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Impact of Reservoir Heterogeneity on the Control of Water Encroachment into Gas-Condensate Reservoirs during CO2 Injection

Impact of Reservoir Heterogeneity on the Control of Water Encroachment into Gas-Condensate... The paper evaluates application of CO injection for the control of water encroachment from the aquifer into gas- condensate reservoir under active natural water drive. The results of numerical simulations indicated that injec- tion of CO at the initial gas-water contact (GWC) level reduces the influx of water into gas-bearing zone and stabilizes the operation of production wells for a longer period. The optimum number of injection wells that leads to the maximum estimated ultimate recovery (EUR) factor was derived based on statistical analysis of the results. The maximum number of injection wells at the moment of CO break-through into production wells for homoge- neous reservoir is equal to 6.41 (6) and for heterogeneous – 7.74 (8) wells. Study results indicated that with the increase of reservoir heterogeneity, denser injection well pattern is needed for the efficient blockage of aquifer water influx in comparison to homogeneous one with the same conditions. Gas EUR factor for the maximum number of injection wells in homogenous model is equal 64.05% and in heterogeneous – 55.56%. Base depletion case the EURs are 51.72% and 49.44%, respectively. The study results showed the technological efficiency of CO injection into the producing reservoir at initial GWC for the reduction of water influx and improvement of ultimate hydrocarbon recovery. Key words: 3D reservoir model, numerical simulation, enhanced gas recovery (EGR), gas-condensate reservoir, water drive, trapped gas, carbon dioxide (CO ) injection INTRODUCTION With active aquifer water encroachment into gas-bearing Rational development of gas-condensate fields under the layers, production wells are being shut after relatively active water drive is based on systematic control of aqui- small cumulative gas production. One of the reasons is the fer water influx into the gas zone and water break- limitation of surface separator and gas treating facilities through to production wells [1, 2]. Majority of the gas that are originally not designed to handle huge volumes fields are represented by multi-stacked heterogeneous of water. Water shut-off well treatments and work-overs reservoirs [3]. During field development planning stage are usually not effective, since they require a very good geological information is limited, and therefore a special understanding of the reasons and paths of water influx. attention must be paid to the selection of well locations That is why control of edge aquifer water influx is the key for maximum drainage of the reservoirs [1]. Non-uniform task of reservoir management [5]. production well spacing with higher well-count in the The majority of gas production in Ukraine is coming from crest of the gas-bearing zone is very common. These leads partially or heavily depleted reservoirs with significant re- to selective water encroachment into the gas zone maining volumes of trapped gas. Research of the opti- through high-permeable rocks and most depleted layers mum ways of macro- and micro-trapped gas recovery is [4]. Selective water invasion causes decrease of gas rela- an important issue especially with constantly decreasing tive permeability and well productivity due to liquid load- quality and quantity of the hydrocarbon reserves. [6]. ing, when mixture velocity in the tubing falls below the critical value of 4-5 m/s. S. MATKIVSKYI et al. – Impact of Reservoir Heterogeneity on the Control… 63 RESEARCH OBJECTIVE factors of gas displacement [16]. Results of numerical sim- The complexity of remaining hydrocarbon in place recov- ulation studies where natural gas was displaced by CO2 ery under water drive is related to water encroachment are presented in [17, 18, 19]. According to the study [18], from the aquifer into gas-bearing zone and further to pro- gas production until the economic limit followed by CO duction wells. To minimize negative impact of formation injection leads to higher EUR than in the case when CO water on reservoir development by CO2 injection at initial injection starts from the beginning of reservoir develop- GWC requires additional research to maximize the ulti- ment. CO2 injection at the final stage is the most efficient mate recovery at minimum costs and negative impact on way to maximize the ultimate gas recovery [19] resulting environment. in EUR of 86% versus 66% in case when it was injected The objective of the research is to evaluate the influence from the beginning. of heterogeneity on the well pattern density (well spacing The presented results proved the efficiency of non-hydro- and well count) during CO2 injection at the level of initial carbon gas injection for EGR but they do not account for GWC for the purpose of water encroachment control into technical complexities of final development stage as well the gas-bearing zone using numerical simulation. as macro-heterogeneity of the reservoirs. The following tasks were solved during the research: The results of physical and mathematical modeling of nat- 1. Investigation of CO2 injection wells number on the ac- ural gas displacement by non-hydrocarbon gases [20, 21, tivity of aquifer and control of water encroachment 22] showed high technological