A Computational Navier-Stokes Fluid-Dynamics-Simulation Study of Wormhole Propagation in Carbonate-Matrix Acidizing and Analysis of Factors Influencing the Dissolution Process
- Olatokunbo O. Akanni (Texas A&M University) | Hisham A. Nasr-El-Din (Texas A&M University) | Deepak Gusain (Carbo Ceramics Incorporated)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2017
- Document Type
- Journal Paper
- 2,049 - 2,066
- 2017.Society of Petroleum Engineers
- modeling, carbonates, efficeincy curves, vugs, acidizing
- 2 in the last 30 days
- 347 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 5.00|
|SPE Non-Member Price:||USD 35.00|
This study demonstrates the application of an alternative numerical-simulation approach to effectively describe the flow field in a two-scale carbonate-matrix-acidizing model. The modified model accurately captures the dissolution regimes that occur during carbonate-matrix acidizing. Sensitivity tests were performed on the model to compare the output with experimental observations and previous two-scale models in the literature. A nonlinear reaction-kinetics model for alternative acidizing fluids is also introduced.
In this work, the fluid-field flow is described by the Navier-Stokes momentum approach instead of Darcy’s law or the Darcy-Brinkman approach used in previous two-scale models. The present model is implemented by means of a commercial computational-fluid- dynamics (CFD) package to solve the momentum, mass-conservation, and species-transport equations in Darcy scale. The software is combined with functions and routines written in the C programming language to solve the porosity-evolution equation, update the pore-scale parameters at every timestep in the simulation, and couple the Darcy and pore scales.
The output from the model simulations is consistent with experimental observations, and the results from the sensitivity tests performed are in agreement with previously developed two-scale models with the Darcy approach. The simulations at very-high injection rates with this model require less computational time than models developed with the Darcy approach. The results from this model show that the optimal injection rate obtained in laboratory coreflood experiments cannot be directly translated for field applications because of the effect of flow geometry and medium dimensions on the wormholing process. The influence of the reaction order on the optimal injection rate and pore volumes (PVs) of acid required to reach breakthrough is also demonstrated by simulations run to test the applicability of the model for acids with nonlinear kinetics in reaction with calcite.
The new model is computationally less expensive than previous models with the Darcy-Brinkman approach, and simulations at very-high injection rates with this model require less computational time than Darcy-based models. Furthermore, the possibility of extending the two-scale model for acid/calcite reactions with more-complex chemistry is shown by means of the introduction of nonlinear kinetics in the reaction equation.
|File Size||2 MB||Number of Pages||18|
ANSYS. 2015. ANSYS Fluent, Version 15.0. Canonsburg, Pennsylvania: ANSYS, Incorporated.
Akanni, O. O. and Nasr-El-Din, H. A. 2015. The Accuracy of Carbonate Matrix-Acidizing Models in Predicting Optimal Injection and Wormhole Propagation Rates. Presented at the SPE Middle East Oil & Gas Show and Conference, Manama, Bahrain, 8–11 March. SPE-172575-MS. https://doi.org/10.2118/172575-MS.
Balakotaiah, V. and West, D. H. 2002 Shape Normalization and Analysis of Mass Transfer Controlled Regime in Catalytic Monoliths. Chem. Eng. Sci. 57 (8): 1269–1286. https://doi.org/10.1016/S0009-2509(02)00059-3.
Bazin, B. 2001. From Matrix Acidizing to Acid Fracturing: A Laboratory Evaluation of Acid/Rock Interactions. SPE Prod & Fac 16 (1): 22–29. SPE-66566-PA. https://doi.org/10.2118/66566-PA.
Bryant, S. L., Mellor, D. W., and Cade, C. A. 1993. Physically Representative Network Models of Transport in Porous Media. AIChE J. 39 (3): 387–396. https://doi.org/10.1002/aic.690390303.
Buijse, M. A. 2000. Understanding Wormholing Mechanisms Can Improve Acid Treatments in Carbonate Formations. SPE Prod & Oper 15 (3): 168–175. SPE-38166-MS. https://doi.org/10.2118/38166-MS.
Buijse, M. A. and Glasbergen, G. 2005. A Semi-Empirical Model to Calculate Wormhole Growth in Carbonate Acidizing. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, 9–12 October. SPE-96892-MS. https://doi.org/10.2118/96892-MS.
Carman, P. C. 1937. Fluid Flow Through Granular Beds. Transactions - Institution of Chemical Engineers 15: 150–166.
Cohen, C. E., Ding, D., Quintard, M. et al. 2008. From Pore Scale to Wellbore Scale: Impact of Geometry on Wormhole Growth in Carbonate Acidization. Chem. Eng. Sci. 63 (12) 3088–3099. https://doi.org/10.1016/j.ces.2008.03.021.
Daccord, G., Touboul, E., and Lenormand, R. 1989. Carbonate Acidizing: Toward a Quantitative Model of the Wormholing Phenomenon. SPE Prod Eng 4 (1): 63–68. SPE-16887-PA. https://doi.org/10.2118/16887-PA.
