稠油热采数值模拟自适应网格法计算软件开发研究及实例应用
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摘要
目前稠油开发的最主要的手段是蒸汽注采。稠油蒸汽注采是一个带有相变的多孔介质中多相流动问题,流场中存在物理量变化十分剧烈的狭窄相变锋面,对于此类问题的数值模拟,为了保证计算精度,锋面处的计算网格尺寸必须很小,如果整个计算区域都采用均匀网格,那么网格节点就会很多,计算量很大。本文利用自适应网格法动态追踪锋面,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地方采用粗网格,从而大幅度提高稠油热采问题数值模拟的计算速度。
油藏数值模拟是油田勘探开发生产部门的重要科研手段。本文自主开发了注蒸汽热采稠油油藏数值模拟自适应网格法计算软件,能够对渗透率空间分布不均匀、油藏区域分布不同种类输运性质岩石、裂缝-孔隙双重介质、不规则边界及内部含有断层和人工压裂裂缝油藏等复杂地层注蒸汽热采稠油问题进行数值模拟。软件通过了信息处理产品标准符合性检测中心的测试并获得了国家版权局的软件著作权。通过简单二维裂缝性稠油油藏SAGD开采过程数值模拟和某稠油油藏注热水驱油过程数值模拟两个算例并与国际著名商业油藏数值模拟软件CMG-STARS对比结果显示,软件具有较高的计算精度和稳定性,并且由于采用了自适应网格法,计算速度比CMG-STARS快,可以满足油田的科研生产需求。
利用自主开发的软件,本文对辅助注入轻质溶剂的SAGD过程进行了数值研究,发现注入不同分子量的轻质溶剂对SAGD开采效率的影响截然不同：辅助注入C2H6可以保持蒸汽腔的压力并减小顶部热损,但是由于生产井过早见气,蒸汽和轻质气堵塞了稠油流通通道,使得油相相对渗透率降低,反而不利于稠油增产；辅助注入的C9H20能够在蒸汽腔壁的蒸汽锋面处凝结并充分溶解到稠油中,大大降低稠油粘度,增强锋面处油相流动能力,从而有效地提高稠油的开采速度,降低了蒸汽使用量,提高了油汽比,有利于节能减排。本文分析了辅助注入C9H20溶剂开采稠油的经济效益,结果表明辅助注入C9H20有一定的经济价值并且特别适用于快采。
稠油、高含水原油以及低渗透地层中原油均显示出非牛顿流体的特性,三次采油中利用聚合物溶液、胶束溶液、乳状液和压缩系数大的泡沫液等非牛顿流体作为驱油剂,钻井液和水力压裂工艺中的压裂液通常也是非牛顿流体。因此,研究非牛顿流体的渗流规律对于油气田开发具有重要的实际意义。幂律流体是工程上常见的非牛顿流体,其本构方程能够较好地反映稠油的流变特性。本文从幂律流体的基本流动控制方程出发,利用Whitaker的体积平均方法,将多孔介质中幂律流体的细观运动和宏观渗流运动联系起来；采用多尺度分析,使得体积平均意义下的宏观渗流运动方程得到进一步的简化：在将细观的下的流体物理量和宏观下的流体物理量联系起来的封闭性假设的基础上,理论推导得到幂律流体宏观渗流的广义Darcy定律。研究结果显示渗流速度和压力梯度之间存在幂函数关系,但幂律流体表观渗透率仅在一维流动情况下由多孔介质的空间结构以及幂律流体的流变特性所确定,对于二维及以上空间的流动,由于非线性项的存在,其表观渗透率还依赖于宏观渗流速度的具体方向,该渗流特性和牛顿流体完全不同。数值算例显示本文理论推导的表观渗透率对于渗流速度方向的依赖属性和国际上现有的基于直接求解幂律流体流动控制方程的数值模拟结果相符。
综上,本文的主要工作是开发具有自主知识产权的稠油热采数值模拟自适应网格法计算软件,软件能够对复杂地层的稠油蒸汽注采问题进行快速模拟。软件对裂缝-孔隙双重介质稠油油藏SAGD开采过程和某稠油油藏热水驱采油过程模拟的两个实例表明软件能对复杂地层的稠油热采问题利用自适应网格法进行快速数值模拟；本文利用开发的软件研究不同轻质溶剂对SAGD过程开采效率的影响和作用机理；针对稠油的非牛顿流体特性,本文利用体积平均方法对幂律流体在多孔介质中的渗流规律进行研究并推导其广义Darcy定律。
The numerical reservoir simulation has become an important tool for the petroleum research and exploration. The thermal recovery by steam injection can be thought as the problem of multi-phase flow in porous media with the phase-change. In the processes, there are sharp moving interfaces of temperature and phase saturations in the reservoir. Due to the rapid variations of the physical quantities across the interface, very fine grids are required. As a result, a huge CPU time and memory are needed if applying a uniform grid to the whole calculation area. In this paper, the adaptive mesh refinement (AMR) technique is applied to the numerical simulations for the processes of thermal recovery by steam injection, where the different heterogeneous cases of the reservoir are considered, like the reservoir with the permeability variations, the different rock-types, the heterogeneous fractured porous media, the complex boundary or complex faulted reservoir. In the AMR technique, the front is tracked, in order to have fine grid blocks in the region with steep gradients but coarser grid blocks ahead and behind of the front. The proposed AMR technique is fast and can give good accuracy. On the basis of theoretical research, a software package for the reservoir simulations, where including the AMR technique, is developed. This software package has good precision and numerical stability to meet the demands of scientific research.
