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Research Papers: Energy Systems Analysis

Lattice Boltzmann Simulation of Wormhole Propagation in Carbonate Acidizing

[+] Author and Article Information
Xinfang Ma

College of Petroleum Engineering,
China University of Petroleum,
18th, Fuxue Road, Changping District,
Beijing 102249, China
e-mail: maxinfang@cup.edu.cn

Jianye Mou

College of Petroleum Engineering,
China University of Petroleum,
18th, Fuxue Road, Changping District,
Beijing 102249, China
e-mail: moujianye@cup.edu.cn

Hun Lin

College of Petroleum Engineering,
China University of Petroleum,
18th, Fuxue Road, Changping District,
Beijing 102249, China
e-mail: linhun016@aliyun.com

Feng Jiang

Anhui Special Equipment Inspection Institute,
45th, Dalian Road,
Hefei 230051, Anhui Province, China
e-mail: jiangfeng_N@163.com

Kaiyu Liu

CNPC Great Wall Drilling Company,
Panjin 124100, Liaoning Province, China
e-mail: liukaiyu666@163.com

Xinzhe Zhao

College of Petroleum Engineering,
China University of Petroleum,
18th, Fuxue Road, Changping District,
Beijing 102249, China
e-mail: bsyzhaoxinzhe@163.com

1Corresponding author.

Contributed by the Advanced Energy Systems Division of ASME for publication in the JOURNAL OF ENERGY RESOURCES TECHNOLOGY. Manuscript received September 6, 2016; final manuscript received January 30, 2017; published online February 24, 2017. Assoc. Editor: Reza Sheikhi.

J. Energy Resour. Technol 139(4), 042002 (Feb 24, 2017) (10 pages) Paper No: JERT-16-1361; doi: 10.1115/1.4035909 History: Received September 06, 2016; Revised January 30, 2017

In acidizing operations, the acid flows selectively through large pores to create wormholes. Wormhole propagation has been studied by many experts at macroscopic scale. In this paper, the lattice Boltzmann model (LBM), which is a mesoscopic scale method, is adopted to simulate the flow, acid–rock reaction, and rock dissolution in porous media at mesoscopic scale. In this model, a new method based on nonequilibrium extrapolation is proposed to deal with the reactive boundary. On the basis of the model, extensive simulations are conducted on the propagation behavior of wormholes, and the factors influencing wormhole propagation are investigated systematically. The results show that the LBM is a reliable numerical technique to study chemical dissolution in porous media at mesoscopic scale, and that the new method of dealing with the reaction boundary performs well. The breakthrough time decreases with the increase of acid concentration, but acid concentration does not affect the ultimate dissolution pattern. As the reaction rate constant increases, shorter wormholes are created. A higher hydrogen ion diffusion coefficient will result in shorter but wider wormholes. These findings agree well with the previous experimental and theoretical analyses. This study demonstrates the mechanism of wormholing that the unstable growth of pores by the acid rock reaction makes the acid selectively flow through a few large pores which finally form wormholes.

