Experimental Investigation on the Permeability Evolution of Compacted Broken Coal

Given the importance of airflow seepage properties to coal self-oxidation in gob, this paper develops a method and self-designed apparatus to assess seepage properties of compacted broken coal. This study mainly focuses on the strain, porosity and permeability evolution under the different conditions of particle size, vertical stress and temperature. The studied results show: (1) The strain, porosity and permeability were enlarged when the particle size increased under the same loading stress. The porosity and permeability reduced when the vertical stress increased. (2) The non-Darcy coefficient was negative in all tests, but the absolute value of the non-Darcy coefficient generally increased when the vertical stress increased. (3) The experiment results indicated that the larger the particle was, the easier to be compacted. The larger the grain diameter was, the lower the porosity and permeability were, which shown that the void volume in broken coal with larger grain diameters could be easily compacted. (4) The permeability was reduced when the temperature increased, which indicated the permeability of the compacted broken coal decreased during low-temperature oxidation in gob. (5) By the effects of stress and the particle size diameter on the porosity and permeability, the vertical stress recovery and generally increase are advantageous to reduce the porosity and permeability in gob. It is favorable to reduce the porosity and permeability and prevent coal self-heating by reducing the degree of fragmentation and percentage of small particles or consolidate the small particles.     

Prediction of Non-Darcy Coefficients for Inertial Flows Through the Castlegate Sandstone Using Image-Based Modeling

Near wellbore flow in high rate gas wells shows the deviation from Darcy??s law that is typical for high Reynolds number flows, and prediction requires an accurate estimate of the non-Darcy coefficient (?? factor). This numerical investigation addresses the issues of predicting non-Darcy coefficients for a realistic porous media. A CT-image of real porous medium (Castlegate Sandstone) was obtained at a resolution of 7.57???m. The segmented image provides a voxel map of pore-grain space that is used as the computational domain for the lattice Boltzmann method (LBM) based flow simulations. Results are obtained for pressure-driven flow in the above-mentioned porous media in all directions at increasing Reynolds number to capture the transition from the Darcy regime as well as quantitatively predict the macroscopic parameters such as absolute permeability and ?? factor (Forchheimer coefficient). Comparison of numerical results against experimental data and other existing correlations is also presented. It is inferred that for a well-resolved realistic porous media images, LBM can be a useful computational tool for predicting macroscopic porous media properties such as permeability and ?? factor.     

Positive Effect of Flow Velocity on Gas–Condensate Relative Permeability: Network Modelling and Comparison with Experimental Results

Positive velocity dependency of relative permeability of gas–condensate systems, which has been observed in many different core experiments, is now well acknowledged. The above behaviour, which is due to two-phase flow coupling in condensing systems at low interfacial tension (IFT) conditions, was simulated using a 3D pore network model. The steady-dynamic bond network model developed for this purpose was also equipped with a novel anchoring technique, which was based on the equivalent hydraulic length concept adopted from fluid flow through pipes. The available rock data on the co-ordination number, capillary pressure, absolute permeability, porosity and one set of measured relative permeability curves were utilised to anchor the capillary, volumetric and flow characteristics of the constructed network model to those properties of the real core sample. Then the model was used to predict the effective permeability values at other IFT and velocity levels. There is a reasonable quantitative agreement between the predicted and measured relative permeability values affected by the coupling rate effect.     

超临界CO2在低渗透煤层中渗流规律的实验研究

利用自主研发的THM三场耦合渗流实验系统,进行不同孔隙压力和温度条件下的超临界CO2在低渗透煤层中的渗流实验,得出不同温度下流速和压力梯度之间的关系,从而得到了低渗透煤层注入超临界CO2的非达西渗流规律,即流速与压力梯度变化规律呈现正指数关系.随着压力梯度的增大,渗透系数也不断的增大,且呈现正指数关系;在同一体积应力和压力梯度的条件下,温度越高,流速越快;温度在临界点附近,流速和渗透系数增加很快.     

