heating of the reservoir with a small temperature gradient. Numerical calculations show that the bottom-hole pressure and the EM generator power are essential factors in determining the heat transfer processes and heavy oil production. The method of RF-EM radiation is also compared to “cold” production (without any influence of heating). © 2011 Elsevier B.V. All rights reserved.
1. Introduction Heavy-oil and bitumen recovery from difficult geological media such as deep, heterogeneous and high shale content sands and carbonates, and water repellent oilshale reservoirs requires techniques other than conventional thermal and miscible injection methods. Materials in oil reservoirs (formation water, crude oil, oil–water emulsions, bitumen and their components like resins, asphaltenes, and paraffin) are nonmagnetic dielectric materials with low electrical conductivity. If an electromagnetic field can be created to change these properties, electrothermo controlled hydrodynamics could improve the displacement and recovery of heavy-oil/bitumen. This paper deals with the recovery improvement of heavy-oil by Radio-Frequency (RF) Electromagnetic (EM) radiation. The RF-EM fields in the form of waves can penetrate deeply enough – from fractions of a meter to several hundred meters – into oil and gas containing reservoirs to generate heat and eventually improve recovery mainly due to the reduction of oil viscosity. Results of RF-EM treatment experiments were well documented in numerous studies (Chakma and Jha, 1992; Kasevich et al., 1994; Nigmatulin et al., 2001; Ovalles et al., 2002). Theoretical aspects of heavy-oil production were covered by Abernethy (1976), Islam et al. (1991), Sahni et al. (2000), Sayakhov et al. (2002), and Carrizales et al. ⁎ Corresponding author at: Department of Civil and Environmental Engineering, School of Mining and Petroleum Eng., 3-112 Markin CNRL-NREF, Edmonton, AB, Canada T6G 2W2. E-mail address: [email protected] (T. Babadagli). 0920-4105/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2011.07.006
(2008). Several other studies investigated the heat and mass transfer processes in heavy oil reservoirs stimulated by EM radiation (Davletbaev et al., 2008, 2009; Kovaleva and Khaydar, 2004; Kovaleva et al., 2004; Sayakhov et al., 1998). A number of other investigations proposed analytical models of lab experiments (Nigmatulin et al., 2001; Ovalles et al., 2002). Various methods of EM treatment of hydrocarbon deposits were reported over more than five decades (Bridges, 1979; Dyblenko et al., 1981; Haagensen, 1965, 1986; Jeambey, 1989, 1990; Ritchey, 1956; Sayakhov, 1992, 1996, 2003; Sresty et al., 1984). Field tests of bottomhole heating by RF-EM radiation were carried out in a number of oil fields in Russia, the USA, and Canada (e.g., Kasevich et al., 1994; Sayakhov et al., 1980; Spencer, 1987, 1989). Abernethy (1976), in one of the pioneering works, solved the problem of heat transmission within the production well under the RF-EM field influence. The following expression for the oil flow rate, taking into account the effect of temperature on the oil viscosity, and the one-dimensional expression for the density of heat sources, was adapted in that paper: q = 2αd Jb
rd expð−2αd ðr−rd ÞÞ; r
ð1Þ
where αd is the damping factor of the EM-wave, Jb is the intensity of radiation at the well bottom, and rd is the radius of EM-wave radiator. The use of two horizontal wells for bitumen recovery by EM heating in Alaska was simulated by Islam et al. (1991). According to the model presented, one of the wells is intended for water or gas injection and
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another well is intended for fluid recovery. Sahni et al. (2000) analyzed the use of low-frequency electric field (ohmic) heating (ω = 60 Hz) and microwave electromagnetic heating (ω = 0.915 GHz). Application of the EM heating for oil recovery in two oil reservoirs was tested. The heat equation with a heat source in a one-dimensional formulation was solved by Ovalles et al. (2002). The aim of this work was to mathematically model the physical experiments described in the same paper. A satisfactory agreement between the calculated and the laboratory data was obtained. Then, the mathematical model was used for EM simulation in three hypothetical oil fields in Venezuela with different viscosities of heavy oil. EM oil recovery by horizontal oil wells was also considered by Kovalyova (Kovaleva) and Khaydar (2004) and Kovaleva et al. (2004). Later, EM radiation and electrical heating methods were compared by Carrizales et al. (2008). Mathematical models were developed for one-dimensional radial and linear cases. The