Electrical-heating-assisted recovery for heavy oil

Electrical-heating-assisted recovery for heavy oil

Journal of Petroleum Science and Engineering 45 (2004) 213 – 231 www.elsevier.com/locate/petrol Electrical-heating-assisted recovery for heavy oil E...

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Journal of Petroleum Science and Engineering 45 (2004) 213 – 231 www.elsevier.com/locate/petrol

Electrical-heating-assisted recovery for heavy oil E.R. Rangel-German a, J. Schembre a, C. Sandberg b, A.R. Kovscek a,* a

Petroleum Engineering Department, Stanford University, Stanford, CA 94305-2220, USA b Tyco Thermal Controls, 300 Constitution Drive, Menlo Park, CA 94025, USA Received 21 August 2003; accepted 9 June 2004

Abstract Warming heavy oil (940 – 1000 kg/m3, 10j – 20j API) reduces its viscosity substantially; however, conventional thermal recovery by steam injection is not applicable to a number of heavy-oil reservoirs. This paper explores localized electric resistance heating provided by mineral-insulated cable and a novel heater – well arrangement. Two-dimensional (2-D) and heterogeneous three-dimensional (3-D) reservoir simulation models employing single- and dual-lateral completion horizontal wells illustrate that an electric resistance heating element with a modest power output enhances recovery several fold. Important parameters for improved recovery are (1) solution gas, (2) formation and fluid thermal conductivity that permits conductive heating, and (3) the ability to achieve relatively low bottom-hole pressure in production wells. Economic analysis suggests that the cost of electricity is about 1.25 USD per barrel of incremental oil. D 2004 Elsevier B.V. All rights reserved. Keywords: Thermal oil recovery; Thermal conduction; Heavy oil; Electric resistance heating

1. Introduction In excess of 4 billion bbl of oil have been recovered in the United States alone as a result of thermal recovery operations, chiefly steam injection (Moritis, 2002). The addition of heat reduces the viscosity of heavy oil (density z 940 kg/m3 or API V 20j) substantially, thereby improving oil mobility and the productivity of wells. Nevertheless, conventional steam injection candidates are limited to relatively shallow, thick, permeable, and homogeneous sands that are onshore.

* Corresponding author. Tel.: +1-650-723-1218; fax: +1-650725-2099. E-mail address: [email protected] (A.R. Kovscek). 0920-4105/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2004.06.005

Consider the Alaskan North Slope field of Ugnu as an example of a reservoir where the addition of heat might enhance recovery greatly, but conventional steam injection does not appear to be feasible. Oil viscosity at reservoir conditions is estimated to range from 2 to 300 Pa-s (2,000 – 300,000 cP; Hallam et al., 1991; Islam et al., 1991). The reservoir has permeable sands (100 – 3000 md, 1 md = 10 15 m2) that should allow reasonable productivity if oil viscosity is reduced. The presence of hundreds of feet of permafrost, concerns about permafrost disruption, and Arctic surface conditions deters consideration of thermal recovery. Use of electricity to enhance oil recovery is not a new topic. Electrical heating of reservoir formations employing alternating current was field tested as early as 1969 for enhanced oil recovery (Pizarro and Trevisan, 1990), and a number of variants of the process patented in the

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1970s (Gill, 1970; Crowson, 1971; Kern, 1974; Hagedorn, 1976; Pritchett, 1976). Others have studied the flow of direct current through a formation as a means to increase fluid flux and the relative permeability to oil (Chillingar et al., 1970). Some heating occurs as a result. Most investigations have explored alternating current applications for in situ heating (Pizarro and Trevisan, 1990). The mode of heating depends on the frequency of the electrical current. In the radio frequency and microwave range (i.e., short wavelength) dielectric heating prevails (cf. Sahni et al., 2000 for a review). Polar molecules tend to align and relax with the alternating electric field. The molecular movement may result in significant heating. Unfortunately, it appears difficult with available microwave antennae to propagate this short wavelength radiation deep within the formation (Sahni et al., 2000). When lowfrequency alternating current flows through a reservoir, resistive or ohmic heating of the formation occurs (Harvey et al., 1979; Hiebert et al., 1986; Pizarro and Trevisan, 1990; Sierra et al., 2001). An electrical path through the formation is provided by brine, and electrical energy is dissipated as heat. Unfortunately, ohmic heating is reduced as water saturation decreases or if a majority of the water has been heated to form steam. The resistive heating process was also combined with water injection to overcome such problems (Harvey et al., 1979; Harvey and Arnold, 1980). Rather than rely on the reservoir to carry electrical current or electromagnetic radiation, commercially available mineral-insulated (MI) cables are selfcontained electric resistance heaters (Afkhampur, 1985). Formation brine need not be present to carry electrical current or heat. Alternating current flows between two conductors packed in a resistive core composed of graphite and polymers. As heater temperature increases, electrical resistance of the mineral insulation increases. Thus, a self-regulating mechanism is achieved that eliminates overheating of the element and coking of the oil. An MI downhole heater has a cross-section of 2.5 by 0.8 cm and is supplied in lengths ranging from 300 to 1000 m, making them practical for installation in horizontal wells. Heat output varies between 48 and 288 W/m (50 and 300 BTU/h/ft). The device described by Afkhampur (1985) operates with 480 VAC. A simulation study is presented of alternative thermal recovery employing MI cables. The intent is

