Evaluation of orthogonal collocation and orthogonal collocation on finite element method using genetic algorithm in the pressure profile prediction in petroleum reservoirs

Abstract

The diffusivity equation in the porous media is the basis of pressure profile prediction in the petroleum reservoir. The aim of this work is to solve this equation by two approximate analytical solutions including the OC (Orthogonal Collocation) and OCFE (Orthogonal Collocation on Finite Element) methods. The advantage of these methods is in the cases that the values of reservoir properties such as porosity and permeability are presented as a function of position or pressure in the reservoir or sometimes in the discrete values form. In these cases, the exact analytical solution is difficult or impossible which justifies the priority of the OC and OCFE methods. In the OC method, the results of different numbers of collocation points for two oil reservoirs demonstrate that there is a systematic trend for the odd and even number of collocation points while the former has less error than the later. Also, there is a minimum AAD % (Average Absolute Deviation percent) from the exact solution that is related to 17 collocation points and 0.26 and 0.42 AAD % for two oil reservoirs which justifies that the increasing of the number of collocation points may not increase the accuracy of computations. Also, the results obtained by the OCFE method show that this method is sensitive to the division ratio of domain and the number of collocation points in each sub-domain. Therefore, the GA (Genetic Algorithm) method has been applied for the optimization of these parameters. The results of GA show 0.07 AAD % which is related to 0.24 for the division ratio and 18 and 2 collocation points for the first and second subdomain, respectively.