[论文解读] 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 analysis参考文献 20被引用 3

一句话总结

本文提出了一种新的化学组分储层模拟数学公式，通过考虑吸附引起的孔隙体积变化，严格保证质量与能量守恒。该方法重新表述了控制方程，以解决现有模型中的不一致问题，从而实现更稳定、更准确的顺序求解方法，提升模拟精度与物理一致性。

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.

研究动机与目标

• 解决现有化学组分储层模拟器中违反质量与能量守恒定律的不一致问题。
• 开发一种数学公式，以考虑吸附效应引起的有效孔隙尺寸变化。
• 确保整体组分平衡方程与能量守恒方程之间的一致性。
• 通过建立物理解释一致的控制方程，实现稳健的顺序求解方法。
• 通过修正现有模型对吸附作用和孔隙体积变化处理中的缺陷，提升模拟精度。

提出的方法

• 推导出一组新的偏微分方程，明确建模组分在岩心表面吸附引起的孔隙体积变化。
• 重新表述质量守恒方程，将可变孔隙体积作为吸附组分浓度的函数纳入其中。
• 修订能量守恒方程，以考虑有效孔隙尺寸的变化，确保热力学一致性。
• 提出一种基于新公式的顺序求解策略，实现组分输运方程与压力方程的解耦求解。
• 通过将守恒定律的物理原理嵌入控制方程，扩展现有组分模拟器模型。
• 采用一种数学框架，保持组分输运、能量平衡与孔隙体积动态之间的一致性。

实验结果

研究问题

• RQ1 如何数学建模吸附引起的孔隙体积变化，以在组分储层模拟中保持质量守恒？
• RQ2 为确保组分平衡与能量守恒之间的一致性，控制方程需要进行哪些修改？
• RQ3 是否可以将可靠的顺序求解方法应用于考虑可变孔隙体积的新公式化方程组？
• RQ4 为何当前的化学组分模拟器在吸附改变孔隙结构时无法保持能量守恒？
• RQ5 忽略孔隙体积变化对组分模拟结果的准确性有何影响？

主要发现

• 所提出的公式通过将孔隙体积建模为吸附组分浓度的函数，严格保证了质量守恒。
• 能量守恒方程得到修正，以反映吸附引起的有效孔隙尺寸变化，解决了先前的不一致问题。
• 新公式确保了组分平衡方程与能量方程之间的热力学一致性。
• 该模型支持稳定的顺序求解方法，这对复杂化学过程的高效模拟至关重要。
• 重构后的方程消除了现有模拟器中存在物理不一致的问题，尤其是在吸附主导的流动情景下。
• 该方法为更精确、更可靠的化学组分储层模拟奠定了基础。