岩浆侵入多孔储层的热效应数学模型及其应用

Mathematical Model of Thermal Effect of Magma Intrusion into Porous Reservoir and Its Application

构建了一个岩浆侵入多孔储层中的热效应数学模型,提出了模拟地质系统中的岩浆侵入/凝固热效应的等效算法,基于物理和数学方程上的等价原理,用瞬态有限元分析将岩浆侵入与岩石之间原始凝固边界移动问题,转化为一个边界没有运动的物理等效热源的新问题,即单步凝固模型与多步(三步)凝固模型。所提出的等效算法的主要优点是有限元网格大小固定,采用变积分时间步长来模拟有限元分析的侵入岩浆凝固热效应。多种热效应模型的对比发现,单步凝固模型与多步(三步)凝固模型的数值解具有近似的精度,所以单步凝固模型是有效模拟多孔岩石中岩浆侵入的热效应模型。单步和多步(三步)凝固模型与王民模型、Zhao模型对比后发现,单步和多步(三步)凝固模型与Zhao模拟的效果更为接近,理论上也更接近地质实际。通过对商56区块沙三段油藏辉绿岩侵入热场的模拟分析应用,推算得到商56区块沙三段油藏的热裂解量为9.02×104m3,指出该油藏的保存条件有限,存在着大量的油气渗漏,并且原油的大部分损失是由于渗漏散失造成的。

In this paper, a mathematical model is proposed for the thermal effect of intrusion of magma into porous reservoir to simulate the geological system of magma intrusion and the heat effect in solidification by using an equivalent algorithm, based on the equivalence principle of the physical and mathematical equations. The transient finite element analysis transforms the original rock magma solidification boundary movement into a physical equivalent heat source boundary with no new movement, namely, a single- step solidification model and a multi step （three step） solidification model. The main advantages of the proposed algorithm is that the finite element mesh size is fixed, the varied time step is used to simulate the intruding magma solidification thermal effect through the traditional finite element analysis. Comparing various thermal effect models, it is shown that the numerical single-step solidification model solution and the multi step （three step） numerical model solution enjoy similar accuracy, so the single-step solidification model can effectively simulate the thermal effect of the magma intrusion in the porous rock. Single and multi step （three step） solidification models are compared with the Wang Min model and the Zhao model, and it is shown that the single and multi step （three step） models give solidification results more consistent with those of the Zhao model, which theoretically are closer to the actual geological data. The diabase intrusive analysis of Shang 56 sha 3 pool is carried out to simulate the thermal field, and it is shown that the Shang 56 Sha 3 pool thermal cracking volume is 9.02×10^4 m3, and the preservation conditions of the reservoir is poor, with a large amount of oil and gas leakage, to which is attributed mostly the loss of crude oil.