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References

Hofmann, H. , Babadagli, T. , and Zimmermann, G. , 2014, “ Numerical Simulation of Complex Fracture Network Development by Hydraulic Fracturing in Naturally Fractured Ultratight Formations,” ASME J. Energy Resour. Technol., 136(4), p. 042905. [CrossRef]
Wang, W. , and Dahi Taleghani, A. , 2014, “ Simulation Multizone Fracturing in Vertical Wells,” ASME J. Energy Resour. Technol., 136(4), p. 042902. [CrossRef]
Guo, T. , Zhang, S. , Qu, Z. , Zhou, T. , Xiao, Y. , and Gao, J. , 2014, “ Experimental Study of Hydraulic Fracturing for Shale by Stimulated Reservoir Volume,” Fuel, 128, pp. 373–380. [CrossRef]
Mahmoud, M. , and Nasr-EI-Din, H. , 2014, “ Challenges During Shallow and Deep Carbonate Reservoirs Stimulation,” ASME J. Energy Resour. Technol., 137(1), p. 012902. [CrossRef]
Bastami, A. , and Pourafshary, P. , 2016, “ Development of a New Model for Carbonate Matrix Acidizing to Consider the Effects of Spent Acid,” ASME J. Energy Resour. Technol., 138(5), p. 052905. [CrossRef]
Barri, A. , Mahmoud, M. , and EIkatatny, S. , 2016, “ Evaluation of Rock Mechanical Properties Alteration During Matrix Stimulation With Chelating Agents,” ASME J. Energy Resour. Technol., 138(3), p. 032907. [CrossRef]
Nunes, M. , Bedrikovetsky, P. , Newbery, B. , Paiva, R. , Furtado, C. , and Souza, A. L. D. , 2010, “ Theoretical Definition of Formation Damage Zone With Applications to Well Stimulation,” ASME J. Energy Resour. Technol., 132(2), pp. 87–94.
Daccord, G. , Lenormand, R. , and Lietard, O. , 1993a, “ Chemical Dissolution of a Porous Medium by a Reactive Fluid-1. Model for the ‘Wormholing’ Phenomenon,” Chem. Eng. Sci., 48(1), pp. 169–178. [CrossRef]
Daccord, G. , Lenormand, R. , and Lietard, O. , 1993b, “ Chemical Dissolution of a Porous Medium by a Reactive Fluid-2. Convection versus Reaction, Behavior Diagram,” Chem. Eng. Sci., 48(1), pp. 179–186. [CrossRef]
Fredd, C. N. , and Fogler, H. S. , 1999, “ Optimum Conditions for Wormhole Formation in Carbonate Porous Media: Influence of Transport and Reaction,” SPE J., 4(3), pp. 196–205. [CrossRef]
Frick, T. P. , Mostofizadeh, B. , and Economides, M. J. , 1994, “ Analysis of Radial Core Experiments for Hydrochloric Acid Interaction With Limestones,” International Symposium on Formation Damage Control, Lafayette, LA, Feb. 7–10, Paper No. SPE27402.
Buijse, M. A. , 2000, “ Understanding Wormholing Mechanisms Can Improve Acid Treatments in Carbonate Formations,” SPE Prod. Facil., 15(3), pp. 168–175. [CrossRef]
Bazin, B. , 2001, “ From Matrix Acidizing to Acid Fracturing: A Laboratory Evaluation of Acid/Rock Interactions,” SPE Prod. Facil., 16(1), pp. 22–29. [CrossRef]
Ortoleva, P. J. , Chadam, J. , Merino, E. , and Sen, A. , 1987, “ Geochemical Self-Organization—Part II: The Reactive-Infiltration Instability,” Am. J. Sci., 287(10), pp. 1008–1040. [CrossRef]
Wei, C. , and Ortoleva, P. , 1990, “ Reaction Front Fingering in Carbonate-Cemented Sandstones,” Earth-Sci. Rev., 29(1–4), pp. 183–198. [CrossRef]
Steefel, C. I. , and Lasaga, A. C. , 1994, “ A Coupled Model for Transport of Multiple Chemical-Species and Kinetic Precipitation Dissolution Reactions With Application to Reactive Flow in Single-Phase Hydrothermal Systems,” Am. J. Sci., 294(5), pp. 529–592. [CrossRef]
Liu, X. , Ormond, A. , Bartko, K. , Ying, L. , and Ortoleva, P. , 1997, “ A Geochemical Reaction-Transport Simulator for Matrix Acidizing Analysis and Design,” J. Pet. Sci. Eng., 17(1), pp. 181–196. [CrossRef]
Ormond, A. , and Ortoleva, P. , 2000, “ Numerical Modeling of Reaction-Induced Cavities in a Porous Rock,” J. Geophys. Res. Atmos., 105(B7), pp. 16737–16747. [CrossRef]
Panga, M. K. R. , 2003, “ Multiscale Transport and Reaction: Two Case Studies,” Ph.D. dissertation, The University of Houston, Houston, TX.
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), pp. 3231–3248. [CrossRef]
Izgec, O. , Keys, R. , Zhu, D. , and Hill, A. D. , 2008, “ An Integrated Theoretical and Experimental Study on the Effects of Multiscale Heterogeneities in Matrix Acidizing of Carbonates,” SPE Annual Technical Conference and Exhibition, Denver, CO, Sept. 21–24, Paper No. SPE115143.
Izgec, O. , Zhu, D. , and Hill, A. D. , 2009, “ Models and Methods for Understanding of Early Acid Breakthrough Observed in Acid Core-Floods of Vuggy Carbonates,” SPE European Formation Damage Conference, Scheveningen, The Netherlands, May 27–29, Paper No. SPE122357.
Wells, J. T. , Janecky, D. R. , and Travis, B. J. , 1991, “ A Lattice Gas Automata Model for Heterogeneous Chemical Reactions at Mineral Surfaces and in Pore Networks,” Phys. D Nonlinear Phenom., 47(1–2), pp. 115–123. [CrossRef]
Boek, E. S. , and Venturoli, M. , 2010, “ Lattice-Boltzmann Studies of Fluid Flow in Porous Media With Realistic Rock Geometries,” Comput. Math. Appl., 59(7), pp. 2305–2314. [CrossRef]
