Bayesian seismic inversion for estimating fluid content and fracture parameters in a gas-saturated fractured porous reservoir

Understanding the effects of in situ fluid content and fracture parameters on seismic characteristics is important for the subsurface exploration and production of fractured porous rocks. The ratio of normal-to-shear fracture compliance is typically utilized as a fluid indicator to evaluate anisotropy and identify fluids filling the fractures, but it represents an underdetermined problem because this fluid indicator varies as a function of both fracture geometry and fluid content. On the bases of anisotropic Gassmann's equation and linear-slip model, we suggest an anisotropic poroelasticity model for fractured porous reservoirs. By combining a perturbed stiffness matrix and asymptotic ray theory, we then construct a direct relationship between the PP-wave reflection coefficients and characteristic parameters of fluids(P-and S-wave moduli) and fractures(fracture quasi-weaknesses), thereby decoupling the effects of fluid and fracture properties on seismic reflection characterization.By incorporating fracture quasi-weakness parameters, we propose a novel parameterization method for elastic impedance variation with offset and azimuth(EIVOA). By incorporating wide-azimuth observable seismic reflection data with regularization constraints, we utilize Bayesian seismic inversion to estimate the fluid content and fracture parameters of fractured porous rocks. Tests on synthetic and real data demonstrate that fluid and fracture properties can be reasonably estimated directly from azimuthal seismic data and the proposed approach provides a reliable method for fluid identification and fracture characterization in a gas-saturated fractured porous reservoir.     

A constitutive model for water flow in unsaturated fractured rocks

A conceptual model for describing effective saturation in fractured hard rock is presented. The fracture network and the rock matrix are considered as an equivalent continuum medium where each fracture is conceptualized as a porous medium of granular structure and the rock matrix is assumed to be impermeable. The proposed model is based on the representation of a rough‐walled fracture by an equivalent porous medium, which is described using classical constitutive models. A simple closed‐form equation for the effective saturation is obtained when the van Genuchten model is used to describe saturation inside fractures and fractal laws are assumed for both aperture and number of fractures. The relative hydraulic conductivity for the fractured rock is predicted from a simple relation derived by Liu and Bodvarsson. The proposed constitutive model contains three independent parameters, which may be obtained by fitting the proposed effective saturation curve to experimental data. Two of the model parameters have physical meaning and can be identified with the reciprocal of the air entry pressure values in the fractures of minimum and maximum apertures. Effective saturation and relative hydraulic conductivity curves match fairly well the simulated constitutive relations obtained by Liu and Bodvarsson. Copyright © 2008 John Wiley & Sons, Ltd.     

Characterization of fractured reservoirs using a consistent stiffness‐permeability model: focus on the effects of fracture aperture

In this paper we propose a method for the characterization of naturally fractured reservoirs by quantitative integration of seismic and production data. The method is based on a consistent theoretical frame work to model both effective hydraulic and elastic properties of fractured porous media and a (non‐linear) Bayesian method of inversion that provides information about uncertainties as well as mean (or maximum likelihood) values. We model a fractured reservoir as a porous medium containing a single set of vertical fractures characterized by an unknown fracture density, azimuthal orientation and aperture. We then look at the problem of fracture parameter estimation as a non‐linear inverse problem and try to estimate the unknown fracture parameters by joint inversion of seismic amplitude versus angle and azimuth data and dynamic production data. Once the fracture parameters have been estimated the corresponding effective stiffness and permeability tensors can be estimated using consistent models. A synthetic example is provided to clearly explain and test the workflow. It shows that seismic and production data complement each other, in the sense that the seismic data resolve a non‐uniqueness in the fracture orientation and the production data help to recover the true fracture aperture and permeability, because production data are more sensitive to the fracture aperture than the seismic data.     

