Skip to main content Accessibility help
×
Hostname: page-component-8448b6f56d-42gr6 Total loading time: 0 Render date: 2024-04-20T02:46:25.170Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  22 July 2019

Knut-Andreas Lie
Affiliation:
SINTEF, Norway
HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
An Introduction to Reservoir Simulation Using MATLAB/GNU Octave
User Guide for the MATLAB Reservoir Simulation Toolbox (MRST)
, pp. 631 - 649
Publisher: Cambridge University Press
Print publication year: 2019
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This content is Open Access and distributed under the terms of the Creative Commons Attribution licence CC-BY-NC-ND 4.0 https://creativecommons.org/cclicenses/

References

[1] Aarnes, J. E. 2004. On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation. Multiscale Model. Simul., 2(3), 421439. doi:10.1137/030600655.Google Scholar
[2] Aarnes, J. E., Gimse, T., and Lie, K.-A. 2007b. An introduction to the numerics of flow in porous media using Matlab. In Hasle, G., Lie, K.-A., and Quak, E. (eds), Geometrical Modeling, Numerical Simulation and Optimisation: Industrial Mathematics at SINTEF. Berlin, Heidelberg, New York: Springer-Verlag, pp. 265306.CrossRefGoogle Scholar
[3] Aarnes, J. E., Hauge, V. L., and Efendiev, Y. 2007a. Coarsening of three-dimensional structured and unstructured grids for subsurface flow. Adv. Water Resour., 30(11), 21772193. doi:10.1016/j.advwatres.2007.04.007.Google Scholar
[4] Aarnes, J. E., Kippe, V., and Lie, K.-A. 2005. Mixed multiscale finite elements and streamline methods for reservoir simulation of large geomodels. Adv. Water Resour., 28(3), 257271. doi:10.1016/j.advwatres.2004.10.007.CrossRefGoogle Scholar
[5] Aarnes, J. E., Krogstad, S., and Lie, K.-A. 2006. A hierarchical multiscale method for two-phase flow based upon mixed finite elements and nonuniform coarse grids. Multiscale Model. Simul., 5(2), 337363. doi:10.1137/050634566.CrossRefGoogle Scholar
[6] Aarnes, J. E., Krogstad, S., and Lie, K.-A. 2008. Multiscale mixed/mimetic methods on corner-point grids. Comput. Geosci., 12(3), 297315. doi:10.1007/s10596-007-9072-8.Google Scholar
[7] Aavatsmark, I. 2002. An introduction to multipoint flux approximations for quadrilateral grids. Comput. Geosci., 6, 405432. doi:10.1023/A:1021291114475.CrossRefGoogle Scholar
[8] Aavatsmark, I. 2007. Interpretation of a two-point flux stencil for skew parallelogram grids. Comput. Geosci., 11(3), 199206. doi:10.1007/s10596-007-9042-1.CrossRefGoogle Scholar
[9] Aavatsmark, I., Barkve, T., Bøe, Ø., and Mannseth, T. 1994. Discretization on non-orthogonal, curvilinear grids for multi-phase flow. In: ECMOR IV – 4th European Conference on the Mathematics of Oil Recovery. doi:0.3997/2214-4609.201411179.Google Scholar
[10] Aavatsmark, I., Eigestad, G. T., and Klausen, R. A. 2006. Numerical convergence of the MPFA O-method for general quadrilateral grids in two and three dimensions. In: Arnold, D. N., Bochev, P. B., Lehoucq, R. B., Nicolaides, R. A., and Shashkov, M. (eds), Compatible Spatial Discretizations. New York: Springer.Google Scholar
[11] Aavatsmark, I., Eigestad, G. T., Klausen, R. A., Wheeler, M. F., and Yotov, I. 2007. Convergence of a symmetric MPFA method on quadrilateral grids. Comput. Geosci., 11(4), 333345. doi:10.1007/s10596-007-9056-8.CrossRefGoogle Scholar
[12] Aavatsmark, I., Eigestad, G. T., Mallison, B. T., and Nordbotten, J. M. 2008. A compact multipoint flux approximation method with improved robustness. Numer. Meth. Partial Diff. Eqs., 24(5), 13291360. doi:10.1002/num.20320.CrossRefGoogle Scholar
[13] Aavatsmark, I., and Klausen, R. 2003. Well index in reservoir simulation for slanted and slightly curved wells in 3D grids. SPE J., 8(01), 4148. doi:10.2118/75275-PA.Google Scholar
[14] Abou-Kassem, J. H., Farouq-Ali, S. M., and Islam, M. R. 2006. Petroleum Reservoir Simulations: A Basic Approach. Houston: Gulf Publishing Company.Google Scholar
[15] AGMG. 2012. Iterative solution with AGgregation-based algebraic MultiGrid. http://agmg.eu. [Online; accessed July 11, 2018].Google Scholar
[16] AllenIII, M. B., Behie, G. A., and Trangenstein, J. A. 1988. Multiphase Flow in Porous Media: Mechanics, Mathematics, and Numerics. New York: Springer-Verlag.Google Scholar
[17] Alpak, F. O., Pal, M., and Lie, K.-A. 2012. A multiscale method for modeling flow in stratigraphically complex reservoirs. SPE J., 17(4), 10561070. doi:10.2118/140403-PA.CrossRefGoogle Scholar
[18] Alvestad, J., Holing, K., Christoffersen, K., and Stava, O. 1994. Interactive modelling of multiphase inflow performance of horizontal and highly deviated wells. In: European Petroleum Computer Conference. Society of Petroleum Engineers. doi:10.2118/27577-MS.CrossRefGoogle Scholar
[19] Andersen, O. 2017. Simplified models for numerical simulation of geological CO2 storage. PhD. thesis, University of Bergen. url: http://hdl.handle.net/1956/15477.Google Scholar
[20] Andersen, O., Gasda, S. E., and Nilsen, H. M. 2015. Vertically averaged equations with variable density for CO2 flow in porous media. Transp. Porous Media, 107(1), 95127. doi:10.1007/s11242-014-0427-z.CrossRefGoogle Scholar
[21] Andersen, O., Lie, K.-A., and Nilsen, H. M. 2016. An open-source toolchain for simulation and optimization of aquifer-wide CO2 storage. Energy Procedia, 86(Jan.), 324333. doi:10.1016/j.egypro.2016.01.033.Google Scholar
[22] Andersen, O., Nilsen, H. M., and Raynaud, X., 2017a. Coupled geomechanics and flow simulation on corner-point and polyhedral grids. In: SPE Reservoir Simulation Conference. doi:10.2118/182690-MS.CrossRefGoogle Scholar
[23] Andersen, O., Nilsen, H. M., and Raynaud, X. 2017b. Virtual element method for geomechanical simulations of reservoir models. Comput. Geosci., 21(5–6), 877– 893. doi:10.1007/s10596-017-9636-1.Google Scholar
[24] Appleyard, J. R., and Cheshire, I. M. 1983. Nested factorization. In: SPE Reservoir Simulation Symposium. doi:10.2118/12264-MS.Google Scholar
[25] Arbogast, T., Cowsar, L. C., Wheeler, M. F., and Yotov, I. 2000. Mixed finite element methods on nonmatching multiblock grids. SIAM J. Num. Anal., 37(4), 12951315. doi:10.1137/S0036142996308447.CrossRefGoogle Scholar
[26] Arbogast, T., Dawson, C. N., Keenan, P. T., Wheeler, M. F., and Yotov, I. 1998. Enhanced cell-centered finite differences for elliptic equations on general geometry. SIAM J. Sci. Comp., 19(2), 404425. doi:10.1137/S1064827594264545.CrossRefGoogle Scholar
[27] Ates, H., Bahar, A., El-Abd, S., et al. 2005. Ranking and upscaling of geostatistical reservoir models using streamline simulation: A field case study. SPE Res. Eval. Eng., 8(1), 2232. doi:10.2118/81497-PA.CrossRefGoogle Scholar
[28] Aziz, K., and Settari, A. 1979. Petroleum Reservoir Simulation. London, New York: Elsevier Applied Science Publishers.Google Scholar
[29] Baker, L. E. 1988. Three-phase relative permeability correlations. In: SPE Enhanced Oil Recovery Symposium. doi:10.2118/17369-MS.Google Scholar
[30] Bao, K., Lie, K.-A., Møyner, O., and Liu, M. 2017. Fully implicit simulation of polymer flooding with MRST. Comput. Geosci., 21(5–6), 12191244. doi:10.1007/s10596-017-9624-5.Google Scholar
[31] Barker, J., and Thibeau, S. 1997. A critical review of the use of pseudorelative permeabilities for upscaling. SPE Reservoir Engineering, 12(2), 138143. doi:10.2118/35491-PA.Google Scholar
[32] Batycky, R. P., Thieles, M. R., Baker, R. O., and Chugh, S. H. 2008. Revisiting reservoir flood-surveillance methods using streamlines. SPE Res. Eval. Eng., 11(2), 387394. doi:10.2118/95402-PA.Google Scholar
[33] Baxendale, D., Rasmussen, A., Rustad, A. B., et al. 2018. Open porous media: Flow documentation manual. 2018-10 Rev-2 edn. http://opm-project.org.Google Scholar
[34] Bear, J. 1988. Dynamics of Fluids in Porous Media. Mineola, NY: Dover.Google Scholar
[35] Bear, J. 2007. Hydraulics of Groundwater. Mineola, NY: Dover.Google Scholar
[36] Bear, J., and Bachmat, Y. 1990. Introduction to Modeling of Transport Phenomena in Porous Media. Dordrecht: Springer.Google Scholar
[37] Begg, S. H., Carter, R. R., and Dranfield, P. 1989. Assigning effective values to simulator gridblock parameters for heterogeneous reservoirs. SPE Res. Eng., 4(4), 455463. doi:10.2118/16754-PA.Google Scholar