De Oliveira, T. J. L., De Melo, A. R., Oliveira, J. A. et al. 2012. Numerical Simulation of the Acidizing Process and PVBT Extraction Methodology Including Porosity/Permeability and Mineralogy Heterogeneity. Presented at the SPE International Symposium and Exhibition on Formation Damage Control. Lafayette, Louisiana, 15–17 January. SPE-151823-MS. https://doi.org/10.2118/151823-MS.
Fatt, I. 1956. The Network Model of Porous Media. Published in Petroleum Transactions, AIME, Vol. 207, 144–181. SPE-574-G.
Fredd, C. N. and Fogler, H. S. 1998. Influence of Transport and Reaction on Wormhole Formation in Porous Media. AIChE J. 44 (9): 1933–1949. https://doi.org/10.1002/aic.690440902.
Fredd, C. N. and Fogler, H. S. 1999. Optimal Conditions for Wormhole Formation in Carbonate Porous Media: Influence of Transport and Reaction. SPE J. 4 (3): 196–205. SPE-56995-PA. https://doi.org/10.2118/56995-PA.
Fredd, C. N. and Miller, M. J. 2000. Validation of Carbonate Matrix Stimulation Models. Presented at the SPE International Symposium on Formation Damage Control, Lafayette, Louisiana, 23–24 February. SPE-58713-MS. https://doi.org/10.2118/58713-MS.
Frick, T. P., Kurmayr, M., and Economides, M. J. 1994. An Improved Modeling Of Fractal Patterns in Matrix Acidizing and Their Impact on Well Performance. SPE Prod & Oper 9 (1): 61–68. SPE-23789-PA. https://doi.org/10.2118/23789-PA.
Furui, K., Burton, R., Burkhead, D. et al. 2012. A Comprehensive Model of High-Rate Matrix-Acid Stimulation for Long Horizontal Wells in Carbonate Reservoirs: Part I–ScalingUp Core-Level Acid Wormholing to Field Treatments. SPE J. 17 (1): 271–279. SPE-134265-PA. https://doi.org/10.2118/134265-PA.
Ghommem, M. and Brady, B. 2015. Multifidelity Modeling and Analysis of Matrix Acidizing under Radial Flow Conditions. Oral presentation given at the International Petroleum Technology Conference, Doha, Qatar, 6–9 December.
Ghommem, M., Zhao, W., Dyer, S. et al. 2015. Carbonate Acidizing: Modeling, Analysis, and Characterization of Wormhole Formation and Propagation. J. Pet. Sci. Eng. 131 (July): 18–33. https://doi.org/10.1016/j.petrol.2015.04.021.
Glasbergen, G., Kalia, N., and Talbot, M. S. 2009. The Optimal Injection Rate for Wormhole Propagation: Myth or Reality? Presented at the 8th European Formation Damage Conference, Scheveningen, The Netherlands, 27–29 May. SPE-121464-MS. https://doi.org/10.2118/121464-MS.
Golfier, F., Zarcone, C., Bazin, B. et al. 2002. On the Ability of a Darcy-Scale Method Model To Capture Wormhole Formation During the Dissolution of a Porous Medium. J. Fluid Mech. 457 (April): 213–254. https://doi.org/10.1017/S0022112002007735.
Gupta, N. and Balakotaiah, V. 2001. Heat and Mass Transfer Coefficients in Catalytic Monoliths. Chem. Eng. Sci. 56 (16): 4771–4786. https://doi.org/10.1016/S0009-2509(01)00134-8.
Hoefner, M. L. and Fogler, H. S. 1988. Pore Evolution and Channel Formation During Flow and Reaction in Porous Media. AIChE J. 34 (1): 45–54. https://doi.org/10.1002/aic.690340107.
Huang, T., Hill, A. D., and Schechter, R. S. 1997. Reaction Rate and Fluid Loss: The Keys to Wormhole Initiation and Propagation in Carbonate Acidizing. Presented at the International Symposium on Oilfield Chemistry, Houston, 18–21 February. SPE-37312-MS. https://doi.org/10.2118/37312-MS.
Hung, K. M., Hill, A. D., and Sepehrnoori, K. 1989. A Mechanistic Model of Wormhole Growth in Carbonate Matrix Acidizing and Acid Fracturing. J Pet Technol 41 (1): 59–66. SPE-16886-PA. https://doi.org/10.2118/16886-PA.
Izgec, O., Zhu, D., and Hill, A. D. 2010. Numerical and Experimental Investigation of Acid Wormholing during Acidization of Vuggy Carbonate Rocks. J. Pet. Sci. Eng. 74 (1): 51–66. https://doi.org/10.1016/j.petrol.2010.08.006.
Kalia, N. and Balakotaiah, V. 2007. Modeling and Analysis of Wormhole Formation in Reactive Dissolution of Carbonate Rocks. Chem. Eng. Sci. 62 (4): 919–928. https://doi.org/10.1016/j.ces.2006.10.021.
Kalia, N. and Balakotaiah, V. 2009. Effect of Medium Heterogeneities on Reactive Dissolution of Carbonates. Chem. Eng. Sci. 64 (2): 376–390. https://doi.org/10.1016/j.ces.2008.10.026.
