非均匀多孔介质中多相渗流的有限分析算法

发布时间：2018-04-28 02:32

本文选题：非常规油气藏 + 数值模拟　；参考：《中国科学技术大学》2015年博士论文

【摘要】：非常规油气资源已经成为21世纪能源结构中的重要组成部分,非常规油气的埋藏、赋存状态与常规油气资源有较大区别,这给油藏数值模拟带来了新的挑战。地质参数的非均质性,特别是绝对渗透率的强非均质性,是非常规油气藏数值模拟的一大难点。实际应用于非常规油气藏数值模拟的计算网格都是建立在较大尺度上的,一个计算网格往往包含很多特性不同的子区域,为了给定相应大尺度网格上的特性参数,必须要对地质参数,特别是渗透率进行大尺度化处理。传统的数值算法会严重低估多孔介质的渗流能力,为了得到更加准确的结果,需要对网格进行细分,细分的程度通常会依赖于非均匀性的强弱,即使在非均匀性不强的情况下也需要上千次的细分,这是大尺度化不能接受的。本文的主要研究内容就是针对非均质多孔介质中多相渗流的数值模拟建立高效而准确的数值计算格式,将非均匀单项渗流的有限分析算法应用到非均匀多相渗流的数值模拟中,并对“大孔道”现象进行相关研究。首先,本文对二维不可压缩非均匀两相渗流问题展开研究,将油、水连续方程相加得到总渗方程,忽略毛管力梯度项,得到一个和单相渗流形式相同的类拉普拉斯方程,将该方程的奇点压力幂律解析解作为总渗方程的一个近似解,推导出两相渗流网格界面绝对渗透率的有限分析格式,建立非均匀两相渗流的有限分析算法。该格式得到的网格界面绝对渗透率与控制体周边网格的绝对渗透率都相关。在压力线性分布的特别情况下,有限分析格式自动退化为传统格式。渗透率棋盘分布算例显示有限分析算法在少量的网格加密情况下即可算出准确的饱和度场以及见水时间,特别地,在渗透率log-normal分布的算例中,有限分析法在原始网格下的计算结果已经具备很高的精度；无论是渗透率棋盘分布还是log-normal分布传统算法严重低估了饱和度锋面的移动速度和出口边界的见水时间,随着网格的加密,计算结果向着有限分析结果收敛,收敛的速度完全受控于介质的非均匀强弱,而有限分析法几乎不受其影响。进一步地,本文对二维非均匀三相渗流展开了研究。两相渗流有限分析算法的推导过程实际上提供了一种网格界面绝对渗透率的求解思路,本文借鉴这一思路重构了网格界面绝对渗透率的有限分析格式,建立了非均匀三相渗流的有限分析算法。渗透率棋盘分布的三相渗流算例显示,有限分析算法能够准确的计算出温度场、各相饱和度场以及见气时间,同时看到高渗透率网格之间会形成一个质量和能量的高速流通通道,这一通道会加速蒸汽及热量的流通,在渗透率棋盘分布的蒸汽驱算例中,这条通道会导致生产井快速见气;传统算法得到的温度场、各相饱和度场以及见气时间远远落后于有限分析的结果,为了得到收敛结果,需要对原始网格进行上万次的细分,大大降低了计算效率。渗透率log-normal分布的算例结果显示,与两相渗流类似,有限分析算法在原始网格下的计算结果已经具有很好的计算精度,生产井的见气时间也基本不随网格加密参数变化,但传统算法收敛的速度完全依赖于介质的非均匀性强弱,即使在非均匀性不强的情况下,也需要对原始网格进行几百甚至上千次的细分。在实际生产中,准确的生产井见气时间对产量以及残余油饱和度的预估具有重要意义。最后,本文利用渗透率log-normal分布蒸汽驱算例的结果,对“大孔道”现象进行了相关探究。有限分析结果显示注入井和生产井之间会形成高渗通道使得生产井快速见气,将高渗通道所在计算区域内网格的绝对渗透率按照生产井产量与有限分析结果一致的原则调高相应倍数后,用传统算法进行数值计算,得到了与有限分析法相近的温度场、各相饱和度场以及生产井见气时间。这个过程正好重现了对渗透率历史拟合的过程。因此,本文认为传统算法严重低估多孔介质的渗流能力可能是“大孔道”现象的一个合理解释。综上,本文对非常规油藏数值模拟中的渗透率非均匀问题展开研究,建立了非均匀不可压缩两相渗流和非均匀三相渗流的有限分析算法。文中的数值算例显示有限分析算法在计算精度和计算效率上相比于传统算法有着巨大的优势,同时可能对现今数值模拟中的相关现象做出相应的解释。有限分析算法有望解决非常规油气藏数值模拟的更多实际问题。
[Abstract]:Unconventional oil and gas resources have become an important part of the energy structure in the twenty-first Century. The burial of unconventional oil and gas is very different from the conventional oil and gas resources. This brings new challenges to the reservoir numerical simulation. The heterogeneity of geological parameters, especially the strong heterogeneity of absolute permeability, is the numerical model of the unconventional oil and gas reservoirs. A computational grid applied to the numerical simulation of unconventional oil and gas reservoirs is based on a large scale. A computational grid often contains many subregions with different characteristics. In order to give the characteristic parameters on the large scale grid, the number of geological parameters, especially the permeability, must be processed in large scale. The numerical algorithm will seriously underestimate the percolation capacity of porous media. In order to get more accurate results, the mesh needs to be subdivided. The degree of subdivision usually depends on the strength of non-uniformity. Even in the case of inhomogeneous inhomogeneity, it needs a thousand subdivisions, which is unacceptable in large scale. The content is to establish an efficient and accurate numerical calculation scheme for the numerical simulation of heterogeneous porous media in heterogeneous porous media. The finite analysis algorithm of non-uniform single term percolation is applied to the numerical simulation of heterogeneous multiphase seepage, and the phenomenon of "large pass" is studied. The two phase seepage problem is studied. The oil and water continuity equations are added to the total seepage equation, and the force gradient term of the capillary is ignored. A Laplasse equation is derived from the same form of the single-phase seepage. The analytic solution of the singular point pressure power law of the equation is used as an approximate solution of the total seepage equation. Finite analysis scheme is used to establish a finite analysis algorithm for non-uniform two-phase flow. The absolute permeability of the grid interface is related to the absolute permeability of the surrounding meshes of the control body. In the special case of pressure distribution, the finite analysis scheme automatically degenerates into the traditional form. The numerical example of the permeability chessboard distribution shows the finite analysis The method can calculate the exact saturation field and water time