Status and Progress of Reactive Flow Simulations for Carbonate Reservoirs
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摘要: 酸岩反应流动模拟可用于指导油藏酸化施工，优选注入参数，从而以最小的成本最大程度地改善地层.国内外很多学者基于不同的方法建立了不同的模型对碳酸盐岩油藏酸岩反应流进行了研究，但这些模型尚缺乏科学的归纳与整理.以研究对象的空间尺度为依据，将现有的碳酸盐岩油藏酸岩反应流模型分为孔隙尺度模型、岩心尺度模型及井筒尺度模型，简要概括了每类模型的适用条件及其在应用中的局限性.结合本课题组在酸岩反应流模拟方面所做的工作，重点论述了岩心尺度模型的最新研究进展和发展趋势，给出了岩心尺度模型下一步的研究方向，主要包括：建立更接近地层实际的数学模型，如考虑酸化过程中存在的非达西流和地应力的影响；发展高效的数值算法，将模型的计算区域扩大到油藏尺度；将岩心尺度模型进行尺度升级，得到可以指导油藏酸化施工的优化参数.Abstract: Simulation results of the reactive flow of the acid in the rock generally are used to optimize the operation of reservoir acidization so that the optimal injection rate is determined to stimulate the formation effectively with minimum cost. Many models have been developed based on variety of methods to study the reactive flow in carbonate reservoir during acidizing. However, these models are still short of scientific classification and systematization. According to the spatial scale of the study objects, the existing models for reactive flow in carbonate rocks are classified into three types, namely pore-scale model, core-scale model and wellbore-scale model in this study. The assumptions and limitations of each type are summarized. Based on the works we have done in the simulation of reactive flow in carbonate rock, the latest research progress and development trend of the core-scale model are presented in this paper. Besides, suggestions on the future studies on core-scale model are proposed, which include developing more accurate mathematical model, such as considering the effect of non-Darcy flow and the influence of stress, developing the efficient numerical algorithms to extend the computational domain to the whole reservoir, upscaling the core-scale model to obtain the optimal operating parameters during carbonate reservoir acidization.
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Key words:
- carbonate reservoir /
- reactive flow /
- acidization /
- wormhole /
- numerical simulation /
- upscaling
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图 1 基于三维孔隙网络模型计算得到的溶蚀模式
不同注入速度对应的溶蚀模式：① 低注入速度；② 中等注入速度；③ 高注入速度；据Fredd and Fogler(1998)
Fig. 1. Dissolution patterns obtained from the numerical simulation using the 3-D network model
图 2 基于连续模型计算得到的溶蚀模式与岩心酸化实验得到的溶蚀模式对比
a.岩心实验结果，据Fredd and Fogler(1999)；b.数值模拟结果.溶蚀模式：① 面溶蚀；② 锥形溶蚀；③ 蚓孔；④ 分枝蚓孔；⑤ 均匀溶蚀
Fig. 2. Comparison of dissolution patterns obtained from numerical simulations using continuum model and linear flow experiments
图 3 基于非结构网格计算得到的二维径向流条件下的不同溶蚀模式
Fig. 3. Radial dissolution patterns obtained from the numerical simulation using the unstructured grid method
图 4 应用基于非结构网格的通用算法计算复杂边界形状条件下的反应溶蚀
Fig. 4. The simulation of reactive flow in carbonate rock with complex geometry using the general method based on unstructured grid
图 5 基于Forchheimer方程计算得到的三维条件下的不同溶蚀模式
Fig. 5. 3-D dissolution patterns obtained from simulation using Forchheimer equation