Han, Y. , and Cundall, P. A. , 2010, “ Lattice Boltzmann Modeling of Pore-Scale Fluid Flow Through Idealized Porous Media,” Int. J. Numer. Methods Fluids, 67(11), pp. 1720–1734. [CrossRef]
Gao, Y. , Zhang, X. , Rama, P. , Liu, Y. , Chen, R. , Ostadi, H. , and Jiang, K. , 2012, “ Calculating the Anisotropic Permeability of Porous Media Using the Lattice Boltzmann Method and X-Ray Computed Tomography,” Transp. Porous Media, 92(2), pp. 457–472. [CrossRef]
Jiang, B. , and Zhang, X. , 2014, “ An Orthorhombic Lattice Boltzmann Model for Pore-Scale Simulation of Fluid Flow in Porous Media,” Transp. Porous Media, 104(1), pp. 145–159. [CrossRef]
Angelopoulos, A. D. , Paunov, V. N. , Burganos, V. N. , and Payatakes, A. C. , 1998, “ Lattice Boltzmann Simulation of Nonideal Vapor-Liquid Flow in Porous Media,” Phys. Rev. E: Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., 57(3), pp. 3237–3245.
Kang, Q. , Zhang, D. , and Chen, S. , 2002, “ Displacement of a Two-Dimensional Immiscible Droplet in a Channel,” Phys. Fluids, 14(9), pp. 3203–3214. [CrossRef]
Pan, C. , Hilpert, M. , and Miller, C. T. , 2004, “ Lattice-Boltzmann Simulation of Two-Phase Flow in Porous Media,” Water Resour. Res., 40(1), pp. 62–74. [CrossRef]
Benzi, R. , Biferale, L. , Sbragaglia, M. , Succi, S. , and Toschi, F. , 2006, “ Mesoscopic Modeling of a Two-Phase Flow in the Presence of Boundaries: The Contact Angle,” Phys. Rev. E, 74(2 Pt. 1), pp. 79–97.
He, X. , Chen, S. , and Doolen, G. D. , 1998, “ A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit,” J. Comput. Phys., 146(1), pp. 282–300. [CrossRef]
Ibrahem, A. M. , El-Amin, M. F. , Mohammadein, A. A. , and Gorla, R. S. R. , 2016, “ Lattice Boltzmann Technique for Heat Transport Phenomena Coupled With Melting Process,” Heat Mass Transfer, 52(333), pp. 1–9.
Kelemen, P. B. , Whitehead, J. A. , Einat, A. , and Jordahl, K. A. , 1995, “ Experiments on Flow Focusing in Soluble Porous-Media, With Applications to Melt Extraction From the Mantle,” J. Geophys. Res. Atmos., 100(B1), pp. 475–496. [CrossRef]
Xiaoyi, He. , Ning, Li. , and Goldstein, B. , 2000, “ Lattice Boltzmann Simulation of Diffusion-Convection Systems With Surface Chemical Reaction,” Mol. Simul., 25(3), pp. 145–156.
Kang, Q. , Zhang, D. , Chen, S. , and He, X. , 2002, “ Lattice Boltzmann Simulation of Chemical Dissolution in Porous Media,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys., 65(3 Pt. 2B), p. 036318. [CrossRef]
He, X. , and Luo, L. S. , 1997, “ A Priori Derivation of the Lattice Boltzmann Equation,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., 55(6), pp. R6333–R6336.
Abe, T. , 1997, “ Derivation of the Lattice Boltzmann Method by Means of the Discrete Ordinate Method for the Boltzmann Equation,” J. Comput. Phys., 131(1), pp. 241–246. [CrossRef]
Succi, S. , 2001, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, Brussels, Belgium.
Chen, S. , and Doolen, G. D. , 2003, “ Lattice Boltzmann Method for Fluid Flows,” Annu. Rev. Fluid Mech., 30(1), pp. 329–364. [CrossRef]
Wolf-Gladrow, D. A. , 2000, Lattice-Gas Cellular Automata and Lattice Boltzmann Models, Springer, Berlin.
Bhatnagar, P. , Gross, E. , and Krook, M. , 1954, “ A Model for Collisional Processes in Gases I: Small Amplitude Processes in Charged and Neutral One-Component System,” Phys. Rev., 94(3), pp. 511–525. [CrossRef]
Qian, Y. H. , D'Humières, D. , and Lallemand, P. , 1992, “ Lattice BGK Models for Navier–Stokes Equation,” Europhys. Lett., 17(6BIS), p. 479. [CrossRef]
Li-Shi Luo, P. L. , 2000, “ Theory of the Lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., 61(6 Pt. A), pp. 6546–6562.
Kang, Q. , Lichtner, P. C. , and Zhang, D. , 2007, “ An Improved Lattice Boltzmann Model for Multicomponent Reactive Transport in Porous Media at the Pore Scale,” Water Resour. Res., 43(12), pp. 2578–2584. [CrossRef]
Noble, D. R. , 1997, “ Lattice Boltzmann Study of the Interstitial Hydrodynamics and Dispersion in Steady Intertial Flows in Large Randomly Packed Beds,” Ph.D. thesis, University of Illinois at Urbana–Champaign, Champaign, IL.
Dawson, S. P. , Chen, S. , and Doolen, G. D. , 1993, “ Lattice Boltzmann Computations for Reaction-Diffusion Equations,” J. Chem. Phys., 98(2), pp. 1514–1523. [CrossRef]
Huber, C. , Shafei, B. , and Parmigiani, A. , 2014, “ A New Pore-Scale Model for Linear and Non-Linear Heterogeneous Dissolution and Precipitation,” Geochim. Cosmochim. Acta, 124(1), pp. 109–130. [CrossRef]
Carslaw, H. S. , Jaeger, J. C. , and Feshbach, H. , 1959, Conduction of Heat in Solids, Clarendon Press, Gloucestershire, UK.
Hoefner, M. L. , and Fogler, H. S. , 1988, “ Porous Evolution and Channel Formation During Flow and Reaction in Porous Media,” Am. Inst. Chem. Eng. J., 34(1), pp. 45–54. [CrossRef]