基于数字岩心的含裂隙储层砂岩介电性质研究

了解储层岩石的介电特性在石油工业的各个方面都有重要的应用.小尺度裂隙是影响岩石介电性质的地质因素之一,获得裂隙对含裂隙岩石介电性质影响的定量关系具有重要的理论和实践意义.以含裂隙人造砂岩的三维微观数字结构为基础,通过基于三维有限差分算法计算的岩石介电性质与实验数据的对比验证数值计算方法的有效性.在此基础上,通过理论模型获得不同孔隙度基质的介电性质,并在不含裂隙人造砂岩的三维微观数字结构中人为添加以裂隙密度和纵横比为定量表征参数的裂隙,应用验证后的数值算法模拟随频率变化的含裂隙砂岩的介电性质,分析和研究不同孔隙度基质中定向排列裂隙对砂岩介电性质的影响.结果表明,当裂隙孔隙度随裂隙纵横比或裂隙密度发生改变时,含裂隙砂岩的介电性质与裂隙密度以及裂隙纵横比呈正相关关系,而当裂隙孔隙度保持不变时,含裂隙砂岩的介电性质随裂隙纵横比的减小而增大;裂隙参数的改变对不同基质孔隙度的含裂隙砂岩的介电性质的影响趋势较为一致,但随着基质孔隙度的减小,裂隙对砂岩介电性质的影响逐渐增大.裂隙参数和基质孔隙度对含裂隙砂岩介电性质影响的研究结果为基于介电特性的裂缝性油气储层的定量表征提供了依据,在油气勘探开发中具有重要的应用前景.     

基于两级尺度粗化的裂缝-多孔隙介质地震响应分析方法

实际地震勘探中,储层物性参数的差异是导致地震波响应特征发生变化的根本原因,而建立储层物性参数与地震响应特征之间的联系,需要跨越微观孔隙尺度、介观测井尺度以及宏观地震尺度等三个不同尺度空间.本文基于已知井的岩石物理实验数据和测井数据,利用复杂多孔隙介质理论将微观尺度孔隙岩石粗化到介观测井尺度,利用Backus平均理论将介观测井尺度的模型进一步粗化到宏观地震尺度,最终,得到地震尺度裂缝-多孔隙介质模型.其数值计算结果与测井数据和地震数据的对比表明：基于两级尺度粗化算法的裂缝多孔隙介质模型在给定参数下是有效的,且基于该模型的地震响应特征分析方法能够对储层的地震响应特征随物性参数的变化进行分析.     

An equivalent medium model for wave simulation in fractured porous rocks

Seismic wave propagation in reservoir rocks is often strongly affected by fractures and micropores. Elastic properties of fractured reservoirs are studied using a fractured porous rock model, in which fractures are considered to be embedded in a homogeneous porous background. The paper presents an equivalent media model for fractured porous rocks. Fractures are described in a stress‐strain relationship in terms of fracture‐induced anisotropy. The equations of poroelasticity are used to describe the background porous matrix and the contents of the fractures are inserted into a matrix. Based on the fractured equivalent‐medium theory and Biot's equations of poroelasticity, two sets of porosity are considered in a constitutive equation. The porous matrix permeability and fracture permeability are analysed by using the continuum media seepage theory in equations of motion. We then design a fractured porous equivalent medium and derive the modified effective constants for low‐frequency elastic constants due to the presence of fractures. The expressions of elastic constants are concise and are directly related to the properties of the main porous matrix, the inserted fractures and the pore fluid. The phase velocity and attenuation of the fractured porous equivalent media are investigated based on this model. Numerical simulations are performed. We show that the fractures and pores strongly influence wave propagation, induce anisotropy and cause poroelastic behaviour in the wavefields. We observe that the presence of fractures gives rise to changes in phase velocity and attenuation, especially for the slow P‐wave in the direction parallel to the fracture plane.     

