Math GeosciDOI 10.1007/s11004-013-9516-8

SPECIAL ISSUE

Modified Method for Estimating Geothermal Resourcesin Oil and Gas Reservoirs

Kewen Li · Wenjie Sun

Received: 16 July 2013 / Accepted: 19 December 2013© International Association for Mathematical Geosciences 2014

Abstract Increasing attention has been paid to the power generated by utilizing hotfluids that are co-produced from oil and gas reservoirs, as well as other geother-mal resources. It is thus essential to evaluate the geothermal resource in oil and gasreservoirs accurately. Although there are a number of approaches for determining thegeothermal resource associated with oil and gas fields, a lot of problems are yet tobe solved. Previous studies on the effects of oil and gas saturation on the geothermalresource were considered; however, it was assumed that the oil and gas saturationswere constant during the development, which is not true. To this end, the existingvolumetric approach of evaluating geothermal resource in oil and gas reservoirs wasmodified by considering the change of oil and gas saturation with time. An oil reservoirfrom Huabei oilfield with a moderately high temperature was chosen as a target reser-voir to apply the modified method. The effects of porosity, oil and gas saturations, andreservoir rock type on the geothermal resource were studied and the results comparedto existing approaches. Also, the possible energy and income that might be generatedfrom this geothermal system were estimated. The results indicate that the geothermalresource, energy, and possible income have been overestimated by the existing models,and the difference becomes more significant as the oil or gas saturation increases.

K. Li (B)China University of Geosciences, Beijing 100083, Chinae-mail: likewen@cugb.edu.cn

K. LiStanford Geothermal Program, Stanford University, Stanford, CA 94305, USA

W. SunSchool of Earth and Space Sciences, Peking University, Beijing 100871, China

W. SunResearch Institute of Petroleum Exploration and Development,China National Petroleum Corporation, Beijing 100083, China

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Keywords Modified method · Geothermal resource · Fluid saturation · Porosity ·Oil and gas reservoirs

1 Introduction

Currently, a large number of oil and gas fields are in the late period of development.Water cut in these mature oil and gas fields is very high, even up to 97 %. Thetraditional oilfield has become a water field (Xin et al. 2012). The produced wateris usually considered a nuisance to oil and gas producers, because it is required todispose or re-inject the water into reservoirs. This process costs a lot and reduces thenet profit value of the oil and gas producers. The development of these oil and gas fieldsbecomes a huge challenge because of its high cost, and one of the solutions to thisproblem may be electricity generated by utilizing the geothermal resource co-producedfrom the oil and gas reservoirs (Erdlac et al. 2006, 2007; Li et al. 2007, 2012, 2013;Xin et al. 2012). This is because many of the high water cut oil and gas reservoirsproduce water with a temperature over 100◦C, high enough to generate electricityusing modern power generation technology. In fact, electricity can still be producedcommercially even when the temperature of the produced water is as low as 70 ◦C,if binary cycle power plants are used (Bliem 1988; Hudson 1988; Hung et al. 1997;Kalina 1983; Naga and Gutp 1998). Electricity generated from the produced waterwill give a new life to low-yield oil and gas producers because of high water cut.

According to some of the reported studies (Erdlac et al. 2006, 2007; Johnson andWalker 2010; Xin et al. 2012), the geothermal resource co-existing in oil and gasreservoirs for power generation is huge. One of the benefits of utilizing geothermalresource in oil and gas reservoirs is that injection and production wells along withother facilities in oil and gas fields already exist. So, the cost of electricity generatedfrom hot water is relatively low, which is even closer to that from gas (Evans et al.2009). Moreover, because geothermal energy is environmentally friendly comparedwith traditional fossil energy, the direct use of geothermal energy and power generatedby using hot fluids co-produced from oil and gas reservoirs is increasingly important(Erdlac et al. 2006, 2007; Li et al. 2007; McKenna et al. 2005; Milliken 2007). Recently,Johnson and Walker (2010) reported that a 250 kW power plant was designed andinstalled at the Naval Petroleum Reserve No. 3 (NPR-3) using the water produced fromthe field with a temperature of about 76.7 ◦C, which has already operated successfullyfor over 3 years. Xin et al. (2012) reported on progress related to a 400 kW pilotpower plant using the water produced from the field with a temperature of about110 ◦C, which was installed at Huabei oilfield, China.

