基于PEBI网格的油藏数值计算及其实现
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摘要
目前我国是仅次于美国的世界第二大石油消费国,而我国石油进口依存度也逐年增长,在2008年进口依存度约为50%左右,而且随着国家经济的快速发展,对石油的需求也持续增长。然而,我国的很多老油田生产已进入中后期阶段,石油产量逐渐下降。为了实现老油田的稳产,提高采收率,必须对油田进行精细开发。
精细开发的重要内容之一是利用多种动态监测技术获得油藏层间构造、砂体连通、大孔道及剩余油分布变化。经过长期注采以及加密井不断增加,我国老油田的井网密度大、油水分布变化复杂,开采挖潜的主要对象转向高度分散而又局部相对富集的剩余油。这给测试数据的解释、评价与数值模拟提出了新的要求：由于解析方法难以解决油藏的非均匀性、复杂边界与多相流问题,须发展数值方法；规则网格难以描述复杂的油藏边界,应使用不规则网格划分方法；数值计算方法应与一般意义的数模有所区别,能准确模拟瞬态压力,以满足压力等数据的解释需要。
为此,本文研究了PEBI非结构网格下的多层多相非均值油藏的数值计算模型,数值模型包括以下部分。
1、网格划分。在综合比较了笛卡尔网格、角点网格、曲线网格、中点网格、径向网格与PEBI网格的特点后,选择使用PEBI网格来对油藏区域进行空间离散。提出了针对油藏区域PEBI网格点生成的限定边算法,算法通过对油藏区域的垂直井、裂缝井、水平井、断层和边界进行分类,将油藏区域划分为点模块、线模块、圆模块、圆角矩形模块和平面模块,通过对模块之间的干扰情况分别考虑,可以得到各模块的限定边,对每个模块在其限定边内生成网格点,就可以得到整个油藏区域的网格点。对所得到的网格点作Delaunay剖分,继而生成出网格点的Voronoi图。可以根据此Voronoi图生成二维与三维油藏区域的PEBI网格。本算法可以对存在复杂边界、复杂断层、复杂的井间干扰、复杂的井与断层间干扰的情况生成正确的PEBI网格。
2、油藏模型。数值计算模型以黑油模型方程为基础,使用有限体积法对其方程在PEBI网格上进行离散；对单相和多相方程的离散格式进行了详细推导,推导过程中对方程的非线性项进行了线性化处理。对单相方程中的非线性项可以使用显式方法或迭代的隐式方法进行线性化；对多相方程中的非线性项分成弱非线性项和强线性项,对弱非线性项的处理方法和单相类似,可以使用显式方法或迭代的隐式方法进行线性化,对强非线性项的处理方法使用线性隐式或全隐式方法进行线性化。
3、井模型。文中对已有的井模型如源汇模型、van Pollen模型和Peaceman模型进行了介绍,并分别针对垂直井、裂缝井和水平井的提出了相应的内边界模型。针对不同井型,讨论了其相应的网格划分方法,并根据达西定律推导出井的生产指数。由于水平井通常需要离散到不同的网格中,分别对无限传导和均匀流量两种模型推导出其流量方程。
4、根据以上研究成果,已开发出可生产应用的数值试井软件。该软件能解决多层多相非均值各向异性油藏的数值计算。PEBI网格划分部分可对各种复杂油藏进行正确、快速的PEBI网格划分,计算部分可对单相、两相、三相问题进行计算,并能正确处理PVT设置、非均质、各相异性、过泡点等情况。通过实例计算对数值试井软件进行检验,并对若干问题如井间干扰问题、水平井网格划分问题、两相注水问题、过泡点问题进行了数值分析,表明计算结果正确可靠。经过某油田的大量实测资料检验及其与国外软件的对比表明：此软件已可在油田现场应用,在精度与稳定性方面不低于国外同类软件。
Recently, China is the second largest oil consumption nation in the world. As the rapid development of national economic, the requirement of oil is continuously rising, this results in that the oil import dependency is about 50%. While After years of production, many old oil fields in our country already entered middle or later period. Fine development is necessary to keep the stable production in old oil fields.
One of fine development's contents is to retrieve the connectivity of sand bodies, the macro-pores and the distribution of remaining oil by various dynamic monitor technologies. Over a long period of injection-production and increases of infilling wells in old oil fields, the consistency of well network is compact and the transformation of oil-water distribution becomes very complicated, so the target of production has been shifted to the remaining oil which highly disperses but relatively concentrates in certain spot. And this puts new demands on the interpretation, evaluation and simulation of testing data. Because the analytical method is difficult to solve problems with heterogeneous reservoir, reservoir with complicated boundaries or multi-phase flow, numerical method is necessary to be developed. The regular grids are not effective to describe complicated boundaries, so the development of unstructured grids is obligatory. The numerical calculation should be able to accurately simulate the transient pressure to fulfill the demands of explanation of pressure data.
