Fracture Flow Model Research Articles

A Laplace-Domain Hybrid Model for Representing Flow Behavior of Multifractured Horizontal Wells Communicating Through Secondary Fractures in Unconventional Reservoirs

Summary In a multiwell pad, the chance of interwell communication increases because of the creation of primary and secondary fractures during hydraulic-fracture stimulation. The flow behavior associated with communicating wells is significantly different from that of a single isolated well, because of interplay of flow caused by the interconnected fractures, complex connections, and multiple production conditions. The main purpose of this paper is to develop a rigorous and efficient flow model and quantify flow characteristics of multiple pad wells communicating through primary and secondary fractures. In the model, matrix and primary- and secondary-fracture flows are captured. Fractures are explicitly represented by discrete segments. The Laplace-transform finite-difference (LTFD) method is used to numerically model fracture flow, with sufficient flexibility to consider arbitrary fracture geometries and fracture-conductivity distributions. The analytical matrix-flow model, derived with the line-source function in the Laplace domain, is dynamically coupled with the fracture-flow model, by imposing the continuity of pressure and flux on the fracture surface. Thus, a hybrid model in the Laplace domain is constructed. The main advantage of the solution occurring in Laplace domain is that computations can be performed at predetermined, discrete times, and with grids only for fractures. Thus, stability and convergence problems caused by time discretization are avoided, and the burden of gridding and computation is decreased without loss of important fracture characteristics. The model is validated through comparison with a fully numerical simulator and a semi-analytical model. Detailed flow-regime analysis reveals that pressure interference caused by communication significantly alters the flow signature compared with single (isolated) wells. Before interference, the communicating wells behave as single isolated wells, and will exhibit a fracture linear-flow period and possibly even a matrix linear-flow period. After interference, the flow behavior of the system will vary largely with different production strategies. When the communicating wells all operate under the constant-rate condition, the transient responses of the wells will gradually merge to develop another matrix linear-flow period. If the wells are operated under the constant-bottomhole-pressure (BHP) conditions, the response deviation caused by interference will increase with production; therefore, one of the wells will undergo a rate loss. The results of a sensitivity analysis for a two-well system demonstrate that the time to well interference is primarily determined by secondary-fracture conductivity, number of connections, and communicating-well operating conditions. With larger contrasts in these properties, interference time is accelerated. However, for different production strategies, the effects on the flow behavior after interference are variable.

A comprehensive model combining Laplace-transform finite-difference and boundary-element method for the flow behavior of a two-zone system with discrete fracture network

This paper provides a comprehensive model for the flow behavior of a two-zone system with discrete fracture network. The discrete fracture network within the inner zone is represented explicitly by fracture segments. The Laplace-transform finite-difference method is used to numerically model discrete fracture network flow, with sufficient flexibility to consider arbitrary fracture geometries and conductivity distributions. Boundary-element method and line-source functions in the Laplace domain are employed to derive a semi-analytical flow solution for the two-zone system. By imposing the continuity of flux and pressure on discrete fracture surfaces, the semi-analytical two-zone system flow model and the numerical fracture flow model are coupled dynamically. The main advantage of the approach occurring in the Laplace domain is that simulation can be done with nodes only for discrete fractures and elements for boundaries and at predetermined, discrete times. Thus, stability and convergence problems caused by time discretization are avoided and the burden of gridding and computation is decreased without loss of important fracture characteristics. The model is validated by comparison with the results from an analytical solution and a fully numerical solution.Flow regime analysis shows that a two-zone system with discrete fracture network may develop six flow regimes: fracture linear flow, bilinear flow, inner zone linear flow, inner zone pseudosteady-state flow, outer zone pseudoradial flow and outer zone boundary-dominated flow. Especially, local solutions for the inner-zone linear flow have the same form with that of a finite conductivity planar fracture and can be correlated with the total length of discrete fractures and an intercept term. In the inner zone pseudosteady-state flow period, the discrete fractures, along with the boundary of the inner zone, will act as virtual closed boundaries, due to the pressure interference caused by fracture network and the mobility contrast of the two zones. The dimensionless fracture conductivity of the fracture network determines the characteristics of the bilinear flow and the inner zone linear flow. The mobility ratio, M, and storability ratio, Fs, primarily influence the flow behavior of the middle to later time. For a larger M, the ending time of the inner zone pseudosteady-state flow will be advanced and the beginning time of the outer-zone pseudoradial flow will be delayed. And the larger M also results in increasing of the values of the transient responses in these two periods. Duration of the outer-zone pseudoradial flow becomes longer, as Fs increases; the development of the outer-zone boundary-dominated flow is therefore postponed. Finally, idealization of dual-porosity model for the two zones will introduce two dips on the pressure derivatives on the log/log plot. Depending on the interporosity flow parameter, the time of the two dips varies. However, the dips are not very appreciable for the transient dual-porosity model, when the permeability of matrix system or fracture density is relatively high.

