A Stability Criterion for the Negative Compressibility Problem in Geothermal Simulation and Discrete Modeling of Failure in Oil Shale Pyrolysis Process

Advisor

Hamdi Tchelepi

Abstract

This report includes two distinct parts: ”A Stability Criterion for the Negative Compressibility Problem in Geothermal Simulation” and ”Discrete Modeling of Failure in Oil Shale Pyrolysis Process”. The first part analyzes the negative compressibility problem in geothermal simulation, which was conceived and preliminarily analyzed by K. Coats in 1980. He found that although a fully implicit scheme is applied, a conditionally stable behavior still happens in some processes with a real ”negative compressibility”, such as the steam flooding process. In analogy to the nonlinear compressibility designed by Coats in a single block steam/water problem, we derive a linear compressibility from the linearized pressure equation. We analyze the behavior of these compressibilities and convergence under different timestep size and initial guesses. Different from Moncorge and Tchelepi [1]’s argument that the unsta- ´ ble behavior in negative compressibility problems relates to the different sign of linear and nonlinear compressibility, we find that the instability is a more direct result of negative pressure value generated during the iterations. Based on this analysis, a new timestep criterion is proposed, and an improved algorithm is developed. Then, we verify this algorithm in a one-dimensional test case, where the cold water injects into a fully saturated steam reservoir. In the second part, we develop a workflow to translate the actual rock tests to a wellposed simulation problem for using lattice and discrete element hybrid model (L-DEM) v developed by R. Affes (2015). In this report, we provide a complete example of the conventional triaxial rock strength test using this workflow. Then, the results are compared with experiment data to validate the model. The lattice/discrete element hybrid method is flexible and extendable for modeling failure in oil shale pyrolysis process. To model the entire oil shale pyrolysis process, a coupled thermo-mechanical-fluid dynamic modeling is needed, and it will be based on the extension of L-DEM.