solvent injection combined with RF electromagnetic radiation in a producing well for extra-heavy oil recovery was presented by Davletbaev et al. (2008, 2009). These models considered the heat losses in the well and surrounding formations. Nigmatulin et al. (2001) studied the effects of RF-EM radiation when applied simultaneously with miscible oil displacement. The high-viscosity oil production method introduced in Dyblenko et al. (1981) and Spencer (1987,1989) defines production stimulation by thermal excitation of the producing wells. In these methods, a hydrocarbon reservoir saturated by heavy-oil or bitumen is exposed to radio-frequency electromagnetic radiation (RF-EM) produced by a surface generator. Due to dielectric losses in the pay zone, the transmitted EM energy is converted into thermal energy that generates volume heat sources in the rock. Due to finite conductivity of the coaxial conductor (the tubing and casing strings), part of the EM energy traveling from the well head to its bottom hole transforms again into thermal energy. The heat released prevents paraffin dropout along the wellbore and provides additional heating of the oil in place, thereby increasing its mobility. The results of field tests in Russia (heavy oil reservoir by Ishimbayneft, Yultimirovskaya and Mordovo_Karmalskaya tar sands) and basic mathematical model of RF-EM application were described by Davletbaev et al. (2010). This paper begins with mathematical modeling of the RF-EM process to determine the optimal application conditions. The model was described and a critical sensitivity analysis using the model was provided as a sample exercise. Field case results (Yultimirovskaya tar sands) were used to test and validate the model. The algorithm of calculation included the refinement of the unknown parameters, in particular, an estimate of the damping factor of EM waves in the reservoir (adaptation of the measured and theoretical data temperature).
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The heating process has a volumetric character and is largely governed by the structure of the electromagnetic wave, the frequency and power of radiation, and the dielectric properties of the medium. The emergence of volume heat sources in the substance serves to heat and ultimately reduce the viscosity of oil.
3. Definition of the model: geometry and basic equations This paper presents a two-dimensional mathematical model and numerical results of the heavy oil recovery by EM radiation from a well, taking into account the convective heat transfer along the well and heat losses into the surrounding rock. The EM radiation effect and usual “cold” recovery of high-viscosity oil were also compared. The heat propagation process and fluid filtration in the layer were assumed as radial. An axial-symmetric coordinate system (r, z) with the axis z, oriented along a well axis from top to bottom was used. The well, pay zone and surrounding rocks were a multilayer system consisting of six layers along the coordinate r, and 3 layers along the coordinate z (Fig. 1). The first layer along the coordinate r is a layer from the well axis to the inner radius of tubing 0 b r b R1, the second layer is the tube itself from its inner to outer radiuses R1 b r b R2, the third layer is the well annulus filled with air R2 b r b R3, the fourth layer is the casing of a well from the inner to the outer radius of R3 b r b R4, the fifth layer is baffle plate R4 b r b R5, and the sixth layer is a surrounding rock from the outer radius of the baffle plate to the boundary of a layer R5 b r b re. Oil flows through the borehole from the well bottom to the wellhead. The first layer along the coordinate z in the model is a nonproductive layer, i.e., the layer from the wellhead to the roof of pay zone 0 b z b Z1; the second layer is the producing layer from the roof to the subface Z1 b z b Z2; the third layer is non-productive layer (surrounding rock) Z2 b z b Z3. It is assumed that in each elementary volume of the porous medium, the heat transfer between the skeleton of the porous medium and fluid occurs instantaneously. The deformation of the skeleton of the porous medium is absent and the filtration of fluid in a porous medium is described by Darcy's law. The general system of equations describing the processes in the system (well-pay zone-rocks surrounding the well and the pay zone), includes the continuity equation for the fluid in a porous medium (diffusion equation), the Darcy law, and the equation of heat. Appendix A presents the mathematical model in detail. The boundary-condition differential equation system was solved by the finite difference method using the implicit scheme.