efficiency of this EGR into homogeneous and heterogeneous gas-conden- method, resulting in higher recoveries and financial indi- sate reservoir. cators based on full-field projects implemented in Ukraine 2. Define the optimum number of CO2 injection wells and in other countries [23, 24, 25, 26, 27]. that leads to the maximum ultimate recovery factor in The water encroachment and break-through to produc- the presence of active water drive. tion wells is important issue for Ukrainian and interna- tional gas operators, and therefore, require additional in- LITERATURE REVIEW vestigation also by means of numerical simulation. Majority of hydrocarbon reservoirs is associated with ac- tive aquifer systems providing influx of water by bottom METHODOLOGY OF RESEARCH or edge water drive. Field data indicates that active water Influence of heterogeneity on water encroachment dur- drive can produce up to 70-85% of gas initially in place [7, ing carbon dioxide injection into different number of in- 8]. Due to the high value of remaining gas in presence of jection wells (well count and spacing) was studied by nu- water drive, there is a need in establishment of optimum merical simulation using Schlumberger software ECLIPSE ways for increase of EUR under such conditions. and Petrel [28, 29]. Synthetic homogeneous and hetero- Different methods and technologies for gas reservoir geneous anticline numerical gas-condensate reservoir management and water encroachment control were al- models were used in this study (Fig. 1). ready proposed. However, those solutions are normally non-economic and technologically non-feasible since they do not consider reservoir heterogeneity and spatial and vertical variation of petrophysical properties within the reservoir [9, 10]. In addition to that, there is a necessity to recover macro- and micro-trapped gas due to high de- mand of gas resources. Enhanced gas recovery is a very perspective technology that is based on the introduction of additional energy into the reservoir system from the surface. The results of nu- merous research studies and publications showed high ef- ficiency of non-hydrocarbon gas injection, for example, ni- trogen, carbon dioxide, flue gases and their mixtures, etc. [11, 12, 13]. Methane displacement and gas recovery factor is highly dependent on the type of the injected gas, reservoir het- erogeneity and mutual disposition of layers with different Fig. 1 Conceptual numerical reservoir simulation model show- permeabilities [14]. Molecular diffusion between two lay- ing gas saturation and position of production and injection ers of different permeabilities, partially reduces the nega- wells tive influence of heterogeneity. CO2 is known to have the best displacing properties in Simulated gas-condensate reservoir contains 800 mln. m comparison to nitrogen and flue gases [15], resulting in of gas in place at initial reservoir pressure of 35 MPa, res- EUR of 81.0-97.4%. Density and viscosity of carbon diox- ervoir temperature 358 K, net thickness 15.4 m, effective ide under reservoir conditions are significantly higher porosity 0.18, absolute permeability 8.65 mD, initial gas than those of hydrocarbon gases. High solubility of CO in 2 saturation 0.8. oil, gas-condensate and formation water are additional 64 Management Systems in Production Engineering 2022, Volume 30, Issue 1 𝑚𝑖𝑛 Effective porosity for the layers in heterogeneous model (from top to bottom) are equal 0.17, 0.22, 0.14 and 0.18 1 ∧ ∧ 𝑣 ,𝑎 {𝜎 = ∑[𝑓 (𝑎 , 𝑥 )− 𝑦 ]2}{𝑣 ,𝑎 } 𝑣 𝑎𝑣 𝑣 𝑣 𝑖 𝑖 𝑣 (Fig. 2), and respective values of absolute permeability 𝑛 − 𝑟 𝑣 𝑣 𝑖 =1 6.55, 17.64, 3.62 and 7.99. (1) 𝑚𝑖𝑛 1 ∧ ∧ [ ] } 𝜀 ,𝑎 {𝜎 = ∑ 𝑓 (𝑎 ,𝑥 )− 𝑦 2 {𝜀 ,𝑎 } 𝜀 𝑎𝜀 𝜀 𝜀 𝑖 𝑖 𝜀 𝑛 − 𝑟 𝜀 𝜀 𝑖 =1 ∧ ∧ 𝑓 (𝑎 ,𝑥 ) − 𝑓 (𝑎 ,𝑥 ) = 0 ⇒ 𝑥 (2) 𝑣 𝑣 ∗ 𝜀 𝜀 ∗ ∗ where: 2 2 𝜎 ,𝜎 −measure of dispersion efficiency 𝑓 та 𝑓 𝑣 𝜀 𝑟 ,𝑟 – number of evaluated parameters in the model 𝑣 𝜀 𝑓 (𝑎 ,𝑥 ) та 𝑓 (𝑎 ,𝑥 ) 𝑣 𝑣 і 𝜀 𝜀 і Parameters a , a , a ,…, a are selected by solving the 0 1 2 n above given system of equations. Obtained parameters Fig. 2 Porosity distribution in heterogeneous model of gas-con- are used in a function y=f(x) and in such a way the linear densate reservoir equations are obtained for accurate description of calcu- lated values. After that, the plots are built for particular Duration of CO injection into the gas-condensate reser- calculated data and approximated each one by straight voir at the level of initial GWC was equal 16 months. Pro- duction wells were controlled by constant gas rate of lines, with the crossing point representing the optimum 3 3 value. 50×10 m /d as well as CO2 injection wells. Production wells are located 400 m away from each other. Composi- RESULTS OF RESEARCH tional PVT model was used for proper calculation of com- Using 3D numerical model of gas-condensate reservoir plex phase behavior during fluid flow and CO injection the influence of heterogeneity on aquifer water encroach- [30, 31, 33]. ment during CO injection at the level of initial GWC was CO2 injection was evaluated using different number of in- studied. Based on the results, it was concluded, that the jection wells (4, 6, 8, 12, 16) equally spaced within the number of injection wells (well spacing) makes a signifi- outer boundary of the reservoir. The distance between cant impact on reservoir production performance. De- the injectors for each evaluated case were 1100, 800, 600, pendency between CO break-through time into produc- 400, 