多种岩石油藏数值模拟自适应网格法的研究

发布时间：2018-05-12 16:29

本文选题：自适应网格法 + 油藏数值模拟　；参考：《中国科学技术大学》2015年博士论文

【摘要】：稠油由于其丰富的储量在碳氢能源领域占据的地位越来越重要。蒸汽注采作为稠油开采的主要工艺,其数值模拟研究也引起了学者们的重视。该类问题是一种带有相变的多孔介质多相流动问题,渗流流场内存在变化剧烈且狭窄的温度与饱和度锋面,为了准确模拟流场变化动态,锋面附近网格的尺度必须足够小,若直接对全场采用均匀网格,庞大的网格数据与计算量是难以承受的。考虑于此,可以动态追踪流场锋面的自适应网格法成为本文的主要研究对象。该方法在流场内的网格结构会随着注采过程推进而实时变化,在物理量变化剧烈的区域采用细网格而在物理量变化缓慢的区域采用粗网格,从而大幅度降低计算规模并提高计算速度。由于地质模型与数值模型在尺度上存在较大差异,地质参数一般需要进行粗化,并产生渗透率张量,因而需要单独处理网格界面的流量。借助各网格内压力线性分布的假设以及流量守恒,本文介绍了张量渗透率下网格界面上的流量求解方法,同时结合二维油藏的自适应网格法,研究了绝对渗透率为张量时的自适应网格法。对于自适应网格法中相邻不同层次的网格,由于它们的空间尺度不同,本文引入粗网格的子网格使其与相邻网格层次匹配,从而有效解决了不同层次网格界面上的流量求解问题。通过张量渗透率下的二维蒸汽驱以及注蒸汽辅助重力泄油的具体算例验证了自适应网格法的准确性与高效性。实际油藏往往包含多种流动单元,即分布着不同输运性质的岩石,不同岩石对应不同的相对渗透率、毛管力函数、残余油水饱和度以及初始油水饱和度,这些因素导致相饱和度在跨越不同岩石界面时产生间断,从而给自适应网格法的网格划分以及粗细化操作带来较大困难。本文对于此类油藏数值模拟的自适应网格法展开研究：当重力可忽略,且毛管力梯度影响不大时,根据网格界面处流量守恒的条件,推导出在同一个粗网格内都连续的变量一一不同相相对渗透率的比值,进而给出自适应网格法的网格划分以及粗细化操作的具体方案。二维水平剖面下的蒸汽驱算例验证了理论推导的合理性,并说明了自适应网格法的准确性与高效性；当重力不可忽略时,三相区内油气毛管力在同一个粗网格内保持连续,且油水相对渗透率之比在同一个粗网格内也是不依赖于岩石种类的。借助于该相对渗透率之比以及油气毛管力,本文解决了自适应网格法在考虑重力的多种岩石蒸汽注采问题中网格划分与粗细化等主要难点。二维下的注蒸汽辅助重力泄油算例表明自适应网格法较精细网格法在该类问题中的速度优势。上述蒸汽注采问题中,本文假设各流动单元毛管力总体相差不大,并忽略了毛管力梯度的影响。但是对于某些特殊情况,毛管力在不同介质中可能会存在较大差异,例如裂缝性油藏中的裂缝与基质,此时界面上毛管力梯度较大。本文对包含有两种岩石且一侧考虑毛管力一侧不考虑毛管力的多孔介质进行了研究。考虑到不同岩石界面处毛管力函数关系的不同,本文给出了该界面需要满足的条件,包括流量守恒以及与毛管力相关的条件,针对上述界面条件做出了基于控制方程的数学证明,同时发现在界面上有时会有饱和度梯度发散或者毛管力间断的特殊现象。为了解界面处的流动特性,本文初步研究了相应的数值算法,在岩石界面附近进行了稳态假设下的解析求解,并基于该局部近似解构造了流量的离散格式。数值结果表明毛管力的非均质性会影响界面处的流动特性,当含有毛管力的岩石位于上游,不含有毛管力的岩石位于下游时,界面上的毛管力可以保持连续,但是在含毛管力侧的岩石界面处,润湿相饱和度会趋向于1.0,且其梯度趋于无穷大；相反,不含有毛管力的岩石位于上游时,若毛管力不能进行匹配,会出现毛管力间断的现象,此时润湿相压力间断,非润湿相压力连续。综上,本文主要对渗透率张量下多种岩石油藏蒸汽注采问题的自适应网格法进行了研究,解决了自适应网格法在该类应用中遇到的一系列问题。相应的蒸汽驱以及注蒸汽辅助重力泄油的算例表明自适应网格法在保证计算精度的同时,较精细网格法有巨大的计算速度优势。同时本文还对毛管力非均质的一维不可压缩不混溶两相流问题进行了研究,给出了相应的界面条件以及数值算法。文中的数值算例也说明了岩石界面上的流动特性。
[Abstract]:Heavy oil is becoming more and more important in the field of hydrocarbon energy because of its rich reserves. As the main process of heavy oil mining, the numerical simulation of steam injection has also aroused the attention of scholars. This kind of problem is a multi-phase flow problem with a porous medium with phase change, and there is a severe and narrow temperature in the flow field. With the saturation front, in order to simulate the dynamics of flow field, the scale of the grid near the front must be small enough. If a uniform grid is used directly to the whole field, the large grid data and calculation are difficult to bear. Considering this, the adaptive mesh method that can dynamically track the front of the flow field is the main object of this paper. The grid structure in the flow field will change in real time as the injection and production process advance, and the coarse grid is adopted in the area with intense physical quantity, and the coarse mesh is adopted in the region of slow change of physical quantity, which greatly reduces the calculation scale and improves the calculation speed.
Due to the large difference between the geological model and the numerical model on the scale, the geological parameters generally need to be coarsened and the permeability tensor is generated. Therefore, the flow of the grid interface needs to be treated separately. With the assumption of the linear distribution of pressure in each grid and the conservation of flow, the flow solution on the mesh interface under the tensor permeability is introduced. At the same time, combining the adaptive grid method of two dimensional reservoir, the adaptive mesh method of the absolute permeability as the tensor is studied. For the grid adjacent to the different layers in the adaptive grid method, because of the different spatial scales, this paper introduces the coarse mesh subgrid to match the adjacent grid layer, thus effectively solving the different layers. The accuracy and efficiency of the adaptive mesh method are verified by a specific example of two dimensional steam flooding and steam injection assisted gravity drainage under the tensor permeability.