Matrix diffusion-derived plume attenuation in fractured bedrock

Matrix diffusion can attenuate the rate of plume migration in fractured bedrock relative to the rate of ground water flow for both conservative and nonconservative solutes of interest. In a system of parallel, equally spaced constant aperture fractures subject to steady-state ground water flow and an infinite source width, the degree of plume attenuation increases with time and travel distance, eventually reaching an asymptotic level. The asymptotic degree of plume attenuation in the absence of degradation can be predicted by a plume attenuation factor, beta, which is readily estimated as R' (phi(m)/phi(f)), where R' is the retardation factor in the matrix, phi(m) is the matrix porosity, and phi(f) is the fracture porosity. This dual-porosity relationship can also be thought of as the ratio of primary to secondary porosity. Beta represents the rate of ground water flow in fractures relative to the rate of plume advance. For the conditions examined in this study, beta increases with greater matrix porosity, greater matrix fraction organic carbon, larger fracture spacing, and smaller fracture aperture. These concepts are illustrated using a case study where dense nonaqueous phase liquid in fractured sandstone produced a dissolved-phase trichloroethylene (TCE) plume approximately 300 m in length. Transport parameters such as matrix porosity, fracture porosity, hydraulic gradient, and the matrix retardation factor were characterized at the site through field investigations. In the fractured sandstone bedrock examined in this study, the asymptotic plume attenuation factors (beta values) for conservative and nonconservative solutes (i.e., chloride and TCE) were predicted to be approximately 800 and 12,210, respectively. Quantitative analyses demonstrate that a porous media (single-porosity) solute transport model is not appropriate for simulating contaminant transport in fractured sandstone where matrix diffusion occurs. Rather, simulations need to be conducted with either a discrete fracture model that explicitly incorporates matrix diffusion, or a dual-continuum model that accounts for mass transfer between mobile and immobile zones. Simulations also demonstrate that back diffusion from the matrix to fractures will likely be the time-limiting factor in reaching ground water cleanup goals in some fractured bedrock environments.     

Unified fractional differential approach for transient interporosity flow in naturally fractured media

A unified approach to modeling flows of slightly compressible fluids through naturally fractured media is presented. The unified fractional differential model is derived by combining the flow at micro scale for matrix blocks and macro scale for fractures, using the transient interporosity flow behavior at the interface between matrix blocks and fractures. The derived model is able to unify existing transient interporosity flow models formulated for different shapes of matrix blocks in any medium dimensions. The model is formulated in the form of a fractional order partial differential equation that involves Caputo derivative of order 1/2 with respect to time. Explicit solutions for the unified model are derived for different axisymmetrical spatial domains using Hankel or Hankel–Weber finite or infinite transforms. Comparisons between the predictions of the unified model and those obtained from existing transient interporosity flow models for matrix blocks in the form of slabs, spheres and cylinders are presented. It is shown that the unified fractional derivative model leads to solutions that are very close to those of transient interporosity flow models for fracture-dominant and transitional fracture-to-matrix dominant flow regimes. An analysis of the results of the unified model reveals that the pressure varies linearly with the logarithm of time for different flow regimes, with half slope for the transitional fracture-to-matrix dominant flow regime vs. the fracture and matrix dominant flow regimes. In addition, a new re-scaling that involves the characteristic length in the form of matrix block volume to surface area ratio is derived for the transient interporosity flow models for matrix blocks of different shapes. It is shown that the re-scaled transient interporosity flow models are governed by two dimensionless parameters Θ and Λ compared to only one dimensionless parameter Θ for the unified model. It is shown that the solutions of the transient interporosity flow models for different shapes of matrix blocks are almost identical for the re-scaled variables. Furthermore, the driving parameters for solution behavior are identified based on asymptotic approximations for different flow regimes. It is found that the matrix diffusion and the matrix area-to-volume ratio affect the solution behavior only for the transitional fracture-to-matrix dominant flow regime, that the capacitance ratio affects the solution behavior only for transitional and matrix dominant flow regimes and that the fracture diffusion is involved in all three flow regimes. Similar identification of the driving parameters is also presented in the re-scaled case.     