2. Physics of RF-EM heating of oil The distribution of electromagnetic waves in oil is associated with frequency dispersion of dielectric inductivity (capacitance) caused by orientational polarization of polar components. Under the RF-EM influence, additional heat (besides the Joule heat) is generated owing to electric polarization effects. The dissipation of the EM energy is accompanied by the occurrence of heat sources distributed in the medium. Such distribution is, in the general case, given by the following equation (Landay and Lifshitz, 1984; Ramo and Whinnery, 1944): q=
ωε0 ε′ tgδ 2 E ; 2
ð2Þ
where ω— frequency of EM waves, ε0— electric constants, ε' — relative permittivity of the medium to liquid, tgδ— dielectric loss (dissipation) tangent, and E— electric field intensity.
Fig. 1. Structural model used in the development of mathematical model: (1) well, (2) pay zone, (3) and (4) surrounding rock (matrix).
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An example calculation was performed using the following hypothetical data for a sensitivity analysis in the next section: Pi = 1 MPa; Pwf = 0; 0:25; 0:5; 0:75 MPa; kr = 0:183 10−12 m2 ; kz = 0; T0 = 8:8˚С; ϕ = 0:25; γo = 0:042 K−1 ; ct = 10−9 Pa−1 ; R1 = 0:03 m; R2 = 0:035 m; R3 = 0:105 m; R4 = 0:11 m; R5 = 0:115 m; re = 60 m; Ng = 0; 10; 20; 30 kW; αd = 0:03267 m−1 ; αo = 1912680 J = m3 ·K ; ρo = 950 kg = m3 ; λo = 0:125 W = ðm·KÞ; αm = 1200000 J = m3 ·K ; λm = 3 W = ðm·KÞ; h = 10 m; f = 13:56 MHz; μat = 3:42·10−6 ; σt = 3:4·106 ; Z1 = 83 m; Z2 = 93 m; Z3 = 96 m; Zc = 376:8 Ohm; λR2;R4 = 45 W = ðm·KÞ; αR2; R4 = 3641900 J = m3 ·K ; λR3 = 0:0315 W = ðm·KÞ; αR3 = 142977 J = m3 ·K ; λR5 = 1:2 W = ðm·KÞ; αR5 = 2500000 J = m3 ·K ; λZ1;Z3 = 3:95 W = ðm·KÞ; αZ1;Z3 = 2926000 J = m3 ·K ; μ0 = 1 Pa·s: The average parameters were chosen in the range typical of highviscosity oil deposits of the Urals region of Russia. Details about the field characteristics can be found in Davletbaev et al. (2010). Note that the electromagnetic radiation we use is of radio frequency range (f =13.56 MHz) and therefore, its absorption is mostly in oil. The water absorbs high frequency waves really high in microwave. In addition, the saturation of water in the collector is small and it can be neglected. 4. Application of the model and analysis of the results The results obtained using the solution of the mathematical model for the RF-EM treatment/continuous oil production process and applying the data given above are presented in Figs. 2–6. Fig. 2 shows reservoir temperature distribution curves at different times for μ0 = 1 Pa·s Pwf = 0.5 MPa, Ng = 10 kW. The temperature of the medium at the bottom can reach sufficiently high values due to enhanced absorption of energy by electromagnetic waves near the radiator (in this case ~100 °C). We can also observe increasing temperature and its gradient in the borehole zone during electromagnetic radiation into the reservoir. Fig. 3 shows reservoir temperature distribution curves for different output performance settings of the RF-EM generator for μ0= 1 Pa·s, Pwf = 0.5 MPa and time t = 3 days. It is apparent that by changing the
Fig. 3. Temperature distribution across the reservoir during simultaneous RF EM heating and production for different RF generator performance settings: Ng = 10, 20, 30 kW for μ0 = 1 Pa·s; t= 3 days, Pwf = 0.5 MPa.
