Abstract
The paper presents results of numerical experiments performed to evaluate the effective viscosity of a fluid-proppant mixture, used in hydraulic fracturing. The results, obtained by two complimenting methods (the particle dynamics and the smoothed particle hydrodynamics), coincide to the accuracy of standard deviation. They provide an analytical equation for the dependence of effective viscosity on the proppant concentration, needed for numerical simulation of the hydraulic fracture propagation.
Similar content being viewed by others
References
Economides, M.J. and Nolte, K.G., Reservoir Stimulation. Englewood Cliffs, New Jersey: Prentice Hall, 1989.
Zheltov, Yu.N. and Khristianovich, A.S., Oil Stratum Hydrofracturing, Izv. AN SSSR, Otd. Tekh. Nauk, 1955, no. 5.
Khristianovich, S.A. and Zheltov, V.P., Formation of Vertical Fractures by Means of Highly Viscous Liquid, Proc. 4th World Petroleum Congress, Rome, 1955.
Alekseenko, O.P. and Vaisman, A.M., Certain Aspects of a Two-Dimensional Pon the Hydraulic Fracturing of an Elastic Medium, Journal of Mining Science, 1999, vol 35, no. 3, pp. 269–275.
Savitski, A.A. and Detournay, E., Propagation of a Fluid-Driven Penny-Shaped Fracture in an Impermeable Rock: Asymptotic Solutions, Int. J. Solids Structures, 2002, vol. 39.
Adachi, J., Siebrits, E., et al., Computer Simulation of Hydraulic Fractures, Int. J. Rock Mech. Mining Sci., 2007, vol. 44.
Peirce, A. and Detournay, E., An Implicit Level Set Method for Modeling Hydraulically Driven Fractures, Comput. Methods Appl. Mech. Engng., 2008, vol. 197.
Garagash, D.I., Detournay, E., Adachi, J.I., Multiscale Tip Asymptotics in Hydraulic Fracture with Leak-Off, J. Fluid Mech., 2011, vol. 669.
Linkov, A.M., On Efficient Simulation of Hydraulic Fracturing in Terms of Particle Velocity, Int. J. Engineering Sci., 2012, vol. 52.
Lecampion, B., Peirce, A., Detournay, E., Zhang, X., Chen, Z., Bunger, A., Detournay, C., Napier, J., Abbas, S., Garagash, D., and Cundall, P., The Impact of the Near-Tip Logic on the Accuracy and Convergence Rate of Hydraulic Fracture Simulators Compared to Reference Solutions, Effective and Sustainable Hydraulic Fracturing, Andrew, J.M., Bunger, P., Jerey, R. (Eds.), Rijeka, Croatia, 2013.
Linkov, A.M., Analytical Solution of Hydralic Fracture Problem for a Non-Newtonian Fluid, Journal of Mining Science, 2013, vol. 49, no. 1, pp. 8–18.
Einstein, A., Eine neue Bestimmung der Molekuldimensionen, Ann. Phys., 1906, vol. 19.
Brady, J.F., The Einstein Viscosity Correction in n Dimensions, Int. J. Mult. Flow, 1983, vol. 10.
Mooney, M., The Viscosity of a Concentrated Suspension of Spherical Particles, J. Colloid Sci., 1951, vol. 6.
Maron, S.H. and Pierce, P.E., Application of Ree-Eyring Generalized Flow Theory to Suspensions of Spherical Sarticles, J. Colloid Sci., 1956, vol. 11.
Krieger, I.M. and Dougherty, T.J., A Mechanism for Non-Newtonian Flow in Suspensions of Rigid Spheres, T. Soc. Rheol., 1959, vol. 3.
Dorr, A., Sadiki, A., and Mehdizadeh, A., A Discrete Model for the Apparent Viscosity of Polydisperse Suspensions Including Maximum Packing Fraction, J. Rheol., 2013, vol. 57.
Mueller, S., Llewellin, E.W., et al., The Rheology of Suspensions of Solid Particles, Proc. R. Soc. A, 2010, vol. 466.
Foss, D.R. and Brady, J.F., Structure, Diffusion and Rheology of Brownian Suspensions by Stokesian Dynamics Simulations, J. Fluid Mech., 2000, vol. 407.
Martys, N.S., Study of a Dissipative Particle Dynamics Based Approach for Modeling Suspensions, J. Rheol., 2005, vol. 49.
Martys, N.S., George, W.L., et al., A Smoothed Particle Hydrodynamics-Based Fluid Model with a Spatially Dependent Viscosity: Application to Flow of a Suspension with a Non-Newtonian Fluid Matrix, Rheol. Acta, 2010, vol. 49.
Wang, Y., Keblinski, P., et al., Viscosity Calculation of a Nanoparticle Suspension Confined in Nanochannels, Phys. Rev. E, 2012, vol. 86.
Ladd, A.J.C., Colvin, M.E., et al., Application of Lattice-Gas Cellular Automata to the Brownian Motion of Solids in Suspension, Phys. Rev. Let., 1988, vol. 60.
Hoover, W.G., Molecular Dynamics, Lecture Notes in Physics, Springer, Berlin, 1986, vol. 258
Krivtsov, A.M., Deformirovanie i razrushenie tverdykh tel s mikrostrukturoi (Deformation and Failure of Microstructure Solids), Moscow: Fizmatlit, 2007.
Lucy, L.B., A Numerical Approach to the Testing of the Fission Hypothesis, Astronomical J., 1977, vol. 82.
Monaghan, J.J., Smoothed Particle Hydrodynamics, Rep. Prog. Phys., 2005, vol. 68.
Hoover, W.G., Smooth Particle Applied Mechanics: The State of the Art, World Scientific Publishing, 2006.
Kuzkin, V.A., Krivtsov, A.M., and Linkov, A.M., Proppant Transport in Hydraulic Fractures: Computer Simulation of Effective Properties and Movement of the Suspension, Proc. 41 Summer-School Conference Advanced Problems in Mechanics, 2013.
Verlet, L., Computer “Experiments” on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules, Phys. Rev., 1967, vol. 159.
Berendsen, H.J.C., Postma, J.P.M., van Gunsteren, W.F., Di Nola, A., and Haak, J.R., Molecular-Dynamics with Coupling to an External Bath, J. Chem. Phys., 1984, vol. 81.
Berryman, J.G., Random Close Packing of Hard Spheres and Disks, Phys. Rev. A, 1983, vol. 27.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.A. Kuzkin, A.M. Krivtsov, A.M. Linkov, 2014, published in Fiziko-Tekhnicheskie Problemy Razrabotki Poleznykh Iskopaemykh, 2014, No. 1, pp. 3–12.
Rights and permissions
About this article
Cite this article
Kuzkin, V.A., Krivtsov, A.M. & Linkov, A.M. Computer simulation of effective viscosity of fluid-proppant mixture used in hydraulic fracturing. J Min Sci 50, 1–9 (2014). https://doi.org/10.1134/S1062739114010013
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1062739114010013