The compositional module in the MATLAB Reservoir Simulation Toolbox (MRST) implements two different formulations of a three-phase compositional system that consists of a pair of multicomponent phases and an optional immisicible phase. In petroleum engineering, the aqueous phase is taken to be immiscible and the hydrocarbon liquid and vapor phases are governed by an equation of state (EoS). The overall composition formulation uses pressure and overall mole fractions as primary variables, whereas the natural variable formulation relies on solving for phase mole fractions and phase saturations simultaneously. Thermodynamic behavior is modeled using $K$-values or a (standard) cubic EoS. In the chapter, you will learn about the model equations, choice of primary variables, and numerical strategies for solving the thermodynamic problem, alone or coupled to the flow equations. We discuss details of the implementation, which builds upon the object-oriented, automatic differentiation (AD-OO) framework and utilizes state functions and generic model classes for increased modularity. We also present a few relatively simple simulation examples to illustrate typical behavior and teach you how to set up simulation cases yourself.

The ad-core module in MRST offers an object-oriented framework for rapid prototyping of new reservoir simulators based on automatic differentiation (AD-OO). The framework simplifies the task of changing and extending existing simulation models in MRST or implementing brand new ones. The MRST textbook (Lie, Cambridge University Press, 2019, Chapter 12) presents a model hierarchy for the black-oil equations, discretized by a standard fully implicit method, and describes how to (automatically) select time steps and configure linear and nonlinear solvers. Herein, we present a further modularization of the AD-OO framework that aims to simplify the implementation of more complex flow models and other types of discretizations and solution strategies. To this end, we view the reservoir simulator as a graph of functional relationships and their dependencies and introduce the new concept of so-called state functions to define these functional relationships and compute discrete quantities required for the linearized governing equations. Using the graph perspective, it is relatively simple to not only visualize and understand the data flow of highly complex reservoir simulators, but also replace components of the graph and/or extend the graph with new branches as needed. The result is a versatile family of reservoir simulators that can easily be configured to run different types of multiphase, multicomponent models and at the same time support a number of different spatial and temporal discretizations. The state-function concept also has a built-in compute cache that helps you to systematically eliminate redundant function evaluations. The chapter explains the new concept in detail and exemplifies its use by showcasing implicit, explicit, and adaptive-implicit versions of the same physical processes. We also demonstrate the use of consistent and high-resolution schemes to improve simulation accuracy. Applications to complex flow physics (EOR models, compositional flow, fractured reservoirs) are discussed in other chapters.

Surfactant and polymer flooding, alone or in combination, are common and effective chemical EOR methods. This chapter reviews the main physical mechanisms and presents how the corresponding mathematical flow models are implemented as an add-on module to MRST to provide a powerful and flexible tool for investigating flooding processes in realistic reservoir scenarios. Using a so-called limited-compositional models, surfactant and polymer are both assumed to be transported in the water phase only, but also adsorbed within the rock. The hydrocarbon phases are described with the standard three-phase black-oil equations. The resulting flow models also take several physical effects into account, such as chemical adsorption, inaccessible pore space, permeability reduction, effective solution viscosities, capillary pressure alteration, relative permeability alteration, and so on. The new simulator is implemented using the object-oriented, automatic differentiation (AD-OO) framework from MRST, and can readily utilize features such as efficient iterative linear solvers with constrained pressure residual (CPR) preconditioners, efficient implicit and sequential solution strategies, advanced time-step controls, improved spatial discretizations, etc. We describe how the computation of fluid properties can be decomposed into state functions for better granularity and present several numerical examples that demonstrate the software and illustrate different physical effects. We also discuss the resolution of trailing chemical waves and validate our implementation against a commercial simulator.