Therefore, this paper researches on the numerical calculation model of multi-layer, multi-phase, heterogeneous reservoir on PEBI grid. The model contain the below parts.
1. Meshing. After comparing the Cartesian grid, corner grid, curvilinear grid, the mid-point grid, radial grid and PEBI grid, PEBI grid are chosen to discrete the space of the reservoir. Restricted edge algorithm is proposed to generate PEBI grids in the reservoir. By classifying vertical wells, fractural wells, horizontal wells, faults and boundaries, the algorithm split the reservoir into point modules, line modules, circle module, rounded rectangular modules and flat modules. By considering the interferences between the modules, restricted edges of each module are obtained. After generating grid points within restricted edges of every module, grid points of the reservoir are obtained. After making Delaunay triangulation to the mesh points, the Voronoi graph of the grid points is generated. Then the 2-D or 3-D PEBI grid of the reservoir can be obtained. This algorithm can generate correct PEBI grids of reservoir which involves complicated boundaries, faults, interferences between wells, interferences between wells and fault.
2. Reservoir model. The numerical model is based on black-oil model, and it discretizes the equations on PEBI grid. The single-phase and multi-phase discretized equations are derived in detail. The non-linear item of the equations is linearized. In the single-phase equation, explicit method or iterating implicit method can be used to linearize the non-linear item. The non-linear item of the multi-phase equation can be divided into weak non-linear item and strong non-linear item. The processing method of the weak non-linear item is similar to the single-phase. The half explicit method or full explicit method can be use to linearize the strong non-linear item.
3. Well models. The existing models are introduced, such as source-sink model, van Pollen model and Peaceman model. Internal boundary model is proposed for vertical well, vertical fractural well and horizontal well. Correspondingly, the mesh methods are analyzed, and the well index is derived from Darcy law. Because horizontal well usually need to be discretized into separate grids, the flow equation has been derived from infinite conduction model and average flow model.
4. Numerical well testing software is developed based on the above research. The software can generate correct PEBI mesh of complicated quickly, and can calculate single-phase, two-phase and three-phase flow. After compared to foreign softwares, this software is proved to be correct and stable, and can be applied in oil fields.
精细开发的重要内容之一是利用多种动态监测技术获得油藏层间构造、砂体连通、大孔道及剩余油分布变化。经过长期注采以及加密井不断增加,我国老油田的井网密度大、油水分布变化复杂,开采挖潜的主要对象转向高度分散而又局部相对富集的剩余油。这给测试数据的解释、评价与数值模拟提出了新的要求：由于解析方法难以解决油藏的非均匀性、复杂边界与多相流问题,须发展数值方法；规则网格难以描述复杂的油藏边界,应使用不规则网格划分方法；数值计算方法应与一般意义的数模有所区别,能准确模拟瞬态压力,以满足压力等数据的解释需要。
为此,本文研究了PEBI非结构网格下的多层多相非均值油藏的数值计算模型,数值模型包括以下部分。
1、网格划分。在综合比较了笛卡尔网格、角点网格、曲线网格、中点网格、径向网格与PEBI网格的特点后,选择使用PEBI网格来对油藏区域进行空间离散。提出了针对油藏区域PEBI网格点生成的限定边算法,算法通过对油藏区域的垂直井、裂缝井、水平井、断层和边界进行分类,将油藏区域划分为点模块、线模块、圆模块、圆角矩形模块和平面模块,通过对模块之间的干扰情况分别考虑,可以得到各模块的限定边,对每个模块在其限定边内生成网格点,就可以得到整个油藏区域的网格点。对所得到的网格点作Delaunay剖分,继而生成出网格点的Voronoi图。可以根据此Voronoi图生成二维与三维油藏区域的PEBI网格。本算法可以对存在复杂边界、复杂断层、复杂的井间干扰、复杂的井与断层间干扰的情况生成正确的PEBI网格。
2、油藏模型。数值计算模型以黑油模型方程为基础,使用有限体积法对其方程在PEBI网格上进行离散；对单相和多相方程的离散格式进行了详细推导,推导过程中对方程的非线性项进行了线性化处理。对单相方程中的非线性项可以使用显式方法或迭代的隐式方法进行线性化；对多相方程中的非线性项分成弱非线性项和强线性项,对弱非线性项的处理方法和单相类似,可以使用显式方法或迭代的隐式方法进行线性化,对强非线性项的处理方法使用线性隐式或全隐式方法进行线性化。
3、井模型。文中对已有的井模型如源汇模型、van Pollen模型和Peaceman模型进行了介绍,并分别针对垂直井、裂缝井和水平井的提出了相应的内边界模型。针对不同井型,讨论了其相应的网格划分方法,并根据达西定律推导出井的生产指数。由于水平井通常需要离散到不同的网格中,分别对无限传导和均匀流量两种模型推导出其流量方程。
4、根据以上研究成果,已开发出可生产应用的数值试井软件。该软件能解决多层多相非均值各向异性油藏的数值计算。PEBI网格划分部分可对各种复杂油藏进行正确、快速的PEBI网格划分,计算部分可对单相、两相、三相问题进行计算,并能正确处理PVT设置、非均质、各相异性、过泡点等情况。通过实例计算对数值试井软件进行检验,并对若干问题如井间干扰问题、水平井网格划分问题、两相注水问题、过泡点问题进行了数值分析,表明计算结果正确可靠。经过某油田的大量实测资料检验及其与国外软件的对比表明：此软件已可在油田现场应用,在精度与稳定性方面不低于国外同类软件。