300 m respectively. Production from the reservoir tion wells and number of CO injectors is shown on Fig. 3. stopped at the moment when carbon dioxide broke- through into the last production well. In the case of CO injection, the break-through time to each production well was recorded in order to make a proper comparison to depletion case, in which production wells were stopped in exactly same times. Different number of injection wells leads to different well operation time until the moment of CO break-through. Therefore, for each CO injection case there was a respec- tive depletion case of different duration of production. Reservoir production performance was calculated and compared at the moment of CO2 break-through into one of the production wells based on the cumulative water production for the cases with different injection well count. Graphical method combined with statistical analysis was used for identification of optimum values of the key per- formance parameters in of results interpretation [32]. Fig. 3 Dependence of CO break-through time from number of Statistical analysis of function parameters f(x)=a +a x a 0 1 injection wells for homogeneous and heterogeneous reservoir chosen in such a way that difference of evaluated points During CO injection into homogeneous reservoir model (xi; yi) і = 1..𝑁 from the selected trend curve will be min- the duration of production well operation depends on imal. Parameters a0, a1 must be such that sum of square number of injection wells (well spacing) and respectively root deviations of observed values yi from calculated by a equal for 4 wells – 44 months, for 6 wells – 46 months, for function f(x)=a +a x will be minimal. After a few transfor- 0 1 8 wells – 47 months, for 12 wells – 40 months and for 16 mations, the system of two linear equations for the re- wells – 34 months. gression on unknown parameters was obtained. 𝑎𝜀 𝑎𝑣 S. MATKIVSKYI et al. – Impact of Reservoir Heterogeneity on the Control… 65 a) In a case of the model with layered heterogeneity the forecasted duration of production time until the moment of CO2 break-through depending on number of injectors: for 4 wells – 41 months, for 6 wells – 42 months, for 8 wells – 43 months, for 12 months – 41 months, for 16 wells – 36 months. It is necessary to point out that during CO2 injection, the production period from homogeneous model with mini- mum number of injectors (4 and 8) significantly longer b) than in the case of heterogeneous model. However, dur- ing future increase of the number of injectors the produc- tion period of homogeneous reservoir becomes shorter in comparison to heterogeneous. Analysis of reservoir pressure behavior at the time of CO break-through into production wells indicated that in- crease of injection wells number from 4 to 8 in case of het- erogeneous model leads to higher values of reservoir pressure in comparison to homogeneous one. However, Fig. 5 Carbon dioxide concentration in homogeneous (a) the further increase of injectors count is causing the re- and heterogeneous (b) models at the moment of break- duction of reservoir pressure in comparison to homoge- through into first production well for the case of 16 injectors neous case. Such relationship between reservoir pressure According to the simulation results, cumulative water pro- and number of injection wells is due to different produc- tion periods until the moment of CO break-through. The duction is reducing with the increase of number of CO2 in- change of reservoir pressure as a function of injection well jectors in comparison to depletion case. Calculated values of cumulative water production at the moment of CO2 count for homogeneous and heterogeneous cases is pre- break-through and for the depletion cases are compared sented on Fig. 4. in Table 1. Table 1 Comparison of cumulative water production between depletion and CO injection case, at the moment of CO 2 2 break-through as a function of injection wells number Cumulative water production, m Number of injection Homogeneous model Heterogeneous model wells Depletion Injection Depletion Injection 4 99.47 19.93 5.93 0.32 6 561.38 98.07 12.58 0.34 8 2304.04 298.12 137.45 0.41 12 0.47 0.07 1.62 0.06 16 0.06 0.03 0.06 0.03 We also calculated the ultimate gas recovery factor for both injection cases at the moment of CO break-through and for the respective depletion cases both for homoge- Fig. 4 Change of reservoir pressure at the moment of CO break- neous and heterogeneous models (Table 2). through into production wells for homogeneous and heteroge- Table 2 neous reservoirs as a function of CO injection wells number Comparison of gas ultimate recovery factors between depletion and CO injection case, at the moment of CO 2 2 Looking at the concentrations of carbon dioxide in the res- break-through as a function of injection wells number ervoir at the moment of CO break-through into the first Ultimate gas recovery factor, frac. production well of heterogeneous model it is obvious (Fig. Number Homogeneous Heterogeneous 5) that intake capacity is proportional to the permeability of injection wells model model of the particular layer. The higher the permeability the Depletion Injection Depletion Injection faster break-through of injected CO2 is observed in heter- 4 40.01 41.48 36.71 39.30 ogeneous model in comparison to homogeneous one. 6 41.33 43.24 37.21 40.38 8 42.46 43.37 37.50 41.15 12 33.61 37.83 33.77 38.61 16 19.03 32.27 22.11 34.13 