外文翻译-煤的渗透率决定的变形在煤层气回收及与CO2分离中的应用

Deformation Dependent Permeability of Coal for Coalbed Methane (CBM) Recovery and CO2 SequestrationG. X. Wang1, Z. T Wang1,2, V. Rudolph1 and P. Massarotto11 Division of Chemical Engineering, University of Queensland, Qld 4074, AUSTRALIA2 Department of Mining Engineering, China University of Mining and Technology, Xuzhou 221008, CHINAAbstractAn alternative approach is proposed in this paper to address the difficult issue on permeability of coal so as to improve the numerical simulation of Coalbed methane (CBM) and/or enhanced CBM (ECBM) recovery and CO2 storage processes. This approach integrates the coal structural properties with its mechanical behavior in cleat scale, resulting in two basic models, i.e. stress induced deformation model and deformation dependent permeability model. The deformation model is described using stress-strain correlations that cover the elastic and brittle deformations of coal. The permeability model, build up based on the stress-strain correlations, accounts for the contributions from the deformations of individual cleats and coal matrix in coal and formulates in a generalized strain-permeability relationship. Coupling these two models with the associated structural and mechanic properties of a given coal allows determination of directional permeability of the coal under any progressive stress conditions. Verification of the models has been discussed with experimental investigations and the results showed the reasonable agreements between the model predictions and the experimental measurements for the given coal under laboratory conditions.Keywords: Coal; Coalbed methane (CBM); CO2 enhanced CBM (ECBM); Stress/strain; Deformation; Permeability.1. INTRODUCTIONCoalbed methane (CBM) recovery and CO2 sequestration have become more attractive technologies in recent decades due to advantages in optimal utilization of energy sources and effective storage of carbon dioxide, a greenhouse gas (GHG). It is particularly attractive to develop a combined CBM recovery and CO2 sequestration in deep, unmineable coalbeds, i.e. CO2-enhaced CBM (ECBM) process in which CO2 or flue gas (i.e. a mixture of carbon dioxide and nitrogen) can be injected and stored into the coalbed to replace the adsorbed methane . Thus the revenue of methane production can significantly reduce capital cost by offsetting the expenditures of CO2 storage operation. There are many factors that affect the efficiency of CBM or ECBM process. Darcy flow, for example, may control the gases and water flows through coal seams , and hence determine the well pattern and the (production and/or injection) well rates. Generally speaking, the Darcy flow is basically related to the permeability and pressure gradient which are controlled by the structural and mechanical properties of the coal. The most important requirement in the CBM/ECBM process is to achieve the required gas flow rate without obvious loss of permeability in coal seams. Therefore it is essential to understand the relevant mechanical properties and its impacts on the transport characteristics of fluid through coal seams for this particular process. In the past three decades, the mining industry has expended a large number of resources to understand the physical behavior of coal, such as its deformation, elasticity, as well as the correlations between laboratory and field data. Focus of such efforts, however, has been on most aspects of coal pillar loading behavior and design approaches to develop more accurate and reliable coal pillar design methods for underground coal mining . Very less attention is paid to the impact of the physical behavior of coal on permeability which is one of major concerns in processes for CBM/ECBM recovery and CO2 sequestration . There exists another knowledge gap between the structural properties and mechanical behavior of coal which significantly limit generalized application of the common geological/mechanical models in deep coals. Today the structure of coal, consisting of two distinct constitution, i.e. matrix and cleat, can be well characterized by means of many advanced techniques and their combination, such as geographical measurement, light microscope (LM), scanning electronic microscope (SEM) and x-ray diffraction (XRD). Thus the structure of coal can statistically described with average dimensional parameters such as cleat spacing of both butt and face cleats and so-called cleat density . On the other hand it is apparently easy and reliable to measure the mechanical properties of singe constituent materials than ones of multi-constituent coal. These features are helpful in developing somehow or other correlations between coal structure and its mechanical behavior. It is particularly significant to understand and describe the influence of structural properties on mechanical behavior in optimizing CBM or ECBM process in deep coal. Both experimental and field data have revealed that the permeability of coal would be changing during CBM extraction and/or enhanced fluid injection . The dynamical change in permeability mainly subjects to two mechanisms, i.e. effective stress determined by pore pressure of fluid and overload from upper rock layer , and swelling/shrinkage induced accompanying with gaseous absorption and desorption in coal . Regardless of whatever mechanism, the result seems same, i.e. the coal structure is deformed in terms of increased or decreased porosity. As a result of deformation the demanded permeability for CBM or ECBM process would unpredictably variable and may lead to failure in well operation.Many attempts have been made in development of the predictive models of dynamical permeability for CBM or ECBM process. Two approaches were commonly used in such the permeability models. The