emitting performance of the generator, it is possible to achieve the target bottom-hole temperature and bottom-hole zone heating depth. Fig. 4 illustrates the 3-D distributions (for r-φ coordinates, corresponding to 10 m from the wellhead) of temperature after 3 days of treatment for an RF-EM generator power of 10 kW (Fig. 4-a) and 20 kW (Fig. 4-b), μ0 = 1 Pa·s, Pwf = 0.5 MPa. The generated thermal field in the first case (Fig. 4) is characterized by high temperatures (because of intense absorption of EM energy) in the borehole environment, decreasing monotonically with distance from the borehole. We consider the combined technology, including radiofrequency electromagnetic field impact and injection of solvent into the formation in other studies (Davletbaev et al., 2008, 2009). We noticed that such technology is more effective for extra-heavy crude oil and can increase the processing of well bottom zone in comparison with RF treatment only more than twice. Fig. 5 illustrates wellbore temperature distributions after 3 days of treatment, at different distances from the wellbore central axis: 0.035 m (on the tubing surface); 0.7 m (in the annular space); 0.11 m (on the inner wall surface of the cement casing); 0.5 m (in the surrounding rock). The absolute bottom-hole temperatures correspond to the values of the reservoir temperature distribution curves
a
100
T, °C
100
75
50 0 10
50 25 5
0
5
y, m
10
10
0
5
5
10 0
x, m
b
200
T, °C
100
150
50 0 10
100 50 5
0 y, m
Fig. 2. Temperature distribution across the reservoir during simultaneous RF-EM heating and production at different times: t = 0.1, 0.5, 1.5, 3 days forμ0 = 1 Pa·s; Pwf = 0.5 MPa, Ng = 10 kW.
5
10
10
0
5
5
10 0
x, m
Fig. 4. Temperature distribution across the reservoir during simultaneous RF EM heating and production for different RF generator performance settings: Ng = 10 kW (a) and Ng = 20 kW (b); t = 3 days, μ0 = 1 Pa·s, Pwf = 0.5 MPa.
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of the wellbore caused by the EM wave absorption by the tubing string and the influx of ‘hot’ oil from the matrix can help prevent paraffin formation and produce heated oil coming to the surface, which is more mobile than the initial oil in place. Fig. 6 shows the flow dynamics for different generator output performance settings (Fig. 6a) for different reservoir/bottom-hole differential pressures (Fig. 6b). At the initial stage of production, the liquid rate falls rapidly; this decreasing trend then slows and turns into a monotonous upward tendency. The initial rate drop is due to the well reaching the stationary flow regime; the succeeding rate increase is the result of reduction in oil viscosity. The greater the duration of stimulation and the power of the emitter of EM waves, the greater is the increased oil production as compared with the production of cold oil. Pressure differential between the borehole and the formation has no significant effect on the dynamics of change in flow rate (in the case considered here the range of pressure difference between wellbore and formation, the duration of oil production and the duration of EM radiation). The greater the pressure differential between the borehole and formation, the greater is the flow of oil from the reservoir. Fig. 5. Temperature distribution along the wellbore during simultaneous RF EM heating and production for different RF generator performance settings: Ng = 10 kW (a), Ng = 20 kW (b); Pwf = 0.5 MPa, μ0 = 1 Pa·s, t = 3 days.
(Figs. 2–5). An abrupt fall in temperature is observed on the border between the pay zone and the reservoir bottom, which can be attributed to the absence of heat sources in this zone. Within the pay zone, the wellbore temperature curves indicate the presence of hightemperature spots. This is due to well/rock interaction effects in the bottom-hole zone — volume heating occurring within the pay zone 83 ≤ z ≤ 93 m is caused by EM energy absorption by the medium and a convective heat transport from the heated oil in the reservoir. Heating
Fig. 6. Production rate dynamics during RF EM treatment for “cold oil” production Ng = 0 kW and for generator performance settings Ng = 10, 20, 30 kW (a); and for different reservoir/bottom-hole differential pressures P0 − Pwf = 0.25, 0.5, 0.75 MPa (b).