66 Management Systems in Production Engineering 2022, Volume 30, Issue 1 In case of homogeneous reservoir, increasing the injection DISCUSSION wells number from 4 to 8 results in maximum EUR of gas Evaluation of the efficiency of CO2 injection into gas-con- equal to 43.37% at the moment of CO2 break-through, but densate reservoir at the level of initial GWC for the control with further increase of the injector count quickly reduces of aquifer water encroachment into gas zone was per- the gas recovery due to very fast break-through of CO . formed with help of numerical simulation software from During the carbon dioxide injection into heterogeneous Schlumberger – ECLIPSE and Petrel. Results analysis of the reservoir, the maximum gas recovery of 41.15% is development indicators for homogeneous and heteroge- achieved with 8 injection wells. Further increase of the in- neous reservoirs allowed establishment of the key de- jection wells number to 16 leads to decrease of gas recov- pendencies. ery towards 34.13%. The respective plots for the change Simulation results showed that presence of layered reser- of gas recover factor with the number of wells for homo- voir heterogeneity requires higher number of injection geneous and heterogeneous models are shown on Fig. 6. wells (smaller well number) for efficient blockage of water encroachment from the aquifer in comparison to homo- geneous reservoir. This is due to the presence of high-per- a) meable layers that serve as a flow passage for water and injected CO2. It is also confirmed by calculations of period of production until the CO2 break-through to production wells when 4, 6 and 8 injection wells were used. The fur- ther increase of the number of injection wells from 8 to 16 in the case of heterogeneous reservoir increases the operational period of heterogeneous reservoir in compar- ison to homogeneous. This is caused by the blockage of water within the greater area and volume of high-perme- able layers by CO injection proving the high efficiency of the proposed method of CO injection at the initial level of GWC. CONCLUSIONS 1. Effect of CO injection wells number during injection at b) the level of initial GWC on the activity of aquifer system was studied with help of numerical simulation. Homoge- neous and heterogeneous gas-condensate reservoir cases were evaluated. The simulation results showed that increase of well count (reduction of well spacing) provides the decrease of aqui- fer water production in both homogeneous and heteroge- neous models in comparison to depletion cases. CO2 in- jection well count increase improves the spatial distribu- tion of CO , creating a better barrier against water en- croachment. The method application enables efficient water movement control from the aquifer into the gas- bearing zone. 2. Statistical result analysis derived the optimum number of injection wells for CO injection at the level of initial GWC for control of water encroachment from the aquifer Fig . 6 Gas recovery factor at the moment of CO breakthrough into production wells for homogeneous (a) and heterogeneous into the gas-bearing zone. The optimum number of CO2 (b) reservoirs as a function of CO injection wells number 2 injectors for homogeneous reservoir is equal to 6 and for heterogeneous – 8 wells. Based on the statistical results analysis, the necessary In case of high level of layer heterogeneity in the reservoir number of injection wells for the efficient blockage of aq- the higher number (smaller well spacing) is needed for ef- uifer water encroachment was defined. At the moment of ficient blockage of aquifer water encroachment in com- CO2 break-through the maximums number of injection parison to homogeneous reservoir with the same condi- wells is equal to 6.41 (6) for homogeneous reservoir and tions. 7.74 (8) for heterogeneous gas-condensate reservoir. The The gas ultimate recovery factor for optimum number of forecasted gas recovery factor for the stated above opti- injection wells in homogeneous model is equal 64.05% mum number of injection wells for homogeneous reser- and in heterogeneous model – 55.56%. voir is equal to 64.05% and 55.65% for heterogeneous one. S. MATKIVSKYI et al. – Impact of Reservoir Heterogeneity on the Control… 67 [14] A.T. Turta, S.S.K. Sim, A.K. 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[28] ECLIPSE* Technical Description. Version 2020.1 © Schlum- https://doi.org/10.3997/2214-4609.202010155 berger, 2020, pp. 1078. *Mark of Schlumberger. [29] Petrel* Help. Version 2019.2. *Mark of Schlumberger. [30] O.V. Burachok, D.V. Pershyn, S.V. Matkivskyy, Ye.S. Bikman, O.R. Kondrat. “Osoblyvosti vidtvorennya rivnyannya stanu hazokondensatnykh sumishey za umovy obmezhenoyi vkhidnoyi informatsiyi”, Rozvidka ta rozrobka naftovykh i hazovykh rodovyshch, № 1(74), 2020, pp. 82-88. https://doi.org/10.31471/1993-9973-2020- 1(74)-82-88 Serhii Matkivskyi ORCID ID: 0000-0002-4139-1381 JSC "Ukrgasvydobuvannya" Department of analysis and 3D modeling of hydrocarbon field Kudriavska Street, 26/28, 04053, Kyiv, Ukraine e-mail: matkivskij@gmail.com Oleksandr Burachok ORCID ID: 0000-0001-9935-3970 Ivano-Frankivsk National Technical University of Oil and Gas Karpatska St., 15, 76019, Ivano-Frankivsk, Ukraine e-mail: oburachok@googlemail.com http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Management Systems in Production Engineering de Gruyter