An efficient numerical model for incompressible two-phase flow in fractured media

Various numerical methods have been used in the literature to simulate single and multiphase flow in fractured media. A promising approach is the use of the discrete-fracture model where the fracture entities in the permeable media are described explicitly in the computational grid. In this work, we present a critical review of the main conventional methods for multiphase flow in fractured media including the finite difference (FD), finite volume (FV), and finite element (FE) methods, that are coupled with the discrete-fracture model. All the conventional methods have inherent limitations in accuracy and applications. The FD method, for example, is restricted to horizontal and vertical fractures. The accuracy of the vertex-centered FV method depends on the size of the matrix gridcells next to the fractures; for an acceptable accuracy the matrix gridcells next to the fractures should be small. The FE method cannot describe properly the saturation discontinuity at the matrix–fracture interface. In this work, we introduce a new approach that is free from the limitations of the conventional methods. Our proposed approach is applicable in 2D and 3D unstructured griddings with low mesh orientation effect; it captures the saturation discontinuity from the contrast in capillary pressure between the rock matrix and fractures. The matrix–fracture and fracture–fracture fluxes are calculated based on powerful features of the mixed finite element (MFE) method which provides, in addition to the gridcell pressures, the pressures at the gridcell interfaces and can readily model the pressure discontinuities at impermeable faults in a simple way. To reduce the numerical dispersion, we use the discontinuous Galerkin (DG) method to approximate the saturation equation. We take advantage of a hybrid time scheme to alleviate the restrictions on the size of the time step in the fracture network. Several numerical examples in 2D and 3D demonstrate the robustness of the proposed model. Results show the significance of capillary pressure and orders of magnitude increase in computational speed compared to previous works.     

A new upscaling method for fractured porous media

We present a method to determine equivalent permeability of fractured porous media. Inspired by the previous flow-based upscaling methods, we use a multi-boundary integration approach to compute flow rates within fractures. We apply a recently developed multi-point flux approximation Finite Volume method for discrete fracture model simulation. The method is verified by upscaling an arbitrarily oriented fracture which is crossing a Cartesian grid. We demonstrate the method by applying it to a long fracture, a fracture network and the fracture network with different matrix permeabilities. The equivalent permeability tensors of a long fracture crossing Cartesian grids are symmetric, and have identical values. The application to the fracture network case with increasing matrix permeabilities shows that the matrix permeability influences more the diagonal terms of the equivalent permeability tensor than the off-diagonal terms, but the off-diagonal terms remain important to correctly assess the flow field.     

Anisotropic azimuthal surface-wave inversion for a vertically fractured and transverse isotropy medium: Theory and examples from a controlled field experiment

Fractures in elastic media add compliance to a rock in the direction normal to the fracture strike. Therefore, elastic wave velocities in a fractured rock will vary as a function of the energy propagation direction relative to the orientation of the aligned fracture set. Anisotropic Thomson–Haskell matrix Rayleigh-wave equations for a vertically transverse isotropic media can be used to model surface-wave dispersion along the principal axes of a vertically fractured and transversely isotropic medium. Furthermore, a workflow combining first-break analysis and azimuthal anisotropic Rayleigh-wave inversion can be used to estimate P-wave and S-wave velocities, Thomsen's ε, and Thomsen's δ along the principal axes of the orthorhombic symmetry. In this work, linear slip theory is used to map our inversion results to the equivalent vertically fractured and transversely isotropic medium coefficients. We carried out this inversion on a synthetic example and a field example. The synthetic data example results show that joint estimation of S-wave velocities with Thomsen's parameters ε and δ along normal and parallel to the vertical fracture set is reliable and, when mapped to the corresponding vertically fractured and transversely isotropic medium, provides insight into the fracture compliances. When the inversion was carried out on the field data, results indicated that the fractured rock is more compliant in the azimuth normal to the visible fracture set orientation and that the in situ normal fracture compliance to tangential fracture compliance ratio is less than half, which implies some cementation may have occurred along the fractures. Such an observation has significant implications when modelling the transport properties of the rock and its strength. Both synthetic and field examples show the potential of azimuthal anisotropic Rayleigh-wave inversion as the method can be further expanded to a more general case where the vertical fracture set orientation is not known a priori.     

