AN IMPROVED GLOBAL UPSCALING APPROACH FOR RESERVOIR SIMULATION

Realistic upscaling of fine-scale reservoir models is a great challenge for reservoir engineers. The common problem of conventional upscaling methods is that they may smear out the spatially continuous permeability extremes, such as shale barriers and open fractures. Recent studies have shown that such smearing effect has a significant impact on recovery in heterogeneous reservoirs, especially the breakthrough oil recovery. The conventional methods are considered as local upscaling which concentrate on only local areas and ignore geologically important structural information. A recent global upscaling approach attempts to solve this problem, but the resulting grid system may be over-irregular and becomes impractical for field applications. This paper presents an improved global upscaling approach based on the representative elemental volume (REV) theory and the stepwise idea from renormalization. The new method focuses on the use of a new concept of REVGS (REV Grid System) for constructing coarse blocks, which taking into account the spatial connectivity of a global permeability field. Mathematically, the variance of permeability in the coarse blocks is the smallest within the blocks, and the largest between the blocks. The resulting system can be readily used in flow simulators. The proposed method is applied to two case studies. Compared to the conventional methods, the coarse grid system derived from our improved global method successfully retains the permeability extremes observed in the fine-scale models. The flow simulation results show that the consistency of the reservoir behavior before and after upscaling is excellent.     

REV Grid Technique for Reservoir Upscaling

Lasseter et al. (Lasseter, T. J., Waggoner, J. R., Lake, L. W. (1986). Reservoir Heterogeneities and Their Influence on Ultimate Recovery. Reservior Characterization, Orlando, Florida: Academic Press Inc., 545.) proposed that scale-up of properties should be done from the scale of a representative elementary volume (REV), a volume for which the measured property does not change with an increase in scale over a given limit of scale. The notion of REV has been a quite argued concept owing to its definition is not unequivocal, and it did not address how to obtain it in real system, some people even argue if REV really exists. Qi et al. (Qi, D., Wong, P. M., Liu, K. (2001). An improved global upscaling approach for reservoir simulation. Petroleum Science and Technology 19(7-8):779-795.) based on REV concept, proposed the new idea of REVG (representative elemental volume grid). This article further developed this idea, and based on it, proposed the REV grid upscaling technique. This new technique uses an algorithm, which is a combination of two-procedure-upgridding with reverse stepwise approach, it is a field-oriented 3D model. The new method concentrates on constructing a unique coarse grid, referred to as pseudo-REVG, which could best describe the heterogeneity of the original model at given scale. Mathematically, the variance of properties in REVG is the smallest within each block, and largest between the blocks. The proposed method is applied to two case studies, one of them is a 3D multiphase real reservoir, and the flow simulation results show that the consistency of the reservoir behavior before and after upscaling with REV grid technique is excellent. It is much better than that of the conventional upscaling methods.     

Sensitivity-based upscaling for history matching of reservoir models

Simulation of reservoir flow processes at the finest scale is computationally expensive and in some cases impractical. Consequently, upscaling of several fine-scale grid blocks into fewer coarse-scale grids has become an integral part of reservoir simulation for most reservoirs. This is because as the number of grid blocks increases, the number of flow equations increases and this increases, in large proportion, the time required for solving flow problems. Although we can adopt parallel computation to share the load, a large number of grid blocks still pose significant computational challenges. Thus, upscaling acts as a bridge between the reservoir scale and the simulation scale. However as the upscaling ratio is increased, the accuracy of the numerical simulation is reduced; hence, there is a need to keep a balance between the two. In this work, we present a sensitivity-based upscaling technique that is applicable during history matching. This method involves partial homogenization of the reservoir model based on the model reduction pattern obtained from analysis of the sensitivity matrix. The technique is based on wavelet transformation and reduction of the data and model spaces as presented in the 2Dwp–wk approach. In the 2Dwp–wk approach, a set of wavelets of measured data is first selected and then a reduced model space composed of important wavelets is gradually built during the first few iterations of nonlinear regression. The building of the reduced model space is done by thresholding the full wavelet sensitivity matrix. The pattern of permeability distribution in the reservoir resulting from the thresholding of the full wavelet sensitivity matrix is used to determine the neighboring grids that are upscaled. In essence, neighboring grid blocks having the same permeability values due to model space reduction are combined into a single grid block in the simulation model, thus integrating upscaling with wavelet multiscale inverse modeling. We apply the method to estimate the parameters of two synthetic reservoirs. The history matching results obtained using this sensitivity-based upscaling are in very close agreement with the match provided by fine-scale inverse analysis. The reliability of the technique is evaluated using various scenarios and almost all the cases considered have shown very good results. The technique speeds up the history matching process without seriously compromising the accuracy of the estimates.     

Major Challenges for Reservoir Upscaling

Abstract

In the past two decades, many upscaling procedures have been proposed. The major methods are power-law average, renormalization technique, pressure-solver method, tenser method, and pseudo-function technique. The common problem of conventional upscaling methods is that they tend to smear out the spatially continuous extremes, such as shale barriers and open fractures. However, experience and previous simulation work in heterogeneous reservoirs have shown that oil recovery (especially water breakthrough oil recovery) mainly depends on the spatial connectivity of the extreme permeability values.

Lasseter et al. (1986) Lasseter, T. J., Waggoner, J. R. and Lake, L. W. 1986. “Reservoir heterogeneities and their influence on ultimate recovery.”. In Reservoir characterization Edited by: Schatzinger, R. A. and Jordan, J. F. 545Orlando: Academic Press, Inc..  [Google Scholar] proposed that scale-up of properties should be done from the scale of a representative elementary volume (REV), a volume for which the measured property does not change with an increase in scale over a given limit of scale. The notion of REV is physical-model oriented and proposed a criterion for upscaling technique. However, the decisive factor in upscaling is the grid system rather than individual physical point.