Evaluating the geothermal resource in oil and gas reservoirs accurately is of seri-ous importance. Several approaches, including volumetric, analytical and numericalapproaches (Muffler and Cataldi 1978), can be used to estimate the energy capacityof a geothermal system. In this study, the volumetric approach was chosen to esti-mate geothermal resources in oil and gas reservoirs, and the reasons are describedbriefly as follows. The volumetric approach has been well established in the geother-mal industry (Ciptomulyono 2007; Clotworthy 2006; Sanyal 2003, 2007; Sanyal andSarmiento 2005; Yan and Yu 2000) and is a convenient and fast method to calculate

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the geothermal potential. Sanyal and Sarmiento (2005) mentioned that the volumetricestimation technique is one of the methods consistently applicable for the estimationof a geothermal resource, which might still be true even now. Volumetric estimationapproach is usually used at a later stage of geothermal exploration after drilling hasstarted, although it can also be used in the early period of development as long as goodsurface indications and geophysical surveys are available (Clotworthy 2006). There-fore, the volumetric approach is suitable for the estimation of a geothermal resource inoil and gas reservoirs, because plenty of wells have already been drilled and geothermalenergy is usually utilized at the later period of oil production when water cut is high.

The estimation of a geothermal resource in oil and gas reservoirs differs from thatin geothermal reservoirs as there are differences between geothermal and petroleumreservoirs in which oil and gas phases exist (Ciptomulyono 2007; Clotworthy 2006;Sanyal 2003, 2007; Sanyal and Sarmiento 2005; Yan and Yu 2000; Zhang et al. 2009).Zhang et al. (2009) modified the volumetric approach by including three phases (oil,water and gas). However, in their study, the values of the oil and gas saturation wereassumed constant from the beginning to the end of the development of the reservoir,which is obviously not the case. During the development of oil reservoirs, the watersaturation may increase, while the oil and gas saturations decrease. This increases themean specific heat of fluids residing in the rock. With all of the above considerations,a modified volumetric method was proposed by considering the saturation changeduring the development of oil and gas reservoirs. Then the new model was appliedto estimate the geothermal resource in Hexaw reservoir from Huabei oilfield with amoderately high temperature. Finally, the effects of porosity, oil and gas saturation,as well as reservoir rock type on the geothermal resource were also studied in thisresearch.

2 Theoretical Background

The volumetric approach is widely used in geothermal engineering because it does notneed as much information to apply as other more sophisticated evaluation approaches(Clotworthy et al. 2006). To consider the effects of oil and gas saturation on thegeothermal resource in petroleum reservoirs with both oil and gas phases, the volu-metric method is described as follows (Zhang et al. 2009)

QR = A · h · (Tr − Ta) · C, (1)

where QR is the total available heat resource of the geothermal system, A is the areaof the geothermal reservoir, h is the reservoir thickness, Tr is the initial temperature ofthe geothermal reservoir, Ta is the abandonment temperature of the reservoir, and Cis the mean specific heat of rock and fluids residing in the rock and can be expressedas below

C = ρr · Cr · (1 − φ) + (ρw · Cw · Sw + ρo · Co · So + ρg · Cg · Sg)φ, (2)

Sw + So + Sg = 1. (3)

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Here, ρr, ρg, ρw and ρo are the density of rock, gas, water and oil, respectively,Cr, Cg, Cw and Co are the specific heat of rock, gas, water and oil, respectively, φ

is the porosity of the rock, and Sw, So and Sg are the saturations of water, oil and gas.Note that the above volumetric approach does not consider the saturation alteration

during the development of oil and gas reservoirs. However, as stated previously, watersaturation increases while oil and gas saturations decrease when the development ofoil reservoirs reaches the phase of abandonment. Assuming that the reservoir develop-ment process is balanced between injection and production and taking the saturationalteration into account, the volumetric model as shown in Eq. (1) is modified in thisstudy and expressed as follows

QR = Qi − Qa. (4)

Where Qi is the initial heat resource of the geothermal system and Qa is the heatresource of the geothermal system at the abandonment time, Qi and Qa can be calcu-lated as below