Seismic prediction method of multiscale fractured reservoir

Common prestack fracture prediction methods cannot clearly distinguish multiplescale fractures. In this study, we propose a prediction method for macro- and mesoscale fractures based on fracture density distribution in reservoirs. First, we detect the macroscale fractures (larger than 1/4 wavelength) using the multidirectional coherence technique that is based on the curvelet transform and the mesoscale fractures (1/4–1/100 wavelength) using the seismic azimuthal anisotropy technique and prestack attenuation attributes, e.g., frequency attenuation gradient. Then, we combine the obtained fracture density distributions into a map and evaluate the variably scaled fractures. Application of the method to a seismic physical model of a fractured reservoir shows that the method overcomes the problem of discontinuous fracture density distribution generated by the prestack seismic azimuthal anisotropy method, distinguishes the fracture scales, and identifies the fractured zones accurately.     

Influence of frequency-dependent anisotropy on seismic amplitude-versus-offset signatures for fractured poroelastic rocks

Frequency-dependent amplitude variation with offset offers an effective method for hydrocarbon detections and analysis of fluid flow during production of oil and natural gas within a fractured reservoir. An appropriate representation for the frequency dependency of seismic amplitude variation with offset signatures should incorporate influences of dispersive and attenuating properties of a reservoir and the layered structure for either isotropic or anisotropic dispersion analysis. In this study, we use an equivalent medium permeated with aligned fractures that simulates frequency-dependent anisotropy, which is sensitive to the filled fluid of fractures. The model, where pores and fractures are filled with two different fluids, considers velocity dispersion and attenuation due to mesoscopic wave-induced fluid flow. We have introduced an improved scheme seamlessly linking rock physics modelling and calculations for frequency-dependent reflection coefficients based on the propagator matrix technique. The modelling scheme is performed in the frequency-slowness domain and can properly incorporate effects of both bedded structure of the reservoir and velocity dispersion quantified with frequency-dependent stiffness. Therefore, for a dispersive and attenuated layered model, seismic signatures represent a combined contribution of impedance contrast, layer thickness, anisotropic dispersion of the fractured media and tuning and interference of thin layers, which has been avoided by current conventional methods. Frequency-dependent amplitude variation with offset responses was studied via considering the influences of fracture fills, layer thicknesses and fracture weaknesses for three classes amplitude variation with offset reservoirs. Modelling results show the applicability of the introduced procedure for interpretations of frequency-dependent seismic anomalies associated with both layered structure and velocity dispersion of an equivalent anisotropic medium. The implications indicate that anisotropic velocity dispersion should be incorporated accurately to obtain enhanced amplitude variation with offset interpretations. The presented frequency-dependent amplitude variation with offset modelling procedure offers a useful tool for fracture fluid detections in an anisotropic dispersive reservoir with layered structures.     

Development of a new semi-analytical model for cross-borehole flow experiments in fractured media

Analysis of borehole flow logs is a valuable technique for identifying the presence of fractures in the subsurface and estimating properties such as fracture connectivity, transmissivity and storativity. However, such estimation requires the development of analytical and/or numerical modeling tools that are well adapted to the complexity of the problem. In this paper, we present a new semi-analytical formulation for cross-borehole flow in fractured media that links transient vertical-flow velocities measured in one or a series of observation wells during hydraulic forcing to the transmissivity and storativity of the fractures intersected by these wells. In comparison with existing models, our approach presents major improvements in terms of computational expense and potential adaptation to a variety of fracture and experimental configurations. After derivation of the formulation, we demonstrate its application in the context of sensitivity analysis for a relatively simple two-fracture synthetic problem, as well as for field-data analysis to investigate fracture connectivity and estimate fracture hydraulic properties. These applications provide important insights regarding (i) the strong sensitivity of fracture property estimates to the overall connectivity of the system; and (ii) the non-uniqueness of the corresponding inverse problem for realistic fracture configurations.     

