Comparison of Lanczos Decomposition Method LDM and Conventional Implicit Time-Stepping Method ITSM for Numerical Reservoir Simulation

Abstract

Reservoir simulations constitute a cornerstone to predict the flow of fluids through porous media. Various numerical models called simulators are developed to simulate the performance of hydrocarbon reservoirs. These models are used in field development since production forecasts are necessary to make investment decisions. Nowadays, numerical simulators are widely used by reservoir engineers. In recent times, machine learning applications have garnered the interest of the oil and gas industry due their unorthodox approach to creating complex models. The more historical data that can be provided in the training phase of the computation, the more accurate the predictions utilizing less time and computational power required by the alternative. The alternative, reservoir simulation applications, require more robust hardware for processing large amounts of data in sophisticated ways. This will require several iterations and may require long computation to validate the model. Running time for a simulation is dependent on software, which can be dependent on hardware. This creates a matrix of time and resources needed to complete simple to complicated simulations. A few studies have proposed the use of the Lanczos decomposition method in reservoir simulation studies. The attractiveness of this method appears to be the avoidance of time stepping in simulation and allows the computation of reservoir pressures at any given time directly. In this study, two new simulators were developed using Lanczos Decomposition Method (LDM) and Conventional Implicit Time-Stepping Method (ITSM). The study focuses on 2-D flow for slightly compressible fluid of constant viscosity with multiple wells. Derivation of the model equations was performed using the continuity equation for both methods through the use of MATLAB. The simulators were written using the MATLAB programming language. The simulators developed in this study are capable of assigning uniform and non-uniform gridblock distribution; porosity and permeability distributions, as well as developing various production and injection scenarios for single or multiple wells depending on different areas of application. Validity and accuracy of the 2D flow simulator were examined by comparing simulation results with that obtained from the commercial software called ECRIN. The results of the simulator were almost identical with the results obtained from the commercial software. During the model runs, the CPU time of the two simulators were compared. A special case was also studied for a single well with variable rate history using both ITSM and LDM written with FORTRAN. To date, in petroleum engineering literature, there is no work published that compares the performances (in terms of computational aspects as well as CPU times) of the Lanczos method and the conventional implicit-time stepping method.