Development and Testing of a New 3-D Field Scale Fully Implicit Multi-Phase Compositional Steam Injection Simulator
Authors: Cicek O. , Ertekin T. 
Published: December 2007

Abstract
A 3-D field scale steam injection simulator is developed and tested. The three-dimensional multi-phase mass and energy flow equations are based on compositional balances. A fully implicit numerical solution method is implemented in the solution of the nonlinear system of equations. The model solves for (nhcd+5) primary variables simultaneously where n, denotes the number of hydrocarbon components permissible. The accuracy and efficiency of the model is verified and benchmarked against the compositional problem of the Fourth SPE Comparative Solution Project: Comparison of Steam Injection Simulators.
Large computational time and extensive hardware facility requirements are the two major sources of difficulty on compositional simulation of hydrocarbon reservoirs. Nonetheless, it is important to include the correct physics of the problem to be modeled in fine details. The problem is aggravated more by the highly nonlinear nature of most of the improved oil recovery operations requiring computationally demanding, numerically stable fully implicit solutions. Although explicit formulations or semi-implicit formulations are computationally less demanding, they cannot adequately handle highly nonlinear nature of the chemistry and physics encountered in most of the oil recovery operations making their application almost impossible for this class of problems.
In this paper by investigating a trade-off between the degree of implicitness and stability as well as a required level of accuracy of the results and computational time, we present a sensitivity analysis of the research results obtained by solving the mathematical model via various implicit formulations with different sets and numbers of primary variables. Understanding the relationship between the degree of implicitness and the accuracy of the simulation results will help in deciding on the degree of refinement of the grid blocks and level of detail of the actual problem representation in the simulation model.
In order to speed up the simulator, for each of the implicit formulations implemented, various primary variable/equation alignment schemes are considered in the construction of the Jacobian. The simulator is tested using a wide range of compiler/CPU combinations. While performing well on a certain computational environment the very same alignment may result in logarithmically singular Jacobian on another compiler/CPU combination. An analysis on the round off error dependence of the mathematical stability of the Jacobian as a function of primary variable/equation alignment schemes is presented. Accordingly, a set of criteria for the optimum primary variable/equation alignment is proposed to increase the efficiency of the model.
To the authors' knowledge, the model presented in this paper is one of the more implicit models reported in the literature. The developed simulator is found to be strongly stable and internally consistent even for the most dynamic and stiff systems as the ones studied in this research. This is benchmarked by the model's ability in accommodating large average time step sizes of over 50 days and its high average convergence rates of less than three Newtonian iterations per time step.