5. Model validation using a field case RF-EM tests were conducted in the Yultimirovskoye bitumen field located in Sugushlinskaya Square operated by Tatneft. An experimental section was selected for these tests in the field. The test section included two wells: no. 150 and no. 1. The distance between these wells is 5 m. The pay zone has 25% porosity, 3.6% bitumen saturation and the permeability ranges between 0 and 183 mD. The EM energy was produced by a RF generator and transmitted by a coaxial conductor (well). Initially, water from Well 150 was displaced by air at an injection pressure of 0.4–0.6 MPa. The temperature in both wells was measured by thermocouple elements. One measuring element was lowered through the tubing string into Well 150 and positioned at 87.5 m (the middle part of the radiator), and the other element was lowered into Well 1 at 83.5 m. The EM heating of the bitumen reservoir was performed in several stages for different RF generator operation modes. Initially, the generator was switched to the prolonged heating mode and its output performance was set to approximately 20 kW. Fig. 7 shows the changes in temperature recorded in the bottom-hole zones of the wells during the RF-EM treatment. Fig. 2 indicates that after t1 =1.39 days (33.4 h) of continuous heating in this mode, the temperature at the bottomhole of Well 150 increased from 8.8 °C to 117.9 °C. At the next stage, the generator was readjusted to output 30 kW. As a result, after 6 h (by t2 =1.64 days), the temperature in Well 150 reached 149.8 °C. After that, the generator was
Fig. 7. Temperature distribution in Well 150 during RF-EM heating, with the generator performance set to 20 kW, 30 kW, 60 kW, and 0 kW.
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6. Energy balance calculation
Fig. 8. Temperature distribution across the reservoir during simultaneous RF-EM heating for different stages.
set to its maximum output capacity of 60 kW. As seen in Fig. 2, the heating dynamics soared and within 3.7 h (t3 =1.64–1.80 days) of operation at the maximum-output mode, the temperature at the well bottom hole increased from 149.8 to 191.3 °C. After that, the RF generator was switched out for 1.72 h (t4 =1.80– 1.87 days). Then, the RF-EM system worked at maximum output of the generator with electromagnetic waves of ~60 kW for 32 h (t5 =1.87– 3.21 days). The RF-EM generator was shut for 72 h (t6 =3.21–6.20 days). During the RF-EM treatment of Well 150 the temperature on the bottom of Well 1 which was on distance of 5 m from Well 150 was registered. The increase in temperature to 44.8 °C was detected. Fig. 8 shows the theoretical curves of temperature distribution in the reservoir from borehole 150 in different time periods. The results indicate, after the 5th (t5 = 1.87–3.21 days of generator at 60 kW operating) and 6th stages (t6 = 3.21–6.20 days generator stop), the temperature at 5 m from the well (Well-150) increased to 32 °C. Fig. 9 illustrates the theoretical and measured temperature distributions along the borehole (from the wellhead to bottom). As seen, the measured and theoretical curves are in good agreement. Note that the mathematical model did not take into account the geothermal gradient of temperature, hence, the absolute values of temperature do not coincide. The distribution of temperature along the borehole (Fig. 9) calculated after a few days shows a small loss of heat at the top and bottom of the reservoir. When modeling, the damping factor of the EM waves in the reservoir was used as a parameter to match the measured and theoretical data in Figs. 7 and 9. The best combination of measured and theoretical data was obtained at the value of αd = 0.03267 m − 1. This value of damping coefficient of EM waves in the reservoir was used for mathematical modeling of the RF-EM field and the production of extra-heavy oil.