Frequency-dependent PP and PS reflection coefficients in fractured media

When a porous layer is permeated by mesoscale fractures, wave-induced fluid flow between pores and fractures can cause significant attenuation and dispersion of velocities and anisotropy parameters in the seismic frequency band. This intrinsic dispersion due to fracturing can create frequency-dependent reflection coefficients in the layered medium. In this study, we derive the frequency-dependent PP and PS reflection coefficients versus incidence angle in the fractured medium. We consider a two-layer vertical transverse isotropy model constituted by an elastic shale layer and an anelastic sand layer. Using Chapman's theory, we introduce the intrinsic dispersion due to fracturing in the sand layer. Based on the series coefficients that control the behaviour of velocity and anisotropy parameters in the fractured medium at low frequencies, we extend the conventional amplitude-versus-offset equations into frequency domain and derive frequency-dependent amplitude-versus-offset equations at the elastic–anelastic surface. Increase in fracture length or fracture density can enlarge the frequency dependence of amplitude-versus-offset attributes of PP and PS waves. Also, the frequency dependence of magnitude and phase angle of PP and PS reflection coefficients increases as fracture length or fracture density increases. Amplitude-versus-offset type of PP and PS reflection varies with fracture parameters and frequency. What is more, fracture length shows little impact on the frequency-dependent critical phase angle, while the frequency dependence of the critical phase angle increases with fracture density.     

裂缝性储层的电各向异性响应特征研究

以水平裂缝分布的孔隙介质模型为基础,建立了水平裂缝面的平行裂缝分布和带粗糙表面的点接触裂缝模型,导出了两类裂缝模型的水平和垂直电阻率响应关系,分析了两类裂缝模型在没有围压和存在围压条件下的水平电阻率、垂直电阻率变化规律和电各向异性系数的变化特征.讨论了裂缝开度、裂缝密度和裂缝粗糙度等裂缝特征参数对裂缝性储层电各向异性的影响.为简化讨论,所有电性响应特征的分析都忽略了裂缝和孔隙表面的导电性和极化的影响.利用平行分布水平裂缝面模型和带粗糙面的裂缝模型,考察了围压条件下的裂缝性岩石的电各向异性响应特征,得到了对实际应用有意义的结果.     

裂缝型储层流体识别方法

裂缝型储层的描述包括预测裂缝分布特征和识别裂隙充填物.依据等效介质理论计算的纵波速度随裂缝密度的增大而减小.正演地震记录显示,裂缝介质含气时反射振幅最大,且变化程度比含油或含水时大.叠前方位AVO反演所得的各向异性梯度Bani与裂缝密度成正比,可用于描述有效裂缝发育强度.对于不同的裂缝密度,各向异性梯度Bani与各向同性梯度Biso的比值I(1)fluid近似为常数,且对流体敏感.经裂缝纵横比和背景介质拉梅常数修正后,流体因子Ifluid既不随纵横比变化,又不受背景介质的影响,是裂缝型储层敏感的流体识别因子.在塔里木盆地塔北哈拉哈塘地区热瓦普区块碳酸盐岩储层裂缝发育区域,运用该参数在井点处的流体识别效果与钻井结果一致.     

Azimuthally pre-stack seismic inversion for orthorhombic anisotropy driven by rock physics