to explore if the modest heating available with such cables is sufficient to enhance oil recovery and to draw out important oil and formation parameters that influence recovery. This heating process stimulates oil recovery primarily by reducing oil viscosity around the well bore and secondly by thermal expansion of reservoir fluids. To illustrate the improvement of well injectivity or productivity, we review the calculation of the well index (WI) for a single well, with fixed well bore pressure, single-phase flow at steady state, producing or injecting in a finite domain with fixed pressure boundaries: WI ¼

2pkh   lln rrwo

ð1Þ

where k is permeability, l is viscosity, h is the formation thickness, ro is the drainage radius, and rw is the well radius. Fig. 1 shows that the well index is a composite of heated and unheated regions (Dake, 1978). The heated region, between rw and ra, is assumed to undergo a constant temperature change, while the outer region is unaffected. Enhanced production is described by the ratio   ro ln rw WIV     ¼ ð2Þ WI l ln ra þ ln ro r

rw

ra

where lr is the ratio between the warm-oil viscosity and the original viscosity. Thus, the enhancement of well productivity is related directly to oil viscosity reduction; however, the size of the region where temperature

Fig. 1. The simple well model: the area of reduced oil viscosity around the wellbore is shaded.

E.R. Rangel-German et al. / Journal of Petroleum Science and Engineering 45 (2004) 213–231 Table 1 Properties of components Component

Molecular weight kg/mol

Critical temperature Tc (K)

Critical pressure pc (kPa)

Water Heavy fraction Medium fraction Methane Propane

0.01802 0.600 0.450 0.016 0.0443

647.3 – 783.2 190.6 369.8

22.100 – 0.96500 4.5989 4.2448

is elevated modifies WI in a logarithmic fashion. The latter implies relatively less sensitivity to heated zone size. 2. Model description The reservoir simulation model approximates some facets of the Ugnu and West Sak reservoirs (Werner, 1985; Panda et al., 1989; Sharma et al., 1989; Gondouin and Fox, 1991; Hallam et al., 1991; Foerster et al., 1997). The oil is modeled compositionally as a live oil. In the first section, simulations are conducted in a two-dimensional (2-D) vertical cross-section. Second, a three-dimensional (3-D) model incorporating heterogeneity is used. All flow simulations were performed using the commercial simulator Steam, Thermal, and Advanced Processes Reservoir Simulator (STARS; CMG, 1998). Details of the model for fluid properties as well as grids used for computations are given below. Reservoir heating with MI cables occurs locally around well bores, and the method does not rely on the formation to carry electrical current. Accordingly, conventional thermal reservoir simulators are capable of predicting the effects of this type of electrical heating provided that they allow the introduction of a heat source or sink. STARS provides such an option. Hence, the flow equations, mathematics, and solution procedure are standard for thermal reservoir simulation and well established (Aziz et al., 1987). 2.1. 2-D vertical section The flow simulation grid is a two-dimensional Cartesian vertical section. A vertical section captures critical physical phenomena, such as gravity, thermal conduction, and production mechanisms. The layer

