On the application of the LET-model for the approximation of core relative phase permeabilities

Abstract

The article deals with the problem of adequate interpretation of core relative phase permeabilities and the use of the LET-model in application to this problem. Some existing analytical dependencies for the interpretation of laboratory studies of the OFP are briefly analyzed: the Corey model, the Sigmund and McCaffery model, the Chierici model, the LET-model. The advantage of the LET-model and the high evaluation of this model in independent studies of the authors are described. In the process of preliminary analysis, the authors of the article revealed that the non-trivial issue of determining the adjustable coefficients of the model using mathematical methods was not sufficiently covered, which became the central object of the work. Further, the application of the LET-model is formalized and the methodology for determining the adjustable coefficients of the model (L, E and T) is described. The task of selecting model parameters is interpreted as a multidimensional optimization problem. Also, a class of nonlinear least squares methods was defined to solve the problem. Several common numerical optimization methods for selecting the coefficients of the model are considered: the brute-force search method, the Levenberg-Marquardt algorithm method, the trust region method. Computational experiments were carried out to assess their applicability and comparative analysis of optimization algorithms. Based on the results of the experiments, it was concluded that the method of confidence domains is suitable for practical application, since they converge to the optimal solution quickly enough and demonstrates high accuracy in the selection of coefficients L, E, T. The final part of the article demonstrates the difference between the LET-model and the basic Corey model when approximating core relative phase permeabilities.