【专家技术贴】孔隙尺度建模和本构关系预测

Lin879

Pore-scale Modeling and Predicting Constitutive Relationships

孔隙尺度建模和本构关系预测

Dr. Arash, 高级数岩工程师

孔隙建模和本构关系是数字岩石技术模拟最基本的问题，也是最复杂的问题。搞清楚建模理论和本构关系才能保证模拟结果的可信，从而正确指导生产，解决生产问题，产生客观的经济效益。数字岩石如何做到神奇的建模模拟呢？数岩妹今天请来了FEI高级数岩工程师Arash博士讲一讲他的想法。

I often get the question that how the simulations that I run are different than a reservoir simulation. The answer that I usually give is that I perform pore-scale simulations. But what does a pore-scale simulation really mean? Does it just have a different scale than a reservoir simulation, or are there fundamental differences in the way the physical phenomena are simulated? I am going to try to answer this questionin this article. To understand the differences between a reservoir simulation and a pore-scale simulation we first need to understand how a porous medium is modeled.

作为数岩工程师，最经常思考的一个问题就是我做的模拟和常见的油藏数值模拟有什么区别。对于这个问题，最常见的答案是，我做的是孔隙尺度的模拟。但是究竟什么是孔隙尺度的模拟呢？它和油藏数值模拟只有尺度差异，还是在模拟的物理理论差异？本文中，将会和大家交流相关的想法。为了更好的区分油藏模拟和孔隙尺度的模拟，首先我们需要知道孔隙介质模型是如何得到的。

There are generally 2 or maybe 3 (if you differentiate pore-scale from grain-scale) methods for modeling aporous medium, namely continuum-scale, pore-scale and grain-scale. In acontinuum-scale model a porous medium is considered as a continuous materialwith a known porosity, permeability, and saturation at every single location.This is the way reservoir simulators model rock formations in a reservoir. The porosity, permeability, and saturation values in these models need to be determined from various sources. Typically well logs, cores, seismic and outcrop data are used to assign rock properties to formations in a reservoir. The variations are usually modeled using a random distribution. However, the challenge arises when it is time to assign capillary pressure and relative permeability curves to these formations. The most common way of assigning the seconstitutive relationships is using semi-empirical equations. The end points ofthe relative permeability curves are usually treated as adjustable parameters when performing a history match. In rare cases full special core analysis (i.e.SCAL) results are available on a select number of core plugs from the wells that were cored. These results are often used after being up-scaled.

孔隙模型建模方法有多种，比如连续性模型，孔隙尺度模型和基质尺度模型。在连续性模型中认为孔隙介质是拥有特定孔隙度、渗透率和在特定位置有对应饱和度的连续材料。这就是储层模拟器模拟储层岩石的方式。模型中孔隙度、渗透率和饱和度的值需要用其他途径来确定。通常情况下，这些数据通过测井曲线、岩石分析、地震数据和露头数据可以得到。这些数据的差异性通常通过数据值的随机分布来模拟。因此对于毛管压力和相对渗透率曲线这样的值如何赋给模型是一个很大的挑战。将这些本构关系复制的最常用办法就是利用半经验公式。相对渗透率曲线上的束缚水饱和度和残余油饱和度通常认为是历史拟合的参考数据。少数情况下，特殊岩心分析（SCAL）的结果对于取心井的一批岩心都具有代表性。其他情况下，这些数据通常要粗化之后才使用。

In a pore-scale model, the pore-space of the rock is modeled as open space for fluid flow. The simplest form of a pore-scale model is the bundle of capillary tubes model. The exact geometry of the pore-space is needed to create an accurate model. Rock imageswith different modalities, e.g. optical, X-ray CT and SEM, are used to create amodel of the pore-space. That is why this type of models are also known asimage-based models. In pore-scale models, every point in the rock is either solid or open to flow. In more advanced types of pore-scale models different minerals may be assigned to different solid points in the model.

对于孔隙尺度的模型而言，认为岩石孔隙空间就是岩石中流体流动的空间。最简单的孔隙尺度模型就是我们常说的毛管束模型。对于复杂的孔隙结构而言，就需要更精细更精准的模型来描述孔隙空间。现在我们可以利用真实岩石的图像信息来进行孔隙结构建模。常用的图像信息包括光学图像，X射线CT扫描以及SEM扫描电镜图像等。因此此类型的孔隙结构建模又被成为基于图像的建模。在孔隙尺度的建模中，模型中的每个点的值都有两个可能，非流动的岩石固体基质或者可供流动的孔隙。在一些更前沿的孔隙模型中，甚至可以考虑到固体基质由不同的矿物组成。

When it comes to simulating the physical phenomena in a rock. it matters what type of model you are using.If you have a continuum-scale model the Darcy’s law is used to simulate the fluid flow in the medium with known porosity, permeability, saturation values.However, if you are using a pore-scale model you have the description of the geometry of the pore-space, therefore, you can use the fluid flow equations for open spaces, i.e. Navier-Stokes equations. The results that you are going toget from these two models are also different. From a pore-scale model you canget a porosity value for the entire system and also for different parts of the sample. The results that you are going to get from these two models are also different. From a pore-scale model you can get a porosity value for the entire system and also for different parts of the sample. Permeability and other flow parameters can also be predicted using a pore-scale model. However the true strengths of these models are demonstrated when they are used to predictrelative permeability and capillary pressure curves. These saturation dependent relationships are some of the most difficult data to come by in E&Pworkflows. The table below lists some of the differences between pore-scale and reservoir-scale simulations.

在进行岩石物理模拟的时候，模型的选择非常重要。比如，对于连续性孔隙结构模型而言，已知孔隙度、渗透率和饱和度的值，就应该利用达西定律进行流动模拟。同时，如果考虑的孔隙的形状，运用更复杂的孔隙模型，就可以利用比如纳维斯托克斯方程来求解孔隙空间中的流动。不同的模型不同的理论得到的结果差异很大。对于孔隙模型而言，通过模拟不仅可以得到整个模型的孔隙度值，还可以得到样品不同部分的孔隙度值。渗透率等其他流动参数也可以通过孔隙模型来预测。光着两点还没有发挥孔隙模型的真正实力。孔隙模型最大的优势体现在相对渗透率和毛管压力曲线的预测。这两个与饱和度相关的模拟通常是勘探开发以及研究过程中中最难得到的数据。下表中列出了一些孔隙模型和油藏模型的区别：

查看原文，可关注科吉思石油公众号