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studied is 29 m (95 ft) tall and 160 m (525 ft) in length. Wells are assumed to be developed in multiple patterns, and thus all boundaries are no flux (i.e., 160-m well spacing). The gross formation volume is 4636 m3/m, and the formation pore volume is 1626 m3/m. Initial volumes of oil and water are 975 and 648 m3/m, respectively. A variety of grids were studied to minimize the run time and numerical dispersion. The different grids provided the same final oil recovery. Oil and gas rates as a function of time displayed discrepancies. Block boundaries in the horizontal direction were selected in a pattern similar to that proposed by Aziz et al. (1987). A locally refined grid of 15  19 blocks was used with the following dimensions: Dy = 42.7, 21.3, 9.10, 9  1.52, 9.10, 21.3, 42.7 for 160 m (525 ft) total, and D z = 19  1.52 m for a 29 m (95 ft) total. This grid provided realistic performance by the simulator and was also validated by replicating previous results of Aziz et al. (1987). This adds confidence to the physical correctness of the input data files used in this study. The reservoir fluids are modeled compositionally with five components, as detailed in Tables 1 and 2. The initial oil phase is modeled using methane ( f1 = 0.35), medium ( f2 = 0.02), and heavy ( f3 = 0.63) components, where f is the species mole fraction. Water is assumed to be immiscible in the oil, and propane is used as a solvent. The solution gas – oil ratio (GOR) is about 21 m3/m3 (120 SCF/STB). This is a common value for heavy-oil reservoirs (Jaubert et al., 2002). The effect of the solution gas – oil ratio was examined for four different initial molar concentrations of gas: 10%, 20%, 30%, and 35%, as presented later. A correlation for the gas –oil equilibrium ratio, kij, is used to represent the gas – liquid phase behavior as a function of temperature and pressure (CMG, 1998):     A C þ B exp kij ¼ ð3Þ p T D where T is temperature in K, p is pressure in kPa, A, B, C, and D are coefficients summarized in Table 2. Table 2 Coefficients in the correlation for gas – oil equilibrium ratios

A B C D

Water

Heavy

Medium

Methane

Propane

0 0 0 0

0 0 0 0

3.14E + 06 212  2777.8 266.5

1.03E + 06 0  1032.2 0

2.12E + 06 0  2222.22  0.1833

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The initial pressure in the model is 8.96 MPa (1300 psi), and the initial reservoir temperature is 14 jC (58 jF) at the formation top located at a depth of 884 m (2900 ft). The sand porosity is 35%. It is assumed that initially there is no free gas and, the water saturation is 40%. The permeability is homogeneous, isotropic, and equal to 500 md. The water – oil and gas –liquid relative permeability data shown in Figs. 2 and 3 correspond to those for the Schrader Bluff field, Alaska (Hallam et al., 1991). Rock and reservoir properties are summarized in Table 3. Fig. 4 shows viscosity as a function of temperature for the medium and heavy components of the oil phase. The viscosity of both components decreases drastically with temperature. Oil-phase viscosity, lo, is computed according to (CMG, 1998) lnðlo Þ ¼

nc X

2.2. 3-D model In this case, a 3-D heterogeneous model is used with a mean permeability of 500 md. Permeability is distributed within the model using sequential Gaussian simulation (Deutsch and Journel, 1998; Fig. 5). There are 16  8  19 grids of variable size with grid refinement of the y-direction in the area of the well: D x = 16  30.5 m; Dy = 5  1.52, 9.14, 21.34, 42.67 m; D z = 16  1.52 m. The total dimensions are thus 488 m long  80.72 m wide  29.0 m thick. The length of the horizontal section of the well is 488 m (1600 ft). The compositional description as well as the viscosity versus temperature relationships are identical to the 2-D case.

3. Results—two-dimensional model fi lnðli Þ

ð4Þ

i¼1

where li is the component viscosity and nc is the number of components in the oil phase.

First, the effect of continuous heating on depletion is studied. The horizontal well is centered in the y-direction and located vertically in the middle of the formation. The producer operates under a constant flowing bottom-hole

Fig. 2. Water – oil relative permeability data (Hallam et al., 1991).

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Fig. 3. Gas – liquid relative permeability data (Hallam et al., 1991).

pressure (BHP), as described below. A heating device, such as MI cable, is located in the production well. In practice, the heater is placed outside the casing and cemented in place, or inside the casing and adjacent to any tubing. Eight cases are considered: 1. No heating (base case); BHP = 3.1 MPa (450 psi). 2. Continuous heat input of 300 BTU/(h/ft) and BHP = 3.1 MPa (450 psi). Table 3 Rock and reservoir properties Porosity, / Horizontal permeability, kh Vertical permeability, kv Initial pressure, pi Initial temperature, Ti Initial So Initial Sw API Effective formation compress Volumetric heat capacity Thermal conductivity

0.35 500 md 500 md 8.96 MPa 14.4 jC 60% 40% 11.3 0.0725 MPa 1 2.34  106 J/m3/jC 1.49  105 J/m /day/jC