Impact of Reservoir Heterogeneity on the Control of Water Encroachment into Gas-Condensate Reservoirs during CO2 Injection

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Abstract

The paper evaluates application of CO injection for the control of water encroachment from the aquifer into gas- condensate reservoir under active natural water drive. The results of numerical simulations indicated that injec- tion of CO at the initial gas-water contact (GWC) level reduces the influx of water into gas-bearing zone and stabilizes the operation of production wells for a longer period. The optimum number of injection wells that leads to the maximum estimated ultimate recovery (EUR) factor was derived based on statistical analysis of the results. The maximum number of injection wells at the moment of CO break-through into production wells for homoge- neous reservoir is equal to 6.41 (6) and for heterogeneous – 7.74 (8) wells. Study results indicated that with the increase of reservoir heterogeneity, denser injection well pattern is needed for the efficient blockage of aquifer water influx in comparison to homogeneous one with the same conditions. Gas EUR factor for the maximum number of injection wells in homogenous model is equal 64.05% and in heterogeneous – 55.56%. Base depletion case the EURs are 51.72% and 49.44%, respectively. The study results showed the technological efficiency of CO injection into the producing reservoir at initial GWC for the reduction of water influx and improvement of ultimate hydrocarbon recovery. Key words: 3D reservoir model, numerical simulation, enhanced gas recovery (EGR), gas-condensate reservoir, water drive, trapped gas, carbon dioxide (CO ) injection INTRODUCTION With active aquifer water encroachment into gas-bearing Rational development of gas-condensate fields under the layers, production wells are being shut after relatively active water drive is based on systematic control of aqui- small cumulative gas production. One of the reasons is the fer water influx into the gas zone and water break- limitation of surface separator and gas treating facilities through to production wells [1, 2]. Majority of the gas that are originally not designed to handle huge volumes fields are represented by multi-stacked heterogeneous of water. Water shut-off well treatments and work-overs reservoirs [3]. During field development planning stage are usually not effective, since they require a very good geological information is limited, and therefore a special understanding of the reasons and paths of water influx. attention must be paid to the selection of well locations That is why control of edge aquifer water influx is the key for maximum drainage of the reservoirs [1]. Non-uniform task of reservoir management [5]. production well spacing with higher well-count in the The majority of gas production in Ukraine is coming from crest of the gas-bearing zone is very common. These leads partially or heavily depleted reservoirs with significant re- to selective water encroachment into the gas zone maining volumes of trapped gas. Research of the opti- through high-permeable rocks and most depleted layers mum ways of macro- and micro-trapped gas recovery is [4]. Selective water invasion causes decrease of gas rela- an important issue especially with constantly decreasing tive permeability and well productivity due to liquid load- quality and quantity of the hydrocarbon reserves. [6]. ing, when mixture velocity in the tubing falls below the critical value of 4-5 m/s. S. MATKIVSKYI et al. – Impact of Reservoir Heterogeneity on the Control… 63 RESEARCH OBJECTIVE factors of gas displacement [16]. Results of numerical sim- The complexity of remaining hydrocarbon in place recov- ulation studies where natural gas was displaced by CO2 ery under water drive is related to water encroachment are presented in [17, 18, 19]. According to the study [18], from the aquifer into gas-bearing zone and further to pro- gas production until the economic limit followed by CO duction wells. To minimize negative impact of formation injection leads to higher EUR than in the case when CO water on reservoir development by CO2 injection at initial injection starts from the beginning of reservoir develop- GWC requires additional research to maximize the ulti- ment. CO2 injection at the final stage is the most efficient mate recovery at minimum costs and negative impact on way to maximize the ultimate gas recovery [19] resulting environment. in EUR of 86% versus 66% in case when it was injected The objective of the research is to evaluate the influence from the beginning. of heterogeneity on the well pattern density (well spacing The presented results proved the efficiency of non-hydro- and well count) during CO2 injection at the level of initial carbon gas injection for EGR but they do not account for GWC for the purpose of water encroachment control into technical complexities of final development stage as well the gas-bearing zone using numerical simulation. as macro-heterogeneity of the reservoirs. The following tasks were solved during the research: The results of physical and mathematical modeling of nat- 1. Investigation of CO2 injection wells number on the ac- ural gas displacement by non-hydrocarbon gases [20, 21, tivity of aquifer and control of water encroachment 22] showed high technological efficiency of this EGR into homogeneous and heterogeneous gas-conden- method, resulting in higher recoveries and financial indi- sate reservoir. cators