Upscaling LBM-TPM simulation approach of Darcy and non-Darcy fluid flow in deformable,heterogeneous porous media

This paper presents a numerical approach for the simulation of fluid flow through porous media by proposing a theoretical and numerical meso-to-macro multiscale framework, which combines the advantages of the lattice Boltzmann method (LBM) with the continuum Theory of Porous Media (TPM) to efficiently and accurately model fluid transport in heterogeneous porous media. In particular, LBM presents an alternative to experiments by studying the flow from a mesoscopic perspective, which in turn, allows the derivation of the material parameters needed for simulating the flow in the macroscopic TPM model. In this work, a meso-macro hierarchic upscaling scheme is applied to investigate the deformation-dependent intrinsic permeability properties and the Darcy/non-Darcy fluid flow regime. Concerning the mesoscale, the intrinsic permeability of the porous domain is computed by means of the LBM model at the first stage. Subsequently, deformation of the medium takes place in furtherance of determining the relation of the aforementioned deformation dependency. Thereupon, these findings are input into the TPM model in order to compute the primary unknown variables, where special focus is laid on the stability challenges in the compaction and near compaction states. With respect to the criteria of non-Darcy fluid flow, the conditions of its onset, i.e. the induced pressure gradient and mean fluid flow velocity, are computed as well using the LBM solver and conveyed afterwards to the macroscopic TPM model. Herein, the non-Darcy intrinsic permeability has been investigated in the TPM approach based on the Forchheimer equation. Simulations done on a synthetic porous micro-structure show that the combined framework proved to stand well between the two approaches.     

Gas-gas displacement in a fractured porous reservoir

The results of an experimental investigation of the process of miscible displacement of a gas from a fractured porous reservoir by another gas are presented. It is established that the displacement process is influenced by convective and molecular diffusion. The displacement coefficient depends both on the reservoir properties of the formation and on the technological displacement parameters. The experiments revealed a decrease in the displacement coefficient with increase in the permeability ratio of the joints and the blocks and with decrease in formation pressure. The dependence of the displacement coefficient on the average gas velocity in the reservoir, i.e., the ratio of the gas flow rate to the product of the flow area and the total reservoir porosity coefficient (including the blocks and the joints), is established.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 74–79, May–June, 1991.     

A New Non-Darcy Flow Model for Low-Velocity Multiphase Flow in Tight Reservoirs

The pore and pore-throat sizes of shale and tight rock formations are on the order of tens of nanometers. The fluid flow in such small pores is significantly affected by walls of pores and pore-throats. This boundary layer effect on fluid flow in tight rocks has been investigated through laboratory work on capillary tubes. It is observed that low permeability is associated with large boundary layer effect on fluid flow. The experimental results from a single capillary tube are extended to a bundle of tubes and finally to porous media of tight formations. A physics-based, non-Darcy low-velocity flow equation is derived to account for the boundary layer effect of tight reservoirs by adding a non-Darcy coefficient term. This non-Darcy equation describes the fluid flow more accurately for tight oil reservoir with low production rate and low pressure gradient. Both analytical and numerical solutions are obtained for the new non-Darcy flow model. First, a Buckley–Leverett-type analytical solution is derived with this non-Darcy flow equation. Then, a numerical model has been developed for implementing this non-Darcy flow model for accurate simulation of multidimensional porous and fractured tight oil reservoirs. Finally, the numerical studies on an actual field example in China demonstrate the non-negligible effect of boundary layer on fluid flow in tight formations.     

考虑二次梯度项及动边界的双重介质低渗透油藏流动分析

在传统试井模型的非线性偏微分方程中根据弱可压缩流体的假设,忽略了二次梯度项,对于低渗透油藏这种方法是有疑问的.低渗透问题一个显著的特点就是流体的流动边界随着时间不断向外扩展.为了更好地研究双重介质低渗透油藏中流体的流动问题,考虑了二次梯度项及活动边界的影响,同时考虑了低渗透油藏的非达西渗流特征,建立了双重介质低渗透油藏流动模型.采用Douglas-Jones预估-校正差分方法获得了无限大地层定产量生产时模型的数值解,分别讨论了不同参数变化时压力的变化规律及活动边界随时间的传播规律,还分析了考虑和忽略二次梯度项影响时模型数值解之间的差异随时间的变化规律,做出了典型压力曲线图版,这些结果可用于实际试井分析.     

高温高压气体在低含水率介质中迁移的数值模拟

针对气液两相非等温渗流模型高度非线性的特点,发展了适宜的数值离散方法。根据相态转换准则和控制方程的性质,采用最低饱和度法简化算法。空间离散方面,使用有限体积法;时间离散方面,设计了一套包含合理求解顺序的Picard迭代法,解决了方程组强耦合的问题。利用上述数值方法对高温高压气体的迁移行为进行数值模拟,证明了气体在低含水率介质和等效孔隙度的干燥介质内的运动基本一致,并分析了空腔内的气液相态转变过程。在此基础上,研究了多孔介质孔隙度和渗透率对气体压强演化和示踪气体迁移的影响。研究表明,孔隙度越小（相同渗透率）、渗透率越高（相同孔隙度）,示踪气体的迁移距离越远,并给出了估算不同孔隙度和渗透率下迁移距离的半经验公式。     