The impact of in-situ stress and outcrop-based fracture geometry on hydraulic aperture and upscaled permeability in fractured reservoirs

Aperture has a controlling impact on porosity and permeability and is a source of uncertainty in modeling of naturally fractured reservoirs. This uncertainty results from difficulties in accurately quantifying aperture in the subsurface and from a limited fundamental understanding of the mechanical and diagenetic processes that control aperture. In the absence of cement bridges and high pore pressure, fractures in the subsurface are generally considered to be closed. However, experimental work, outcrop analyses and subsurface data show that some fractures remain open, and that aperture varies even along a single fracture. However, most fracture flow models consider constant apertures for fractures. We create a stress-dependent heterogeneous aperture by combining Finite Element modeling of discrete fracture networks with an empirical aperture model. Using a modeling approach that considers fractures explicitly, we quantify equivalent permeability, i.e. combined matrix and stress-dependent fracture flow. Fracture networks extracted from a large outcropping pavement form the basis of these models. The results show that the angle between fracture strike and σ1 has a controlling impact on aperture and permeability, where hydraulic opening is maximum for an angle of 15°. At this angle, the fracture experiences a minor amount of shear displacement that allows the fracture to remain open even when fluid pressure is lower than the local normal stress. Averaging the heterogeneous aperture to scale up permeability probably results in an underestimation of flow, indicating the need to incorporate full aperture distributions rather than simplified aperture models in reservoir-scale flow models.

Fully Coupled XFEM Model for Flow and Deformation in Fractured Porous Media with Explicit Fracture Flow

AbstractA hydromechanical model with explicit fracture flow is presented for the fully coupled analysis of flow and deformation in fractured porous media. Extended finite-element method (XFEM) was utilized to model the fracture discontinuity in the two-dimensional plane-strain mechanical model. Two flow models, a one-dimensional laminar flow within the fracture and a two-dimensional Darcy flow through porous media, were considered. The flow domains were coupled through a mass exchange term (leak-off) accounting for discontinuous Darcy flow velocity across the fracture. Particular attention was given to the coupling of the flow domains with the mechanical model. Spatial and temporal discretization was achieved using the standard Galerkin method and the finite-difference technique, respectively. Unlike the successive coupled models in which the results of the mechanical model are used to update the fracture flow model and vice versa, the fully coupled hydromechanical formulation is solved simultaneously. Th...

A general productivity model for optimization of multiple fractures with heterogeneous properties

The principle focus of this work is on developing a general productivity model to fill the gap in simultaneously optimizing multiple hydraulic fractures with different properties in heterogeneous spaced fracture configuration. Based on the instantaneous point source solutions, a rigorous mathematical model is established by coupling reservoir flow model with fracture flow model in a box-shaped reservoir, which takes into account fracture interaction, fracture conductivity, contacted reservoir area with fractures, and heterogeneity of fracture properties. A corresponding semi-analytical solution is further proposed to solve the model by using a new discretization algorithm called multi direct boundary element methodology (MDBEM). Based on the general model, the maximum productivity index (PI) is obtained by optimizing properties of fractures under the limitation of given proppant volume, which puts a constraint on number of fractures, fracture conductivity and fracture length. The heterogeneity effect of fracture properties on optimization is discussed in detail, and results indicate that it is more advantageous and practical to create more fractures with identical properties in homogeneous fractured configuration.

