基于GPU的页岩储层裂缝建模及压力模拟
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摘要
我国老油田普遍进入了高含水开采阶段,新探明储量的70%为低渗透油气藏,为保持国内油气产量的稳定,必须对开采难度较大的低渗、特低渗油田进行开发。由于特低渗油气田大多为页岩等致密性储层,地质结构复杂,天然裂缝及人工压裂裂缝形态难以描述,储层裂缝模型建立的精确程度直接影响着后续的油田开发。因此,开展储层裂缝建模研究和地层压力研究,对特低渗油气田的开发有重要的意义。
目前,三维建模的研究主要通过地质统计学理论。由于传统地质统计学方法在描述空间分布方面的限制,多点地质统计方法成为主要的储层建模手段。随着多点统计方法的深入研究,在大规模地质模拟时,CPU串行方法受到一些参数数值的限制而导致计算效率缓慢,甚至出现因内存过度消耗而计算崩溃等问题,使得逐点模拟算法的实际应用难以达到理想效果。
页岩储层的精细构造及天然裂缝发育的研究使得裂缝性油气储层的压力模拟研究也更加的全面精细。目前,主要有等效连续模型、离散模型及综合模型等模型用以裂缝性储层的建模及其流体流动模拟研究。而如何将建模得到的裂缝表征成果应用到渗流模型中去,研究裂缝参数对渗流压力场和产能的影响规律,是致密油气藏渗流研究的重要组成部分。
本文首先研究了多点地质统计SNESIM方法的并行实现,采用随机模拟方法得到储层裂缝模型。并分别从解析和数值方法两方面对致密油气藏中的垂直裂缝井和多段压裂水平井进行求解。主要研究成果如下：
1.提出使用多点地质统计方法随机模拟页岩油藏天然裂缝的空间分布。实现了SNESIM随机模拟策略的单网格方法和多重网格方法,并将计算待模拟结点概率分布函数的模块任务在GPU上进行了多线程并行执行。以300数据模板为例,GPU并行方法的总模拟时间比CPU串行方法加快了约25倍,内存消耗降低了800倍,显著提高了储层天然裂缝的三维空间建模效率。
2.优化并行方法中,因GPU和CPU之间的数据交互而形成的计算缓慢问题。针对多重网格方法,提出在GPU内部设置数据缓冲区的方案,来减少CPU主机和GPU之间的数据读取交互时间。针对计算数据模板偏移量时所需的大量重复计算问题,采用预缓冲方法减轻CUDA线程计算的负荷,通过偏移量的增减对数据模板的节点位置进行快速定位,优化了并行算法的计算效率。
3.开展页岩储层压力解析求解研究。利用瞬时源函数推导出各种类型边界条件下,多层垂直裂缝井以及水平井多段压裂的压力分布表达式,提出压裂裂缝与各种井型之间为任意角度时的模型,并推导出该模型在不同边界条件下的压力表达式。将理论计算结果与国内某油田实际井例进行压力分析比较,验证了模型及其解析方法的精确性。
4.研究储层压力模拟的数值计算方法。使用非结构PEBI网格对特低渗油气藏储层模型的断层、压裂裂缝等进行网格划分,并采用有限体积法对渗流力学方程进行离散,建立数值模型。最后通过GMRES迭代算法求解线性方程组,得到水平井多段压裂模型的地层压力场分布。
5.利用页岩储层的压力场数值分析方法,对一口多段压裂水平井进行压力场数值实验分析。模拟了特低渗油气藏中,均质地层情况下不同水平渗透率对产量的影响,以及非均质地层情况时渗透率的变化对水平井井底流压和地层压力场的影响,提出不能用常规油气藏渗流规律中的产量与压差关系,来描述在特低渗油气藏(如致密气、页岩气等储集层)中的渗流特征。
6.研究双孔地层中水平井多段压裂的渗流特征。采用随机模拟方法得到的裂缝性油藏中天然裂缝模型的水平井多段压裂双孔渗流方程,推导出水平井多段压裂情况下的压力表达式。通过压力表达式的求解分析了实际生产过程中,多段压裂水平井的七个较为明显的流动段,与实际生产过程吻合。
With continuous exploitation, a lot of existing oil and gas fields in our country have entered a late-time production stage, and the oil production is declining year by year. Further, within the new reservoirs whose reserves have been proven,70%of them are low permeability reservoirs. In order to enhance oil recovery, efforts must be made on the exploitation of oil fields with low and ultralow permeability. Among these fields, oil shale is the most commonly seen, which is typically characterized with complex geological structures. Oil shale typically involves two kinds of fracture systems, i.e. the natural fractures and the hydraulic fractures, and the modeling of such systems has direct impact on the subsequent development strategy. Thus, the studies on modeling and simulation of reservoirs with complex fracture systems have great implication on development of oil and gas fields with ultra-low permeability.