based on full-field projects implemented in Ukraine 2. Define the optimum number of CO2 injection wells and in other countries [23, 24, 25, 26, 27]. that leads to the maximum ultimate recovery factor in The water encroachment and break-through to produc- the presence of active water drive. tion wells is important issue for Ukrainian and interna- tional gas operators, and therefore, require additional in- LITERATURE REVIEW vestigation also by means of numerical simulation. Majority of hydrocarbon reservoirs is associated with ac- tive aquifer systems providing influx of water by bottom METHODOLOGY OF RESEARCH or edge water drive. Field data indicates that active water Influence of heterogeneity on water encroachment dur- drive can produce up to 70-85% of gas initially in place [7, ing carbon dioxide injection into different number of in- 8]. Due to the high value of remaining gas in presence of jection wells (well count and spacing) was studied by nu- water drive, there is a need in establishment of optimum merical simulation using Schlumberger software ECLIPSE ways for increase of EUR under such conditions. and Petrel [28, 29]. Synthetic homogeneous and hetero- Different methods and technologies for gas reservoir geneous anticline numerical gas-condensate reservoir management and water encroachment control were al- models were used in this study (Fig. 1). ready proposed. However, those solutions are normally non-economic and technologically non-feasible since they do not consider reservoir heterogeneity and spatial and vertical variation of petrophysical properties within the reservoir [9, 10]. In addition to that, there is a necessity to recover macro- and micro-trapped gas due to high de- mand of gas resources. Enhanced gas recovery is a very perspective technology that is based on the introduction of additional energy into the reservoir system from the surface. The results of nu- merous research studies and publications showed high ef- ficiency of non-hydrocarbon gas injection, for example, ni- trogen, carbon dioxide, flue gases and their mixtures, etc. [11, 12, 13]. Methane displacement and gas recovery factor is highly dependent on the type of the injected gas, reservoir het- erogeneity and mutual disposition of layers with different Fig. 1 Conceptual numerical reservoir simulation model show- permeabilities [14]. Molecular diffusion between two lay- ing gas saturation and position of production and injection ers of different permeabilities, partially reduces the nega- wells tive influence of heterogeneity. CO2 is known to have the best displacing properties in Simulated gas-condensate reservoir contains 800 mln. m comparison to nitrogen and flue gases [15], resulting in of gas in place at initial reservoir pressure of 35 MPa, res- EUR of 81.0-97.4%. Density and viscosity of carbon diox- ervoir temperature 358 K, net thickness 15.4 m, effective ide under reservoir conditions are significantly higher porosity 0.18, absolute permeability 8.65 mD, initial gas than those of hydrocarbon gases. High solubility of CO in 2 saturation 0.8. oil, gas-condensate and formation water are additional 64 Management Systems in Production Engineering 2022, Volume 30, Issue 1 𝑚𝑖𝑛 Effective porosity for the layers in heterogeneous model (from top to bottom) are equal 0.17, 0.22, 0.14 and 0.18 1 ∧ ∧ 𝑣 ,𝑎 {𝜎 = ∑[𝑓 (𝑎 , 𝑥 )− 𝑦 ]2}{𝑣 ,𝑎 } 𝑣 𝑎𝑣 𝑣 𝑣 𝑖 𝑖 𝑣 (Fig. 2), and respective values of absolute permeability 𝑛 − 𝑟 𝑣 𝑣 𝑖 =1 6.55, 17.64, 3.62 and 7.99. (1) 𝑚𝑖𝑛 1 ∧ ∧ [ ] } 𝜀 ,𝑎 {𝜎 = ∑ 𝑓 (𝑎 ,𝑥 )− 𝑦 2 {𝜀 ,𝑎 } 𝜀 𝑎𝜀 𝜀 𝜀 𝑖 𝑖 𝜀 𝑛 − 𝑟 𝜀 𝜀 𝑖 =1 ∧ ∧ 𝑓 (𝑎 ,𝑥 ) − 𝑓 (𝑎 ,𝑥 ) = 0 ⇒ 𝑥 (2) 𝑣 𝑣 ∗ 𝜀 𝜀 ∗ ∗ where: 2 2 𝜎 ,𝜎 −measure of dispersion efficiency 𝑓 та 𝑓 𝑣 𝜀 𝑟 ,𝑟 – number of evaluated parameters in the model 𝑣 𝜀 𝑓 (𝑎 ,𝑥 ) та 𝑓 (𝑎 ,𝑥 ) 𝑣 𝑣 і 𝜀 𝜀 і Parameters a , a , a ,…, a are selected by solving the 0 1 2 n above given system of equations. Obtained parameters Fig. 2 Porosity distribution in heterogeneous model of gas-con- are used in a function y=f(x) and in such a way the linear densate reservoir equations are obtained for accurate description of calcu- lated values. After that, the plots are built for particular Duration of CO injection into the gas-condensate reser- calculated data and approximated each one by straight voir at the level of initial GWC was equal 16 months. Pro- duction wells were controlled by constant gas rate of lines, with the crossing point representing the optimum 3 3 value. 50×10 m /d as well as CO2 injection wells. Production wells are located 400 m away from each other. Composi- RESULTS OF RESEARCH tional PVT model was used for proper calculation of com- Using 3D numerical model of gas-condensate reservoir plex phase behavior during fluid flow and CO injection the influence of heterogeneity on aquifer water encroach- [30, 31, 33]. ment during CO injection at the level of initial GWC was CO2 injection was evaluated using different number of in- studied. Based on the results, it was concluded, that the jection wells (4, 6, 8, 12, 16) equally spaced within the number of injection wells (well spacing) makes a signifi- outer boundary of the reservoir. The distance between cant impact on reservoir production performance. De- the injectors for each evaluated case were 1100, 800, 600, pendency between CO break-through time into produc- 400, 300 m respectively. Production from the reservoir tion wells and number of CO injectors is shown on Fig. 3. stopped at the moment when