3. No heating; BHP = 0.69 MPa (100 psi). 4. Continuous heat input of 48 W/m [50 BTU/(h/ft)] and BHP = 0.69 MPa (100 psi). 5. Continuous heat input of 96 W/M [100 BTU/(h/ft)] and BHP = 0.69 MPa (100 psi). 6. Continuous heat input of 144 W/m [150 BTU/(h/ft)] and BHP = 0.69 MPa (100 psi). 7. Continuous heat input of 192 W/m [200 BTU/(h/ft)] and BHP = 0.69 MPa (100 psi). 8. Continuous heat input of 288 W/m [300 BTU/(h/ft)] and BHP = 0.69 MPa (100 psi). Fig. 6(a) shows the cumulative oil recovery on a per meter basis, and Fig. 6(b) presents the production rate as a function of time for these eight cases. The worst recoveries are obtained under cold conditions (no heat input), and the best recovery is obtained with the minimum bottom-hole pressure and maximum heat input, case 8. Here, cumulative recovery relative to the base case increased by over 100%. Fig. 6 also teaches that the flowing bottom-hole pressure is a critical parameter for maximizing oil recovery. Compare cases

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Fig. 4. Viscosity of medium and heavy crude-oil components as a function of temperature.

1 and 3 that have no heating but differ in the bottomhole pressure. Cumulative recovery is increased by more than 35% if the bottom-hole pressure is reduced from 3.1 MPa (450 psi) to 0.79 MPa (100 psi).

Fig. 7 compares the pressure distribution for case 1 and case 8 after 10 years of fluid production. Dark shading represents lower pressure. The top image of Fig. 7 shows that after 10 years of production without

Fig. 5. Pattern and permeability distribution used for the 3-D heterogeneous case.

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Fig. 6. Effect of heating on oil recovery: (a) cumulative oil recovery and (b) oil rate.

heating, areas far away from the producer do not ‘feel’ the effects of the well; these areas remain at the initial reservoir pressure (9.0 MPa, 1300 psi). On the other hand, a combination of heating and a small bottom-hole pressure develops a pressure gradient extending through

the entire reservoir, as shown in the bottom image of Fig. 7. Greater reservoir volumes are contacted by one well when operated in a fashion similar to case 8. Fig. 8 presents the temperature distribution for case 8. White shading represents temperatures of 54 jC

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Fig. 7. Comparison of the pressure (mPa) distributions of cases 1 and 8 after 10 years of fluid production.

(130 jF) or greater. The extent of the heated region is about 18.3 m (60 ft) in the horizontal direction and covers practically the entire height of the layer. The temperatures in the heated zone vary from 20 jC (68 jF) to more than 48 jC (120 jF) very close to the well bore; this represents a considerable increment to the initial reservoir temperature. Fig. 4 shows that an increment in temperature of only 5.5 jC (10 jF) reduces the oil viscosity significantly, and therefore, the resistance to flow is reduced in proportion to heating.

3.1. GOR and recovery The initial GOR of the oil was varied to test its effect on recovery. Fig. 9 illustrates the cumulative oil recovery for different gas (methane) mole fractions: 10%, 20%, 30%, and 35% (6, 12, 18, and 21 m3/m3, respectively). The producer bottom-hole pressure is constant at 3.1 MPa (450 psi). Cold-production results indicate that oils with large GOR give greater oil recoveries. For example, compare 10 mol% gas versus 35 mol% gas. This result is a function of increasing

Fig. 8. Temperature (jC) distribution for case 8 after 10 years of fluid production.

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Fig. 9. Effect of GOR on cumulative oil recovery.

compressibility and decreasing oil-phase viscosity as the gas content increases. When the production is heated, oil recovery is greater as expected. The curve for recovery of the heated GOR = 21 m3/m3 case is more than four times that of the case of the GOR = 6 m3/ m3 case under cold production.

3.2. Well location Additional simulations were performed placing the producer in every cell (i.e., every 1.5 m) from the lower limit to the upper limit of the reservoir and the oil production evaluated. The producer was at a

Fig. 10. Temperature (jC) distribution for different locations of the producer after 10 years of fluid production.

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Fig. 11. Effect of location of producer on cumulative oil recovery. Distances are from the top of the reservoir.

constant bottom-hole pressure of 3.1 MPa (450 psi), and the heat input was 288 W/m (300 BTU/h/ft). As in the previous cases, the heater and producer were located together. Fig. 10 shows the temperature distribution for three different locations of the producer after 10 years of fluid production: top, middle, and bottom of the formation, respectively. For a single-well pro-

cess, a large amount of heat is lost to the overburden or underburden if the well is placed very close to the layer boundary. Thus, the well is placed near the middle of the layer. Fig. 11 shows the cumulative oil recovery for 9 of the 19 locations studied, that is every 3.0 m. The recovery curve for cold production of a well placed 2.3 m from the bottom boundary is also included in

Fig. 12. Temperature distribution for the best combination of locations of producer – heater/injector after 10 years of fluid production (jC), BHP = 3.10 MPa, and heat input is 288.4 W/m.