Currently, studies of3-dimensional modeling are mostly based on the geostatistical theory. Due to limitations of the traditional geostatistical methods on description of the spatial distribution, the multi-point geostatistical methods are becoming a major tool for reservoir modeling. But during application of multi-point statistical methods to the large-scale geological modeling, CPU serial implementation is typically limited by some parameters, which may lead to the slow computational efficiency, excessive memory consumption and even program collapse. Above restrictions make it difficult to achieve the desired effect during practical application of point simulation.
Study on fine scale structure and natural fracture distribution of shale reservoirs lead to a more comprehensive level of pressure simulation of fractured reservoirs. Current fluid flow simulation model of fractured reseroir include equivalent continuous model, discrete model and integrated model, and the key point during flow mechanism investigation of such fields is how to implement the fracture distribution obtained with geostatistics into the percolation simulation model and the study of fracture parameters on pressure distribution and production.
Parallel implementation of the SNESIM multi-point geostatistics is carried out in this paper, and the fractured reservoir model is obtained with stochastic simulation. Investigations on the percolation mechanism and pressure distribution are then provided for vertical fracture wells and multi-stage fractured horizontal wells with both analytical and numerical methods. Main contents of the thesis are as follows:
1. Multi-point geostatistics is introduced into the simulation of spatial distribution in shale reservoirs. Single grid and multi-grid implementation of SNESIM stochastic simulation strategy is given, and the module task of probability distribution function of the node to be simulated is allocated to GPU parallel execution. Taking the data template which contains300positions as example, the parallel methods is about25times faster than the serial version, and the memory cost reduces about800times, which leads to significant improvement of the three-dimensional modeling efficiency of naturally fractured reservoirs.
2. Improvement is made to the GPU based SNESIM parallel approach. For multi-grid method, buffer is set in the GPU memory to reduce the interaction time of the data transfer between the CPU and GPU. Considering the large amount of repeated execution during calculation of data template offset, pre-buffer method is introduced to reduce the calculation load, the fast locating of the node is realized by changing the offset value, and optimization is made on the memory usage effciency of parallel algorithms.
3. Research on seepage behavior of shale reservoir is conducted. Applying the transient source function, the analytical solutions to the vertical fracture well and the multi-stage fractured horizontal well with various boundary conditions are derived. Comparison of the calculated pressure to an in-situ field data in our country is made, which validates the analytical method proposed.
4. Numerical simulation of reservoir pressure distribution is studied. The PEBI grid method is applied for mesh generation to the3-dimensional model obtained with stochastic simulation, and the seepage equation is then discretized. The obtained linear equations are solved with GMRES iterative method, and the pressure distribution of multi-fractured horizontal well is given out.
5. With the numerical simulation method proposed, the pressure field of multi-stage fractured horizontal wells in shale reservoir is provided and then analyzed. The influence of permeability in the horizontal direction on homogeneous reservoirs with ultralow permeability, as well as influence of permeability on heterogeneous reservoir is investigated. The calculated results are consistent with in situ production data.
6. Considering the natural fracture distribution model obtained with the stochastic simulation in fractured reservoirs, a dual-porosity single permeability quasi-steady seepage equation is proposed, and the bottom-hole pressure of the horizontal well is derived. The seven obvious flow regimes during production of multi-stage fractured horizontal well are analyzed.