The energy balance calculations were performed for: (1) “cold” oil production at a constant bottomhole pressure in the well (the period of 30 days of oil production), and (2) 5 days — oil production and RFEM radiation and 25 days — oil production stopped RF-EM generator (the total duration of 30 days). These two cases were compared and the additional oil production by high-frequency electromagnetic radiation into the reservoir was calculated. These data were used to estimate the energy balance, i.e. energy equivalent of additional oil production to compare the expenditure of energy of using RF-EM radiation. Power consumption, RF electromagnetic generator, its efficiency, energy losses in transmission lines from the thermal station (where oil production is burned conventionally) to the location of RF-EM generator, and the efficiency of power transmission lines were included in this exercise. RF-EM generator has efficiency ηG = 0.67. Transmission line of EM waves from the wellhead to the bottom is a coaxial system of tubing and casing, the efficiency is ηL = 0.476. It is assumed that the efficiency of the transmission line from the thermoelectric power station to the location of the RF-EM generator is ηTF = 0.563. Efficiency of thermoelectric power station is ηEPS = 0.35. Heat loss EM energy in the borehole that are associated with oxidation and contamination of surface pipe tubing, with the presence of water in the well production is ηLH = 0.75. Total power consumption with all the loss is determined from the following expression:
NPC =
N0 : ηG ηL ηEPS ηTF ηLH
Assessment of energy balance is described by the form factor Kem, which equal to the ratio of produced additional energy, WAP to the consumed energy due to the RF generator WPC:
Kem =
WAP : WPC
Here, the energy consumption is equal to the product consumed by power RF-EM generator NPC on the duration of RF-EM radiation t1: WPC =NPC ⋅t1. In addition the energy obtained is determined by the formula of WAP =M⋅G, where G— calorific value of oil, which is assumed to be 4.61∙107 J/kg, M=ΔQo ⋅ ρo— the mass of additional oil, which is determined from the density of oil ρo and the volume of additional oil ΔQo. In calculating the energy balance was taken 5 days of oil production with RF-EM heating and then 25 days production without RF-EM radiation. The base case is accepted by the “cold” oil production 30 days without RF-EM radiation. The analysis showed that the ratio of the energy balance is 5.29. 7. Conclusions
Fig. 9. Wellbore temperature distribution in Well 150 (from the well head) after RF-EM treatment (measured and calculated curves).
1. We formulated a two-dimensional mathematical model of heavy oil recovery for RF-EM radiation heating. This model allowed us to quantify the degree of heating the reservoir. The mathematical model takes into account the heat losses into the rock surrounding the wellbore and reservoir, and can be used to quantify the magnitude of heat loss. 2. Simulation results were compared with those of a field test. The damping coefficient of EM waves in a reservoir was evaluated to match the measured and calculation data. 3. Numerical simulations suggest that bottom-hole temperature and heat/mass transfer effects in the reservoir can be controlled by setting the output performance of the RF generator and by the difference between the reservoir and bottom-hole pressure.
A. Davletbaev et al. / Journal of Petroleum Science and Engineering 78 (2011) 646–653
4. The RF-EM energy loss along the wellbore (between the generator and the bottom hole) can be considered an advantage as it prevents paraffin deposition and boosts the mobility of the produced oil. Nomenclature ω frequency of EM waves, MHz; ε0 and χ0 electric and magnetic constants, respectively; ε' relative permittivity of the medium to liquid; tgδ dielectric loss (dissipation) tangent; E electric field intensity; λ0 length of the EM wave produced by the generator, m; P pressure, MPa; P0 initial reservoir pressure, MPa; Pwf bottom-hole pressure, MPa; T temperature, °C; ΔT = T − T0, T0 initial temperature of the medium, °C; R1 and R2 inside and outside radius of tubing, respectively, m; R3 and R4 inside and outside radius of casing, respectively, m; R5 outside radius of baffle plate, m; Z1 and Z2 coordinates of the roof and subface of stratum, respectively, m; Z3 maximal observed distance along coordinate z, m; rd radius of EM-wave radiator (rw = R2), m; re pool boundary along coordinate r, m; ρo density of the oil, kg/m 3; ñ specific heat capacity of oil, J/(kg·K); α heat capacity per unit volume, J/(m 3·K); αm heat capacity of the rock skeleton, J/(m 3·K); αo heat capacity of oil, J/(m 3·K); λ thermal conductivity of the medium, W/(m·K); λm thermal conductivity of the rock skeleton, W/(m·K); λo thermal conductivity of oil, W/(m·K); ϕ porosity of the medium; kr and kz permeability of productive stratum along coordinates r and z, respectively, m 2; h stratum thickness, m; ct total compressibility of the system, Pa − 1; cm and co compressibility of the rock skeleton and of oil, Pa − 1; υr and υz rate of filtering in the stratum along and across stratification, m/s; ωw flow in the tubing, m/s; Q flow rate, m 3/c, m 3/day; μ0 value of viscosity at T = T0, Pa·s, mPa·s, cP; γo coefficient allowing for temperature dependence of the viscosity of oil, 1/K; N0 power of EM-wave radiator, kW; Ng power of RF EM generator, kW; Sb area of EM-wave radiator, m 2; Jb = N0/Sb intensity of radiation at the well bottom, kW/m2; αd damping factor of EM-wave, m − 1; αd2 and αd4 damping factor of EM waves in the tubing and casing, respectively, m − 1; Rs active part of surface resistance of tubes; Zc wave resistance of air filling the intertube space, Ohm; f cyclic frequency of EM waves, MHz; μat and σat absolute magnetic permeability and specific electrical conductivity of the tubes, respectively; ηG efficiency of RF-EM generator; ηL efficiency of transmission line of EM waves of a coaxial system of tubing and casing; ηTF efficiency of transmission line from the thermoelectric power station to the location of the RF-EM generator; ηEPS efficiency of thermoelectric power station; ηLH efficiency of heat loss EM energy; Kem energy balance factor; WAP produced additional energy, J; WPC energy due to the RF generator working, J;
NPC t1 G ρo ΔQo
651
total power, J/s; duration of RF-EM radiation; calorific value of oil, J/kg; density of oil, kg/m 3; volume of additional oil, m 3.