Based on the long-wavelength approximation, a set of parallel vertical fractures embedded in periodic thin interbeds can be regarded as an equivalent orthorhombic medium. Rock physics is the basis for constructing the relationship between fracture parameters and seismic response. Seismic scattering is an effective way to inverse anisotropic parameters. In this study, we propose a reliable method for predicting the Thomsen’s weak anisotropic parameters and fracture weaknesses in an orthorhombic fractured reservoir using azimuthal pre-stack seismic data. First, considering the influence of fluid substitution in mineral matrix, porosity, fractures and anisotropic rocks, we estimate the orthorhombic anisotropic stiffness coefficients by constructing an equivalent rock physics model for fractured rocks. Further, we predict the logging elastic parameters, Thomsen’s weak parameters, and fracture weaknesses to provide the initial model constraints for the seismic inversion. Then, we derive the P-wave reflection coefficient equation for the inversion of Thomsen’s weak anisotropic parameters and fracture weaknesses. Cauchy-sparse and smoothing-model constraint regularization taken into account in a Bayesian framework, we finally develop a method of amplitude variation with angles of incidence and azimuth (AVAZ) inversion for Thomsen’s weak anisotropic parameters and fracture weaknesses, and the model parameters are estimated by using the nonlinear iteratively reweighted least squares (IRLS) strategy. Both synthetic and real examples show that the method can directly estimate the orthorhombic characteristic parameters from the azimuthally pre-stack seismic data, which provides a reliable seismic inversion method for predicting Thomsen’s weak anisotropic parameters and fracture weaknesses.     

A numerical method for two-phase flow in fractured porous media with non-matching grids

We propose a novel computational method for the efficient simulation of two-phase flow in fractured porous media. Instead of refining the grid to capture the flow along the faults or fractures, we represent the latter as immersed interfaces, using a reduced model for the flow and suitable coupling conditions. We allow for non matching grids between the porous matrix and the fractures to increase the flexibility of the method in realistic cases. We employ the extended finite element method for the Darcy problem and a finite volume method that is able to handle cut cells and matrix-fracture interactions for the saturation equation. Moreover, we address through numerical experiments the problem of the choice of a suitable numerical flux in the case of a discontinuous flux function at the interface between the fracture and the porous matrix. A wrong approximate solution of the Riemann problem can yield unphysical solutions even in simple cases.     

Vertically fractured transversely isotropic media: dimensionality and deconstruction

A vertically fractured transversely isotropic (VFTI) elastic medium is one in which any number of sets of vertical aligned fractures (each set has its normal lying in the horizontal x₁, x₂‐plane) pervade the medium and the sets of aligned fractures are the only features of the medium disturbing the axi‐symmetry about the x₃‐axis implying that in the absence of fractures, the background medium is transversely isotropic (TI). Under the assumptions of long wavelength equivalent medium theory, the compliance matrix of a fractured medium is the sum of the background medium's compliance matrix and a fracture compliance matrix. For sets of parallel rotationally symmetric fractures (on average), the fracture compliance matrix is dependent on 3 parameters − its normal and tangential compliance and its strike direction. When one fracture set is present, the medium is orthorhombic and the analysis is straightforward. When two (non‐orthogonal) or more sets are present, the overall medium is in general elastically monoclinic; its compliance tensor components are subject to two equalities yielding an 11 parameter monoclinic medium. Constructing a monoclinic VFTI medium with n embedded vertical fracture sets, requires 5 TI parameters plus 3×n fracture set parameters. A deconstruction of such an 11 parameter monoclinic medium involves using its compliance tensor to find a background transversely isotropic medium and several sets of vertical fractures which, in the long wavelength limit, will behave exactly as the original 11 parameter monoclinic medium. A minimal deconstruction, would be to determine, from the 11 independent components, the transversely isotropic background (5 parameters) and two fracture sets (specified by 2 × 3 = 6 parameters). Two of the background TI medium's compliance matrix components are known immediately by inspection, leaving nine monoclinic components to be used in the minimal deconstruction of the VFTI medium. The use of the properties of a TI medium, which are linear relations on its compliance components, allows the deconstruction to be reduced to solving a pair of non‐linear equations on the orientations of two fracture sets. A single root yielding a physically meaningful minimum deconstruction yields a unique minimal representation of the monoclinic medium as a VFTI medium. When no such root exists, deconstruction requires an additional fracture set and uniqueness is lost. The boundary between those monoclinic media that have a unique minimal representation and those that do not is yet to be determined.