carbon dioxide broke- through into the last production well. In the case of CO injection, the break-through time to each production well was recorded in order to make a proper comparison to depletion case, in which production wells were stopped in exactly same times. Different number of injection wells leads to different well operation time until the moment of CO break-through. Therefore, for each CO injection case there was a respec- tive depletion case of different duration of production. Reservoir production performance was calculated and compared at the moment of CO2 break-through into one of the production wells based on the cumulative water production for the cases with different injection well count. Graphical method combined with statistical analysis was used for identification of optimum values of the key per- formance parameters in of results interpretation [32]. Fig. 3 Dependence of CO break-through time from number of Statistical analysis of function parameters f(x)=a +a x a 0 1 injection wells for homogeneous and heterogeneous reservoir chosen in such a way that difference of evaluated points During CO injection into homogeneous reservoir model (xi; yi) і = 1..𝑁 from the selected trend curve will be min- the duration of production well operation depends on imal. Parameters a0, a1 must be such that sum of square number of injection wells (well spacing) and respectively root deviations of observed values yi from calculated by a equal for 4 wells – 44 months, for 6 wells – 46 months, for function f(x)=a +a x will be minimal. After a few transfor- 0 1 8 wells – 47 months, for 12 wells – 40 months and for 16 mations, the system of two linear equations for the re- wells – 34 months. gression on unknown parameters was obtained. 𝑎𝜀 𝑎𝑣 S. MATKIVSKYI et al. – Impact of Reservoir Heterogeneity on the Control… 65 a) In a case of the model with layered heterogeneity the forecasted duration of production time until the moment of CO2 break-through depending on number of injectors: for 4 wells – 41 months, for 6 wells – 42 months, for 8 wells – 43 months, for 12 months – 41 months, for 16 wells – 36 months. It is necessary to point out that during CO2 injection, the production period from homogeneous model with mini- mum number of injectors (4 and 8) significantly longer b) than in the case of heterogeneous model. However, dur- ing future increase of the number of injectors the produc- tion period of homogeneous reservoir becomes shorter in comparison to heterogeneous. Analysis of reservoir pressure behavior at the time of CO break-through into production wells indicated that in- crease of injection wells number from 4 to 8 in case of het- erogeneous model leads to higher values of reservoir pressure in comparison to homogeneous one. However, Fig. 5 Carbon dioxide concentration in homogeneous (a) the further increase of injectors count is causing the re- and heterogeneous (b) models at the moment of break- duction of reservoir pressure in comparison to homoge- through into first production well for the case of 16 injectors neous case. Such relationship between reservoir pressure According to the simulation results, cumulative water pro- and number of injection wells is due to different produc- tion periods until the moment of CO break-through. The duction is reducing with the increase of number of CO2 in- change of reservoir pressure as a function of injection well jectors in comparison to depletion case. Calculated values of cumulative water production at the moment of CO2 count for homogeneous and heterogeneous cases is pre- break-through and for the depletion cases are compared sented on Fig. 4. in Table 1. Table 1 Comparison of cumulative water production between depletion and CO injection case, at the moment of CO 2 2 break-through as a function of injection wells number Cumulative water production, m Number of injection Homogeneous model Heterogeneous model wells Depletion Injection Depletion Injection 4 99.47 19.93 5.93 0.32 6 561.38 98.07 12.58 0.34 8 2304.04 298.12 137.45 0.41 12 0.47 0.07 1.62 0.06 16 0.06 0.03 0.06 0.03 We also calculated the ultimate gas recovery factor for both injection cases at the moment of CO break-through and for the respective depletion cases both for homoge- Fig. 4 Change of reservoir pressure at the moment of CO break- neous and heterogeneous models (Table 2). through into production wells for homogeneous and heteroge- Table 2 neous reservoirs as a function of CO injection wells number Comparison of gas ultimate recovery factors between depletion and CO injection case, at the moment of CO 2 2 Looking at the concentrations of carbon dioxide in the res- break-through as a function of injection wells number ervoir at the moment of CO break-through into the first Ultimate gas recovery factor, frac. production well of heterogeneous model it is obvious (Fig. Number Homogeneous Heterogeneous 5) that intake capacity is proportional to the permeability of injection wells model model of the particular layer. The higher the permeability the Depletion Injection Depletion Injection faster break-through of injected CO2 is observed in heter- 4 40.01 41.48 36.71 39.30 ogeneous model in comparison to homogeneous one. 6 41.33 43.24 37.21 40.38 8 42.46 43.37 37.50 41.15 12 33.61 37.83 33.77 38.61 16 19.03 32.27 22.11 34.13 66 Management Systems in Production Engineering 2022, Volume 30, Issue 1 In case of homogeneous reservoir, increasing the injection DISCUSSION