Qi = AhTrCi, (5)

Qa = AhTaCa, (6)

where Ci is the initial mean specific heat of rock and fluids resided in the rock, Ca isthe mean specific heat of rock and fluids resided in the rock at the abandonment time.Ci and Ca are expressed as follows:

Ci = ρrcr(1 − φ) + ρwcwφSwi + ρocoφSoi + ρgcgφSgi, (7)

Ca = ρrcr(1 − φ) + ρwcwφSwa + ρocoφSoa + ρgcgφSga, (8)

Swi + Soi + Sgi = 1, (9)

Swa + Soa + Sga = 1, (10)

Here, Swi, Soi and Sgi are the initial saturations of water, oil and gas phases; Swa, Soaand Sga are the saturations of water, oil and gas phases at the abandonment time,respectively. The values of these parameters can be provided by the operators of theoil reservoirs. Equations (4)–(10) constitute the modified volumetric method proposedin this paper. One can see from Eqs. (7) to (8) that the effect of the change in fluidsaturation along with the production time on the geothermal resource is considered bytaking the parameters of initial and abandonment saturations into account. In addition,the electric energy that could be generated from geothermal energy can be describedas follows:

E = QR · η, (11)

where η is the efficiency factor and E is the electric energy generated from geothermalenergy.

3 Results

In this study, the Hexaw reservoir in the Huabei oilfield is chosen as a case study ofthe modified volumetric approach. The Huabei oilfield is a mature oilfield of China

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National Petroleum Corporation (CNPC), which is now at the late period of devel-opment. The Hexaw oil reservoir is located in the Hexaw structural belt in Lang-gudepression. It is one of the main water flooding carbonate reservoirs of the Huabeioilfield. The basic geological data of the Hexaw reservoir, including formation thick-ness, porosity, reservoir rock density, specific heat and formation fluid specific heat,are listed in Table 1. Using both the existing volumetric approach [Eqs. (1)–(3)] andthe modified volumetric approach [Eqs. (4)–(10)], the geothermal resource, energyand the possible income from the Hexaw reservoir were calculated and compared. Inthis study, the abandonment temperature (Ta) was assumed as 50 ◦C, while Soa was40 %, a typical value in the Huabei oilfield. In the assessment, the efficiency factorwas set as 12 % and the price of electric energy was 0.5 Yuan/kW h (1 dollar equalsto 7 Yuan approximately).

Figure 1 shows the effect of water saturation on the geothermal resource for the casein which only oil and water phases exist in the oil reservoir (Tr = 120 ◦C). It indicates

Table 1 The basic geologicaldata of the Hexaw reservoir inthe Huabei oilfield

Area (A, km2) 452

Thickness (h, m) 117

Porosity (φ, %) 30

The density of rock (ρr , kg/m3) 1,956

The specific heat of rock (Cr , J/(kg ◦C)) 857

The density of oil (ρo, kg/m3) 850

The specific heat of oil (Co, J/(kg ◦C)) 2,468

The density of water (ρw, kg/m3) 1,000

The specific heat of water (Cw, J/(kg ◦C)) 4,190

The density of gas (ρg, kg/m3) 0.717

The specific heat of gas (Cg, J/(kg ◦C)) 2,227

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Fig. 1 Effect of water saturation on the geothermal resource in the case in which only oil and water phasesexist in the oil reservoir (Tr = 120 ◦C, φ = 30 %)

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that the geothermal resource increases with water saturation and decreases with theincrease in oil saturation significantly. Furthermore, it is obvious that the geothermalresource evaluated by the modified volumetric method (labeled as new model in thefigures) is less than that calculated by the volumetric method (Zhang et al. 2009)(labeled as existing model in the figures). As water saturation decreases, the differencebetween the geothermal resources calculated by Eqs. (1) and (4) becomes increasinglysignificant. When the water saturation is close to 0.6, the difference approaches zeroas expected. This observation is reasonable because the specific heat of oil is lessthan that of water. It can be seen from Fig. 1 that the geothermal resource in the oilreservoir is overestimated if the saturation alteration is simply neglected as is done inthe existing volumetric approach, especially in the reservoir with high oil saturation.In Fig. 2, the effect of water saturation on the electric energy in the case where only oil