[38] Beirão da Veiga, L., Brezzi, F., Cangiani, A., et al. 2013. Basic principles of virtual element methods. Math. Mod. Meth. Appl. Sci., 23(01), 199214. doi:10.1142/S0218202512500492.Google Scholar
[39] Beirão da Veiga, L., Brezzi, F., Marini, L. D., and Russo, A. 2014. The hitchhiker’s guide to the virtual element method. Math. Mod. Meth. Appl. Sci., 24(08), 1541– 1573. doi:10.1142/S021820251440003X.Google Scholar
[40] Beirao da Veiga, L., Lipnikov, K., and Manzini, G. 2014. The Mimetic Finite Difference Method for Elliptic Problems. New York: Springer.Google Scholar
[41] Benesoussan, A., Lions, J.-L., and Papanicolaou, G. 1978. Asymptotic Analysis for Periodic Structures. Amsterdam: Elsevier Science Publishers.Google Scholar
[42] Berge, R. L. 2016. Unstructured PEBI grids adapting to geological feautres in subsurface reservoirs. M.Sc. thesis, Norwegian University of Science and Technology. http://hdl.handle.net/11250/2411565.Google Scholar
[43] Bischof, C. H., Bücker, H. M., Lang, B., Rasch, A., and Vehreschild, A. 2002. Combining source transformation and operator overloading techniques to compute derivatives for MATLAB programs. Proceedings of the Second IEEE International Workshop on Source Code Analysis and Manipulation (SCAM 2002). Los Alamitos, CA, pp. 65–72 doi:10.1109/SCAM.2002.1134106.CrossRefGoogle Scholar
[44] Blunt, M. J. 2017. Multiphase Flow in Permeable Media: A Pore-Scale Perspective. Cambridge: Cambridge University Press.Google Scholar
[45] Braess, D. 1997. Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
[46] Branets, L., Ghai, S. S., Lyons, S. L., and Wu, X.-H. 2009a. Efficient and accurate reservoir modeling using adaptive gridding with global scale up. In: SPE Reservoir Simulation Symposium. doi:10.2118/118946-MS.Google Scholar
[47] Branets, L. V., Ghai, S. S., Lyons, S. L., and Wu, X.-H. 2009b. Challenges and technologies in reservoir modeling. Commun. Comput. Phys., 6(1), 123.CrossRefGoogle Scholar
[48] Branets, L., Kubyak, V., Kartasheva, E., Shmyrov, L., and Kandybor, D. 2015. Capturing geologic complexity in simulation grid. In: SPE Reservoir Simulation Symposium. doi:10.2118/173270-MS.CrossRefGoogle Scholar
[49] Brenier, Y., and Jaffré, J. 1991. Upstream differencing for multiphase flow in reservoir simulation. SIAM J. Numer. Anal., 28(3), 685696. doi:10.1137/0728036.Google Scholar
[50] Brenner, S. C., and Scott, L. R. 2007. The Mathematical Theory of Finite Element Methods. 3rd edn. New York: Springer-Verlag.Google Scholar
[51] Brewer, M., Camilleri, D., Ward, S., and Wong, T. 2015. Generation of hybrid grids for simulation of complex, unstructured reservoirs by a simulator with MPFA. In: SPE Reservoir Simulation Symposium. doi:10.2118/173191-MS.CrossRefGoogle Scholar
[52] Brezzi, F., Lipnikov, K., and Simoncini, V. 2005. A family of mimetic finite difference methods on polygonial and polyhedral meshes. Math. Models Methods Appl. Sci., 15, 15331553. doi:10.1142/S0218202505000832.CrossRefGoogle Scholar
[53] Brezzi, F., and Fortin, M. 1991. Mixed and Hybrid Finite Element Methods. New York: Springer-Verlag.CrossRefGoogle Scholar
[54] Brooks, R. H., and Corey, A. T. 1966. Properties of porous media affecting fluid flow. J. Irrigation Drainage Div., 92(2), 6190.CrossRefGoogle Scholar
[55] Buckingham, E. 1907. Studies on the Movement of Soil Moisture. Bulletin, no. 38. United States. Bureau of Soils. https://archive.org/details/studiesonmovemen38buck.Google Scholar
[56] Buckley, S. E., and Leverett, M. C. 1942. Mechanism of fluid displacement in sands. Trans. AIME, 146(01), 107116. doi:10.2118/942107-G.Google Scholar
[57] Caers, J. 2005. Petroleum Geostatistics. Richardson, TX: Society of Petroleum Engineers.CrossRefGoogle Scholar
[58] Cao, H. 2002. Development of techniques for general purpose simulators. PhD. thesis, Stanford University.Google Scholar
[59] Castellini, A., Edwards, M. G., and Durlofsky, L. J. 2000. Flow based modules for grid generation in two and three dimensions. In: ECMOR VII – 7th European Conference on the Mathematics of Oil Recovery. doi:10.3997/2214-4609.201406120.CrossRefGoogle Scholar
[60] Cayuga Research. ADMAT. www.cayugaresearch.com/admat.html. [Online; accessed Jul 11, 2018].Google Scholar
[61] Chavent, G., and Jaffré, J. 1982. Mathematical Models and Finite Elements for Reservoir Simulation. Amsterdam: North Holland.Google Scholar
[62] Chavent, G., and Jaffré, J. 1986. Mathematical Models and Finite Elements for Reservoir Simulation: Single Phase, Multiphase and Multicomponent Flows through Porous Media. Amsterdam: Elsevier.Google Scholar
[63] Chen, Y., and Durlofsky, L. J. 2006. Adaptive local-global upscaling for general flow scenarios in heterogeneous formations. Transport Porous Media, 62, 157182. doi:10.1007/s11242-005-0619-7.Google Scholar
[64] Chen, Y., Durlofsky, L. J., Gerritsen, M., and Wen, X. H. 2003. A coupled local-global upscaling approach for simulating flow in highly heterogeneous formations. Adv. Water Resour., 26(10), 10411060. doi:10.1016/S0309-1708(03)00101-5.Google Scholar
[65] Chen, Z. 2000. Formulations and numerical methods of the black oil model in porous media. SIAM J. Numer. Anal., 38(2), 489514. doi:10.1137/S0036142999304263.Google Scholar
[66] Chen, Z. 2007. Reservoir Simulation: Mathematical Techniques in Oil Recovery. Philadelphia: Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
[67] Chen, Z., and Ewing, R. E. 1997. Comparison of various formulations of three-phase flow in porous media. J. Comput. Phys., 132(2), 362373. doi:10.1006/jcph. 1996.5641.Google Scholar
[68] Chen, Z., and Hou, T. Y. 2003. A mixed multiscale finite element method for elliptic problems with oscillating coefficients. Math. Comp., 72, 541576. doi:10.1090/S0025-5718-02-01441-2.CrossRefGoogle Scholar
[69] Chen, Z., Huan, G., and Ma, Y. 2006. Computational Methods for Multiphase Flows in Porous Media. Philadelphia: Society of Industrial and Applied Mathematics. doi:10.1137/1.9780898718942.Google Scholar
[70] Christie, M. A. 1996. Upscaling for reservoir simulation. J. Pet. Tech., 48(11), 1004– 1010. doi:10.2118/37324-MS.Google Scholar
[71] Christie, M. A., and Blunt, M. J. 2001. Tenth SPE comparative solution project: A comparison of upscaling techniques. SPE Reservoir Eval. Eng., 4, 308317. doi:10.2118/72469-PA.Google Scholar
[72] Cirpka, O. A., Frind, E. O., and Helmig, R. 1999. Streamline-oriented grid generation for transport modelling in two-dimensional domains including wells. Adv. Water Resour., 22(7), 697710. doi:10.1016/S0309-1708(98)00050-5.Google Scholar
[73] Coats, K. H. 2000. A note on IMPES and some IMPES-based simulation models. SPE J., 05(03), 245251. doi:10.2118/65092-PA.Google Scholar
[74] Cordes, C., and Kinzelbach, W. 1992. Continous groundwater velocity fields and path lines in linear, bilinear, and trilinear finite elements. Water Resour. Res., 28(11), 29032911. doi:10.1029/92WR01686.Google Scholar
[75] Courant, R., Friedrichs, K., and Lewy, H. 1928. Über die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann., 100(1), 3274. doi:10.1007/BF01448839.Google Scholar
[76] Dafermos, C. M. 2010. Hyperbolic Conservation Laws in Continuum Physics. Berlin, Heidelberg: Springer.Google Scholar
[77] Darcy, H. P. G. 1856. Les Fontaines Publiques de la Ville de Dijon. Paris: Dalmont.Google Scholar
[78] Datta-Gupta, A., and King, M. J. 1995. A semianalytic approach to tracer flow modeling in heterogeneous permeable media. Adv. Water Resour., 18, 924. doi:10.1016/0309-1708(94)00021-V.Google Scholar
[79] Datta-Gupta, A., and King, M. J. 2007. Streamline Simulation: Theory and Practice. Richardson, TX: Society of Petroleum Engineers.Google Scholar
[80] DeBaun, D., et al. 2005. An extensible architecture for next generation scalable parallel reservoir simulation. In: SPE Reservoir Simulation Symposium. doi:10.2118/93274-MS.CrossRefGoogle Scholar
[81] Demidov, D. 2017 (Oct.). amgcl-sdd-scaling. https://zenodo.org/record/1002948#.XE_CAFxKiUk.Google Scholar
[82] Deutsch, C. V., and Journel, A. G. 1998. GSLIB: Geostatistical Software Library and User’s Guide. 2nd edn. New York: Oxford University Press.Google Scholar