first is basically empirical and was adopted by Gray , Harpalani and Zhao and Shi and Durucan . This approach makes use of experimental observation and usually formulates in an empirical correlation between permeability and effective stress acting on the given coal. The second is based on the designated exponent relationship for porosity/permeability ratio, in which the porosity can be determined by means of a theoretical or semi-empirical model. This approach was typically used by Sawyer and Palmer and Mansoori , and further extended to use in several commercial simulators . However all permeability models developed using the aforementioned approaches have at least two deficiencies, i.e., incapability of addressing to the directional feature of permeability in deep coal and lack of he meaningful linkage between the coal structural properties and its permeability. This paper describes an alternative permeability model for improvement of the numerical simulation of CBM and ECBM recovery/storage process that have increasingly occurred over the past few years. The model is developed based on stress induced deformation in coal under confined stress conditions. The stress induced deformation is related to characterization of coal cleat structure and its mechanical behavior and can be described using a stress-strain correlation . The model has unique features that integrate the coal structural properties with its mechanical behavior and allow determination of directional permeability. 2. THEORETICAL ANALYSIS 2.1 Stress induced deformation Deep coals usually suffer high stresses under diverse geology, which may dramatically change due to mining operation or water/gas injection/extraction via wellbores. High stresses and adverse geology in deep coal mines might cause bursts , which is beyond the scope of this study. Concerns here are about stress induced deformation and its impact on transport of gas and water through the deforming deep coal associated with CBM/ECBM recovery and CO2 sequestration processes. A better understanding of the mechanisms and stress/strain levels involved in these processes is needed to help develop improved stress control and wellbore design. In general, coal seams can be characterized in two parts: large fracture system, comprising of face and butt cleats, and coal matrix. The face and butt cleats are essentially mutually perpendicular and form a continuous network structure containing individual coal matrixes according to microstructure characterizations of various coals . Such a structure can be approximately represented using a simplified physical model , as shown in Figure 1. Here digits 1 to 3 indicate the cleats corresponding to the axes in rectangular coordinates, respectively. Matrix is marked with digit 4. denotes the confined stresses accordingly in i-th () axial direction. and are half widths of cleat and matrix, respectively.Coal described as Figure 1 can be considered as a composite material because of distinct physics in the cleat and matrix. A successively analyzing approach has been proposed elsewhere to determine the mechanical properties of such a material using the relevant properties and structural parameters of the cleat and matrix. According to the approach, the general stress-strain analysis is applied to the individual elements, i.e. cleat and matrix, respectively. Then a successively joining procedure that subjects to the mechanical and geometric constraints simultaneously is used to sum up the individual contributions to the net deformation of the composite coal . It is easily to extend the aforementioned approach to determination of stress induced deformation. Lets start from the discussion on a simple case as shown in Figure 2, in which Cleat 1 is in series with the composite matrix consisting of Cleats 2, 3 and coal matrix under the axial stress . The stress induced deformation will occur as increases, giving(1)where , and are component strains of cleat 1 and composite matrix, and total strain in Y direction due to the progressive stress , respectively. and are stress increments transferring to the cleat 1 and the composite matrix.Rewetting Eq. (1) in the form of (1a)and introducing the definition of pliability(1b)Eq. (1) can be expressed in terms of pliability, i.e. the property of being easily bent without breaking, as follows (2)Thus the component and resultant stress-induced deformations under the axial stress can respectively be described in the generic forms of(3) 2.2 Deformation curveA general stress-strain correlation under compressive stress for brittle rock can only be determined through experiments, commonly giving a deformation curve as illustrated in Figure 3. It has been revealed experimentally that the deformation involves several distinct stages, i.e. compression due to enclose of pre-existing micro-cracks, deformation controlled by elastic behavior and damage from stable/unstable crack growths . Coal can be considered as special brittle rock and its mechanical behavior of coal under a confined stress subjects to the similar stress-strain correlation which determines the deformations of coal cleats or pores and its matrix. In general speaking, the elastic deformation and non-elastic damage occur in coal sequentially as overburden or stress increases, and are the result from the accumulation of the changes in micro structure under the given stress state. These will promote the further formation and/or growth of the macro faults in the coal, leading to the structural disintegration and hence the precarious mechanical and fluid behaviors. Experiments indicate all the coals almost have the similar deformation and damage features as shown in Figure 3, in which , (i.e. for cleat or for matrix) and are critical (maximum) stress and strain, and