[Paper Review] A New Mathematical Formulation of the Governing Equations for the Chemical Compositional Simulation

Bakhbergen E. Bekbauov, А. Kаltayev+1 more|White Rose Research Online (University of Leeds, The University of Sheffield, University of York)|Dec 27, 2015

Hydrocarbon exploration and reservoir analysis20 references3 citations

TL;DR

This paper proposes a new mathematical formulation for chemical compositional reservoir simulation that enforces strict mass and energy conservation by accounting for pore volume changes due to adsorption. The approach reformulates governing equations to resolve inconsistencies in existing models, enabling a stable sequential solution method for improved simulation accuracy and physical consistency.

ABSTRACT

It is the purpose of this work to develop new approach for chemical compositional reservoir simulation, which may be regarded as a sequential method. The development process can be roughly divided into the following two stages: (1) development of a new mathematical formulation for the sequential chemical compositional reservoir simulation, (2) implementation of a sequential solution approach for chemical compositional reservoir simulation based on the formulation described in this paper. This paper addresses the first stage of the development process by presenting a new mathematical formulation of the chemical compositional reservoir flow equations for the sequential simulation. The newly developed mathematical formulation is extended from the model formulation used in existing chemical compositional simulators. During the model development process, it was discovered that the currently used chemical compositional model estimates the adsorption effect on the transport of a component reasonably well but it violates the principle of mass conservation. The energy conservation equation in the currently used chemical compositional model does not consider any change in the effective pore size caused by adsorption, which leads to inconsistency between the overall compositional balance equations and the energy conservation equation by violating conservation of energy. With these partial differential equations as governing equations, several simulators have been developed. In this article, we propose a formulation to model the change in pore volume due to adsorption that satisfies the conservation laws for mass and energy, and allows applying a sequential solution approach.

Motivation & Objective

• To address inconsistencies in existing chemical compositional reservoir simulators that violate mass and energy conservation laws.
• To develop a mathematical formulation that accounts for changes in effective pore size due to adsorption effects.
• To ensure consistency between the overall compositional balance equations and the energy conservation equation.
• To enable a robust sequential solution approach by formulating physically consistent governing equations.
• To improve simulation accuracy by correcting flaws in current models' treatment of adsorption and pore volume variation.

Proposed method

• Derives a new set of partial differential equations that explicitly model pore volume changes caused by component adsorption on rock surfaces.
• Reformulates the mass conservation equation to include variable pore volume as a function of adsorbed component concentrations.
• Revises the energy conservation equation to account for changes in effective pore size, ensuring thermodynamic consistency.
• Introduces a sequential solution strategy based on the new formulation, allowing decoupled solution of component transport and pressure equations.
• Extends existing compositional simulator models by embedding physical principles of conservation into the governing equations.
• Uses a mathematical framework that maintains consistency between component transport, energy balance, and pore volume dynamics.

Experimental results

Research questions

• RQ1 How can adsorption-induced changes in pore volume be mathematically modeled to preserve mass conservation in compositional reservoir simulation?
• RQ2 What modifications to the governing equations are required to ensure consistency between compositional balance and energy conservation?
• RQ3 Can a sequential solution approach be applied reliably to a reformulated set of equations that account for variable pore volume?
• RQ4 Why do current chemical compositional simulators fail to conserve energy when adsorption alters pore structure?
• RQ5 What is the impact of neglecting pore volume variation on the accuracy of compositional simulation results?

Key findings

• The proposed formulation enforces strict mass conservation by modeling pore volume as a function of adsorbed component concentrations.
• The energy conservation equation is corrected to reflect changes in effective pore size due to adsorption, resolving prior inconsistencies.
• The new formulation ensures thermodynamic consistency between compositional balance and energy equations.
• The model enables a stable sequential solution approach, which is essential for efficient simulation of complex chemical processes.
• The reformulated equations eliminate physical inconsistencies present in existing simulators, particularly in adsorption-dominated flow scenarios.
• The approach provides a foundation for more accurate and reliable chemical compositional reservoir simulations.