Figures

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Fig. 1

Schematics of the D2Q9 lattice model

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Fig. 2

Schematics of the D2Q4 lattice model

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Fig. 3

Boundary types in the simulation

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Fig. 4

The boundary condition in simulation zone

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Fig. 5

The comparison between the numerical and analytical concentration field when Da = 4.0

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Fig. 6

The comparison between the numerical and analytical concentration field when Da = 40.0

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Fig. 7

The initial pore structure of unequal channel

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Fig. 8

The concentration field when simulation is finished

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Fig. 9

The pore structure when simulation is finished

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Fig. 10

Pore structure display generated with PFC

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Fig. 11

Concentration and pore structure at different times (upper: acid concentration pattern; below: pore structure pattern)

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Fig. 12

Change of permeability with time

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Fig. 13

Change of porosity with time

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Fig. 14

Pore structure and concentration distribution at different acid concentrations

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Fig. 15

Change of permeability with time at different concentrations

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Fig. 16

Concentration distribution and pore structure at different concentrations during breakthrough

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Fig. 17

Concentration distribution and pore structure for the reaction rate of 0.1 mm/s

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Fig. 18

Concentration distribution and pore structure for the reaction rate of 0.8 mm/s

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Fig. 19

Concentration distribution and pore structure for four different diffusion coefficients

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