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Fig. 11. The greatest oil recovery is obtained when the heater is placed near the middle of the formation. Exact positioning of the heater is not critical. Results are similar for a well placed 12.2 to 18.3 m (40 to 60 ft) from the reservoir top. Up to this point, the producer and heater/injector have been located together. An arrangement of wells similar to that used for steam-assisted gravity drainage (SAGD) or vapor extraction (VAPEX) is also possible (Butler, 1991). Here, the heater is placed some distance above the producer and oriented parallel to the producer. To study the best combination of a producer –heater/ injector pair, the producer was located 2.3 m above the lower limit of the reservoir, working at constant bottom-hole pressure conditions of 3.1 MPa (450 psi). The heater was placed sequentially at increasing vertical separation above the producer. The heat input was set at 288 W/m (300 BTU/h/ft). This case is similar to the previous (location of single producer), in the sense that heat losses need to be minimized by placing the heater near the center of the vertical layer. When the heater has a location different from the producer, other factors need to be taken into account. If the heater is too far from the producer, the producer does not take full advantage of

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the heat input. On the other hand, if the heater is placed too close to the producer or within the producer, then part of the heat provided by the heater is lost by the immediate production of the hot oil. Fig. 12 illustrates the temperature distribution for the best combination of locations of the producer and heater after 10 years of fluid production. Compared to Figs. 8 and 10, the region of greatest temperature is noticeably larger. Fig. 13 shows the cumulative oil recovery for 9 of the 19 locations studied covering the layer every two grid cells (i.e., 3 m). The optimal distance between producer and heater is a function of the properties of the reservoir. It depends strongly on thermal conductivity, permeability, and oil viscosity. The optimum distance between heater and producer, as gauged by oil production, is around 4.8 to 6.2 m (15 – 20 ft). Similar to Fig. 11, oil production is not especially sensitive to the spacing. Spacings from 3 to 7.6 m give roughly the same recovery. 3.3. Solvent injection In this section, solvent (propane, C3) injection for saturated conditions is presented. The object of

Fig. 13. Effect of location of heater on cumulative oil recovery, BHP = 3.10 MPa. Distances are from the top of the reservoir.

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propane injection is twofold: reestablish the pressure of the reservoir (provide energy) by filling the void space left by the produced oil and reduce the oil viscosity by dissolving gas into the heavy oil. In order to study propane injection with electrical heating, an arrangement similar to the position of the injector/producer pair in the SAGD technique is chosen. The producer is located 2.3 m (7.5 ft) above the lower limit of the reservoir, working at constant bottom-hole pressure conditions of 0.69 MPa (100 psi), as previously. The heater/injector is located 6.1 m (20 ft) above the producer. The heat input is set to 288 W/m (300 BTU/h/ft). The following cases were studied: S1. Cold production (single horizontal well). This case corresponds to a single producer working at a constant bottom-hole pressure of 0.69 MPa (100 psi). Neither solvent nor heat is input into the reservoir. The producer is always open. S2. Heated production (single horizontal well). Similar to case 1, but the producer is heated continuously during the entire production. No solvent is injected. The producer is always open. S3. Solvent injection for 230 days followed by cold production (two horizontal wells) followed by heated production (and no injection) for 500 days. Then the producer is shut in, the heating device is turned off, and C3 is injected at 4.1 MPa (600 psi) for 230 days. Then, the injector is shut in and the producer is open to constant bottomhole pressure cold production. S4. Solvent injection for 230 days followed by heated production (two horizontal wells). Heated production (and no injection) for 500 days. Then, the producer is shut in. The heating device is turned off, and C3 is injected at 4.1 MPa (600 psi) for 230 days. Then the injector is shut in, and the producer is open to constant bottom-hole pressure heated production. S5. Continuous solvent injection followed by cold production (two horizontal wells). Heated production (and no injection) for 500 days. Then, the producer is shut in. The heating device is turned off, and C3 is injected at 4.1 MPa (600 psi) continuously. After 230 days, the producer is open to constant bottom-hole pressure cold production.