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[1] Bastami, A., Pourafshary, P., 2016.Development of a New Model for Carbonate Matrix Acidizing to Consider the Effects of Spent Acid.Journal of Energy Resources Technology, 138(5):052905.doi: 10.1115/1.4032728 [2] Bekibayev, T.T., Beisembetov, I.K., Assilbekov, B.K., et al., 2015.Study of the Impact of Reduced Permeability due to Near-Wellbore Damage on the Optimal Parameters of the Matrix Acidizing in Carbonate Rocks.SPE Annual Caspian Technical Conference & Exhibition, Assilbekov.doi:10.2118/177372-ms [3] Budek, A., Szymczak, P., 2012.Network Models of Dissolution of Porous Media.Physical Review E, 86(5):056318.doi: 10.1103/physreve.86.056318 [4] Buijse, M.A., 2000.Understanding Wormholing Mechanisms Can Improve Acid Treatments in Carbonate Formations.SPE Production & Facilities, 15(3):168-175.doi: 10.2118/65068-pa [5] Cohen, C.E., Ding, D.Y., Quintard, M., et al., 2007.A New Matrix Acidizing Simulator Based on a Large Scale Dual Porosity Approach.European Formation Damage Conference, Scheveningen, doi:10.2118/107755-ms [6] Cohen, C.E., Dong, C.L., Quintard, M., et al., 2008.From Pore Scale to Wellbore Scale:Impact of Geometry on Wormhole Growth in Carbonate Acidization.Chemical Engineering Science, 63(12):3088-3099.doi: 10.1016/j.ces.2008.03.021 [7] Daccord, G., Touboul, E., Lenormand, R., 1989.Carbonate Acidizing:Toward a Quantitative Model of the Wormholing Phenomenon.SPE Production Engineering, 4(1):63-68.doi: 10.2118/16887-pa [8] Deng, H., Molins, S., Steefel, C., et al., 2016.A 2.5D Reactive Transport Model for Fracture Alteration Simulation.Environmental Science & Technology, 50(14):7564-7571.doi: 10.1021/acs.est.6b02184 [9] Detwiler, R.L., Rajaram, H., 2007.Predicting Dissolution Patterns in Variable Aperture Fractures:Evaluation of an Enhanced Depth-Averaged Computational Model.Water Resources Research, 43(4):W04403.doi: 10.1029/2006wr005147 [10] Dong, C.L., Zhu, D., Hill, A.D., 2001.Acid Penetration in Natural Fracture Networks.SPE European Formation Damage Conference, Hague.doi:10.2118/68927-ms [11] Dong, C.L., Zhu, D., Hill, A.D., 2002a.Acidizing in Naturally Fractured Carbonate Reservoirs.SPE/DOE Improved Oil Recovery Symposium, Tulsa.doi:10.2118/75252-ms [12] Dong, C.L., Zhu, D., Hill, A.D., 2002b.Modeling of the Acidizing Process in Naturally Fractured Carbonates.SPE Journal, 7(4):400-408.doi: 10.2118/81816-pa [13] Economides, M.J., Nolte, K.G., 2000.Reservoir Stimulation.Wiley, Chichester. https://www.osti.gov/scitech/biblio/5112212 [14] Fang, Y., Xie, S.Y., He, Z.L., et al., 2016.Thin Section Based Geochemical Dissolution Experiments of Ooid Carbonates.Earth Science, 41(5):779-791 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-DQKX201605005.htm [15] Fredd, C.N., Fogler, H.S., 1998.Influence of Transport and Reaction on Wormhole Formation in Porous Media.AIChE Journal, 44(9):1933-1949.doi: 10.1002/aic.690440902 [16] Fredd, C.N., Fogler, H.S., 1999.Optimum Conditions for Wormhole Formation in Carbonate Porous Media:Influence of Transport and Reaction.SPE Journal, 4(3):196-205.doi: 10.2118/56995-pa [17] Fredd, C.N., Miller, M.J., 2000.Validation of Carbonate Matrix Stimulation Models.SPE International Symposium on Formation Damage Control, Lafayette.doi:10.2118/58713-ms [18] Frick, T.P., Kurmayr, M., Economides, M.J., 1994.An