Efficient and accurate simulation of nonlinearly coupled multiphase flow in porous media

Efficient and accurate simulation of nonlinearly coupled multiphase flow in porous media

Kardale, M.

Cusini, M. (mentor)
Hajibeygi, H. (mentor)

Civil Engineering and Geosciences

Geoscience & Engineering

Section for Petroleum Engineering

2015-08-25

In this work, the non-linear behaviour of saturation transport equations in sequential implicit simulation strategy for multi-phase, immiscible and incompressible displacements are investigated. In reservoir simulation, use of explicit time schemes can lead to severe time-step size restrictions, specially when strong nonlinear terms exist. For highly heterogeneous formations, when a global time step needs to be taken, the CFL numbers can vary by orders of magnitude through the entire domain. In such cases, explicit schemes are not practical, and implicit time schemes are typically followed. The transport equation which describe the fluid flow in porous media in space and time are often highly non-linear and tightly coupled with the flow (pressure) equation. Characterized by S-shaped flux functions, they can also be non-monotone in presence of strong buoyancy (and capillary) forces. Through the phase velocities, which depend on pressure, the transport equation is strongly coupled to pressures equation. In presence of strong capillarity, the pressure solution also depends on the slope of capillary function, which is a function of saturation. An industry standard procedure is to use Newton method to first linearize these coupled governing equations, and iteratively reach a converged solution. To study the nonlinearity within the transport equation, first, a two-dimensional twophase simulator based on all types of Implicit Pressure Explicit Saturation (IMPES), Sequential Implicit, and Fully Implicit strategies are developed. Both capillary and gravitational effects are being considered. As to extend the stability limits of the sequential implicit strategy, flux correction method is investigated and implemented in the transport equation. All cases of viscous, buoyancy and capillary dominated flows are studied, where, in the cases of strong nonlinearities, non-convergence and severe time-step restrictions have been observed. Stability analysis of the flux functions in buoyancy and capillary dominated flows is performed along with a time-step control strategy, which is shown to result in unconditional convergence irrespective of the time-step size selection. Finally, application of flux correction strategies to EOR processes, where foam flows through the rock formation, is presented. Such a study has never been performed in the literature.

reservoir simulation
non-Linear Stability
multiphase flow in porous media

http://resolver.tudelft.nl/uuid:48f59529-f0c9-4a7e-abd5-c81edce3268e

Student theses

master thesis

(c) 2015 Kardale, M.