目前,三维建模的研究主要通过地质统计学理论。由于传统地质统计学方法在描述空间分布方面的限制,多点地质统计方法成为主要的储层建模手段。随着多点统计方法的深入研究,在大规模地质模拟时,CPU串行方法受到一些参数数值的限制而导致计算效率缓慢,甚至出现因内存过度消耗而计算崩溃等问题,使得逐点模拟算法的实际应用难以达到理想效果。
页岩储层的精细构造及天然裂缝发育的研究使得裂缝性油气储层的压力模拟研究也更加的全面精细。目前,主要有等效连续模型、离散模型及综合模型等模型用以裂缝性储层的建模及其流体流动模拟研究。而如何将建模得到的裂缝表征成果应用到渗流模型中去,研究裂缝参数对渗流压力场和产能的影响规律,是致密油气藏渗流研究的重要组成部分。
本文首先研究了多点地质统计SNESIM方法的并行实现,采用随机模拟方法得到储层裂缝模型。并分别从解析和数值方法两方面对致密油气藏中的垂直裂缝井和多段压裂水平井进行求解。主要研究成果如下：
1.提出使用多点地质统计方法随机模拟页岩油藏天然裂缝的空间分布。实现了SNESIM随机模拟策略的单网格方法和多重网格方法,并将计算待模拟结点概率分布函数的模块任务在GPU上进行了多线程并行执行。以300数据模板为例,GPU并行方法的总模拟时间比CPU串行方法加快了约25倍,内存消耗降低了800倍,显著提高了储层天然裂缝的三维空间建模效率。
2.优化并行方法中,因GPU和CPU之间的数据交互而形成的计算缓慢问题。针对多重网格方法,提出在GPU内部设置数据缓冲区的方案,来减少CPU主机和GPU之间的数据读取交互时间。针对计算数据模板偏移量时所需的大量重复计算问题,采用预缓冲方法减轻CUDA线程计算的负荷,通过偏移量的增减对数据模板的节点位置进行快速定位,优化了并行算法的计算效率。
3.开展页岩储层压力解析求解研究。利用瞬时源函数推导出各种类型边界条件下,多层垂直裂缝井以及水平井多段压裂的压力分布表达式,提出压裂裂缝与各种井型之间为任意角度时的模型,并推导出该模型在不同边界条件下的压力表达式。将理论计算结果与国内某油田实际井例进行压力分析比较,验证了模型及其解析方法的精确性。
4.研究储层压力模拟的数值计算方法。使用非结构PEBI网格对特低渗油气藏储层模型的断层、压裂裂缝等进行网格划分,并采用有限体积法对渗流力学方程进行离散,建立数值模型。最后通过GMRES迭代算法求解线性方程组,得到水平井多段压裂模型的地层压力场分布。
5.利用页岩储层的压力场数值分析方法,对一口多段压裂水平井进行压力场数值实验分析。模拟了特低渗油气藏中,均质地层情况下不同水平渗透率对产量的影响,以及非均质地层情况时渗透率的变化对水平井井底流压和地层压力场的影响,提出不能用常规油气藏渗流规律中的产量与压差关系,来描述在特低渗油气藏(如致密气、页岩气等储集层)中的渗流特征。
6.研究双孔地层中水平井多段压裂的渗流特征。采用随机模拟方法得到的裂缝性油藏中天然裂缝模型的水平井多段压裂双孔渗流方程,推导出水平井多段压裂情况下的压力表达式。通过压力表达式的求解分析了实际生产过程中,多段压裂水平井的七个较为明显的流动段,与实际生产过程吻合。
With continuous exploitation, a lot of existing oil and gas fields in our country have entered a late-time production stage, and the oil production is declining year by year. Further, within the new reservoirs whose reserves have been proven,70%of them are low permeability reservoirs. In order to enhance oil recovery, efforts must be made on the exploitation of oil fields with low and ultralow permeability. Among these fields, oil shale is the most commonly seen, which is typically characterized with complex geological structures. Oil shale typically involves two kinds of fracture systems, i.e. the natural fractures and the hydraulic fractures, and the modeling of such systems has direct impact on the subsequent development strategy. Thus, the studies on modeling and simulation of reservoirs with complex fracture systems have great implication on development of oil and gas fields with ultra-low permeability.
Currently, studies of3-dimensional modeling are mostly based on the geostatistical theory. Due to limitations of the traditional geostatistical methods on description of the spatial distribution, the multi-point geostatistical methods are becoming a major tool for reservoir modeling. But during application of multi-point statistical methods to the large-scale geological modeling, CPU serial implementation is typically limited by some parameters, which may lead to the slow computational efficiency, excessive memory consumption and even program collapse. Above restrictions make it difficult to achieve the desired effect during practical application of point simulation.
Study on fine scale structure and natural fracture distribution of shale reservoirs lead to a more comprehensive level of pressure simulation of fractured reservoirs. Current fluid flow simulation model of fractured reseroir include equivalent continuous model, discrete model and integrated model, and the key point during flow mechanism investigation of such fields is how to implement the fracture distribution obtained with geostatistics into the percolation simulation model and the study of fracture parameters on pressure distribution and production.