residual stress, respectively, and can only determined experimentally. In principle it is extremely difficult to describe such deformation and damage features of the coal. Therefore an experimental approach has been developed in this study to analyze the deformation process with the following mathematical model. In this model, two constitutive questions are used to describe the stress-strain correlations in elastic and brittle zones defined in Figure 3, respectively, i.e. (4)for the cleat 1 under the axial stress (refer to Figure 2) and (5)for the matrix containing other cleats. Where (5a)and and are two model parameters which can be evaluated based on the experimental stress-strain curve for a given coal. The parameter presents the Y-directional Yongs module of the matrix containing cleats 2 and 3 under the axial stress and can be calculated analytically using the coal characterization information as shown elsewhere .Eqs. (4) and (5) can be rewritten as (6)for the cleat 1 and(7)for the matrix. Furthermore the relations as described by Eqs. (2) and (3) imply that the total Y-directional strain under the axial stress subjects to (8)Thus the resultant deformation and damage behavior can be described with following stress-strain correlations obtained by substituting Eq. (8) with Eqs. (6) and (7), giving(9) where () is defined as directional dimension ratio of cleat to matrix.2.3 Deformation dependent permeabilityPermeability of coal is an important transport property in reservoir engineering for CBM/ECBM recovery from and CO2 storage in coal seams, which largely depends on the structural deformation of coal induced by various physical and/or chemical processes. In most cases, permeability of coal is directional, relating to orientation and distribution of cleats (fractures) determined by the types and ranks of coal and geological conditions. The directional permeability of coal can generally be described in terms of a nine-component permeability tensor as follows (10) with the matrix elements (). In order to have a physical meaning, the permeability tensor needs to be symmetric and positive definite , i.e. () and ().In general, is given in a form (refer to Figure 4) as(11)where denotes the i component permeability scale, is the Kronecker delta, and and are the component of the vector normal to the cleat plane, n, projected to the axis i and j (), as illustrated in Figure 4. The projections of these normal vector components can be determined by means of the dip direction, defined as the angle, , measured from the X-axis to the projection of the unit normal vector in X-Y plane, and the dip angle of the cleat, , measured from the X-Y plane to the cleat. Detailed formulation can be found elsewhere .Eq. (11) can be simplified if considering the fact that the face and butt cleats in coal are mutually perpendicular which wrap individual coal matrixes, as shown in Figure 1, giving(12)Thus Eq. (10) can rewritten in a simplified form as(13)where are the component permeability in corresponding axial direction respectively. Their values are deformation dependent, resulting from the contributions of the individual cleats and matrix for a given direction. As shown in Figure 1, each direction includes two cleats except for matrix. The deformation of the cleats and matrix in two directions normal to a given axis under an axial stress will change the axial permeability. For example, the Y-directional strain in cleat 1, Z-directional strain in Cleat 3 and matrix strains along 2 and 3 directions will significantly contribute to the X-axial permeability, . Assuming that the fluid flow through the coal obeys Darcys law and cubic law , and the strain is set as positive for compressing and as negative otherwise, the deformation dependent permeability can approximately estimated by(14a)(14b) (14c)where () represents initial directional permeability of matrix and corresponding cleats; and denote directional strains of matrix; and and are directional strains of cleats 2, 1 and 3, respectively; () is a fraction that defined as , which accounts for the directional effect of deformation on permeability. The relationship between directional strains for matrix and cleats can be expressed as (15)with (), and(16)where denotes strains of the j-th cleat () under the i-th axial stress, which can be determined by the corresponding strain-stress correlations such as Eqs. (6) and (7); and are Poissons ratios of cleats and matrix, respectively; and are defined as deformation coefficients for cleats and matrix and will be discussed in details later; and is a compressing coefficient which reflects the impact of matrix expansion due to Poisson effect on the cleat along the i-th axis. 3. CONCLUSIONS Proposed a new concept cleat ratio to characterize the fracture in coal. Correlated the cleat ratio with strain to capture directional feature of coal fractures. Developed a stress-strain model with multi-field coupling. Formulated the permeability tensor which connects to the dynamical properties of coal seam. 中文译文煤的渗透率决定的变形在煤层气回收及与CO2分离中的应用摘 要在本文中提出了煤的渗透性在影响煤的变形对煤层气回收和二氧化碳的分离中的应用，这里有许多因素影响 CBM 或 ECBM 的回收效率。举例来说，达西流可能控制经过煤层的气体和水流 , 因此决定了井的式样和井的比率。 一般而言，达西流主要涉及到渗透率和能控制煤的结构和力学特性的压力梯度。 CBM/ ECBM 过程中最重要的需求是达成气体流率的需要，在煤层中没有明显损失。 因此它是很必要的去了解有关力学特性和它经过煤层在流体的传送特性上的影响。关键词：煤 甲烷 应力 变形 渗透性1 介 绍甲烷 (CBM) 回收和 CO2 分离变成了比较吸引人的技术，由于近几十年来已经在能量来源的最佳利用和一种温室气体 (GHG)即二氧化碳的有效储藏.它特别地是吸引人发展在深部煤层的 CBM 回收联合 CO2 隔离, 也就是 CO2增强了 CBM(ECBM) 回收过程，CO2 或烟洞气体 (也就是一个二氧化碳和氮气的混合) 能进入被注射和储存在煤床之内代替被吸附的甲烷 . 这样甲烷生产的收入能大量地减少以此来弥补 CO2 储藏过程中的成本花费开支。这里有许多因素影响 CBM 或 ECBM 的回收效率。举例来说，达西流可能控制经过煤层的气体和水流 , 因此决定了井的式样和井的比率。 一般而言，达西流主要涉及到渗透率和能控制煤的结构和力学特性的压力梯度。 CBM/ ECBM 过程中最重要的需求是达成气体流率的需要，在煤层中没有明显损失。 因此它是很必要的去了解有关力学特性和它经过煤层在流体的传送特性上的影响。在过去三十年中，采矿业已经消耗了大量的资源去了解自然条件下的煤，如变形、弹性这样煤的试验 , 连同在实验室之间的相互关系和区域数据。 然而,如此努力的焦点在大多