Improved Modeling of Fractal Patterns in Matrix Acidizing and Their Impact on Well Performance.SPE Production & Facilities, 9(1):61-68.doi: 10.2118/23789-pa [19] Gdanski, R., 1999.A Fundamentally New Model of Acid Wormholing in Carbonates.SPE European Formation Damage Conference, Hague.doi:10.2118/54719-ms [20] Ghommem, M., Zhao, W.S., Dyer, S., et al., 2015.Carbonate Acidizing:Modeling, Analysis, and Characterization of Wormhole Formation and Propagation.Journal of Petroleum Science and Engineering, 131:18-33.doi: 10.1016/j.petrol.2015.04.021 [21] Golfier, F., Zarcone, C., Bazin, B., et al., 2002.On the Ability of a Darcy-Scale Model to Capture Wormhole Formation during the Dissolution of a Porous Medium.Journal of Fluid Mechanics, 457:213-254.doi: 10.1017/s0022112002007735 [22] Hanna, R.B., Rajaram, H., 1998.Influence of Aperture Variability on Dissolutional Growth of Fissures in Karst Formations.Water Resources Research, 34(11):2843-2853.doi: 10.1029/98wr01528 [23] Hill, A.D., Zhu, D., Dong, C., Dong, C.L., et al., 2001.Computer Model Predicts Matrix Acidizing of Naturally Fractured Carbonate.Journal of Petroleum Technology, 53(10):20-25.doi: 10.2118/1001-0020-jpt [24] Hoefner, M.L., Fogler, H.S., 1988.Pore Evolution and Channel Formation during Flow and Reaction in Porous Media.AIChE Journal, 34(1):45-54.doi: 10.1002/aic.690340107 [25] Huang, T.P., Hill, A.D., Schechter, R.S., 1997.Reaction Rate and Fluid Loss:The Keys to Wormhole Initiation and Propagation in Carbonate Acidizing.SPE Journal, 5(3):287-292.doi: 10.2118/37312-ms [26] Huang, T.P., Zhu, D., Hill, A.D., 1999.Prediction of Wormhole Population Density in Carbonate Matrix Acidizing.SPE European Formation Damage Conference, Hague.doi:10.2118/54723-ms [27] Huang, Z.Q., Yan, X., Yao, J., 2014.A Two-Phase Flow Simulation of Discrete-Fractured Media Using Mimetic Finite Difference Method.Communications in Computational Physics, 16(3):799-816.doi: 10.4208/cicp.050413.170314a [28] Hung, K.M., Hill, A.D., Sepehrnoori, K., 1989.A Mechanistic Model of Wormhole Growth in Carbonate Matrix Acidizing and Acid Fracturing.Journal of Petroleum Technology, 41(1):59-66.doi: 10.2118/16886-pa [29] Izgec, O., Zhu, D., Hill, A.D., 2010.Numerical and Experimental Investigation of Acid Wormholing during Acidization of Vuggy Carbonate Rocks.Journal of Petroleum Science and Engineering, 74(1-2):51-66.doi: 10.1016/j.petrol.2010.08.006 [30] Kalia, N., 2008.Modeling and Analysis of Reactive Dissolution of Carbonate Rocks (Dissertation).University of Houston, Houston. http://www.amazon.in/Modeling-Analysis-Reactive-Dissolution-Carbonate/dp/1243804734 [31] Kalia, N., Balakotaiah, V., 2007.Modeling and Analysis of Wormhole Formation in Reactive Dissolution of Carbonate Rocks.Chemical Engineering Science, 62(4):919-928.doi: 10.1016/j.ces.2006.10.021 [32] Kalia, N., Balakotaiah, V., 2009.Effect of Medium Heterogeneities on Reactive Dissolution of Carbonates.Chemical Engineering Science, 64(2):376-390.doi: 10.1016/j.ces.2008.10.026 [33] Kalia, N., Balakotaiah, V., 2010.Wormholing in Perforated Completions.SPE International Symposium and Exhibiton on Formation Damage