Acknowledgment This paper is the revised and improved version of SPE 136611 presented at the 2010 SPE Canadian Unconventional Resources and Int. Petr. Conf., Calgary, AB, Canada, 19–21 Oct. Appendix A. Formulation of the problem and basic equations We assumed that the filtration of fluid in the reservoir and the distribution of the thermal field in the radial direction is carried out uniformly, i.e. ∂ T/∂ ϕ = 0 and ∂ P/∂ ϕ = 0. The general system of equations includes the equation of heat transfer, the diffusion equation and Darcy's law. The heat conductivity equation in the system is defined as follows: ∂T 1 ∂ ∂T 1 ∂ ∂T ρ c ∂T = rλ + λ −υr o o α⋅r ∂r α ∂z α ∂r ∂t ∂r ∂z −ωw
ðA 1Þ
∂T q + ; 0 ≤ r ≤ re ; 0 ≤ z ≤ Z3 ; α ∂z
where α— heat capacity per unit volume, λ— thermal conductivity of the medium, υr— rate of filtering in the stratum along stratification, ρo— density of the oil, co— specific heat capacity of oil, ωw— flow in the tubing, q— density of distribution of these heat sources, and Z3— maximal observed distance along coordinate z. The pressure distribution in the reservoir is described by the diffusion equation: ∂P k 1 ∂ r ∂P k ∂ 1 ∂P = r + z ; rw ≤ r ≤ re ; Z1 ≤ z ≤ Z2 ; ϕct r ∂r μ ∂r ϕct ∂z μ ∂z ∂t
ðA 2Þ
where kr and kz— permeability of productive stratum along coordinates r and z, ϕ— porosity of the medium, μ— oil viscosity, ct— total compressibility of the system, rw and re— well radius and pool boundary along coordinate r, Z1 and Z2— coordinates of the roof and subface of stratum, respectively. The rate of fluid flow in a porous medium is determined from Darcy's law: υr = −
kr ∂P ; r ≤ r ≤ re ; Z1 ≤ z ≤ Z2 ; μ ∂r w
ðA 3Þ
It is assumed that the fluid motion along the wellbore from the borehole to the wellhead is defined by ωw =
Q ; 0 ≤ r ≤ R1 ; 0 ≤ z ≤ Z1 ; π⋅R21
ðA 4Þ
where R1— inside radius of tubing, and Q— flow rate. Reservoir oil viscosity is a function of temperature as given by: μ = μ0 expð−γo ⋅ΔT Þ;
ðA 5Þ
where μ0— value of viscosity at T = T0, ΔT = T − T0— change in temperature in the reservoir, and γo— coefficient allowing for temperature dependence of the viscosity of oil.