Parallel implementation of the SNESIM multi-point geostatistics is carried out in this paper, and the fractured reservoir model is obtained with stochastic simulation. Investigations on the percolation mechanism and pressure distribution are then provided for vertical fracture wells and multi-stage fractured horizontal wells with both analytical and numerical methods. Main contents of the thesis are as follows:
1. Multi-point geostatistics is introduced into the simulation of spatial distribution in shale reservoirs. Single grid and multi-grid implementation of SNESIM stochastic simulation strategy is given, and the module task of probability distribution function of the node to be simulated is allocated to GPU parallel execution. Taking the data template which contains300positions as example, the parallel methods is about25times faster than the serial version, and the memory cost reduces about800times, which leads to significant improvement of the three-dimensional modeling efficiency of naturally fractured reservoirs.
2. Improvement is made to the GPU based SNESIM parallel approach. For multi-grid method, buffer is set in the GPU memory to reduce the interaction time of the data transfer between the CPU and GPU. Considering the large amount of repeated execution during calculation of data template offset, pre-buffer method is introduced to reduce the calculation load, the fast locating of the node is realized by changing the offset value, and optimization is made on the memory usage effciency of parallel algorithms.
3. Research on seepage behavior of shale reservoir is conducted. Applying the transient source function, the analytical solutions to the vertical fracture well and the multi-stage fractured horizontal well with various boundary conditions are derived. Comparison of the calculated pressure to an in-situ field data in our country is made, which validates the analytical method proposed.
4. Numerical simulation of reservoir pressure distribution is studied. The PEBI grid method is applied for mesh generation to the3-dimensional model obtained with stochastic simulation, and the seepage equation is then discretized. The obtained linear equations are solved with GMRES iterative method, and the pressure distribution of multi-fractured horizontal well is given out.
5. With the numerical simulation method proposed, the pressure field of multi-stage fractured horizontal wells in shale reservoir is provided and then analyzed. The influence of permeability in the horizontal direction on homogeneous reservoirs with ultralow permeability, as well as influence of permeability on heterogeneous reservoir is investigated. The calculated results are consistent with in situ production data.
6. Considering the natural fracture distribution model obtained with the stochastic simulation in fractured reservoirs, a dual-porosity single permeability quasi-steady seepage equation is proposed, and the bottom-hole pressure of the horizontal well is derived. The seven obvious flow regimes during production of multi-stage fractured horizontal well are analyzed.
引文
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Suzuki, S. and S. Strebelle (2007). "Real-time post-processing method to enhance multiple-point statistics simulation." Petroleum geostatistics:10-14.
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Zhang, T. (2008). "Incorporating geological conceptual models and interpretations into reservoir modeling using multiple-point geostatistics." Earth Science Frontiers 15 (1):26-35.
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Zhang, T. (2008). "Incorporating geological conceptual models and interpretations into reservoir modeling using multiple-point geostatistics." Earth Science Frontiers 15 (1):26-35.
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Technology,2008. ISCSCT'08. International Symposium on, IEEE.
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刘建安与马红星等(2005).”井下微地震裂缝测试技术在长庆油田的应用.”油气井测试(02)：54-56+77.
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曲鸿雁与周生田(2009).”裂缝性油藏开发技术进展.”内蒙古石油化工(08)：106-107.
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吴胜和(2010).储层表征与建模,石油工业出版社.
吴胜和与李文克(2005).”多点地质统计学——理论、应用与展望.”古地理学报(01)：137-144.
尹艳树与吴胜和等(2009).”基于储层骨架的多点地质统计学方法,”中国科学：D辑(S2).
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张挺与卢德唐等(2010).”基于软硬数据的多点地质统计法在图像统计信息重构中的应用研究."计算机研究与发展(1)：43-52.
周德华与焦方正等(2004).”裂缝渗流研究最新进展.”海洋石油(02)：34-38.
周文(1998).裂缝性油气储集层评价方法,四川科学技术出版社.
周新桂与操成杰等(2003).”储层构造裂缝定量预测与油气渗流规律研究现状和进展.”地球科学进展(03)：398-404.
周新桂与邓宏文(2003).”储层构造裂缝定量预测研究及评价方法.”地球学报24(2)：175-180.
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