S6. Propane injection (lower pressure) for 230 days followed by heated production (two horizontal wells). Heated production (and no injection) for 500 days. Then, the producer is shut in, the heating device is turned off, and C3 is injected at 2.8 MPa (400 psi) for 230 days. Then, the injector is shut in, and the producer is open to constant bottom-hole pressure heated production. S7. C3 injection (lower pressure) for 180 days followed by heated production (two horizontal wells). Heated production (and no injection) for 912 days. Then, the producer is shut in, the heating device is turned off, and C3 is injected at 2.8 MPa (400 psi) for 180 days. Then, the injector is shut in, and the producer is open to constant bottom-hole pressure heated production. S8. Cyclic solvent injection and heated production (two horizontal wells). Heated production (and no injection) for 500 days. Then, the producer is shut in, the heating device is turned off, and C3 is injected at 4.1 MPa (600 psi) for 100 days. Then, the injector is shut in, and the producer is open to constant bottom-hole pressure heated production for 500 days. The 500 day producing and 100 day injecting cycles are repeated for 10 years. S9. Huff and puff cyclic C 3 injection heated production (single well). Heated production (and no injection) for 500 days. Then, the production is shut in, the heating device is turned off, and C3 is injected at 4.1 MPa (600 psi) for 100 days (from the same well). Then, the injection is stopped, and the producer is open to constant bottom-hole pressure heated production for 500 days. The 500 day producing and 100 day injecting cycles are repeated for 10 years. The first two cases are single-well schemes that operate more or less continuously. Cases S3 to S8 are various cyclic options employing dual horizontal wells. Case S9 is a single-well cyclic scheme operated in a fashion similar to a huff-n-puff steamed well. Fig. 14 displays the cumulative oil recovery for the different cases. This plot shows that for this particular reservoir and fluid and rock properties, the methods are bounded. The worst oil recovery is obtained in case S1—cold production with no injection; and the best oil recovery is obtained in case S2—continuous heated production with no injection.

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Fig. 14. Cumulative oil recovery for different thermal methods.

All methods (except case S1) were designed in such a way that during the first 500 days, heat is input. Cases S3 and S5 have similar behavior. The only difference is that in case S5, propane is injected until the end of the 10-year period. Case S5 has a smaller cumulative oil recovery as compared to case S3. This is because injecting solvent continuously causes early breakthrough of solvent to the producer, because the solvent has greater mobility relative to oil. Cases S3 and S4 were designed to have the same initial behavior: first 500 days are heated, 230 days of propane injection, and then cold (case 13) and heated (case 14) production. The slope of case S3 in Fig. 14 is similar to case S1 and case S5 that also correspond to cold production conditions. On the other hand, the slope of case S4 is similar to that of case S2 corresponding to heated production conditions. The chief controlling factor for these heavy-oil recovery schemes is the heat input. Cases S4 and S6 are similar, the only difference is the propane injection pressure from 500 to 730 days. Case S6 has a lower injection pressure. Case S4 and case S6 almost overlie each other (Fig. 14). Case S4 has a slightly larger oil recovery associated

with greater injection pressure; however, the injection of propane has no major effect on the oil drive. Both of these cases employ a heated producing condition that increases their recovery with respect to other cases. Case S7 is similar to case S6, except that propane injection in case S7 is applied later and is of lesser duration as compared to case S7. Case S7 exhibits slightly greater recovery than case S6. Cumulative oil production curves for these cases indicate that both the starting time and the length of propane injection have some effect on the oil production. Ultimate oil recovery for any of these propaneinjection-assisted processes still lies under the curve corresponding to case S2 (continuous heating with no injection). In the section on economics, the efficiency or incremental recovery per BTU input is shown in terms of costs. Cases S8 and S9 correspond to cyclic propane injection. Case S8 uses two horizontal wells, and case S9 uses a single well (huff-n-puff). Fig. 14 also displays cumulative oil recovery for these two cases. Their behavior is quite similar. This indicates that the single well huff-n-puff may be more profitable, be-

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cause it does not require the drilling, completion, and maintenance/repairing of a second well. As in the previous cases, case S8 and S9 have a cumulative oil recovery below the best method (case S2). 3.4. Discussion Results for the 2-D model make clear the important effect of heating the region surrounding the well even by only 5.6 jC (10 jF). In general, all scenarios benefit from the addition of thermal energy. In the first set of cases, focus was placed on the early stages of recovery. For these cases, the conditions leading to the largest recovery are to apply heat on the order of 288 W/m so that viscosity is reduced and at the same time maintain the minimum possible bottom-hole pressure. Fig. 6 shows, for example, that the best oil recovery is obtained when both heating and a small bottom-hole pressure are applied. Small bottom-hole pressures allow a pressure gradient to propagate into the reservoir far from the well. The configuration of heater and production well leading to the greatest propagation of temperature into the reservoir is to place the heater above the producer in a SAGD fashion. Warmed fluids flow through the reservoir before being produced and transfer heat to the surrounding formation and fluids. Simulation results are quite sensitive to the solution gas – oil ratio. The increased compressibility and the release of substantial quantities of gas during heating aid production considerably. These results mirror qualitatively the unheated results where production due to depletion is expected to be greatest from a system with the largest GOR. Heating the reservoir without injecting a fluid, while enhancing production relative to the cold case, eventually depletes the reservoir of drive energy. The injection of a solvent such as propane would appear to provide pressure maintenance as well as improved recovery by reducing oil viscosity. Continuous gas injection and heated production would seem to be an additive method, whose production is greater than that of either one alone; however, it was found to have a negative effect on production. All of the scenarios considered with solvent injection actually experienced reduced production relative to an optimal case of large heat input and minimum bottom-hole pressure. There are several problems with solvent injection as imple-