wells number from 4 to 8 results in maximum EUR of gas Evaluation of the efficiency of CO2 injection into gas-con- equal to 43.37% at the moment of CO2 break-through, but densate reservoir at the level of initial GWC for the control with further increase of the injector count quickly reduces of aquifer water encroachment into gas zone was per- the gas recovery due to very fast break-through of CO . formed with help of numerical simulation software from During the carbon dioxide injection into heterogeneous Schlumberger – ECLIPSE and Petrel. Results analysis of the reservoir, the maximum gas recovery of 41.15% is development indicators for homogeneous and heteroge- achieved with 8 injection wells. Further increase of the in- neous reservoirs allowed establishment of the key de- jection wells number to 16 leads to decrease of gas recov- pendencies. ery towards 34.13%. The respective plots for the change Simulation results showed that presence of layered reser- of gas recover factor with the number of wells for homo- voir heterogeneity requires higher number of injection geneous and heterogeneous models are shown on Fig. 6. wells (smaller well number) for efficient blockage of water encroachment from the aquifer in comparison to homo- geneous reservoir. This is due to the presence of high-per- a) meable layers that serve as a flow passage for water and injected CO2. It is also confirmed by calculations of period of production until the CO2 break-through to production wells when 4, 6 and 8 injection wells were used. The fur- ther increase of the number of injection wells from 8 to 16 in the case of heterogeneous reservoir increases the operational period of heterogeneous reservoir in compar- ison to homogeneous. This is caused by the blockage of water within the greater area and volume of high-perme- able layers by CO injection proving the high efficiency of the proposed method of CO injection at the initial level of GWC. CONCLUSIONS 1. Effect of CO injection wells number during injection at b) the level of initial GWC on the activity of aquifer system was studied with help of numerical simulation. Homoge- neous and heterogeneous gas-condensate reservoir cases were evaluated. The simulation results showed that increase of well count (reduction of well spacing) provides the decrease of aqui- fer water production in both homogeneous and heteroge- neous models in comparison to depletion cases. CO2 in- jection well count increase improves the spatial distribu- tion of CO , creating a better barrier against water en- croachment. The method application enables efficient water movement control from the aquifer into the gas- bearing zone. 2. Statistical result analysis derived the optimum number of injection wells for CO injection at the level of initial GWC for control of water encroachment from the aquifer Fig . 6 Gas recovery factor at the moment of CO breakthrough into production wells for homogeneous (a) and heterogeneous into the gas-bearing zone. The optimum number of CO2 (b) reservoirs as a function of CO injection wells number 2 injectors for homogeneous reservoir is equal to 6 and for heterogeneous – 8 wells. Based on the statistical results analysis, the necessary In case of high level of layer heterogeneity in the reservoir number of injection wells for the efficient blockage of aq- the higher number (smaller well spacing) is needed for ef- uifer water encroachment was defined. At the moment of ficient blockage of aquifer water encroachment in com- CO2 break-through the maximums number of injection parison to homogeneous reservoir with the same condi- wells is equal to 6.41 (6) for homogeneous reservoir and tions. 7.74 (8) for heterogeneous gas-condensate reservoir. The The gas ultimate recovery factor for optimum number of forecasted gas recovery factor for the stated above opti- injection wells in homogeneous model is equal 64.05% mum number of injection wells for homogeneous reser- and in heterogeneous model – 55.56%. voir is equal to 64.05% and 55.65% for heterogeneous one. S. MATKIVSKYI et al. – Impact of Reservoir Heterogeneity on the Control… 67 [14] A.T. Turta, S.S.K. Sim, A.K. 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[28] ECLIPSE* Technical Description. Version 2020.1 © Schlum- https://doi.org/10.3997/2214-4609.202010155 berger, 2020, pp. 1078. *Mark of Schlumberger. [29] Petrel* Help. Version 2019.2. *Mark of Schlumberger. [30] O.V. Burachok, D.V. Pershyn, S.V. Matkivskyy, Ye.S. Bikman, O.R. Kondrat. “Osoblyvosti vidtvorennya rivnyannya stanu hazokondensatnykh sumishey za umovy obmezhenoyi vkhidnoyi informatsiyi”, Rozvidka ta rozrobka naftovykh i hazovykh rodovyshch, № 1(74), 2020, pp. 82-88. https://doi.org/10.31471/1993-9973-2020- 1(74)-82-88 Serhii Matkivskyi ORCID ID: 0000-0002-4139-1381 JSC "Ukrgasvydobuvannya" Department of analysis and 3D modeling of hydrocarbon field Kudriavska Street, 26/28, 04053, Kyiv, Ukraine e-mail: matkivskij@gmail.com Oleksandr Burachok ORCID ID: 0000-0001-9935-3970 Ivano-Frankivsk National Technical University of Oil and Gas Karpatska St., 15, 76019, Ivano-Frankivsk, Ukraine e-mail: oburachok@googlemail.com

Journal

Management Systems in Production Engineeringde Gruyter

Published: Mar 1, 2022

Keywords: 3D reservoir model; numerical simulation; enhanced gas recovery (EGR); gas-condensate reservoir; water drive; trapped gas; carbon dioxide (CO 2 ) injection

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