页岩气藏压裂水平井试井分析

页岩气藏资源丰富,开发潜力巨大,已成为目前研究的热点.与常规气藏相比,页岩气藏运移机制复杂,流动模式呈非线性,有必要考虑页岩气的吸附解吸,天然微裂缝的应力敏感性,人工裂缝内的非达西流等非线性因素对压裂水平井压力响应的影响. 基于双重介质和离散裂缝混合模型,分别采用Langmuir等温吸附方程描述吸附解吸,渗透率指数模型描述应力敏感,Forchheimer方程描述非达西效应,建立页岩气藏压裂水平井数值试井模型. 运用伽辽金有限元法对模型进行求解.根据试井特征曲线,划分流动阶段,着重分析非线性因素对压力响应的影响.结果表明:页岩气藏压裂水平井存在压裂裂缝线性流、压裂裂缝径向流、地层线性流、系统径向流及封闭边界影响5 种流动阶段.吸附解吸的影响发生窜流之后,Langmuir吸附体积增大,拟压力导数曲线凹槽更加明显,系统径向流出现时间与压力波传播到边界时间均延迟;天然裂缝系统的应力敏感性主要影响试井曲线的晚期段,拟压力和拟压力导数曲线均表现为上翘,应力敏感效应越强,上翘幅度越大;高速非达西效应对早期段影响较大,非达西效应越强,拟压力降幅度越大,试井曲线上翘.与解析解的对比以及矿场实例验证了模型的正确性与适用性.      

Experimental Study of Seepage Properties of Broken Sandstone Under Different Porosities

In coal mining the water flow in broken rock is a very common phenomenon. Study of seepage properties of broken rock is one of the basic subjects required in order to understand the stability of rock surrounding roadways, preventing disasters such as water inrush and gas outbursts and developing underground resources. So far, quantitative studies on the nonlinear seepage properties of broken sandstone under different porosities are not extensive in the research literature. In this article, by means of an electro-hydraulic servo-controlled test system (MTS815.02) and a patent seepage device, the seepage properties under different conditions of porosity were tested on broken sandstone of five different grain sizes. Based on the loading method of controlling the axial compression displacement and steady permeating method, we obtained curves of the relation of pore pressure with time, as well as the relation curves between the pore pressure gradient for steady seepage and velocity. Furthermore, we calculated the permeability k and non-Darcy coefficient β corresponding to different porosities by fitting these curves with the binomial expression. This study indicates that: (1) the seepage properties of broken sandstone are closely related to grain size, load levels, and porosity structure; (2) the permeability k decreases, while the coefficient β increases with a decrease in porosity φ, but both the k − φ and the β − φ curves show some local fluctuations; (3) the permeability k of the broken sandstone has a magnitude of 10⁻¹⁴–10⁻¹² m², while the coefficient β ranges from 10¹⁰ to 10¹² m⁻¹. The results obtained provide some information for further study of the nonlinear seepage behavior of broken rock theoretically.     

Multiscale, Multiphysics Network Modeling of Shale Matrix Gas Flows

We present a pore network model to determine the permeability of shale gas matrix. Contrary to the conventional reservoirs, where permeability is only a function of topology and morphology of the pores, the permeability in shale depends on pressure as well. In addition to traditional viscous flow of Hagen–Poiseuille or Darcy type, we included slip flow and Knudsen diffusion in our network model to simulate gas flow in shale systems that contain pores on both micrometer and nanometer scales. This is the first network model in 3D that combines pores with nanometer and micrometer sizes with different flow physics mechanisms on both scales. Our results showed that estimated apparent permeability is significantly higher when the additional physical phenomena are considered, especially at lower pressures and in networks where nanopores dominate. We performed sensitivity analyses on three different network models with equal porosity; constant cross-section model (CCM), enlarged cross-section model (ECM) and shrunk length model (SLM). For the porous systems with variable pore sizes, the apparent permeability is highly dependent on the fraction of nanopores and the pores’ connectivity. The overall permeability in each model decreased as the fraction of nanopores increased.     