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Fig. 2 Effect of water saturation on the energy generated in the case where only oil and water phases existin the oil reservoir (Tr = 120 ◦C, φ = 30 %)

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Fig. 3 Effect of water saturation on the possible income in the case in which only oil and water phasesexist in the oil reservoir (Tr = 120 ◦C, φ = 30 %)

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and water phases exist in the oil reservoir (Tr = 120 ◦C) was investigated. The energygenerated increases with water saturation and the energy evaluated by the existingvolumetric method is overestimated. The effect of water saturation alteration duringthe development of the oil reservoir on the electric energy is more significant at higheroil saturation. The possible income at different water saturations in the case in whichonly oil and water phases exist in the oil reservoir (Tr = 120 ◦C) was also calculated.It is obvious that the income increases with water saturation, and the possible incomeevaluated by the modified volumetric method is less than that by the existing volumetricmethod as well (see Fig. 3). Comparing the two models, the trend of overestimatingthe income by the existing model is more significant at a higher oil saturation. Figure 4shows the effect of water saturation on the geothermal resource calculated using the

Fig. 4 Effect of water saturation on the geothermal resource at different reservoir temperatures in the oilreservoir in which only oil and water phases exist (φ = 30 %)

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Fig. 5 Effect of water saturation on the geothermal resource in the case in which only gas and water phasesexist in the gas reservoir (Tr = 120 ◦C, φ = 30 %)

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modified model in the case in which only oil and water phases exist in the oil reservoirat different reservoir temperatures (120, 160, and 180 ◦C). The porosity of the reservoirwas also assumed to be 30 % in this case. In Fig. 4, the geothermal resource calculatedby the modified model increases with the reservoir temperature. As the temperatureof the reservoir increases, the effect of water saturation on the geothermal resource ismuch more significant.

Figures 5, 6, and 7 show the effects of water saturation on the geothermal resource,electric energy, and possible income at a reservoir temperature of 120 ◦C in the casein which only gas and water phases exist in the gas reservoir. In the study, Sga wasassumed as 40 %. Figure 8 shows the effect of water saturation on the geothermalresource in the case where only gas and water phases exist in the gas reservoir atdifferent reservoir temperatures (120, 160, and 180 ◦C). Figures 5, 6, 7, and 8 indicatethe effect of water saturation on the geothermal resource, the electric energy, and

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Fig. 6 Effect of water saturation on the energy in the case in which only gas and water phases exist in thegas reservoir (Tr = 120 ◦C, φ = 30 %)

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Fig. 7 Effect of water saturation on the possible income in the case where only gas and water phases existin the gas reservoir (Tr = 120 ◦C, φ = 30 %)

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Fig. 8 Effect of water saturation on geothermal resource in the case in which only gas and water phasesexist in the gas reservoir at different reservoir temperatures (φ = 30 %)

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Fig. 9 Comparison of the effect of water saturation on the geothermal resource with different abandonmenttemperatures in oil–water system (Tr = 120 ◦C, φ = 30 %, Soa = 40 %)

possible income in gas reservoir, and the results are similar to those observed in theoil reservoir (i.e., Figs. 1, 2, 3, 4).

The above results are all based on the assumption that the abandonment temperature(Ta) was equal to 50 ◦C. With the rapid development of technology, the abandonmenttemperature becomes lower and lower. To investigate the effect of the abandonmenttemperature, geothermal resource was estimated using different values of abandon-ment temperature (Ta), that is, 35, 50, and 65 ◦C. The results are shown in Fig. 9.Note that the geothermal resource in Fig. 9 was calculated in the case in which onlyoil and water phases existed in the oil reservoir. The other parameters used for thecalculations were as follows: Tr = 120◦C, φ = 30 %, and Soa = 40 %. One can seethat the difference between the two models becomes more significant as abandonment

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Fig. 10 Comparison of the effect of water saturation on geothermal resource between oil–water andgas–water systems (Tr = 120 ◦C, φ = 30 %)

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Fig. 11 Effect of water saturation on geothermal resource in the case in which only oil and water phasesexist (Tr = 120 ◦C, φ = 15 %)

temperature increases. It is also observed that the geothermal resource decreases asthe abandonment temperature increases, which is reasonable.