With the use of the software developed by ourselves, a numerical example of SAGD progress in fractured reservoirs and a numerical simulation of the hot water flooding process of block Shan2are carried out, whose results are compared with the one based on CMG-STARS, a well-known commercial reservoir simulation software. The comparison shows that the computing speed of our software is five times of the one of CMG-STARS. The calculated results of day steam injection, day oil production, cumulative water injection and cumulative oil production are in good agreement with those of CMG-STARS. The remaining oil saturation distribution within the reservoir is relatively consistent with the one of CMG-STARS.
Using our own developed software, we perform a numerical study of Steam and Gas Push (SAGP) and Expanding-Solvent Steam-Assisted Gravity Drainage (ES-SAGD), which are both improvements of SAGD. In the gravity drainage process, the key to heavy oil production is the mobility of the oil phase which is dominated by the viscosity of the oil phase. The objective of this numerical study was to investigate the drainage mechanism of co-injecting light and heavy solvents to improve production performance. The light solvent C2H6, delivered in the vapor phase to the entire fluid interface, keeps the pressure of the steam chamber, and reduces the thermosteresis by building a thick gas blanket on the top of the recovery, but the recovery ratio may become lower due to the lower temperature of the steam chamber. The heavy solvent C9H20owould condense, with condensed steam, at the boundary of the steam chamber. Condensed solvent around the interface of the steam chamber which dilutes the oil, in conjunction with heat, reduces its viscosity and increases its mobility thereby increasing the oil production rate and recovery ratio. The conclusions from this study can be used to design suitable solvent mixtures and co-injection strategies to deliver a higher production rate and recovery ratio.
Heavy, high water and low permeability formations crude oil show a characteristic of non-Newtonian fluids. Many non-Newton fluids such as polymer solution, micellar solutions, emulsions and foam concentrate of high compression coefficient are used as oil displacing agents in the EOR process. Usually, the drilling fluid and the fracturing fluid in the hydraulic fracturing technology are usually non-Newtonian fluids. Therefore, the study of transport of non-Newtonian fluids in porous media has important practical significance for oil and gas development.
As a common non-Newtonian fluid, the constitutive equation of power-law fluids is relatively simple and can better reflect the rheological properties of heavy oil. The large-scale continuum models for transport of power-law fluids in porous media is derived from the pore-scale control equations using the volume averaging method. The averaging procedure leads to an equation of motion and a continuity equation expressed in terms of the volume-averaged pressure and velocity. The closure problem for the power-law fluid flow is assumed to be analogous as the Newtonian fluid flow. Then a tensorial form of Darcy-scale filtration equation is obtained and the power-law relation between the averaged velocity and the gradient of the averaged pressure are confirmed. Different from Newtonian fluids, the apparent permeability significantly depends upon the filtration velocity direction for higher dimensional flow (d≥2). Numerical test also validates this conclusion.