The actual reservoir often contains a variety of flow units, that is, the distribution of different transport properties of rock. Different rocks correspond to different relative permeability, capillary force function, residual oil water saturation and initial oil water saturation. These factors cause phase saturation to produce discontinuity across different rock boundaries, thus giving the mesh of adaptive grid method. In this paper, the adaptive grid method for numerical simulation of such reservoirs is studied in this paper. When gravity is negligible and the influence of the capillary force gradient is small, according to the condition of the flow conservation at the grid interface, the relative permeability of the successive variables in the same coarse grid is derived. The ratio is then given to the specific scheme of the grid division and the coarse and fine operation from the adaptive grid method. The steam flooding example under the two-dimensional horizontal section proves the reasonableness of the theoretical deduction and illustrates the accuracy and efficiency of the adaptive grid method. When the gravity can not be ignored, the oil and gas force in the three phase region is in the same coarse grid. The ratio of the relative permeability of oil and water is not dependent on the type of rock in the same coarse mesh. With the aid of the ratio of the relative permeability and the oil and gas capillary force, the paper solves the main difficulties of the grid division and the coarse refinement of the adaptive grid method in the problem of various rock steam injection and production in the consideration of gravity. An example of steam assisted gravity drainage shows that the adaptive grid method is superior to the refined grid method in this kind of problem.
In the above problem of steam injection and production, this paper assumes that the overall difference of capillary force in each flow unit is small and neglects the influence of Mao Guanli gradient. However, for some special cases, there may be great differences in the capillary force in different media, such as cracks and foundations in fractured reservoirs, and the capillary force gradient is larger at this time. A porous medium containing two kinds of rocks and one side considering the force of capillary force is studied. Considering the difference of the capillary force function at different rock interfaces, this paper gives the conditions that the interface needs to be satisfied, including the conservation of flow and the conditions related to the capillary force, which is based on the interface conditions. In order to understand the flow characteristics at the interface, the corresponding numerical algorithm is preliminarily studied in order to understand the flow characteristics at the interface. In order to find out the solution of the solution under the steady state assumption near the rock interface, the flow rate is built on the basis of the local approximate deconstruction. The numerical results show that the heterogeneity of the capillary force affects the flow characteristics at the interface. When the rock with Mao Guanli is located upstream and the rock without the capillary force is located downstream, the capillary force on the interface can be kept continuous, but the wetting phase saturation will tend to 1 at the rock interface with the force side of the capillary force. The gradient tends to infinity; on the contrary, when the rock does not contain the capillary force on the upper reaches, if the capillary force can not be matched, the capillary force discontinuous will occur, at this time the wetting phase pressure discontinuous and the non wetting phase pressure is continuous.
To sum up, this paper mainly studies the adaptive grid method of steam injection and production in various rock reservoirs under permeability tensor, and solves a series of problems encountered in this kind of application by adaptive grid method. The calculation examples of the corresponding steam flooding and steam injection assisted gravity discharge show that the adaptive grid method is at the same time guaranteeing the accuracy of the calculation. The finer grid method has a huge computational speed advantage. At the same time, this paper also studies the one-dimensional incompressible immiscible incompressible two-phase flow problem of the capillary force heterogeneity, and gives the corresponding interface conditions and numerical algorithms. The numerical examples in this paper also show the flow characteristics on the rock interface.

【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TE319

【参考文献】