Control, Lafayette.doi:10.2118/127347-ms [34] Kalia, N., Glasbergen, G., 2009.Wormhole Formation in Carbonates under Varying Temperature Conditions.8th European Formation Damage Conference, Scheveningen.doi:10.2118/121803-ms [35] Kalia, N., Glasbergen, G., 2010.Fluid Temperature as a Design Parameter in Carbonate Matrix Acidizing.SPE Production and Operations Conference and Exhibition, Tunisia.doi:10.2118/135654-ms [36] Kang, Q.J., Lichtner, P.C., Viswanathan, H.S., et al., 2009.Pore Scale Modeling of Reactive Transport Involved in Geologic CO2 Sequestration.Transport in Porous Media, 82(1):197-213.doi: 10.1007/s11242-009-9443-9 [37] Kou, J.S., Sun, S.Y., Wu, Y.Q., 2016.Mixed Finite Element-Based Fully Conservative Methods for Simulating Wormhole Propagation.Computer Methods in Applied Mechanics and Engineering, 298:279-302.doi: 10.1016/j.cma.2015.09.015 [38] Liu, M., Zhang, S.C., Mou, J.Y., 2012.Effect of Normally Distributed Porosities on Dissolution Pattern in Carbonate Acidizing.Journal of Petroleum Science and Engineering, 94-95:28-39.doi: 10.1016/j.petrol.2012.06.021 [39] Liu, M., Zhang, S.C., Mou, J.Y., et al., 2013.Wormhole Propagation Behavior under Reservoir Condition in Carbonate Acidizing.Transport in Porous Media, 96(1):203-220.doi: 10.1007/s11242-012-0084-z [40] Liu, N.Z., Liu, M., 2016.Simulation and Analysis of Wormhole Propagation by VES Acid in Carbonate Acidizing.Journal of Petroleum Science and Engineering, 138:57-65.doi: 10.1016/j.petrol.2015.12.011 [41] Liu, P.Y., Yao, J., Couples, G.D., et al., 2017a.Modeling and Simulation of Wormhole Formation during Acidization of Fractured Carbonate Rocks.Journal of Petroleum Science and Engineering, 154:284-301.doi: 10.1016/j.petrol.2017.04.040 [42] Liu, P.Y., Yao, J., Couples, G.D., et al., 2017b.Numerical Modelling and Analysis of Reactive Flow and Wormhole Formation in Fractured Carbonate Rocks.Chemical Engineering Science, 172:143-157.doi: 10.1016/j.ces.2017.06.02717.04.040 [43] Liu, P.L., Xue, H., Zhao, L.Q., et al., 2016.Simulation of 3D Multi-Scale Wormhole Propagation in Carbonates Considering Correlation Spatial Distribution of Petrophysical Properties.Journal of Natural Gas Science and Engineering, 32:81-94.doi: 10.1016/j.jngse.2016.04.014 [44] Liu, X.H., Ormond, A., Bartko, K., et al., 1997.A Geochemical Reaction-Transport Simulator for Matrix Acidizing Analysis and Design.Journal of Petroleum Science and Engineering, 17(1-2):181-196.doi: 10.1016/s0920-4105(96)00064-2 [45] Maheshwari, P., Balakotaiah, V., 2013a.3D Simulation of Carbonate Acidization with HCl:Comparison with Experiments.SPE Production and Operations Symposium, Oklahoma.doi:10.2118/164517-ms [46] Maheshwari, P., Balakotaiah, V., 2013b.Comparison of Carbonate HCl Acidizing Experiments with 3D Simulations.SPE Production & Operations, 28(4):402-413.doi: 10.2118/164517-pa [47] Maheshwari, P., Maxey, J.E., Balakotaiah, V., 2014.Simulation and Analysis of Carbonate Acidization with Gelled and Emulsified Acids.Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi.doi:10.2118/171731-ms [48] Maheshwari, P., Maxey, J.E., Balakotaiah, V., 2015.Reactive-Dissolution Modeling and Experimental Comparison of Wormhole Formation in Carbonates with Gelled and Emulsified Acids.SPE Production & Operations, 31(2):103-119.doi: 10.2118/171731-pa [49] Maheshwari, P., Ratnakar, R.R., Kalia, N., et al., 2013.3-D Simulation and Analysis of Reactive Dissolution and Wormhole Formation in Carbonate Rocks.Chemical Engineering Science, 90:258-274.doi: 10.1016/j.ces.2012.12.032 [50] Menke, H.P., Bijeljic, B., Andrew, M.G., et al., 2015.Dynamic Three-Dimensional Pore-Scale Imaging of Reaction in a Carbonate at Reservoir Conditions.Environmental Science & Technology, 49(7):4407-4414.doi: 10.1021/es505789f [51] O'Brien, G.S., Bean, C.J., McDermott, F., 2003.Numerical Investigations of Passive and Reactive Flow through Generic Single Fractures with Heterogeneous Permeability.Earth and Planetary Science Letters, 213(3-4):271-284.doi: 10.1016/s0012-821x(03)00342-x [52] Panga, M.K.R., Balakotaiah, V., Ziauddin, M., 2002.Modeling, Simulation and Comparison of Models for Wormhole Formation during Matrix Stimulation of Carbonates.SPE Annual Technical Conference and Exhibition, San Antonio.doi:10.2118/77369-ms [53] Panga, M.K.R., Ziauddin, M., Balakotaiah, V., 2005.Two-Scale Continuum Model for Simulation of Wormholes in Carbonate Acidization.AIChE Journal, 51(12):3231-3248.doi: 10.1002/aic.10574 [54] Panga, M.K.R., Ziauddin, M., Gandikota, R., et al., 2004.A New Model for Predicting Wormhole Structure and Formation in Acid Stimulation of Carbonates.SPE International Symposium and Exhibition on Formation Damage Control, Lafayette.doi:10.2118/86517-ms [55] Pichler, T., Frick, T.P., Economides, M.J., et al., 1992.Stochastic Modeling of Wormhole Growth in Carbonate Acidizing with Biased Randomness.European Petroleum Conference, Cannes.doi:10.2118/25004-ms [56] Qian, H.T., Sun, Q., Wang, S.J., 2014.Effects of Geo-Stress on Carbonate Dissolution and Karst Evolution.Earth Science, 39(7):896-904 (in Chinese with English abstract). [57] Ratnakar, R.R., Kalia, N., Balakotaiah, V., 2012.Carbonate Matrix Acidizing with Gelled Acids:An Experiment-Based Modeling Study.SPE International Production and Operations Conference & Exhibition, Doha.doi:10.2118/154936-ms [58] Ratnakar, R.R., Kalia, N., Balakotaiah, V., 2013.Modeling, Analysis and Simulation of Wormhole Formation in Carbonate Rocks with in Situ Cross-Linked Acids.Chemical Engineering Science, 90(10):179-199.doi: 10.1016/j.ces.2012.12.019 [59] Safari, A., Dowlatabad, M.M., Hassani, A., et al., 2016.Numerical Simulation and X-Ray Imaging Validation of Wormhole Propagation during Acid Core-Flood Experiments in a Carbonate Gas Reservoir.Journal of Natural Gas Science and Engineering, 30:539-547.doi: 10.1016/j.jngse.2016.02.036 [60] Szymczak, P., Ladd, A.J.C., 2009.Wormhole Formation in Dissolving Fractures.Journal of Geophysical Research, 114(B6):258-266.doi: 10.1029/2008jb006122 [61] Tabasy, M., Rashidi, F., 2015.A Qualitative Simulation of a Face Dissolution Pattern in Acidizing Process Using Rotating Disk Apparatus for a Carbonate Gas Reservoir.Journal of Natural Gas Science and Engineering, 26:1460-1469.doi: 10.1016/j.jngse.2015.08.014 [62] Tansey, J., 2014.Pore-Network Modeling of Carbonate Acidization.SPE Annual Technical Conference and Exhibition, Amsterdam.doi:10.2118/173472-stu [63] Tansey, J., Balhoff, M.T., 2016.Pore Network Modeling of Reactive Transport and Dissolution in Porous Media.Transport in Porous Media, 113(2):303-327.doi: 10.1007/s11242-016-0695-x [64] Upadhyay, V.K., Szymczak, P., Ladd, A.J.C., 2015.Initial Conditions or Emergence:What Determines Dissolution Patterns in Rough Fractures?Journal of Geophysical Research:Solid Earth, 120(9):6102-6121.doi: 10.1002/2015jb012233 [65] Wang, Y., Hill, A.D., Schechter, R.S., 1993.The Optimum Injection Rate for Matrix Acidizing of Carbonate Formations.SPE Annual Technical Conference and Exhibition, Houston.doi:10.2118/26578-ms [66] Wang, Y.Y., Yao, J., Huang, Z.Q., 2012.Discrete Medium Modeling Method for Fractured-Vuggy Carbonate Reservoir.Xinjinag Petroleum Geology, 33(2):225-229 (in Chinese with English abstract). http://en.cnki.com.cn/Article_en/CJFDTOTAL-XJSD201202029.htm [67] Wu, Y.Q., Salama, A., Sun, S.Y., 2015.Parallel Simulation of Wormhole Propagation with the Darcy-Brinkman-Forchheimer Framework.Computers and Geotechnics, 69:564-577.doi: 10.1016/j.compgeo.2015.06.021 [68] Yan, X., Huang, Z.Q., Yao, J., et al., 2016.An Efficient Embedded Discrete Fracture Model Based on Mimetic Finite Difference Method.Journal of Petroleum Science and Engineering, 145:11-21.doi: 10.1016/j.petrol.2016.03.013 [69] Yao, J., Huang, Z.Q., Li, Y.J., et al., 2010.Discrete Fracture-Vug Network Model for Modeling Fluid Flow in Fractured Vuggy Porous Media.International Oil and Gas Conference and Exhibition, Beijing, 96.doi:10.2118/130287-ms [70] Yao, J., Huang, Z.Q., Wang, Z.S., et al., 2010.Mathematical Model of Fluid Flow in Fractured Vuggy Reservoirs Based on Discrete Fracture-Vug Network.Acta Petrolei Sinica, 31(5):15-20 (in Chinese with English abstract). http://www.syxb-cps.com.cn/EN/abstract/abstract2034.shtml [71] Yao, J., Liu, P.Y., Huang, Z.Q., et al., 2017.Analysis of Influencing Factors on the Optimum Stimulation Conditions of the Acidizing Treatment in Carbonate Reservoirs.Scientia Sinica Technologica, 47:1-16 (in Chinese with English abstract). doi: 10.1360/N092016-00296 [72] Yuan, T., Ning, Y., Qin, G., 2016.Numerical Modeling and Simulation of Coupled Processes of Mineral Dissolution and Fluid Flow in Fractured Carbonate Formations.Transport in Porous Media, 114(3):747-775.doi: 10.1007/s11242-016-0742-7 [73] 方旸, 谢淑云, 何治亮, 等, 2016.基于岩石薄片的鲕粒碳酸盐岩地球化学溶蚀.地球科学, 41(5): 779-791. http://earth-science.net/WebPage/Article.aspx?id=3292 [74] 钱海涛, 孙强, 王思敬, 2014.地应力对碳酸盐岩溶解和岩溶发育的影响.地球科学, 39(7): 896-904. http://earth-science.net/WebPage/Article.aspx?id=2890 [75] 王月英, 姚军, 黄朝琴, 2012.缝洞型碳酸盐岩储集层离散介质模型的建模方法.新疆石油地质, 33(2): 225-229. http://www.cnki.com.cn/Article/CJFDTOTAL-XJSD201202029.htm [76] 姚军, 黄朝琴, 王子胜, 等, 2010.缝洞型油藏的离散缝洞网络流动数学模型.石油学报, 31(5): 15-20. http://www.cnki.com.cn/Article/CJFDTOTAL-SYXB201005023.htm [77] 姚军, 刘丕养, 黄朝琴, 等, 2017.碳酸盐岩油藏酸化施工最优注入条件影响因素分析.中国科学:技术科学, 47: 1-16. http://www.cnki.com.cn/Article/CJFDTOTAL-JEXK201707003.htm -
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