[83] Ding, X. Y., and Fung, L. S. K. 2015. An unstructured gridding method for simulating faulted reservoirs populated with complex wells. In: SPE Reservoir Simulation Symposium. doi:10.2118/173243-MS.Google Scholar
[84] Dogru, A. H., Fung, L. S.-K., Middya, U., Al-Shaalan, T., and Pita, J. A. 2009. A next-generation parallel reservoir simulator for giant reservoirs. In: SPE/EAGE Reservoir Characterization & Simulation Conference. doi:10.2118/119272-MS.Google Scholar
[85] Dogru, A. H., Fung, L. S. K., Middya, U., et al. 2011. New frontiers in large scale reservoir simulation. In: SPE Reservoir Simulation Symposium. doi:10.2118/142297-MS.CrossRefGoogle Scholar
[86] Douglas, J. Jr., Peaceman, D. W., and Rachford, H. H. Jr. 1959. A method for calculating multi-dimensional immiscible displacement. Petrol. Trans. AIME, 216, 297308.Google Scholar
[87] Duarte, A. C. 2016. Contributions to production optimization of oil reservoirs. PhD. thesis, Norwegian University of Science and Technology. http://hdl.handle.net/11250/2383090.Google Scholar
[88] Duff, I. S. 2004. MA57–A code for the solution of sparse symmetric definite and indefinite systems. ACM Trans. Math. Softw., 30(2), 118144. doi:10.1145/992200.992202.Google Scholar
[89] Duff, I. S., and Reid, J. K. 1983. The multifrontal solution of indefinite sparse symmetric linear. ACM Trans. Math. Software, 9(3), 302325. doi:10.1145/356044.356047.CrossRefGoogle Scholar
[90] Durlofsky, L. J. 1991. Numerical calculations of equivalent gridblock permeability tensors for heterogeneous porous media. Water Resour. Res., 27(5), 699708. doi:10.1029/91WR00107.Google Scholar
[91] Durlofsky, L. J. 2003. Upscaling of Geocellular Models for Reservoir Flow Simulation: A Review of Recent Progress. Presented at 7th International Forum on Reservoir Simulation Bühl/Baden-Baden, Germany, June 23–27, 2003.Google Scholar
[92] Durlofsky, L. J. 2005. Upscaling and Gridding of Fine Scale Geological Models for Flow Simulation. Presented at 8th International Forum on Reservoir Simulation Iles Borromees, Stresa, Italy, June 20–24, 2005.Google Scholar
[93] Durlofsky, L. J., Jones, R. C., and Milliken, W. J. 1997. A nonuniform coarsening approach for the scale-up of displacement processes in heterogeneous porous media. Adv. Water Resour., 20(5-6), 335347. doi:10.1016/S0309-1708(96)00053-X.Google Scholar
[94] Edwards, M. G., and Rogers, C. F. 1994. A flux continuous scheme for the full tensor pressure equation. In: ECMOR IV – 4th European Conference on the Mathematics of Oil Recovery. doi:10.3997/2214-4609.201411178.Google Scholar
[95] Efendiev, Y., and Hou, T. Y. 2009. Multiscale Finite Element Methods: Theory and Applications. New York: Springer-Verlag.Google Scholar
[96] Eigestad, G. T., and Klausen, R. A. 2005. On the convergence of the multi-point flux approximation o-method: Numerical experiments for discontinuous permeability. Num. Meth. Partial Diff. Eqs., 21(6), 10791098. doi:10.1002/num.20079.Google Scholar
[97] Eigestad, G., Dahle, H., Hellevang, B., Riis, F., Johansen, W., and Øian, E. 2009. Geological modeling and simulation of CO2 injection in the Johansen formation. Comput. Geosci., 13(4), 435450. doi:10.1007/s10596-009-9153-y.CrossRefGoogle Scholar
[98] Eikemo, B., Lie, K.-A., Dahle, H. K., and Eigestad, G. T. 2009. Discontinuous Galerkin methods for transport in advective transport in single-continuum models of fractured media. Adv. Water Resour., 32(4), 493506. doi:10.1016/j.advwatres.2008.12.010.Google Scholar
[99] Ertekin, T., Abou-Kassem, J. H., and King, G. R. 2001. Basic Applied Reservoir Simulation. Richardson, TX: Society of Petroleum Engineers.CrossRefGoogle Scholar
[100] Evazi, M., and Mahani, H. 2010a. Generation of Voronoi grid based on vorticity for coarse-scale modeling of flow in heterogeneous formations. Transp. Porous Media, 83(3). doi:10.1007/s11242-009-9458-2.Google Scholar
[101] Evazi, M., and Mahani, H. 2010b. Unstructured-coarse-grid generation using background-grid approach. SPE J., 15(2), 326340. doi:10.2118/120170-PA.Google Scholar
[102] Ewing, R. E., Lazarov, R. D., Lyons, S. L., Papavassiliou, D. V., Pasciak, J., and Qin, G. 1999. Numerical well model for non-Darcy flow through isotropic porous media. Comput. Geosci., 3(3-4), 185204. doi:10.1023/A:1011543412675.Google Scholar
[103] Eymard, R., Gallouët, T., and Herbin, R. 1999. Convergence of finite volume schemes for semilinear convection diffusion equations. Numer. Math., 82(1), 91– 116. doi:10.1007/s002110050412.Google Scholar
[104] Eymard, R., Gallouët, T., and Herbin, R. 2001. Finite volume approximation of elliptic problems and convergence of an approximate gradient. App. Numer. Math., 37(1-2), 3153. doi:10.1016/S0168-9274(00)00024-6.Google Scholar
[105] Eymard, R., Guichard, C., and Herbin, R. 2012a. Small-stencil 3D schemes for diffusive flows in porous media. ESAIM: Math. Model. Numer. Anal., 46(2), 265– 290. doi:10.1051/m2an/2011040.Google Scholar
[106] Eymard, R., Guichard, C., Herbin, R., and Masson, R. 2012b. Vertex-centred discretization of multiphase compositional Darcy flows on general meshes. Comput. Geosci., 16(4), 9871005. doi:10.1007/s10596-012-9299-x.CrossRefGoogle Scholar
[107] Fanchi, J. R. 2005. Principles of Applied Reservoir Simulation. Houston, TX: Gulf Professional Publishing.Google Scholar
[108] Farmer, C. L. 2002. Upscaling: A review. Int. J. Numer. Meth. Fluids, 40(1–2), 63– 78. doi:10.1002/fld.267.Google Scholar
[109] Fayers, F. J., and Matthews, J. D. 1984. Evaluation of normalized Stone’s methods for estimating three-phase relative permeabilities. SPE J., 24(2), 224232. doi:10.2118/11277-PA.Google Scholar
[110] Fink, M. 2007. Automatic Differentiation for Matlab. MATLAB Central. https://tinyurl.com/ycvp6n8a. [Online; accessed July 11, 2018].Google Scholar
[111] Floris, F. J. T., Bush, M. D., Cuypers, M., Roggero, F., and Syversveen, A. R. 2001. Methods for quantifying the uncertainty of production forecasts: a comparative study. Petroleum Geoscience, 7(S), S87–S96. doi:10.1144/petgeo.7.S.S87.Google Scholar
[112] Forth, S. A. 2006. An efficient overloaded implementation of forward mode automatic differentiation in MATLAB. ACM Trans. Math. Software, 32(2), 195222. doi:10.1145/1141885.1141888.Google Scholar
[113] Fung, L. S. K., Ding, X. Y., and Dogru, A. H. 2014. Unconstrained Voronoi grids for densely spaced complex wells in full-field reservoir simulation. SPE J., 19(5), 803815. doi:10.2118/163648-PA.Google Scholar
[114] Gain, A. L., Talischi, C., and Paulino, G. H. 2014. On the virtual element method for three-dimensional linear elasticity problems on arbitrary polyhedral meshes. Comput. Meth. App. Mech. Engng., 282, 132160. doi:10.1016/j.cma.2014.05.005.Google Scholar
[115] Gao, M. 2014. Reservoir and Surface Facilities Coupled through Partially and Fully Implicit Approaches. M.Sc. thesis, Texas A & M University. http://hdl.handle.net/1969.1/154076.Google Scholar
[116] Garcia, M. H., Journel, A. G., and Aziz, K. 1992. Automatic grid generation for modeling reservoir heterogeneities. SPE Reservoir Eng., 7(6), 278284. doi:10.2118/21471-PA.Google Scholar
[117] Gerritsen, M., and Lambers, J. V. 2008. Integration of local-global upscaling and grid adaptivity for simulation of subsurface flow in heterogeneous formations. Comput. Geosci., 12(2), 193208. doi:10.1007/s10596-007-9078-2.Google Scholar
[118] Godunov, S. K. 1959. A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics. Mat. Sb. (N.S.), 47 (89), 271–306.Google Scholar
[119] Gries, S., Stüben, K., Brown, G. L., Chen, D., and Collins, D. A. 2014. Preconditioning for efficiently applying algebraic multigrid in fully implicit reservoir simulations. SPE J., 19(04), 726736. doi:10.2118/163608-PA.Google Scholar
[120] Guérillot, D., Rudkiewicz, J. L., Ravenne, C., Renard, D., and Galli, A. 1990. An integrated model for computer aided reservoir description: From outcrop study to fluid flow simulations. Oil Gas Sci. Technol., 45(1), 7177. doi:10.2516/ogst:1990005.Google Scholar
[121] Gunasekera, D., Cox, J., and Lindsey, P. 1997. The generation and application of K-orthogonal grid systems. In: SPE Reservoir Simulation Symposium. doi:10.2118/37998-MS.Google Scholar