in the case of a small number of grid encrypt, especially in the example of the log-normal distribution of permeability. The finite analysis method has high precision in the original mesh, and the traditional algorithm of the permeability chessboard distribution and the log-normal distribution is seriously underestimated. The moving velocity of the frontal plane and the water seeing time of the outlet boundary are convergent with the finite analysis results as the mesh is encrypted. The speed of convergence is completely controlled by the inhomogeneous strength of the medium, and the finite analysis method is almost unaffected. Further, this paper studies the two dimensional inhomogeneous three phase seepage. The derivation process of the limited analysis algorithm actually provides a solution to the absolute permeability of the grid interface. In this paper, the finite analysis scheme of the absolute permeability of the grid interface is reconstructed by using this idea, and a finite analysis algorithm for the inhomogeneous three-phase seepage is established. The finite analysis algorithm is shown by the three phase seepage calculation example of the permeability chessboard distribution. It can accurately calculate the temperature field, the phase saturation field and the gas time. At the same time, the high permeability grid will form a high speed circulation channel between the mass and the energy. This channel will accelerate the flow of steam and heat. In the steam flooding example of the distribution of the permeability chessboard, this channel will cause the production well to see the gas quickly; The temperature field, the phase saturation field and the gas seeing time are far behind the results of the finite analysis. In order to get the convergence result, we need to subdivide the original mesh tens of thousands of times and greatly reduce the calculation efficiency. The numerical example of the log-normal distribution of the permeability shows that the finite analysis algorithm is similar to the two phase seepage. The calculation results under the lattice have good calculation precision, and the gas viewing time of the production well does not change with the grid encryption parameters, but the convergence rate of the traditional algorithm depends on the inhomogeneity of the medium. Even if the inhomogeneity is not strong, it is necessary to subdivide the original grid hundreds or even thousands of subdivisions. In the intercourse production, the accurate production well see gas time is of great significance to the prediction of the output and the residual oil saturation. Finally, this paper makes use of the results of the log-normal distribution of the permeability of the permeability, and explores the phenomenon of the "big pass". The finite analysis results show that the high permeability channel will be formed between the injection well and the production well. In the production well, the gas is quickly seen. After adjusting the absolute permeability of the grid in the calculated area of the hypertonic channel according to the corresponding multiple of the production well output and the finite analysis result, the numerical calculation is carried out with the traditional algorithm, and the temperature field, the saturation field and the gas time in the production well are obtained. In this paper, it is considered that the traditional algorithm seriously underestimates the percolation capacity of porous media, which may be a reasonable explanation of the "large pass" phenomenon. In this paper, the inhomogeneous and incompressible two-phase flow in the numerical simulation of unconventional reservoirs is studied and the inhomogeneous incompressible two-phase flow is established. The finite analysis algorithm in this paper shows that the finite analysis algorithm has a great advantage over the traditional algorithm in calculation precision and efficiency, and it may explain the relevant phenomena in the current numerical simulation. The finite analysis algorithm is expected to solve the numerical model of the unconventional oil and gas reservoirs. More practical problems to be proposed.

【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】：TE312

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