An Experimental Investigation of Permeability Measurement of Water Flow in Crushed Rocks

Due to the high permeability of water flow in crushed rocks, flow catastrophes and water inrush accidents are apt to take place in the broken zones of aquifers in coal mining engineering. The pore, crack and fracture geometries needed for water transport are strongly influenced by grains diameter size and axial displacement conditions. In order to inspect and quantify the influence, we designed and manufactured a water flow apparatus that can be connected to the electro-hydraulic servo-controlled test system MTS815.02 which provides loading pressure in the experiment. Using the apparatus and MTS system, we tested crushed mudstone, limestone and sandstone specimens and obtained the relationship between permeability and variable grain diameter of a (2.5–5 mm), b (5–10 mm), c (10–15 mm), d (15–20 mm) and e (mixed sizes) under variable axial displacement (10, 15, 20, 25, 30, 35 and 40 mm). In particular, the permeability calculation based on collection of water flow velocity and pore pressure gradient difference has involved the influence of non-Darcy flow. The results show that (1) The porosity decreases with the increase of axial displacement and decrease of bigger particle size, respectively. Particle crushing during compaction is a main cause of size 0–2.5 mm appearing, some fine particles be washed away is a main cause of weight loss because of the effect of water seepage. (2) Water flow properties of crushed rocks are found to be strongly influenced by axial displacement and grain diameter size; in general, the permeability decreases with the increase of axial displacement and the decrease of grain diameter, respectively. (3) The fluctuations of permeability–axial displacement are especially intense for mudstone and sandstone than that for limestone. The permeability of crushed rocks is not only related to loading levels but also to grain diameters, style of arrangement. (4) To each grain diameter sizes, the permeability change of sandstone has a greater value than that of mudstone and limestone. The permeability of crushed mudstone shows much less than that of limestone and sandstone.     

Non-Darcy effects on convective boundary layer flow past a semi-infinite vertical plate in saturated porous media

The composite effects of viscosity, porosity, buoyancy parameter, thermal conductivity ratio and non-Darcy effects of Brinkman friction and Forscheimmer quadratic drag on the mixed convection boundary layer flow past a semi-infinite plate in a fully-saturated porous regime are theoretically and numerically investigated using Keller’s implicit finite-difference technique and a double-shooting Runge-Kutta method. The Brinkman Forcheimer-extended Darcy model is implemented in the hydrodynamic boundary layer equation. The effects of the various non-dimensional thermofluid parameters, viz Grashof number, Darcy number, and Forchheimer number, and also porosity, thermal conductivity and viscosity parameters on the velocity and temperature fields are discussed. Computations for both numerical schemes are made where possible and found to be in excellent agreement.     

Understanding Oil and Gas Flow Mechanisms in Shale Reservoirs Using SLD–PR Transport Model

More and more attention has been paid to the oil and gas flow mechanisms in shale reservoirs. The solid–fluid interaction becomes significant when the pores are in the nanoscale. The interaction changes the fluid’s physical properties and leads to different flow mechanisms in shale reservoirs from those in conventional reservoirs. By using a Simplified Local Density–Peng Robinson transport model, we consider the density and viscosity profiles, which result from solid–fluid interaction. Gas rarefaction effect is negligible at high pressure, so we assume it is viscous flow. Considering the density- and viscosity-changing effects, we proposed a slit permeability model. The velocity profiles are obtained by this newly established model. This proposed model is validated by matching the density profile and velocity profile from molecular dynamic simulation. Then, the effects of pressure and pore size on gas and oil flow mechanisms are also studied in this work. The results show that both gas and oil exhibit enhanced flow rates in nanopores. Gas-phase flow in nanopores is dominated by the density-changing effect (adsorption), while the oil-phase flow is mainly controlled by the viscosity-changing effect. Both gas and oil permeability quickly decrease to the Darcy permeability when the slit aperture becomes large. The results reported in this work are representative and should significantly help us understand the mechanisms of oil and gas flow in shale reservoirs.     

A Numerical Study of Microscale Flow Behavior in Tight Gas and Shale Gas Reservoir Systems

Various attempts have been made to model flow in shale gas systems. However, there is currently little consensus regarding the impact of molecular and Knudsen diffusion on flow behavior over time in such systems. Direct measurement or model-based estimation of matrix permeability for these “ultra-tight” reservoirs has proven unreliable. The composition of gas produced from tight gas and shale gas reservoirs varies with time for a variety of reasons. The cause of flowing gas compositional change typically cited is selective desorption of gases from the surface of the kerogen in the case of shale. However, other drivers for gas fractionation are important when pore throat dimensions are small enough. Pore throat diameters on the order of molecular mean free path lengths will create non-Darcy flow conditions, where permeability becomes a strong function of pressure. At the low permeabilities found in shale gas systems, the dusty-gas model for flow should be used, which couples diffusion to advective flow. In this study we implement the dusty-gas model into a fluid flow modeling tool based on the TOUGH+ family of codes. We examine the effects of Knudsen diffusion on gas composition in ultra-tight rock. We show that for very small average pore throat diameters, lighter gases are preferentially produced at concentrations significantly higher than in situ conditions. Furthermore, we illustrate a methodology which uses measurements of gas composition to more uniquely determine the permeability of tight reservoirs. We also describe how gas composition measurement could be used to identify flow boundaries in these reservoir systems. We discuss how new measurement techniques and data collection practices should be implemented in order to take advantage of this method. Our contributions include a new, fit-for-purpose numerical model based on the TOUGH+ code capable of characterizing transport effects including permeability adjustment and diffusion in micro- and nano-scale porous media.     