[122] Hægland, H., Dahle, H. K., Lie, K.-A., and Eigestad, G. T. 2006. Adaptive streamline tracing for streamline simulation on irregular grids. In: Binning, P. J., Engesgaard, P. K., Dahle, H. K., Pinder, G. F., and Gray, W. G. (eds), XVI International Conference on Computational Methods in Water Resources. http://proceedings.cmwr-xvi.org/.Google Scholar
[123] Hales, H. B. 1996. A method for creating 2-d orthogonal grids which conform to irregular shapes. SPE J, 1(2), 115124. doi:10.2118/35273-PA.Google Scholar
[124] Hauge, V. L. 2010. Multiscale methods and flow-based gridding for flow and transport in porous media. PhD. thesis, Norwegian University of Science and Technology. http://hdl.handle.net/11250/258800.Google Scholar
[125] Hauge, V. L., Lie, K.-A., and Natvig, J. R. 2012. Flow-based coarsening for multiscale simulation of transport in porous media. Comput. Geosci., 16(2), 391– 408. doi:10.1007/s10596-011-9230-x.Google Scholar
[126] He, C., and Durlofsky, L. J. 2006. Structured flow-based gridding and upscaling for modeling subsurface flow. Adv. Water Resour., 29(12), 18761892. doi:10.1016/j.advwatres.2005.12.012.Google Scholar
[127] He, Z., Parikh, H., Datta-Gupta, A., Perez, J., and Pham, T. 2004. Identifying reservoir compartmentalization and flow barriers from primary production using streamline diffusive time of flight. SPE J., 7(3), 238247. doi:10.2118/88802-PA.Google Scholar
[128] Heinemann, Z. E., Brand, C. W., and Munka, M. 1991. Modeling reservoir geometry with irregular grids. SPE Res. Eng., 6(2), 225232. doi:10.2118/18412-PA.Google Scholar
[129] Helmig, R. 1997. Multiphase Flow and Transport Processes in the Subsurface: A Contribution to the Modeling of Hydrosystems. Berlin, Heidelberg: Springer.Google Scholar
[130] Hilden, S. T., Møyner, O., Lie, K.-A., and Bao, K. 2016. Multiscale simulation of polymer flooding with shear effects. Transp. Porous Media, 113(1), 111135. doi:10.1007/s11242-016-0682-2.Google Scholar
[131] Hilden, S. T. 2016. Upscaling of water-flooding scenarios and modeling of polymer flow. PhD. thesis, Norwegian University of Science and Technology. http://hdl.handle.net/11250/2388331.Google Scholar
[132] Hilden, S. T., Lie, K.-A., and Raynaud, X. 2014. Steady state upscaling of polymer flooding. In: ECMOR XIV – 14th European Conference on the Mathematics of Oil Recovery. doi:10.3997/2214-4609.20141802.Google Scholar
[133] Holden, L., and Nielsen, B. F. 2000. Global upscaling of permeability in heterogeneous reservoirs; the output least squares (OLS) method. Trans. Porous Media, 40(2), 115143. doi:10.1023/A:1006657515753.Google Scholar
[134] Holden, H., and Risebro, N. H. 2002. Front Tracking for Hyperbolic Conservation Laws. New York: Springer-Verlag.CrossRefGoogle Scholar
[135] Hornung, U. 1997. Homogenization and Porous Media. New York: Springer-Verlag.Google Scholar
[136] Hoteit, H., and Firoozabadi, A. 2008. Numerical modeling of two-phase flow in heterogeneous permeable media with different capillarity pressures. Adv. Water Resour., 31(1), 5673. doi:10.1016/j.advwatres.2007.06.006.Google Scholar
[137] Hubbert, M. K. 1956. Darcy’s law and the field equations of the flow of underground fluids. Petrol. Trans., AIME, 207, 22239.Google Scholar
[138] Hui, M.-H. R., Karimi-Fard, M., Mallison, B., and Durlofsky, L. J. 2018. A general modeling framework for simulating complex recovery processes in fractured reservoirs at different resolutions. SPE J., 22(1), 2029. doi:10.2118/182621-MS.Google Scholar
[139] Huseby, O., Sagen, J., and Dugstad, Ø. 2012. Single well chemical tracer tests – Fast and accurate simulations. In: SPE EOR Conference at Oil and Gas West Asia. doi:10.2118/155608-MS.Google Scholar
[140] Idrobo, E. A., Choudhary, M. K., and Datta-Gupta, A. 2000. Swept volume calculations and ranking of geostatistical reservoir models using streamline simulation. In: SPE/AAPG Western Regional Meeting. doi:10.2118/62557-MS.Google Scholar
[141] Iemcholvilert, S. 2013. A Research on production optimization of coupled surface and subsurface model. M.Sc. thesis, Texas A & M University. http://hdl.handle.net/1969.1/151189.Google Scholar
[142] Islam, M. R., Hossain, M. E., Moussavizadegan, S. H., Mustafiz, S., and Abou-Kassem, J. H. 2016. Advanced Petroleum Reservoir Simulation: Towards Developing Reservoir Emulators. John Wiley & Sons, Inc. doi:10.1002/9781119038573.Google Scholar
[143] Islam, M. R., Mousavizadegan, S. H., Mustafiz, S., and Abou-Kassem, J. H. 2010. Advanced Petroleum Reservoir Simulations. Hoboken, NJ: John Wiley & Sons, Inc.Google Scholar
[144] Izgec, O., Sayarpour, M., and Shook, G. M. 2011 . Maximizing volumetric sweep efficiency in waterfloods with hydrocarbon f-ϕ curves. J. Petrol. Sci. Eng., 78(1), 5464. doi:10.1016/j.petrol.2011.05.003.Google Scholar
[145] Jansen, J. D. 2017. Nodal Analysis of Oil and Gas Wells-System Modeling and Numerical Implementation. Richardson, TX: Society of Petroleum Engineers.Google Scholar
[146] Jenny, P., Lee, S. H., and Tchelepi, H. A. 2003. Multi-scale finite-volume method for elliptic problems in subsurface flow simulation. J. Comput. Phys., 187, 4767. doi:10.1016/S0021-9991(03)00075-5.Google Scholar
[147] Jenny, P., Tchelepi, H. A., and Lee, S. H. 2009. Unconditionally convergent nonlinear solver for hyperbolic conservation laws with S-shaped flux functions. J. Comput. Phys., 228(20), 74977512. doi:10.1016/j.jcp.2009.06.032.Google Scholar
[148] Jenny, P., Wolfsteiner, C., Lee, S. H., and Durlofsky, L. J. 2002. Modeling flow in geometrically complex reservoirs using hexahedral multiblock grids. SPE J., 7(2). doi:10.2118/78673-PA.Google Scholar
[149] Jikov, V. V., Kozlov, S. M., and Oleinik, O. A. 1994. Homogenization of Differential Operators and Integral Functionals. New York: Springer-Verlag.Google Scholar
[150] Jimenez, E., Sabir, K., Datta-Gupta, A., and King, M. J. 2007. Spatial error and convergence in streamline simulation. SPE J., 10(3), 221232. doi:10.2118/92873-MS.Google Scholar
[151] Journel, A. G., Deutsch, C. V., and Desbarats, A. J. 1986. Power averaging for block effective permeability. In: SPE California Regional Meeting. doi:10.2118/15128-MS.Google Scholar
[152] Karimi-Fard, M., and Durlofsky, L. J. 2012. Accurate resolution of near-well effects in upscaled models using flow-based unstructured local grid refinement. SPE J., 17(4), 10841095. doi:10.2118/141675-PA.Google Scholar
[153] Karimi-Fard, M., and Durlofsky, L. J. 2016. A general gridding, discretization, and coarsening methodology for modeling flow in porous formations with discrete geological features. Adv. Water Resour., 96(Supplement C), 354–372. doi:10.1016/j.advwatres.2016.07.019.Google Scholar
[154] Karypis, G., and Kumar, V. 1998. A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comp., 20(1), 359392. doi:10.1137/S1064827595287997.Google Scholar
[155] Keilegavlen, E., Kozdon, J. E., and Mallison, B. T. 2012. Multidimensional upstream weighting for multiphase transport on general grids. Comput. Geosci., 16, 1021– 1042. doi:10.1007/s10596-012-9301-7.Google Scholar
[156] Keilegavlen, E., and Nordbotten, J. M. 2017. Finite volume methods for elasticity with weak symmetry. Int. J. Numer. Meth. Eng., 112(8), 939962. doi:10.1002/nme.5538.Google Scholar
[157] Keilegavlen, E., Nordbotten, J. M., and Aavatsmark, I. 2009. Sufficient criteria are necessary for monotone control volume methods. Appl. Math. Letters, 22(8), 1178– 1180. doi:10.1016/j.aml.2009.01.048.Google Scholar
[158] Kenyon, D. 1987. Third SPE comparative solution project: Gas cycling of retrograde condensate reservoirs. J. Petrol. Tech., 39(08), 981997. doi:10.2118/12278-PA.Google Scholar
[159] Killough, J. E. 1995. Ninth SPE comparative solution project: A reexamination of black-oil simulation. In: SPE Reservoir Simulation Symposium. doi:10.2118/29110-MS.Google Scholar
[160] King, M. J. 2007. Recent advances in upgridding. Oil Gas Sci. Technol. – Rev. IFP, 62(2), 195205. doi:10.2516/ogst:2007017.Google Scholar
[161] King, M. J., and Mansfield, M. 1999. Flow simulation of geologic models. SPE Res. Eval. Eng., 2(4), 351367. doi:10.2118/57469-PA.Google Scholar