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λ = ð1−ϕÞλm + ϕλo ;
ðA 6Þ
where R4— outside radius of casing, while in the other layers of the well q = 0. The total flow, Q of the injected agent is given by the filtration velocity at the bottom hole:
α = ð1−ϕÞαm + ϕαo ;
ðA 7Þ
Q = 2π rw hυr ;
αj = cj ⋅ρj ; j = m; o;
ðA 8Þ
Thermal conductivity and volumetric heat capacity of the saturated porous medium (defined in rw ≤ r ≤ re, Z1 ≤ z ≤ Z2) are as follows:
where λm and λo— thermal conductivity of the rock skeleton and of oil, respectively, αm and αo— heat capacity of the rock skeleton and of oil, respectively, cm and co— specific heat capacity of the rock skeleton and of oil, respectively, and ρm and ρo— density of the rock skeleton and of the oil. The energy interaction between the EM waves and the reservoir rock causes the emergence of volumetric heat sources distributed across the reservoir. The density of distribution of these heat sources can be formulated as follows (Abernethy, 1976): q = 2αd Jb
rd expð−2αd ðr−rd ÞÞ; rd ≤ r ≤ re ; Z1 ≤ z ≤ Z2 r
ðA 9Þ
where αd— damping factor of EM-wave, Jb— intensity of radiation at the well bottom, and rd— radius of EM-wave radiator. The output performance (power) of the EM radiator is obtained from the known generator output performance, Ng: N0 = Ng exp½−2ðαd2 + αd4 ÞZ1 ;
ðA 10Þ
where Ng— power of RF EM generator, αd 2 and αd4— damping factor of EM waves in the tubing and casing. The EM wave damping factor for the coax conductor (well tubing and casing) is estimated from: αd2 =
Rs 1 ⋅ ; 2Zc ⋅ lnðR3 = R2 Þ R2
ðA 11Þ
αd4 =
Rs 1 ⋅ ; 2Zc ⋅ lnðR3 = R2 Þ R3
ðA 12Þ
where Rs— active part of surface resistance of tubes: 2
Rs =
πf μat ; σt
ðA 13Þ
and Zc— wave resistance of air filling the intertube space: 2
Zc =
χ0 : ε0
ðA 14Þ
Here, f— cyclic frequency of EM waves, μat and σt— absolute magnetic permeability and specific electrical conductivity of the tubes, respectively, χ0 and ε0— electric and magnetic constants, R2— outside radius of tubing, and R3— inside radius of casing. It is assumed that the EM waves, while traveling along the annual space from the head towards the bottom hole of the well, lose part of their energy, which creates a sort of ‘internal distributed heat sources’ in the tubing and casing walls. These are given by: q=
q=
αd2 N0 expð−2ðαd2 + αd4 ÞzÞ; R1 ≤ r ≤ R2 ; 0 ≤ z ≤ Z2 ; π r 2 lnðR2 = R1 Þ ðA 15Þ αd4 N0 expð−2ðαd2 + αd4 ÞzÞ; R3 ≤ r ≤ R4 ; 0 ≤ z ≤ Z1 ; π r 2 lnðR4 = R3 Þ ðA 16Þ
ðA 17Þ
where h— stratum thickness. The initial and boundary conditions for the equations are determined by matching the well/reservoir/surrounding rock system, and are given as follows: P ðr; z; t = 0Þ = P0 ; rw ≤ r ≤ re ; Z1 ≤ z ≤ Z2 ;
ðA 18Þ
T ðr; z; t = 0Þ = T0 ; 0 ≤ r ≤ re ; 0 ≤ z ≤ Z3 ;
ðA 19Þ
P ðr = rw ; z; t Þ = Pwf ; Z1 ≤ z ≤ Z2 ;
ðA 20Þ
∂T ðr = 0; z; t Þ = 0; 0 ≤ z ≤ Z3 ; ∂r
ðA 21Þ
T ðr = re ; z; t Þ = T0 ; 0 ≤ z ≤ Z3 ;
ðA 22Þ
∂T ðr; z = 0; t Þ = 0; 0 ≤ r ≤ re ; ∂z
ðA 23Þ
∂T ðr; z = Z3 ; t Þ = 0; 0 ≤ r ≤ re ; ∂z
ðA 24Þ
P ðr = re ; z; t Þ = P0 ; Z1 ≤ z ≤ Z2 :
ðA 25Þ
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