mented here. Early breakthrough of solvent occurs. Production is lost because the injected solvent short circuits from the injector to the producer without contacting an appreciable reservoir volume. The solvent is heated but does not transfer this heat effectively to the reservoir. Additionally, if heating is switched off, production drops dramatically. Heating continuously appears to be the best method. Economics will determine whether a single heater producer or a SAGD-like orientation is best. Simulation runs with propane injection were also performed on this model with both cold and heated production. The results showed that when the reservoir pressure is above the bubble-point pressure, gas injection has little effect on oil production. As injected gas dissolves in the oil the oil-phase viscosity is reduced, but the solvent effect does not reduce viscosity as effectively as heating. The incremental oil production by means of gas injection above the bubble-point pressure represented a small percentage of the oil in place, and it was not studied further.

4. Heterogeneity—three-dimensional model In this section, the effects of heterogeneities and the third dimension are examined in a depletion mode. Note the position of the well. The horizontal well and heater extend over the same total length. The homogeneous, 3-D case, consists of the same well and heater arrangement with a constant permeability of 500 md used for the 2-D cases. The vertical distance between the heater and producer is 4.6 m (15 ft). Both, reservoir initial conditions and producer operative conditions were the same as those used for the 2-D cases. The heat input was set to 288 W/m (300 BTU/h/ft) and the bottom-hole pressure to 3.1 MPa (450 psi). Fig. 15 shows the cumulative oil recovered for the homogeneous and heterogeneous cases, with and without heat. Note that the heterogeneous unheated case recovers slightly more oil than the homogeneous case due to the presence of permeable paths and the absence of a gas cap. Interestingly, once heat is applied to the system, the heterogeneous and homogeneous case results virtually overlay one another. Thermal conductivity is more or less distributed

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Fig. 15. Cumulative oil recovery for 3-D homogeneous and heterogeneous cases.

Fig. 16. Incremental oil recovery versus energy input for 3-D homogeneous and heterogeneous cases.

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uniformly in the simulation model. Heat conduction smoothes the effects of heterogeneities. Fig. 16 compares the incremental recovery obtained versus the energy input for the homogeneous and heterogeneous cases. The slope of these curves provides the efficiency or the ratio of incremental oil recovered with respect to energy (kW/h) input. The homogeneous case has an averaged efficiency of 62 kW/h (0.018 BTU) per incremental oil barrel recovered, while the heterogeneous has an averaged efficiency of 80 kW/h (0.023 BTU) per incremental oil barrel recovered. Thus, heterogeneities do not significantly affect the overall efficiency, and this is an advantage of this electrical heating method. In this regard, electrical heating may be similar to steam injection. 4.1. Heating distribution Two of the parameters for electrical heating are the total heating power and its distribution. The total amount of heat that MI cables deliver is subject to the lineal length of heating demanded. Therefore, the effects of the heating power distribution were exam-

ined. All cases use the 3-D homogeneous permeability field. In case (A), the heater is the same length as the producer. In case (C), the heater is half as long as the producer. It is centered over the length of the producer and provides twice the heating density of case (A), 576 W/m (600 BTU/h/ft). Case (B) is intermediate between the two: the heater is threequarters of the length of the producer and delivers 1.5 times as much heat density as in case (A), 432 W/m (450 BTU/h/ft). All three cases consume 140 kW (4.8  105 BTU/h). Fig. 17 shows the incremental recovery obtained as a function of the total energy input to the system. Cases (A) and (B) have the same slope. In case (A), the heater had greater contact with the reservoir and incremental oil recovery began earlier. Case (C) had the least efficiency as a result of the least contact of the heater with the reservoir. Although this heater arrangement heats oil to higher temperatures in the vicinity of the well bore, most of this hot oil drains to the producer below transferring little heat to the adjacent formation. Fig. 4 shows that the initial temperature increase reduces viscosity substantially. Further increase in the temperature adds relatively

Fig. 17. Incremental oil recovery versus total energy input for 3-D cases (A), (B), and (C).

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less to oil mobility. In these examples, it was more advantageous to have greater heater – reservoir contact than it was to have greater temperature. In short, the heating power and its distribution are parameters to take into account during the optimization and design of this process.