[162] King, M. J., Burn, K. S., Muralidharan, P. W. V., et al. 2006. Optimal coarsening of 3D reservoir models for flow simulation. SPE Reserv. Eval. Eng., 9(4), 317334. doi:10.2118/95759-PA.Google Scholar
[163] King, M. J., MacDonald, D. G., Todd, S. P., and Leung, H. 1998. Application of novel upscaling approaches to the Magnus and Andrew reservoirs. In: European Petroleum Conference. doi:10.2118/50643-MS.Google Scholar
[164] King, M. J., and Datta-Gupta, A. 1998. Streamline simulation: A current perspective. In Situ, 22(1), 91140.Google Scholar
[165] Kippe, V., Aarnes, J. E., and Lie, K.-A. 2008. A comparison of multiscale methods for elliptic problems in porous media flow. Comput. Geosci., 12(3), 377398. doi:10.1007/s10596-007-9074-6.Google Scholar
[166] Klausen, R. A., Rasmussen, A. F., and Stephansen, A. 2012. Velocity interpolation and streamline tracing on irregular geometries. Comput. Geosci., 16, 261276. doi:10.1007/s10596-011-9256-0.Google Scholar
[167] Klausen, R. A., and Winther, R. 2006. Robust convergence of multi point flux approximation on rough grids. Numer. Math., 104(3), 317337. doi:10.1007/s00211-006-0023-4.Google Scholar
[168] Klemetsdal, Ø. S. 2016. The virtual element method as a common framework for finite element and finite difference methods – numerical and theoretical analysis. M.Sc. thesis, Norwegian University of Science and Technology. http://hdl.handle.net/11250/2405996.Google Scholar
[169] Klemetsdal, Ø. S., Berge, R. L., Lie, K.-A., Nilsen, H. M., and Møyner, O. 2017. Unstructured gridding and consistent discretizations for reservoirs with faults and complex wells. In: SPE Reservoir Simulation Conference. doi:10.2118/182679-MS.Google Scholar
[170] Krogstad, S., Lie, K.-A., Møyner, O., Nilsen, H. M., Raynaud, X., and Skaflestad, B. 2015. MRST-AD – An open-source framework for rapid prototyping and evaluation of reservoir simulation problems. In: SPE Reservoir Simulation Symposium. doi:10.2118/173317-MS.Google Scholar
[171] Krogstad, S., Lie, K.-A., Nilsen, H. M., Berg, C. F., and Kippe, V. 2017. Efficient flow diagnostics proxies for polymer flooding. Comput. Geosci., 21(5-6), 1203– 1218. doi:10.1007/s10596-017-9681-9.Google Scholar
[172] Krogstad, S., Raynaud, X., and Nilsen, H. M. 2016. Reservoir management optimization using well-specific upscaling and control switching. Comput. Geosci., 20(3), 695706. doi:10.1007/s10596-015-9497-4.Google Scholar
[173] Kružkov, S. N. 1970. First order quasilinear equations in several independent variables. Mathematics of the USSR-Sbornik, 10(2), 217. doi:10.1070/SM1970v010n02ABEH002156.Google Scholar
[174] Kurganov, A., Noelle, S., and Petrova, G. 2001. Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton–Jacobi equations. SIAM J. Sci. Comp., 23(3), 707740. doi:10.1137/S1064827500373413.Google Scholar
[175] Kwok, F., and Tchelepi, H. 2007. Potential-based reduced Newton algorithm for nonlinear multiphase flow in porous media. J. Comput. Phys., 227(1), 706727. doi:10.1016/j.jcp.2007.08.012.Google Scholar
[176] Lake, L. W. 1989. Enhanced Oil Recovery. Upper Saddle River, NJ: Prentice-Hall.Google Scholar
[177] Lake, L. W. (ed). 2007. Petroleum Engineering Handbook. Richardson, TX: Society of Petroleum Engineers.Google Scholar
[178] Lax, P., and Wendroff, B. 1960. Systems of conservation laws. Comm. Pure Appl. Math., 13(2), 217237. doi:10.1002/cpa.3160130205.Google Scholar
[179] Le Potier, C. 2009. A nonlinear finite volume scheme satisfying maximum and minimum principles for diffusion operators. Int. J. Finite Vol., 6(2), 120.Google Scholar
[180] Lee, S. H., Jenny, P., and Tchelepi, H. A. 2002. A finite-volume method with hexahedral multiblock grids for modeling flow in porous media. Comput. Geosci., 6(3-4), 353379. doi:10.1023/A:1021287013566.Google Scholar
[181] Leeuwenburgh, O., and Arts, R. 2014. Distance parameterization for efficient seismic history matching with the ensemble Kalman Filter. Comput. Geosci., 18(3– 4), 535–548. doi:10.1007/s10596-014-9434-y.Google Scholar
[182] Leeuwenburgh, O., Peters, E., and Wilschut, F. 2011. Towards an integrated workflow for structural reservoir model updating and history matching. In: SPE EUROPEC/EAGE Annual Conference and Exhibition. doi:10.2118/143576-MS.Google Scholar
[183] LeVeque, R. J. 2002. Finite Volume Methods for Hyperbolic Problems. Cambridge: Cambridge University Press.Google Scholar
[184] Leverett, M. C. 1941. Capillary behavior in porous solids. Trans. AIME, 142, 159– 172. doi:10.2118/941152-G.Google Scholar
[185] Li, X., and Zhang, D. 2014. A backward automatic differentiation framework for reservoir simulation. Comput. Geosci., 18(6), 10091022. doi:10.1007/s10596-014-9441-z.Google Scholar
[186] Lie, K.-A. 2018. On Holden’s seven guidelines for scientific computing and development of open-source community software. In: Gesztesy, F., et al. (eds), Non-Linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis: The Helge Holden Anniversary Volume. European Mathematical Society Publishing House. pp. 389–422.Google Scholar
[187] Lie, K.-A., Kedia, K., Skaflestad, B., et al. 2017a. A general non-uniform coarsening and upscaling framework for reduced-order modeling. In: SPE Reservoir Simulation Conference. doi:10.2118/182681-MS.Google Scholar
[188] Lie, K.-A. 2015a. JOLT 1: Introduction to MRST. SINTEF ICT / ICME, Stanford University. www.sintef.no/mrst-jolts.Google Scholar
[189] Lie, K.-A. 2015b. JOLT 2: Grids and petrophysical data. SINTEF ICT / ICME, Stanford University. www.sintef.no/mrst-jolts.Google Scholar
[190] Lie, K.-A., Mykkeltvedt, T. S., and Møyner, O. 2018. Fully implicit WENO schemes on stratigraphic and fully unstructured grids. In: ECMOR XVI – 16th European Conference on the Mathematics of Oil Recovery.Google Scholar
[191] Lie, K.-A., Møyner, O., and Natvig, J. R. 2017a. Use of multiple multiscale operators to accelerate simulation of complex geomodels. SPE J., 22(6), 19291945. doi:10.2118/182701-PA.Google Scholar
[192] Lie, K.-A., Krogstad, S., Ligaarden, I. S., et al. 2012b. Open-source MATLAB implementation of consistent discretisations on complex grids. Comput. Geosci., 16, 297322. doi:10.1007/s10596-011-9244-4.Google Scholar
[193] Lie, K.-A., Nilsen, H. M., Andersen, O., and Møyner, O. 2016. A simulation workflow for large-scale CO2 storage in the Norwegian North Sea. Comput. Geosci., 20(3), 607622. doi:10.1007/s10596-015-9487-6.Google Scholar
[194] Lie, K.-A., Natvig, J. R., Krogstad, S., Yang, Y., and Wu, X.-H. 2014. Grid adaptation for the Dirichlet–Neumann representation method and the multiscale mixed finite-element method. Comput. Geosci., 18(3), 357372. doi:10.1007/s10596-013-9397-4.Google Scholar
[195] Lie, K.-A., Møyner, O., Natvig, J. R., et al. 2017b. Successful application of multiscale methods in a real reservoir simulator environment. Comput. Geosci., 21(5-6), 981998. doi:10.1007/s10596-017-9627-2.Google Scholar
[196] Lie, K.-A., Natvig, J. R., and Nilsen, H. M. 2012a. Discussion of dynamics and operator splitting techniques for two-phase flow with gravity. Int. J. Numer. Anal. Mod., 9(3), 684700.Google Scholar
[197] Ligaarden, I. S. 2008. Well models for mimetic finite difference methods and improved representation of wells in multiscale methods. M.Sc. thesis, University of Oslo. http://urn.nb.no/URN:NBN:no-19435.Google Scholar
[198] Lipnikov, K., Shashkov, M., Svyatskiy, D., and Vassilevski, Y. 2007. Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes. J. Comput. Phys., 227(1), 492512. doi:10.1016/j.jcp.2007.08.008.Google Scholar
[199] Lipnikov, K., Shashkov, M., and Yotov, I. 2009. Local flux mimetic finite difference methods. Numer. Math., 112(1), 115152. doi:10.1007/s00211-008-0203-5.Google Scholar
[200] Lunati, I., and Lee, S. H. 2009. An operator formulation of the multiscale finite-volume method with correction function. Multiscale Model. Simul., 8(1), 96109. doi:10.1137/080742117.Google Scholar
[201] Mahani, H., Muggeridge, A. H., and Ashjari, M. A. 2009. Vorticity as a measure of heterogeneity for improving coarse grid generation. Petrol. Geosci., 15(1), 91102. doi:10.1144/1354-079309-802.Google Scholar
