Estimation of relative permeability curves using an improved Levenberg-Marquardt method with simultaneous perturbation Jacobian approximation

JOURNAL OF HYDROLOGY

卷:544

Article

Zhou, Kang^1,2  Hou, Jian^1,2  Fu, Hongfei³  Wei, Bei^1,2  Liu, Yongge² 

[1] China Univ Petr, State Key Lab Heavy Oil Proc, Qingdao 266580, Peoples R China

[2] China Univ Petr, Sch Petr Engn, Qingdao 266580, Peoples R China

[3] China Univ Petr, Coll Sci, Qingdao 266580, Peoples R China

关键词: Multiphase flow;    Relative permeability;    Levenberg-Marquardt method;    Simultaneous perturbation;    Jacobian approximation;   

DOI  :  10.1016/j.jhydrol.2016.12.006

来源: Elsevier

【 摘 要 】

Relative permeability controls the flow of multiphase fluids in porous media. The estimation of relative permeability is generally solved by Levenberg-Marquardt method with finite difference Jacobian approximation (LM-FD). However, the method can hardly be used in large-scale reservoirs because of unbearably huge computational cost. To eliminate this problem, the paper introduces the idea of simultaneous perturbation to simplify the generation of the Jacobian matrix needed in the Levenberg-Marquardt procedure and denotes the improved method as LM-SP. It is verified by numerical experiments and then applied to laboratory experiments and a real commercial oilfield. Numerical experiment indicates that LM-SP uses only 16.1% computational cost to obtain similar estimation of relative permeability and prediction of production performance compared with LM-FD. Laboratory experiment also shows the LM-SP has a 60.4% decrease in simulation cost while a 68.5% increase in estimation accuracy compared with the earlier published results. This is mainly because LM-FD needs 2n (n is the number of controlling knots) simulations to approximate Jacobian in each iteration, while only 2 simulations are enough in basic LM-SP. The convergence rate and estimation accuracy of LM-SP can be improved by averaging several simultaneous perturbation Jacobian approximations but the computational cost of each iteration may be increased. Considering the estimation accuracy and computational cost, averaging two Jacobian approximations is recommended in this paper. As the number of unknown controlling knots increases from 7 to 15, the saved simulation runs by LM-SP than LM-FD increases from 114 to 1164. This indicates LM-SP is more suitable than LM-FD for multivariate problems. Field application further proves the applicability of LM-SP on large real field as well as small laboratory problems. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free