A novel binomial deliverability equation for fractured gas well considering non-Darcy effects

Hydraulic fracturing is one of the most effective methods to improve the productivity of low permeability reservoirs. Now, the effects of non-Darcy flow mainly caused by high velocity gas in hydraulic fracture are paid increasing attention to. But the binomial deliverability equation influenced by non-Darcy effects has never been seen in any paper for the difficulty in coupling linear flow model in the fracture and radial flow model in the reservoir.Based on equivalent radius models for hydraulic fracture, the authors put forward the concept of CTER, which is short for conductive thickness between equivalent radii. The value of equivalent radius for finite conductivity fracture is smaller than that of infinite conductivity fracture because of the existence of fracture conductivity. CTER whose permeability is equal to reservoir permeability is a theoretical radial conductive thickness existing between equivalent radius models for finite conductivity fracture and infinite conductivity fracture. By making use of CTER, we deduce the novel binomial deliverability equation with respect to the inertial non-Darcy effects in the fracture. With the help of the new concept and the new equation, it is found that non-Darcy effect caused by high flow rate of gas in the fracture influences high permeability reservoirs (>5 mD) more dramatically than those with low permeability (<1 mD).

A fracture mapping and extended finite element scheme for coupled deformation and fluid flow in fractured porous media

SUMMARYThis paper presents a fracture mapping (FM) approach combined with the extended finite element method (XFEM) to simulate coupled deformation and fluid flow in fractured porous media. Specifically, the method accurately represents the impact of discrete fractures on flow and deformation, although the individual fractures are not part of the finite element mesh. A key feature of FM‐XFEM is its ability to model discontinuities in the domain independently of the computational mesh. The proposed FM approach is a continuum‐based approach that is used to model the flow interaction between the porous matrix and existing fractures via a transfer function. Fracture geometry is defined using the level set method. Therefore, in contrast to the discrete fracture flow model, the fracture representation is not meshed along with the computational domain. Consequently, the method is able to determine the influence of fractures on fluid flow within a fractured domain without the complexity of meshing the fractures within the domain. The XFEM component of the scheme addresses the discontinuous displacement field within elements that are intersected by existing fractures. In XFEM, enrichment functions are added to the standard finite element approximation to adequately resolve discontinuous fields within the simulation domain. Numerical tests illustrate the ability of the method to adequately describe the displacement and fluid pressure fields within a fractured domain at significantly less computational expense than explicitly resolving the fracture within the finite element mesh. Copyright © 2013 John Wiley &amp; Sons, Ltd.

X-ray CT based numerical analysis of fracture flow for core samples under various confining pressures

The X-ray CT based numerical analysis of fracture flow for core samples, recently developed by the authors, was applied to two granite core samples having either a mated artificial or a mated natural fracture at confining pressures of 5 to 50 MPa. A third-generation medical X-ray CT scanner was used to image the samples within a core holder consisting of an aluminum liner and a carbon fiber overwrap. Fracture models (i.e., aperture distributions) were obtained by the CT images, the resolution of which was coarser than the apertures, and a single-phase flow simulation was performed using a local cubic law-based fracture flow model. Numerical results were evaluated by a fracture porosity measurement and a solution displacement experiment using NaCl and NaI aqueous solutions. These numerical results coincided only qualitatively with the experimental results, primarily due to image noise from the aluminum liner of the core holder. Nevertheless, the numerical results revealed flow paths within the fractures and their changes with confining pressure, whereas the experimental results did not provide such results. Different stress-dependencies in the flow paths were observed between the two samples despite the similar stress-dependency in fracture porosity and permeability. The changes in total area of the flow paths with confining pressure coincided qualitatively with changes in breakthrough points in the solution displacement experiment. Although the data is limited, the results of the present study suggest the importance of analyzing fluid flows within naturally fractured core samples under in situ conditions in order to better understand the fracture flow characteristics in a specific field. As demonstrated herein, X-ray CT-based numerical analysis is effective for addressing this concern. Using a multi-phase flow model, as well as a core holder constructed of an engineered plastic, should provide a useful, non-destructive, and non-contaminative X-ray CT-based fracture flow analysis for core samples under in situ conditions in future studies.