[202] Mallison, B., Sword, C., Viard, T., Milliken, W., and Cheng, A. 2014. Unstructured cut-cell grids for modeling complex reservoirs. SPE J., 19(2), 340352. doi:10.2118/163642-PA.Google Scholar
[203] Manzocchi, T., et al. 2008. Sensitivity of the impact of geological uncertainty on production from faulted and unfaulted shallow-marine oil reservoirs: Objectives and methods. Petrol. Geosci., 14(1), 315. doi:10.1144/1354-079307-790.Google Scholar
[204] Matringe, S. F., and Gerritsen, M. G. 2004. On accurate tracing of streamlines. In: SPE Annual Technical Conference and Exhibition. doi:10.2118/89920-MS.Google Scholar
[205] Matringe, S. F., Juanes, R., and Tchelepi, H. A. 2007. Streamline tracing on general triangular or quadrilateral grids. SPE J., 12(2), 217233. doi:10.2118/96411-MS.Google Scholar
[206] Mattax, C. C., and Dalton, R. L. (eds). 1990. Reservoir Simulation. Society of Petroleum Engineers.Google Scholar
[207] McCain, W. D. Jr. 1990. The Properties of Petroleum Fluids. 2nd edn. Tulsa, OK: PennWell Books.Google Scholar
[208] McIlhagga, W. 2010. Automatic Differentiation with Matlab Objects. MATLAB Central. https://tinyurl.com/yavlcra4. [Online; accessed July 11, 2018].Google Scholar
[209] Merland, R., Caumon, G., Lévy, B., and Collon-Drouaillet, P. 2014. Voronoi grids conforming to 3d structural features. Comput. Geosci., 18(3-4), 373383. doi:10.1007/s10596-014-9408-0.Google Scholar
[210] Mlacnik, M. J., Durlofsky, L. J., and Heinemann, Z. E. 2006. Sequentially adapted flow-based PEBI grids for reservoir simulation. SPE J., 11(3), 317327. doi:10.2118/90009-PA.Google Scholar
[211] Møyner, O. 2012. Multiscale finite-volume methods on unstructured grids. M.Sc. thesis, Norwegian University of Science and Technology. http://hdl.handle.net/11250/259015.Google Scholar
[212] Møyner, O. 2016. Next generation multiscale methods for reservoir simulation. PhD. thesis, Norwegian University of Science and Technology. http://hdl.handle.net/11250/2431831.Google Scholar
[213] Møyner, O. 2017. Nonlinear solver for three-phase transport problems based on approximate trust regions. Comput. Geosci., 21(5-6), 9991021. doi:10.1007/s10596-017-9660-1.Google Scholar
[214] Møyner, O., and Lie, K.-A. 2014. The multiscale finite-volume method on stratigraphic grids. SPE J., 19(5), 816831. doi:10.2118/163649-PA.Google Scholar
[215] Møyner, O., and Lie, K.-A. 2016a. A multiscale restriction-smoothed basis method for compressible black-oil models. SPE J., 21(06), 20792096. doi:10.2118/173265-PA.Google Scholar
[216] Møyner, O., and Lie, K.-A. 2016b. A multiscale restriction-smoothed basis method for high contrast porous media represented on unstructured grids. J. Comput. Phys., 304, 4671. doi:10.1016/j.jcp.2015.10.010.Google Scholar
[217] Møyner, O., and Tchelepi, H. A. 2017. A multiscale restriction-smoothed basis method for compositional models. In: SPE Reservoir Simulation Conference. doi:10.2118/182679-MS.Google Scholar
[218] Møyner, O., Krogstad, S., and Lie, K.-A. 2014. The application of flow diagnostics for reservoir management. SPE J., 20(2), 306323. doi:10.2118/171557-PA.CrossRefGoogle Scholar
[219] Muskat, M., and Wyckoff, R. D. 1937. The Flow of Homogeneous Fluids through Porous Media. Vol. 12. New York: McGraw-Hill.Google Scholar
[220] Natvig, J. R., and Lie, K.-A. 2008. Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements. J. Comput. Phys., 227(24), 1010810124. doi:10.1016/j.jcp.2008.08.024.Google Scholar
[221] Natvig, J. R., Lie, K.-A., Eikemo, B., and Berre, I. 2007. An efficient discontinuous Galerkin method for advective transport in porous media. Adv. Water Resour., 30(12), 24242438. doi:10.1016/j.advwatres.2007.05.015.Google Scholar
[222] Natvig, J. R., Skaflestad, B., Bratvedt, F., et al. 2011. Multiscale mimetic solvers for efficient streamline simulation of fractured reservoirs. SPE J., 16(4), 880888. doi:10.2018/119132-PA.Google Scholar
[223] Neidinger, R. 2010. Introduction to automatic differentiation and MATLAB object-oriented programming. SIAM Review, 52(3), 545563. doi:10.1137/080743627.Google Scholar
[224] Nessyahu, H., and Tadmor, E. 1990. Nonoscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys., 87(2), 408463. doi:10.1016/0021-9991(90)90260-8.Google Scholar
[225] Nielsen, B. F., and Tveito, A. 1998. An upscaling method for one-phase flow in heterogeneous reservoirs; A Weighted Output Least Squares (WOLS) approach. Comput. Geosci., 2, 92123. doi:0.1023/A:1011541917701.Google Scholar
[226] Nikitin, K., Terekhov, K., and Vassilevski, Y. 2014. A monotone nonlinear finite volume method for diffusion equations and multiphase flows. Comput. Geos., 18(3-4), 311324. doi:10.1007/s10596-013-9387-6.Google Scholar
[227] Nilsen, H. M., Lie, K.-A., and Andersen, O. 2016b. Robust simulation of sharp-interface models for fast estimation of CO2 trapping capacity. Comput. Geosci., 20(1), 93113. doi:10.1007/s10596-015-9549-9.CrossRefGoogle Scholar
[228] Nilsen, H. M., Lie, K.-A., and Andersen, O. 2016a. Fully implicit simulation of vertical-equilibrium models with hysteresis and capillary fringe. Comput. Geosci., 20(1), 4967. doi:10.1007/s10596-015-9547-y.Google Scholar
[229] Nilsen, H. M., Nordbotten, J. M., and Raynaud, X. 2018. Comparison between cell-centered and nodal based discretization schemes for linear elasticity. Comput. Geosci., 22(1), 233260. doi:10.1007/s10596-017-9687-3.Google Scholar
[230] Nilsen, H. M., Lie, K.-A., Møyner, O., and Andersen, O. 2015b. Spill-point analysis and structural trapping capacity in saline aquifers using MRST-co2lab. Comput. Geosci., 75, 3343. doi:10.1016/j.cageo.2014.11.002.Google Scholar
[231] Nilsen, H. M., Lie, K.-A., and Natvig, J. R. 2012. Accurate modelling of faults by multipoint, mimetic, and mixed methods. SPE J., 17(2), 568579. doi:10.2118/149690-PA.Google Scholar
[232] Nilsen, H. M., Lie, K.-A., and Andersen, O. 2015a. Analysis of CO2 trapping capacities and long-term migration for geological formations in the Norwegian North Sea using MRST-co2lab. Comput. Geosci., 79, 1526. doi:10.1016/j.cageo.2015. 03.001.Google Scholar
[233] Nordbotten, J. M. 2016. Stable cell-centered finite volume discretization for biot equations. SIAM J. Numer. Anal., 54(2), 942968. doi:10.1137/15M1014280.Google Scholar
[234] Nordbotten, J. M., and Eigestad, G. T. 2005. Discretization on quadrilateral grids with improved monotonicity properties. J. Comput. Phys., 203(2), 744760. doi:10.1016/j.jcp.2004.10.002.Google Scholar
[235] Nordbotten, J. M., Aavatsmark, I., and Eigestad, G. T. 2007b. Monotonicity of control volume methods. Numer. Math., 106(2), 255288. doi:10.1007/s00211-006-0060-z.Google Scholar
[236] Nordbotten, J. M., and Aavatsmark, I. 2005. Monotonicity conditions for control volume methods on uniform parallelogram grids in homogeneous media. Comput. Geosci., 9(1), 6172. doi:10.1007/s10596-005-5665-2.Google Scholar
[237] Nordbotten, J. M. 2015. Convergence of a cell-centered finite volume discretization for linear elasticity. SIAM J. Numer. Anal., 53(6), 26052625. doi:10.1137/140972792.Google Scholar
[238] Notay, Y. 2010. An aggregation-based algebraic multigrid method. Electron. Trans. Numer. Anal., 37, 123140.Google Scholar
[239] Nutting, P. G. 1930. Physical analysis of oil sands. AAPG Bulletin, 14(10), 1337– 1349.Google Scholar
[240] Obi, E., Eberle, N., Fil, A., and Cao, H. 2014. Giga cell compositional simulation. In: IPTC 2014: International Petroleum Technology Conference. doi:10.2523/IPTC-17648-MS.Google Scholar
[241] Odeh, A. S. 1981. Comparison of solutions to a three-dimensional black-oil reservoir simulation problem. J. Petrol. Techn., 33(1), 1325. doi:10.2118/9723-PA.Google Scholar
[242] Øren, P.-E., Bakke, S., and Arntzen, O. J. 1998. Extending predictive capabilities to network models. SPE J., 3(4), 324336. doi:10.2118/52052-PA.Google Scholar
[243] Pal, M., Lamine, S., Lie, K.-A., and Krogstad, S. 2015. Validation of the multiscale mixed finite-element method. Int. J. Numer. Meth. Fluids, 77(4), 206223. doi:10.1002/fld.3978.Google Scholar
[244] Park, H.-Y., and Datta-Gupta, A. 2011. Reservoir management using streamline-based flood efficiency maps and application to rate optimization. In: SPE Western North American Region Meeting. doi:10.2118/144580-MS.Google Scholar