The comparison of the effect of water saturation on the geothermal resource calcu-lated by the new model between oil–water (oil reservoir) and gas–water (gas reservoir)systems at the temperature of 120 ◦C (Ta = 50 ◦C) is shown in Fig. 10. The geothermalresource in oil–water system is greater than that in gas–water system at the same reser-voir temperature and water saturation. This is because the specific heat of gas is lowerthan that of oil. The rate of increase of the geothermal resource with water saturationin a gas–water system is greater than that in an oil–water system. Furthermore, therate of geothermal resource increase with water saturation calculated by the modifiedvolumetric approach is greater than that by the volumetric method proposed by Zhang

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Fig. 12 Effect of water saturation on geothermal resource in the case in which only oil and water phasesexist (Tr = 120 ◦C, φ = 5 %)

Fig. 13 Comparison of the effect of porosity on geothermal resource in oil–water system (Tr = 120 ◦C)

et al. (2009). As water saturation decreases, the difference between the two modelsbecomes more significant, while the difference approaches zero when oil saturation iscloser to the residual value.

The above results were calculated assuming a porosity of 30 %, which is the meanporosity of the Hexaw reservoir in the Huabei oilfield. However, the values of porosityvary in different geothermal and petroleum reservoirs. To study the effect of porosity,the geothermal resources were calculated using different porosity values (5, 15 and30 %) and the results are depicted in Figs. 11 and 12. Figure 11 demonstrates theeffect of water saturation on the geothermal resource with a porosity of 15 % in thecase in which only oil and water phases exist in the reservoir. Figure 12 shows theresult calculated with a porosity of 5 %. As porosity decreases, the difference betweenthe two models becomes less significant. There is almost no difference between thetwo models when porosity becomes very small (Fig. 12). It can be seen from Figs. 11and 12 that the effect of water saturation on the geothermal resource in low porosityreservoirs is less significant than that in reservoirs with great values of porosity. All

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Cr=1000J/(kg·°C), existing modelCr=1000J/(kg·°C), new modelCr=900J/(kg·°C), existing modelCr=900J/(kg·°C), new modelCr=760J/(kg·°C), existing modelCr=760J/(kg·°C), new model

Fig. 14 Comparison of the effect of rock types on geothermal resource in the oil–water system(Tr = 120 ◦C, φ = 30 %)

of the results calculated using the modified method are summarized in Fig. 13. Asimilar investigation at different values of porosity for the gas–water system was alsoconducted and similar results were observed. According to the above results, the effectof water saturation on the geothermal resource may be neglected when the porosity issmaller than a specific value (around 5 %).

Oil and gas reservoirs may have different rock types, such as sandstone, limestone,and carbonate. The values of the specific heat of different rocks are different because oftheir different mineral compositions. The geothermal resource for oil–water systemsat a temperature of 120 ◦C was estimated using different values of specific heat ofrocks and the results are shown in Fig. 14. Note that the values of the specific heatused in Fig. 14 represent sandstone (1,000 J/kg ◦C), limestone (900 J/kg ◦C), andcarbonate (760 J/kg ◦C). The geothermal resource increases greatly with the value ofthe specific heat of rock, which indicates that the rock type plays an important role indetermining the geothermal resource. One can also see from Fig. 14 that the existingmodel overestimates the geothermal resource.

4 Conclusions

The following conclusions may be drawn according to the present study. Comparedto the modified volumetric approach, the geothermal resource, energy, and possibleincome have been overestimated by the existing model. It is necessary to consider theeffects of saturation alteration during the development of oil and gas reservoirs onthe estimation of a geothermal resource. The difference in estimating the geothermalresource between the two models becomes more significant as the oil or gas saturationincreases. The difference between the modified volumetric approach and the exist-ing model becomes less significant as the value of porosity decreases, and it may beneglected when the porosity is less than a specific value. The effect of specific heat ofrock on the geothermal resource is significant and may not be ignored in some cases.

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Acknowledgments This research was conducted with financial support from CNPC, the contributions ofwhich are gratefully acknowledged.

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