This article concludes that how to obtain REV for real system, how to evaluate the upscaling results quantitatively, how to treat extremes of permeability, as well as how to perform upscaling for naturally fractured reservoirs and carbonate reservoirs are the remained major challenging problems in this area. It is concluded that a great effort should be made on how to obtain the REV grid, which could best describe the heterogeneity of given reservoir at a given scale. Secondly how to perform the upscaling of all properties based on the REV grid is also a critical aspect and should be considered according to the different extent and pattern of heterogeneity of the original geological model respectively.     

油藏模型网格粗化的理论与方法

近20年来,由于油藏描述与油藏模拟的需要,人们提出了许多油藏模型网格粗化(Resenroir Upscaling)的理论与方法.这些方法大致可归纳为5类:指数律平均法、重正规化技术、解压力方程法、矢量法和拟函数法.传统方法的共同点是它们倾向于抹平一些在空间分布的渗透率极值条带,例如,泥岩夹层和裂缝.然而,非均质油藏的生产实践和模拟实验都表明,这些渗透率极值条带对原油采收率,尤其是无水采收率影响极大.因此,在网格粗化过程中怎样处理渗透率极值条带,怎样对天然裂缝油藏以及石灰岩油藏进行网格粗化,是这一研究领域有待解决的挑战性问题.     

Upscaling Extent vs. Information Loss in Reservoir Upscaling

Abstract

Upscaling has become an increasingly important tool in recent years for converting highly detailed geological models of a reservoir to simulation grids. The main idea of upscaling is to replace a number of heterogeneous fine grid blocks with one equivalent coarse homogeneous grid block. The common method of upscaling is to replace more than one different value with an effective one. So, the essence of upscaling is averaging. It goes without saying that some information loss in upscaling is inevitable. Studies show that upscaling extent (UE) has a strong positive correlation with information loss. So, in reservoir upscaling, large UE should try to be avoided, especially greater than 0.4.     

Performance of combined vorticity-based gridding and dual mesh method for gravity dominated reservoir flows

This paper presents a new combined method for accurate upscaling of two-phase displacements in highly heterogeneous reservoirs. The method has the capability to retain its high performance for various flow regimes, from viscous to gravity dominant displacements, without the need for further modifications and computational steps. Two different grids are incorporated for simulation. The grid on fine scale is used to recognize the complicated physics of flow which depends on dominated driving forces and their interaction with heterogeneity. However, to achieve a fast simulation, the global flow calculation is performed on the coarse scale grid using upscaled equivalent properties. The communication between two different scale grids is achieved by the dual mesh method (DMM) procedure. A simple geometric mean upscaling technique is used to assign effective permeability for coarse grid blocks which introduces a significant error due to homogenization. As a result, DMM is incorporated in conjunction with the vorticity-based coarse grid generation technique to limit the homogenization error. The distribution of the coarse grid is optimized by the vorticity preservation concept which attempts to preserve single-phase vorticity between fine and coarse grid models. To demonstrate accuracy and efficiency, the combined DDM–vorticity method is applied to highly heterogeneous systems in two dimensions with and without gravity. The results reveal that the flow regime has only a minor impact on the performance (accuracy and speed up) of the method.     

化学驱驱替前缘动态追踪数值模拟研究

将快速自适应组合网格方法用于化学驱动态局部网格加密研究,并在国产化学驱软件ASP上实现了动态局部网格加密,局部加密区域可以随驱替前缘的移动而改变。所研制的动态局部网格加密的模拟结果与全细网格计算的结果非常接近,而CPU时间比整个模拟区域都采用细网格减少一半以上。进行化学驱数值模拟实验,给出了用3种网格系统(粗网格、全细网格以及组合网格)模拟得到的生产井含水率、井网格含油饱和度对比曲线以及含油饱和度的平面等值图。数值模拟实验结果还表明,化学驱对网格大小很敏感,采用细网格或动态局部网格加密是必要的。图7表1参7     

化学驱驱替前缘动态追踪数值模拟研究

将快速自适应组合网格方法用于化学驱动态局部网格加密研究,并在国产化学驱软件ASP上实现了动态局部网格加密,局部加密区域可以随驱替前缘的移动而改变.所研制的动态局部网格加密的模拟结果与全细网格计算的结果非常接近,而CPU时间比整个模拟区域都采用细网格减少一半以上.进行化学驱数值模拟实验,给出了用3种网格系统(粗网格、全细网格以及组合网格)模拟得到的生产井含水率、井网格含油饱和度对比曲线以及含油饱和度的平面等值图.数值模拟实验结果还表明,化学驱对网格大小很敏感,采用细网格或动态局部网格加密是必要的.图7表1参7     

对油藏模型网格粗化中REV理论的探讨

Lasseter等（1986）提出油藏模型网格粗化（Reservoir Upscaling）应当在表征体元（Representative Elementary Volume,简称REV）级进行.REV指一种特定的体积元,在这种体积元测取的物性参数将在一定的比例尺范围内保持不变.REV理论一直是一个有争议的概念,因为其定义不十分清晰,且没有说明如何在真实油藏中获取之.因此,甚至有人怀疑在真实油藏中,是否真的存在REV.基于REV理论,提出了一个新的概念--表征体元网格,（Representative Elementary Volume Grid,简称REVG）.该网格体系在给定的比例尺范围内可最佳地描述油藏的非均质性.从物理意义上讲,在REVG系统中,每个网格内的物性差异最小,而网格间的物性差异最大.