[245] Peaceman, D. W. 1983. Interpretation of well-block pressures in numerical reservoir simulation with nonsquare grid blocks and anisotropic permeability. Soc. Petrol. Eng. J., 23(3), 531543. doi:10.2118/10528-PA.Google Scholar
[246] Peaceman, D. W. 1991. Fundamentals of Numerical Reservoir Simulation. New York, NY, USA: Elsevier Science Inc.Google Scholar
[247] Peaceman, D. W. 1978. Interpretation of well-block pressures in numerical reservoir simulation. Soc. Petrol. Eng. J., 18(3), 183—194. doi:10.2118/6893-PA.Google Scholar
[248] Persson, P.-O., and Strang, G. 2004. A simple mesh generator in MATLAB. SIAM Review, 46(2), 329345. doi:10.1137/S0036144503429121.Google Scholar
[249] Peters, L., Arts, R., Brouwer, G., et al. 2010. Results of the Brugge benchmark study for flooding optimization and history matching. SPE Reser. Eval. Eng., 13(03), 391– 405. doi:10.2118/119094-PA.Google Scholar
[250] Pettersen, Ø. 2006. Basics of Reservoir Simulation with the Eclipse Reservoir Simulator. Lecture Notes. Department of Mathematics, University of Bergen. http://folk.uib.no/fciop/index_htm_files/ResSimNotes.pdf.Google Scholar
[251] Pettersen, Ø. 2012. Horizontal simulation grids as alternative to structure-based grids for thin oil-zone problems: A comparison study on a Troll segment. Comput. Geosci., 16(2), 211230. doi:10.1007/s10596-011-9240-8.Google Scholar
[252] Pinder, G. F., and Gray, W. G. 2008. Essentials of Multiphase Flow in Porous Media. Hoboken, NJ: John Wiley & Sons.Google Scholar
[253] Pollock, D. W. 1988. Semi-analytical computation of path lines for finite-difference models. Ground Water, 26(6), 743750. doi:10.1111/j.1745-6584.1988.tb00425.x.Google Scholar
[254] Ponting, D. K. 1989. Corner point geometry in reservoir simulation. In: King, P. R. (ed), ECMOR I – 1st European Conference on the Mathematics of Oil Recovery. Oxford: Clarendon Press, pp. 4565. doi:10.3997/2214-4609.201411305.Google Scholar
[255] Potempa, T. C. 1982. Finite element methods for convection dominated transport problems. PhD. thesis, Rice University. http://hdl.handle.net/1911/15714.Google Scholar
[256] Prevost, M., Edwards, M. G., and Blunt, M. J. 2002. Streamline tracing on curvilinear structured and unstructured grids. SPE J., 7(2), 139148. doi:10.2118/78663-PA.Google Scholar
[257] Prevost, M., Lepage, F., Durlofsky, L. J., and Mallet, J.-L. 2005. Unstructured 3D gridding and upscaling for coarse modelling of geometrically complex reservoirs. Petrol. Geosci., 11(4), 339345. doi:10.1144/1354-079304-657.Google Scholar
[258] Pyrcz, M. J., and Deutsch, C. V. 2014. Geostatistical Reservoir Modeling. Oxford: Oxford University Press.Google Scholar
[259] Rashid, B., Muggeridge, A., Bal, A.-L., and Williams, G. J. J. 2012a. Quantifying the impact of permeability heterogeneity on secondary-recovery performance. SPE J., 17(2), 455468. doi:10.2118/135125-PA.Google Scholar
[260] Rashid, B., Bal, A.-L., Williams, G. J. J., and Muggeridge, A. H. 2012b. Using vorticity to quantify the relative importance of heterogeneity, viscosity ratio, gravity and diffusion on oil recovery. Comput. Geosci., 16(2), 409422. doi:10.1007/s10596-012-9280-8.Google Scholar
[261] Rasmussen, A. F., and Lie, K.-A. 2014. Discretization of flow diagnostics on stratigraphic and unstructured grids. In: ECMOR XIV – 14th European Conference on the Mathematics of Oil Recovery. doi:10.3997/2214-4609.20141844.Google Scholar
[262] Raviart, P. A., and Thomas, J. M. 1977. A mixed finite element method for 2nd order elliptic equations. In: Galligani, I., and Magenes, E. (eds), Mathematical Aspects of Finite Element Methods. Berlin, Heidelberg, New York: Springer-Verlag.Google Scholar
[263] Renard, P., and De Marsily, G. 1997. Calculating equivalent permeability: A review. Adv. Water Resour., 20(5), 253278. doi:10.1016/S0309-1708(96)00050-4.Google Scholar
[264] Richards, L. A. 1931. Capillary conduction of liquids through porous mediums. J. App. Phys., 1(5), 318333. doi:10.1063/1.1745010.Google Scholar
[265] Ringrose, P., and Bentley, M. 2015. Reservoir Model Design: A Practitioner’s Guide. New York: Springer.Google Scholar
[266] Samier, P. 1990. A finite element method for calculation transmissibilities in n-point difference equations using a non-diagonal permeability tensor. In: Guérillot, D. (ed), ECMOR II – 2nd European Conference on the Mathematics of Oil Recovery. Editions TECHNIP, pp. 121–130. doi:10.3997/2214-4609.201411106.Google Scholar
[267] Samier, P., and Masson, R., 2017. Implementation of a vertex-centered method inside an industrial reservoir simulator: Practical issues and comprehensive comparison with corner-point grids and perpendicular-bisector-grid models on a field case. SPE J., 22(02), 660678. doi:10.2118/173309-PA.Google Scholar
[268] Sandve, T. H., Berre, I., and Nordbotten, J. M. 2012. An efficient multi-point flux approximation method for discrete fracture matrix simulations. J. Comput. Phys., 231(9), 37843800. doi:10.1016/j.jcp.2012.01.023.Google Scholar
[269] Schlumberger, . 1999. ECLIPSE 100 User Course. Schlumberger GeoQuest.Google Scholar
[270] Schlumberger, . 2014a. ECLIPSE: Reference Manual. 2014.1 edn. Schlumberger.Google Scholar
[271] Schlumberger, . 2014b. ECLIPSE Reservoir Simulation Software: Technical Description. 2014.1 edn. Schlumberger.Google Scholar
[272] Schneider, M., Flemisch, B., and Helmig, R. 2017. Monotone nonlinear finite-volume method for nonisothermal two-phase two-component flow in porous media. Int. J. Numer. Meth. Fluids, 84(6), 352381. doi:10.1002/fld.4352.Google Scholar
[273] Shah, S., Møyner, O., Tene, M., Lie, K.-A., and Hajibeygi, H. 2016. The multiscale restriction smoothed basis method for fractured porous media. J. Comput. Phys., 318, 3657. doi:10.1016/j.jcp.2016.05.001.Google Scholar
[274] Shahvali, M., Mallison, B., Wei, K., and Gross, H. 2012. An alternative to streamlines for flow diagnostics on structured and unstructured grids. SPE J., 17(3), 768– 778. doi:10.2118/146446-PA.Google Scholar
[275] Shampine, L. F., Ketzscher, R., and Forth, S. A. 2005. Using AD to solve BVPs in MATLAB. ACM Trans. Math. Software, 31(1), 7994. doi:10.1145/1055531.1055535.Google Scholar
[276] Sheldon, J. W., Harris, C. D., and Bavly, D. 1960. A method for general reservoir behavior simulation on digital computers. In: Fall Meeting of the Society of Petroleum Engineers of AIME. doi:10.2118/1521-G.Google Scholar
[277] Shook, G. M., and Forsmann, J. H. 2005. Tracer Interpretation Using Temporal Moments on a Spreadsheet. Tech. rept. INL report 05-00400. Idaho National Laboratory.Google Scholar
[278] Shook, G., and Mitchell, K. 2009. A robust measure of heterogeneity for ranking earth models: The F-Phi curve and dynamic Lorenz coefficient. In: SPE Annual Technical Conference and Exhibition. doi:10.2118/124625-MS.Google Scholar
[279] Shubin, G. R., and Bell, J. B. 1984. An analysis of the grid orientation effect in numerical simulation of miscible displacement. Comput. Methods Appl. Mech. Eng., 47(1), 4771. doi:10.1016/0045-7825(84)90047-1.Google Scholar
[280] Spillette, A. G., Hillestad, J. G., and Stone, H. L. 1973. A high-stability sequential solution approach to reservoir simulation. In: Fall Meeting of the Society of Petroleum Engineers of AIME. doi:542-MS.Google Scholar
[281] Stephansen, A. F., and Klausen, R. A. 2008. Mimetic MPFA. In: ECMOR XI – 11th European Conference on the Mathematics of Oil Recovery. doi:10.3997/2214-4609.20146365.Google Scholar
[282] Stone, H. L. 1970. Probability model for estimating three-phase relative permeability. J. Petrol. Tech., 22(02), 214218. doi:10.2118/2116-PA.Google Scholar
[283] Stone, H. L. 1973. Estimation of three-phase relative permeability and residual oil data. J. Pet. Technol., 12(4). doi:10.2118/73-04-06.Google Scholar
[284] Stone, H. L., and Garder, A. O. Jr. 1961. Analysis of gas-cap or dissolved-gas drive reservoirs. SPE J., 1(02), 92104. doi:10.2118/1518-G.Google Scholar
[285] Stüben, K. 2001. A review of algebraic multigrid. J. Comput. Appl. Math., 128(1), 281309. doi:10.1016/S0377-0427(00)00516-1.Google Scholar
[286] Technische Universität Darmstadt. Automatic Differentiation for Matlab (ADiMat). http://www.adimat.de/. [Online; accessed July 11, 2018].Google Scholar