5. Economics Case S2: heated production, no injection (single well), gave excellent recovery. It might be argued that heating the reservoir continuously is expensive in the long term. Fig. 18 displays the incremental oil recovery against the energy input to the 2-D system. The results are on a per meter basis. In order to facilitate discussion of Fig. 18, three different units systems are used on the x-axis. They are (i) electrical energy input to system in kWh/m, (ii) equivalent thermal energy

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converted to barrels of oil consumed using a conversion factor of 7.6  109 J/m3 (5.6  106 BTU/bbl) of oil, (iii) equivalent thermal energy in standard cubic feet of natural gas assuming 3.7  107 J/m3 (1000 BTU/SCF) of natural gas. These three unit systems help us to interpret the energy required for enhanced recovery. Providing heat during the entire process is inexpensive relative to the oil volumes recovered, Fig. 18. For instance, 2 m3 of oil are consumed for the production of more than 140 m3. Fig. 6 shows the oil rate for the thermal methods analyzed with the well in the middle of the formation. Cases 3 and 8 have identical bottom-hole pressure but differ with respect to heating. Average oil rates for these two cases differ by roughly a factor of two. The average oil rates over 3500 days were estimated for cases 3 and 8 as 0.039 m3/day m (0.074 bbl/day ft) and 0.083 m3/day/m (0.16 bbl/day/ ft), respectively.

Fig. 18. Incremental oil recovery versus system energy input for case S2: 288.5 W/m, 0.7 MPa BHP, no solvent injection.

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Using these average rates and assuming a length of reservoir/heating device of 152 m (500 ft), the revenue per day for the heated and cold production is qoil

heated

¼ 0:083

m3 USD 1 bbl 152m  20 bbl 0:159 m3 day m

USD ¼ 1582 day

qoil

cold

¼ 0:039 ¼ 743

m3 USD 1 bbl 152 m  20 bbl 0:159 m3 day m

USD day

Thus, the average incremental revenue is 839 USD/ day. To find the cost of the electricity consumed by the MI cable heater, the energy input per day is calculated first: 288

J s 1 kWh kWh 8:64  104 ¼ 6:9 6 sm d 3:6  10 J day m

The average cost of electricity for U.S. industrial consumers between 1990 and 2003 was 0.05 USD/ kWh, whereas the average for 2003 was 0.053 USD/ kWh (Energy Information Administration, 2004). The cost of electricity is estimated as 6:9

kWh USD USD 152 m  0:05 ¼ 52 day m kWh day

The difference between the gross revenue and the operating cost is 1530 USD/day, whereas the difference between the incremental revenue and the operating cost is 787 USD/day. The 1530 USD/day difference corresponding to the heated production is about 2.1 times larger than the 743 USD/day corresponding to the cold production. The cost of heating the reservoir to obtain such production is 3.4% of the gross revenue or 6.7% of the incremental profit. Alternately, at 20 USD per barrel of oil, the operating cost is about 1.25 USD per barrel for heating the incremental oil produced. Interestingly, the enhanced production rate is significantly large so that the economics are favorable for a wide range of electricity prices. If the price of electricity increases by a factor of 5, the cost for heating increases to 6.60 USD/BBL, and the cost of

heating relative to the incremental profit climbs to 50%. Thus, the process remains economic even at 0.25 USD/kWh.

6. Conclusions (1) For heavy oils with appreciable solution gas (>18 m3/m3), electrical heating alone enhances depletion significantly relative to the unheated case. In cases with maximum heat input and minimum bottom-hole pressure in the producers, oil production rates more than doubled. (2) The greatest recoveries were found for cases with the addition of thermal energy but without any solvent injection. Solvent injection was accompanied by rather rapid injector to producer linkup and cycling of solvent. This frustrated any additional oil recovery. Despite the success of electric heating of producers with no accompanying solvent injection, some form of pressure maintenance or drive needs to be developed to maintain recovery during the latter stages of heating. (3) Electrical heating using MI cables is an economical method for production of heavy oil.

Nomenclature A, B, C, D Coefficients in the correlation for gas– oil equilibrium ratio BHP Bottom-hole pressure CMG Computer Modelling Group f Mole fraction in a multicomponent mixture GOR Gas oil ratio h Formation thickness k Permeability K Equilibrium ratio MI Mineral insulated nc Number of components p Pressure r Radius SAGD Steam assisted gravity drainage STARS Steam, Thermal, and Advanced Processes Reservoir Simulator T Temperature

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VAPEX Vapor extraction WI Well index l Viscosity Subscripts and superscripts a Heated zone radius o Drainage radius w Well radius V Enhanced well index or oil viscosity

Acknowledgements This work was prepared with the partial support of the Stanford University Petroleum Research Institute (SUPRI-A) Industrial Affiliates. This support is gratefully acknowledged.

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