In summary, the object of this paper is to develop an AMR software package for numerical reservoir simulation in thermal recovery of heavy oil by steam injection, based upon the research of the AMR technique for the thermal recovery of heavy oil in complex stratum. With the use of our own developed software, we studied different light solvent extraction efficiency of SAGD process and mechanism. For non-Newtonian behavior of heavy oil, the volume-average method was used to study the transport of power-law fluids flow in porous media and derive its generalized Darcy's law.
油藏数值模拟是油田勘探开发生产部门的重要科研手段。本文自主开发了注蒸汽热采稠油油藏数值模拟自适应网格法计算软件,能够对渗透率空间分布不均匀、油藏区域分布不同种类输运性质岩石、裂缝-孔隙双重介质、不规则边界及内部含有断层和人工压裂裂缝油藏等复杂地层注蒸汽热采稠油问题进行数值模拟。软件通过了信息处理产品标准符合性检测中心的测试并获得了国家版权局的软件著作权。通过简单二维裂缝性稠油油藏SAGD开采过程数值模拟和某稠油油藏注热水驱油过程数值模拟两个算例并与国际著名商业油藏数值模拟软件CMG-STARS对比结果显示,软件具有较高的计算精度和稳定性,并且由于采用了自适应网格法,计算速度比CMG-STARS快,可以满足油田的科研生产需求。
利用自主开发的软件,本文对辅助注入轻质溶剂的SAGD过程进行了数值研究,发现注入不同分子量的轻质溶剂对SAGD开采效率的影响截然不同：辅助注入C2H6可以保持蒸汽腔的压力并减小顶部热损,但是由于生产井过早见气,蒸汽和轻质气堵塞了稠油流通通道,使得油相相对渗透率降低,反而不利于稠油增产；辅助注入的C9H20能够在蒸汽腔壁的蒸汽锋面处凝结并充分溶解到稠油中,大大降低稠油粘度,增强锋面处油相流动能力,从而有效地提高稠油的开采速度,降低了蒸汽使用量,提高了油汽比,有利于节能减排。本文分析了辅助注入C9H20溶剂开采稠油的经济效益,结果表明辅助注入C9H20有一定的经济价值并且特别适用于快采。
稠油、高含水原油以及低渗透地层中原油均显示出非牛顿流体的特性,三次采油中利用聚合物溶液、胶束溶液、乳状液和压缩系数大的泡沫液等非牛顿流体作为驱油剂,钻井液和水力压裂工艺中的压裂液通常也是非牛顿流体。因此,研究非牛顿流体的渗流规律对于油气田开发具有重要的实际意义。幂律流体是工程上常见的非牛顿流体,其本构方程能够较好地反映稠油的流变特性。本文从幂律流体的基本流动控制方程出发,利用Whitaker的体积平均方法,将多孔介质中幂律流体的细观运动和宏观渗流运动联系起来；采用多尺度分析,使得体积平均意义下的宏观渗流运动方程得到进一步的简化：在将细观的下的流体物理量和宏观下的流体物理量联系起来的封闭性假设的基础上,理论推导得到幂律流体宏观渗流的广义Darcy定律。研究结果显示渗流速度和压力梯度之间存在幂函数关系,但幂律流体表观渗透率仅在一维流动情况下由多孔介质的空间结构以及幂律流体的流变特性所确定,对于二维及以上空间的流动,由于非线性项的存在,其表观渗透率还依赖于宏观渗流速度的具体方向,该渗流特性和牛顿流体完全不同。数值算例显示本文理论推导的表观渗透率对于渗流速度方向的依赖属性和国际上现有的基于直接求解幂律流体流动控制方程的数值模拟结果相符。
综上,本文的主要工作是开发具有自主知识产权的稠油热采数值模拟自适应网格法计算软件,软件能够对复杂地层的稠油蒸汽注采问题进行快速模拟。软件对裂缝-孔隙双重介质稠油油藏SAGD开采过程和某稠油油藏热水驱采油过程模拟的两个实例表明软件能对复杂地层的稠油热采问题利用自适应网格法进行快速数值模拟；本文利用开发的软件研究不同轻质溶剂对SAGD过程开采效率的影响和作用机理；针对稠油的非牛顿流体特性,本文利用体积平均方法对幂律流体在多孔介质中的渗流规律进行研究并推导其广义Darcy定律。
The numerical reservoir simulation has become an important tool for the petroleum research and exploration. The thermal recovery by steam injection can be thought as the problem of multi-phase flow in porous media with the phase-change. In the processes, there are sharp moving interfaces of temperature and phase saturations in the reservoir. Due to the rapid variations of the physical quantities across the interface, very fine grids are required. As a result, a huge CPU time and memory are needed if applying a uniform grid to the whole calculation area. In this paper, the adaptive mesh refinement (AMR) technique is applied to the numerical simulations for the processes of thermal recovery by steam injection, where the different heterogeneous cases of the reservoir are considered, like the reservoir with the permeability variations, the different rock-types, the heterogeneous fractured porous media, the complex boundary or complex faulted reservoir. In the AMR technique, the front is tracked, in order to have fine grid blocks in the region with steep gradients but coarser grid blocks ahead and behind of the front. The proposed AMR technique is fast and can give good accuracy. On the basis of theoretical research, a software package for the reservoir simulations, where including the AMR technique, is developed. This software package has good precision and numerical stability to meet the demands of scientific research.