[287] Thiele, M. R., and Batycky, R. P. 2003. Water injection optimization using a streamline-based workflow. In: SPE Annual Technical Conference and Exhibition. doi:10.2118/84080-MS.Google Scholar
[288] Thomas, G. W. 1981. Principles of Hydrocarbon Reservoir Simulation. Boston: IHRDC.Google Scholar
[289] Todd, M. R. and Longstaff, W. J. 1972a. The development, testing, and application of a numerical simulator for predicting miscible flood performance. J. Petrol. Tech., 24(07), 874882. doi:10.2118/3484-PA.Google Scholar
[290] Todd, M. R., O’Dell, P. M., and Hirasaki, G. J. 1972b. Methods for increased accuracy in numerical reservoir simulators. Soc. Petrol. Eng. J., 12(06), 515530. doi:10.2118/3516-PA.Google Scholar
[291] Tomlab Optimization Inc. Matlab Automatic Differentiation (MAD). http://matlabad.com/. [Online; accessed July 11, 2018].Google Scholar
[292] Toor, S. M., Edwards, M. G., Dogru, A. H., and Shaalan, T. M. 2015. Boundary aligned grid generation in three dimensions and CVD-MPFA discretization. In: SPE Reservoir Simulation Symposium. doi:10.2118/173313-MS.Google Scholar
[293] Toro, E. F. 2009. Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction. 3rd edn. Berlin: Springer-Verlag.Google Scholar
[294] Trangenstein, J. A. 2009. Numerical solution of hyperbolic partial differential equations. Cambridge: Cambridge University Press.Google Scholar
[295] Trangenstein, J. A., and Bell, J. B. 1989. Mathematical structure of the black-oil model for petroleum reservoir simulation. SIAM J. Appl. Math., 49(3), 749783. doi:10.1137/0149044.Google Scholar
[296] Trottenberg, U., Oosterlee, C. W., and Schüller, A. 2000. Multigrid. Academic press.Google Scholar
[297] Ucar, E., Berre, I., and Keilegavlen, E. 2015. Simulation of slip-induced permeability enhancement accounting for multiscale fractures. In: Fourtieth Workshop on Geothermal Reservoir Engineering.Google Scholar
[298] van Genuchten, M. T. 1980. Closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Soc. America J., 44(5), 892898. doi:10.2136/sssaj1980.03615995004400050002x.Google Scholar
[299] Varela, J. 2018. Implementation of an MPFA/MPSA-FV solver for the unsaturated flow in deformable porous media. M.Sc. thesis, University of Bergen. http://hdl.handle.net/1956/17905.Google Scholar
[300] Verma, A. 1999. ADMAT: Automatic differentiation in MATLAB using object oriented methods. In: Henderson, M. E., Anderson, C. R., and Lyons, S. L. (eds), Object Oriented Methods for Interoperable Scientific and Engineering Computing: Proceedings of the 1998 SIAM Workshop. Philadelphia: SIAM, pp. 174183.Google Scholar
[301] Verma, S., and Aziz, K. 1997. A control volume scheme for flexible grids in reservoir simulation. In: SPE Reservoir Simulation Symposium. doi:10.2118/37999-MS.Google Scholar
[302] Voskov, D. V., and Tchelepi, H. A. 2012. Comparison of nonlinear formulations for two-phase multi-component eos based simulation. J. Petrol. Sci. Engrg., 82–83(0), 101111. doi:10.1016/j.petrol.2011.10.012.Google Scholar
[303] Voskov, D. V., Tchelepi, H. A., and Younis, R. 2009. General nonlinear solution strategies for multiphase multicomponent EoS based simulation. In: SPE Reservoir Simulation Symposium. doi:10.2118/118996-MS.Google Scholar
[304] Wallis, J. R. 1983. Incomplete gaussian elimination as a preconditioning for generalized conjugate gradient acceleration. In: SPE Reservoir Simulation Symposium. doi:10.2118/12265-MS.Google Scholar
[305] Wallis, J. R., Kendall, R. P., and Little, T. E. 1985. Constrained residual acceleration of conjugate residual methods. In: SPE Reservoir Simulation Symposium. doi:10.2118/13536-MS.Google Scholar
[306] Wang, X., and Tchelepi, H. A. 2013. Trust-region based solver for nonlinear transport in heterogeneous porous media. J. Comp. Phys., 253, 114137. doi:10.1016/j.jcp.2013.06.041.Google Scholar
[307] Watts, J. W. 1986. A compositional formulation of the pressure and saturation equations. SPE Res. Eng., 1(3), 243252. doi:10.2118/12244-PA.Google Scholar
[308] Weiser, A., and Wheeler, M. F. 1988. On convergence of block-centered finite differences for elliptic problems. SIAM J. Numer. Anal., 25(2), 351375. doi:10.1137/0725025.Google Scholar
[309] Welge, H. J. 1952. A simplified method for computing oil recovery by gas or water drive. J. Petrol. Tech., 4(04), 9198. doi:10.2118/124-G.Google Scholar
[310] Wen, X. H., Durlofsky, L. J., and Edwards, M. G. 2003. Upscaling of channel systems in two dimensions using flow-based grids. Transp. Porous Media, 51(3), 343366. doi:10.1023/A:1022318926559.Google Scholar
[311] Wen, X.-H., and Gómez-Hernández, J. J. 1996. Upscaling hydraulic conductivities in heterogeneous media: An overview. J. Hydrol., 183, ixxxxii. doi:10.1016/S0022-1694(96)80030-8.Google Scholar
[312] Wheeler, J. A., Wheeler, M. F., and Yotov, I. 2002. Enhanced velocity mixed finite element methods for flow in multiblock domains. Comput. Geosci., 6(3-4), 315332. doi:10.1023/A:1021270509932.Google Scholar
[313] Wheeler, M. F., Arbogast, T., Bryant, S., et al. 1999. A parallel multiblock/multidomain approach for reservoir simulation. In: SPE Reservoir Simulation Symposium, pp. 5161.Google Scholar
[314] Wheeler, M. F., and Yotov, I. 2006. A cell-centered finite difference method on quadrilaterals. In: Arnold, D. N., Bochev, P. B., Lehoucq, R. B., Nicolaides, R. A., and Shashkov, M. (eds), Compatible Spatial Discretizations. New York: Springer, pp. 189207.Google Scholar
[315] Whitaker, S. 1986. Flow in porous media I: A theoretical derivation of Darcy’s law. Transp. Porous Media, 1(1), 325. doi:10.1007/BF01036523.Google Scholar
[316] Whitson, C. H., and Brulé, M. R. 2000. Phase Behavior. Richardson, TX: Society of Petroleum Engineers.Google Scholar
[317] Wiener, O. 1912. Abhandlungen der Matematisch. PhD. thesis, Physischen Klasse der Königlichen Sächsischen Gesellscaft der Wissenschaften.Google Scholar
[318] Wu, X.-H., Efendiev, Y., and Hou, T. Y. 2002 . Analysis of upscaling absolute permeability. Discrete Contin. Dyn. Syst. Ser. B, 2(2), 185204. doi:10.3934/dcdsb.2002.2.185.Google Scholar
[319] Wu, X.-H., and Parashkevov, R. 2009. Effect of grid deviation on flow solutions. SPE J., 14(01), 67–77. doi:10.218/92868-PA.Google Scholar
[320] Wyckoff, R. D., Botset, H. G., Muskat, M., and Reed, D. W. 1933. The measurement of the permeability of porous media for homogeneous fluids. Rev. Sci. Instrum., 4(7), 394405. doi:10.1063/1.1749155.Google Scholar
[321] Yanosik, J. L., and McCracken, T. A. 1979. A nine-point, finite-difference reservoir simulator for realistic prediction of adverse mobility ratio displacements. Soc. Petrol. Eng. J., 19(04), 253262. doi:10.2118/5734-PA.Google Scholar
[322] Younis, R. 2009. Advances in modern computational methods for nonlinear problems: A generic efficient automatic differentiation framework, and nonlinear solvers that converge all the time. Ph.D. thesis, Stanford University.Google Scholar
[323] Younis, R., and Aziz, K. 2007. Parallel automatically differentiable data-types for next-generation simulator development. In: SPE Reservoir Simulation Symposium. doi:10.2118/106493-MS.Google Scholar
[324] Zhang, P., Pickup, G. E., and Christie, M. A. 2005. A new upscaling approach for highly heterogenous reservoirs. In: SPE Reservoir Simulation Symposium. doi:10.2118/93339-MS.Google Scholar
[325] Zhou, Y., Tchelepi, H. A., and Mallison, B. T. 2011. Automatic differentiation framework for compositional simulation on unstructured grids with multi-point discretization schemes. In: SPE Reservoir Simulation Symposium. doi:10.2118/141592-MS.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Knut-Andreas Lie
  • Book: An Introduction to Reservoir Simulation Using MATLAB/GNU Octave
  • Online publication: 22 July 2019
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Knut-Andreas Lie
  • Book: An Introduction to Reservoir Simulation Using MATLAB/GNU Octave
  • Online publication: 22 July 2019
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Knut-Andreas Lie
  • Book: An Introduction to Reservoir Simulation Using MATLAB/GNU Octave
  • Online publication: 22 July 2019
Available formats
×