Improving the Numerical Accuracy of Hydrothermal Reservoir Simulations Using the CIP Scheme with Third-Order Accuracy

Abstract

We have developed a numerical algorithm using the CIP scheme, or its enhanced version, the RCIP scheme, for improving the numerical accuracy when simulating fluid flows with a high gradient of temperature or chemical concentration in hydrothermal reservoirs. The CIP and RCIP schemes achieve third-order accuracy, and they can effectively control the numerical diffusion that often causes serious numerical errors when using the conventional first-order upstream-difference scheme. The developed algorithm consists of the following two procedures: 1. Time integration of the equations governing the conservation of mass and enthalpy; 2. Determining the thermodynamic functions and their derivatives by solving the systems of nonlinear and linear equations. This paper presents practical numerical techniques by describing the numerical algorithms using not only the CIP or RCIP scheme but also the conventional first-order upstream-difference scheme, for reference purposes. Using these algorithms, several numerical simulations of one-dimensional cold sweep are demonstrated. From the numerical solutions, we conclude that: 1. the algorithm using the CIP or RCIP scheme can effectively control the numerical diffusion; 2. the algorithm using the RCIP scheme yields more realistic solutions by controlling the overshoot that is caused when using the CIP scheme; 3. spatial steps that are four to eight times longer can be used without compromising numerical accuracy, by replacing the conventional first-order upstream-difference scheme with the RCIP scheme.