

SUPER ELEMENT METHOD OF PETROLEUM RESERVOIR SIMULATION
Mazo A.B., Potashev K.A., Kalinin E.I.
Kazan (Volga Region) Federal University, Kazan, Russia
Citation:
Mazo A.B. Super element method of petroleum reservoir simulation / A.B. Mazo, K.A. Potashev, E.I. Kalinin // Modern Science: Researches, Ideas, Results, Technologies.  Dnepropetrovsk: SPIC "Triacon".  2013.  Iss. #1(12).  PP. 237  243

Keywords: oil reservoir simulation; twophase flow in porous media; coarse unstructured grids; super element method 
Abstracts:
In present work a new effective method of petroleum reservoir simulation is presented. The method is based on a numerical solution of 3D twophase filtration flow equations on coarse unstructured grids. Each grid cell represents a 3D superelement which is bounded by a Voronoi cell around a well projection in a horizontal plane (200 – 400 m. across) and by borders of a geological pack in a vertical direction. Such grid is appropriate to represent average pressure and saturation fields with a sufficient accuracy and promotes hundredfold increase in a computational time as compared to the detailed solvers. A sufficient accuracy of calculation results is provided by upscaling of reservoir properties and by utilization of detailed embedded grids in areas of high pressure gradients (near well bores, geological faults, hydraulic fractures). The superelement method has been successfully used for modeling of a number of real petroleum reservoirs. The comparison of results gained by presented method versus results of detailed grid simulation conﬁrmed wide computational opportunities of the superelement method which provides hundredfold increase of calculation performance and doesn’t entail large computational error. 
References:
Mazo, A.B. and Bulygin, D.V. (2011), "Super elements. New approach to modeling the development of oil reservoirs", Neft, Gas, Novatsii, no. 11, pp. 68.
Mazo, A.B., Potashev, K.A., Kalinin, E.I. and Bulygin, D.V. (2013), "Modeling the development of oil reservoirs by a method of super elements", Matematicheskoe modelirovanie, no. 8, pp. 8387.
Aziz, K. (1993), "Reservoir simulation grids: opportunities and problems", Journal of Petroleum Technology, Vol. 45, no. 7, pp. 658663.
Heinemann, Z.E., Brand, C., Munka, M. and Chen, Y.M. (1991) "Modeling reservoir geometry with irregular grids", Soc. of Petroleum Engineers Reservoir Engineering, Vol. 6, no. 2, p. 225232.
Palagi, C.L. and Aziz, K. (1991) "Use of Voronoi grid in reservoir simulation" Proceedings  SPE Annual Technical Conference and Exhibition, Vol. Sigma, p. 7792.
Du, Q., Faber, V. and Gunzburger, M. (1999), "Centroidal voronoi tessellations: Applications and algorithms", SIAM Review, Vol. 41, pp. 637676.
Nikitin, N.G. (2010), "Nonlinear finite volume method for problems of twophase flow in porous media", Matematicheskoe modelirovanie, Vol. 22, no. 11, pp. 131147.
Kuzmin, D., Moller, M. and Turek, S. (2003), "Highresolution FEMFCT schemes for multidimensional conservation laws", Int.J. Numer. Meth. Fluids, Vol. 42, pp. 265295.
Демидов Д.Е., Егоров А.Г., Нуриев А.Н. Решение задач вычислительной гидродинамики с применением технологии NVIDIA CUDA // Физикоматематические науки, Учен. зап. Казан. гос. унта. 2010. Т. 152, кн.1. С. 142154.
Davis, T.A. (2011), "Algorithm 915: SuiteSparseQR: Multifrontal multithreaded rankrevealing sparse QR factorization", ACM Transactions on Mathematical Software Vol 38, number 1.