Kalia, N. and Glasbergen, G. 2009. Wormhole Formation in Carbonates under Varying Temperature Conditions. Presented at the 8th SPE European Formation Damage Conference. Scheveningen, The Netherlands, 27–29 May. SPE-121803-MS. https://doi.org/10.2118/121803-MS.
Liu, M., Zhang, S., and Mou, J. 2012. Effect of Normally Distributed Porosities on Dissolution Pattern in Carbonate Acidizing. J. Pet. Sci. Eng. 94–95 (September): 28–39. https://doi.org/10.1016/j.petrol.2012.06.021.
Liu, X., Ormond, A., Bartko, K. et al. 1997. A Geochemical Reaction-Transport Simulator for Matrix Acidizing Analysis and Design. J. Pet. Sci. Eng. 17 (1–2): 181–196. https://doi.org/10.1016/S0920-4105(96)00064-2.
Maheshwari, P. and Balakotaiah, V. 2013. Comparison of Carbonate HCl Acidizing Experiments with 3D Simulations. SPE Prod & Oper 28 (4): 402–413. SPE-164517-PA. https://doi.org/10.2118/164517-PA.
Maheshwari, P., Maxey, J., and Balakotaiah, V. 2014. Simulation and Analysis of Carbonate Acidization with Gelled and Emulsified Acids. Presented at the AbuDhabi International PetroleumExhibition and Conference, Abu Dhabi, 10–13 November. SPE-171731-MS. https://doi.org/10.2118/171731-MS.
Maheshwari, P., Ratnakar, R. R., Kalia, N. et al. 2012. 3-D Simulation and Analysis of Reactive Dissolution and Wormhole Formation in Carbonate Rocks. Chem. Eng. Sci. 90 (7 March): 258–274. https://doi.org/10.1016/j.ces.2012.12.032.
Panga, M. K. R., Ziauddin, M., and Balakotaiah, V. 2005. Two-Scale Continuum Model for Simulation of Wormholes in Carbonate Acidization. AIChE J. 51 (12): 3231–3248. https://doi.org/10.1002/aic.10574.
Panga, M. K. R., Balakotaiah, V., and Ziauddin, M. 2002. Modeling, Simulation and Comparison of Models for Wormhole Formation during Matrix Stimulation of Carbonates. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 29 September–2 October. SPE-77369-MS. https://doi.org/10.2118/77369-MS.
Ratnakar, R. R., Kalia, N., and Balakotaiah, V. 2012. Carbonate Matrix Acidizing with Gelled Acids: An Experiment-Based Modeling Study. Presented at the SPE International Production and Operations Conference and Exhibition, Doha, Qatar, 14–16 February. SPE-154936-MS. https://doi.org/10.2118/154936-MS.
Rose, W. 1957. Studies of Waterflood Performance: III. Use of Network Models. Illinois State Geological Survey, Urbana, Illinois.
Rowan, G. 1959. Theory of Acid Treatment of Calcite Formations. J. Inst. Petrol. 45 (431).
Sahimi, M., Gavalas, G. R., and Tsotsis, T. T. 1990. Statistical and Continuum Models of Fluid-Solid Reactions in Porous Media. Chem. Eng. Sci. 45 (6): 1443–1502. https://doi.org/10.1016/0009-2509(90)80001-u.
Schechter, R. S. 1992. Oil Well Stimulation. New York City: Prentice Hall.
Schechter, R. S. and Gidley, J. L. 1969. The Change in Pore Size Distribution from Surface Reactions in Porous Media. AIChE J. 15 (3): 339–350. https://doi.org/10.1002/aic.690150309.
Simon, R. and Kelsey, F. J. 1972. The Use of Capillary Tube Networks in Reservoir Performance Studies: II. Effect of Heterogeneity and Mobility on Miscible Displacement Efficiency. SPE J. 12 (4): 345–351. SPE-3482-PA. https://doi.org/10.2118/3482-PA.
Thompson, K. E. and Fogler, H. S. 1997. Modeling Flow in Disordered Packed Beds from Pore-Scale Fluid Mechanics. AIChE J. 43 (6): 1377–1389. https://doi.org/10.1002/aic.690430602.
Vik, B., Djurhuus, K., Spildo, K. et al. 2007. Characterization of Vuggy Carbonates. Presented at the SPE/EAGE Reservoir Characterization and Simulation Conference, Abu Dhabi, 28–31 October. SPE-111434-MS. https://doi.org/10.2118/111434-MS.
Wang, Y., Hill, A. D., and Schechter, R. S. 1993. The Optimal Injection Rate for Matrix Acidizing of Carbonate Formations. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 3–6 October. SPE 26578-MS. https://doi.org/10.2118/26578-MS.
Zhang, Y., Yang, S., Zhang, S. et al. 2014. Wormhole Propagation Behavior and Its Effect on Acid Leakoff under In Situ Conditions in Acid Fracturing. Transport Porous Med. 101 (1): 99–114. https://doi.org/10.1007/s11242-013-0233-z.