With the use of the software developed by ourselves, a numerical example of SAGD progress in fractured reservoirs and a numerical simulation of the hot water flooding process of block Shan2are carried out, whose results are compared with the one based on CMG-STARS, a well-known commercial reservoir simulation software. The comparison shows that the computing speed of our software is five times of the one of CMG-STARS. The calculated results of day steam injection, day oil production, cumulative water injection and cumulative oil production are in good agreement with those of CMG-STARS. The remaining oil saturation distribution within the reservoir is relatively consistent with the one of CMG-STARS.
Using our own developed software, we perform a numerical study of Steam and Gas Push (SAGP) and Expanding-Solvent Steam-Assisted Gravity Drainage (ES-SAGD), which are both improvements of SAGD. In the gravity drainage process, the key to heavy oil production is the mobility of the oil phase which is dominated by the viscosity of the oil phase. The objective of this numerical study was to investigate the drainage mechanism of co-injecting light and heavy solvents to improve production performance. The light solvent C2H6, delivered in the vapor phase to the entire fluid interface, keeps the pressure of the steam chamber, and reduces the thermosteresis by building a thick gas blanket on the top of the recovery, but the recovery ratio may become lower due to the lower temperature of the steam chamber. The heavy solvent C9H20owould condense, with condensed steam, at the boundary of the steam chamber. Condensed solvent around the interface of the steam chamber which dilutes the oil, in conjunction with heat, reduces its viscosity and increases its mobility thereby increasing the oil production rate and recovery ratio. The conclusions from this study can be used to design suitable solvent mixtures and co-injection strategies to deliver a higher production rate and recovery ratio.
Heavy, high water and low permeability formations crude oil show a characteristic of non-Newtonian fluids. Many non-Newton fluids such as polymer solution, micellar solutions, emulsions and foam concentrate of high compression coefficient are used as oil displacing agents in the EOR process. Usually, the drilling fluid and the fracturing fluid in the hydraulic fracturing technology are usually non-Newtonian fluids. Therefore, the study of transport of non-Newtonian fluids in porous media has important practical significance for oil and gas development.
As a common non-Newtonian fluid, the constitutive equation of power-law fluids is relatively simple and can better reflect the rheological properties of heavy oil. The large-scale continuum models for transport of power-law fluids in porous media is derived from the pore-scale control equations using the volume averaging method. The averaging procedure leads to an equation of motion and a continuity equation expressed in terms of the volume-averaged pressure and velocity. The closure problem for the power-law fluid flow is assumed to be analogous as the Newtonian fluid flow. Then a tensorial form of Darcy-scale filtration equation is obtained and the power-law relation between the averaged velocity and the gradient of the averaged pressure are confirmed. Different from Newtonian fluids, the apparent permeability significantly depends upon the filtration velocity direction for higher dimensional flow (d≥2). Numerical test also validates this conclusion.
In summary, the object of this paper is to develop an AMR software package for numerical reservoir simulation in thermal recovery of heavy oil by steam injection, based upon the research of the AMR technique for the thermal recovery of heavy oil in complex stratum. With the use of our own developed software, we studied different light solvent extraction efficiency of SAGD process and mechanism. For non-Newtonian behavior of heavy oil, the volume-average method was used to study the transport of power-law fluids flow in porous media and derive its generalized Darcy's law.
引文
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