Recently, China is the second largest oil consumption nation in the world. As the rapid development of national economic, the requirement of oil is continuously rising, this results in that the oil import dependency is about 50%. While After years of production, many old oil fields in our country already entered middle or later period. Fine development is necessary to keep the stable production in old oil fields.
One of fine development's contents is to retrieve the connectivity of sand bodies, the macro-pores and the distribution of remaining oil by various dynamic monitor technologies. Over a long period of injection-production and increases of infilling wells in old oil fields, the consistency of well network is compact and the transformation of oil-water distribution becomes very complicated, so the target of production has been shifted to the remaining oil which highly disperses but relatively concentrates in certain spot. And this puts new demands on the interpretation, evaluation and simulation of testing data. Because the analytical method is difficult to solve problems with heterogeneous reservoir, reservoir with complicated boundaries or multi-phase flow, numerical method is necessary to be developed. The regular grids are not effective to describe complicated boundaries, so the development of unstructured grids is obligatory. The numerical calculation should be able to accurately simulate the transient pressure to fulfill the demands of explanation of pressure data.
Therefore, this paper researches on the numerical calculation model of multi-layer, multi-phase, heterogeneous reservoir on PEBI grid. The model contain the below parts.
1. Meshing. After comparing the Cartesian grid, corner grid, curvilinear grid, the mid-point grid, radial grid and PEBI grid, PEBI grid are chosen to discrete the space of the reservoir. Restricted edge algorithm is proposed to generate PEBI grids in the reservoir. By classifying vertical wells, fractural wells, horizontal wells, faults and boundaries, the algorithm split the reservoir into point modules, line modules, circle module, rounded rectangular modules and flat modules. By considering the interferences between the modules, restricted edges of each module are obtained. After generating grid points within restricted edges of every module, grid points of the reservoir are obtained. After making Delaunay triangulation to the mesh points, the Voronoi graph of the grid points is generated. Then the 2-D or 3-D PEBI grid of the reservoir can be obtained. This algorithm can generate correct PEBI grids of reservoir which involves complicated boundaries, faults, interferences between wells, interferences between wells and fault.
2. Reservoir model. The numerical model is based on black-oil model, and it discretizes the equations on PEBI grid. The single-phase and multi-phase discretized equations are derived in detail. The non-linear item of the equations is linearized. In the single-phase equation, explicit method or iterating implicit method can be used to linearize the non-linear item. The non-linear item of the multi-phase equation can be divided into weak non-linear item and strong non-linear item. The processing method of the weak non-linear item is similar to the single-phase. The half explicit method or full explicit method can be use to linearize the strong non-linear item.
3. Well models. The existing models are introduced, such as source-sink model, van Pollen model and Peaceman model. Internal boundary model is proposed for vertical well, vertical fractural well and horizontal well. Correspondingly, the mesh methods are analyzed, and the well index is derived from Darcy law. Because horizontal well usually need to be discretized into separate grids, the flow equation has been derived from infinite conduction model and average flow model.
4. Numerical well testing software is developed based on the above research. The software can generate correct PEBI mesh of complicated quickly, and can calculate single-phase, two-phase and three-phase flow. After compared to foreign softwares, this software is proved to be correct and stable, and can be applied in oil fields.
引文
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