Analysis of Multiphase Non-Darcy Flow in Porous Media

Recent laboratory studies and analyses (Lai et al. Presented at the 2009 Rocky Mountain Petroleum Technology Conference, 14–16 April, Denver, CO, 2009) have shown that the Barree and Conway model is able to describe the entire range of relationships between flow rate and potential gradient from low- to high-flow rates through porous media. A Buckley and Leverett type analytical solution is derived for non-Darcy displacement of immiscible fluids in porous media, in which non-Darcy flow is described using the Barree and Conway model. The comparison between Forchheimer and Barree and Conway non-Darcy models is discussed. We also present a general mathematical and numerical model for incorporating the Barree and Conway model in a general reservoir simulator to simulate multiphase non-Darcy flow in porous media. As an application example, we use the analytical solution to verify the numerical solution for and to obtain some insight into one-dimensional non-Darcy displacement of two immiscible fluids with the Barree and Conway model. The results show how non-Darcy displacement is controlled not only by relative permeability, but also by non-Darcy coefficients, characteristic length, and injection rates. Overall, this study provides an analysis approach for modeling multiphase non-Darcy flow in reservoirs according to the Barree and Conway model.     

Calculating the Anisotropic Permeability of Porous Media Using the Lattice Boltzmann Method and X-ray Computed Tomography

A lattice Boltzmann (LB) method is developed in this article in a combination with X-ray computed tomography to simulate fluid flow at pore scale in order to calculate the anisotropic permeability of porous media. The binary 3D structures of porous materials were acquired by X-ray computed tomography at a resolution of a few microns, and the reconstructed 3D porous structures were then combined with the LB model to calculate their permeability tensor based on the simulated velocity field at pore scale. The flow is driven by pressure gradients imposed in different directions. Two porous media, one gas diffusion porous layer used in fuel cells industry and glass beads, were simulated. For both media, we investigated the relationship between their anisotropic permeability and porosity. The results indicate that the LB model is efficient to simulate pore-scale flow in porous media, and capable of giving a good estimate of the anisotropic permeability for both media. The calculated permeability is in good agreement with the measured date; the relationship between the permeability and porosity for the two media is well described by the Kozeny–Carman equation. For the gas diffusion layer, the simulated results showed that its permeability in one direction could be one order of magnitude higher than those in other two directions. The simulation was based on the single-relaxation time LB model, and we showed that by properly choosing the relaxation time, it could give similar results to those obtained using the multiple-relaxation time (MRT) LB method, but with only one third of the computational costs of MRTLB model.     

A general treatment for non-Darcy film condensation within a porous medium in the presence of gravity and forced flow

Non-Darcy film condensation over a vertical flat plate within a porous medium is considered. The Forchheimer extended Darcy model is adopted to account for the non-Darcy effects on film condensation in the presence of both gravity and externally forced flow. A general similarity transformation is proposed upon introducing a modified Peclet number based on the total velocity of condensate, resulting from both gravitational force and externally forced flow. This general treatment makes it possible to obtain all possible similarity solutions including the asymptotic results in the four different limiting regimes, namely, Darcy forced convection regime, Forchheimer forced convection regime, Darcy body force predominant regime and Forchheimer body force predominant regime. Appropriate dimensionless groups for distinguishing these asymptotic regimes are found to be the micro-scale Grashof and Reynolds numbers based on the square root of the permeability of the porous medium. Correspondingly, the non-Darcy effect on the heat transfer rate are investigated in terms of these micro-scale dimensionless numbers.     

低渗油层压裂水平井两相流研究

依据压裂水平井不同流动区域的流动规律, 将压裂水平井的渗流分为裂缝中的高速非达西流 动区、裂缝控制影响的椭圆渗流区、远离裂缝的基质非达西渗流区, 考虑启动压力梯度的影 响, 对压裂水平井两相渗流进行了分析, 得到了低渗透油层压裂水平井的产量公式. 研究结 果表明, 裂缝的导流能力越大, 压裂水平井的产量越高. 但随着开采时间的增加, 其产量递减幅度越 大; 压裂裂缝长度越小, 压裂水平井的初始产量越高. 但随着生产时间的推移, 压裂裂缝的 长度越大, 产量的递减幅度越小; 中间裂缝长, 两翼裂缝短的情况下, 压裂水平井的产量最 高.