Precise 3D Numerical Modeling of Fracture Flow Coupled With X-Ray Computed Tomography for Reservoir Core Samples

Summary The present study focuses on the feasibility of a precise 3D numerical modeling coupled with X-ray computed tomography (CT), which enables simple analysis of heterogeneous fracture flows within reservoir core samples, as well as the measurement of porosity and permeability. A numerical modeling was developed and applied to two fractured granite core samples. One of the samples had an artificial single fracture (sample dimensions: 100 mm in diameter, 150 mm in length), and the other had natural multiple fractures (sample dimensions: 100 mm in diameter, 120 mm in length). A linear relationship between the CT value and the fracture aperture (fracture-aperture calibration curve) was obtained by X-ray CT scanning for a fracture-aperture calibration standard while varying the aperture from 0.1 to 0.5 mm. With the fracture-aperture calibration curve, 3D distributions of the CT value for the samples (voxel dimensions: 0.35×0.35×0.50 mm3) were converted into fracture-aperture distributions in order to obtain fracture models for these samples. The numerical porosities reproduced the experimental porosities within factors of approximately 1.3 and 1.1 for the single fracture and the multiple fractures, respectively. Using the fracture models, a single-phase flow simulation was also performed with a local cubic law-based fracture-flow model for steady-state laminar flow of a viscous and incompressible fluid. The numerically obtained permeabilities were larger than the experimentally obtained permeabilities by factors of approximately 2.2 and 2.7 for the single fracture and the multiple fractures, respectively. However, these discrepancies can be reduced to approximately 1.3—2.1 and 1.6-2.6, respectively, by simply using the correction factor for the cubic-law equation proposed by Witherspoon et al. (1980). Consequently, a precise numerical modeling coupled with X-ray CT is essentially feasible. Furthermore, the development of preferential flow paths (i.e., channeling flow) was clearly demonstrated for multiple fractures, which is much more challenging to achieve by most other methods. Further progress in modeling should enable the in-situ evaluation of heterogeneous fracture flow within reservoir core samples, as well as the clarification of the impacts of the heterogeneity on the productivity of wells and, for example, the efficiency of recovery by water-/gasflooding.

Flow on a Single Rock Fracture in the Shear Process and the Validity of the Cubic Law Examined through Experimental Results and Numerical Simulations

In order to discuss the flow through a rough surface rock fracture, direct shear and flow coupling tests on various rock fractures are carried out. Through the experimental results, the flow on the fracture and the validity of the cubic law are discussed and estimated. As a result, it is understood that the cubic law cannot sufficiently explain the experimental results, although it can partially take into account the experimental results in the Re range of 0.02 to 0.2. Moreover, a simulation by a 2D model, including the inertia term, has been carried out. The 2D model has been found to show a good performance of the fracture flow in comparison with the representative fracture flow model, namely, LCL (local cubic law). The flow on the fracture shows the channeling flow and a higher Re value. Consequently, the flow on the fracture is thought to be caused by the influence of the inertia term.

Properties of fault damage zones in siliclastic rocks: a modelling approach

Abstract Major faults are surrounded by damage zones of minor faults that, in siliclastic rocks, can form barriers to flow in their own right. Reservoir flow simulation — now a routine part of reservoir management — requires equivalent hydraulic parameters on the scale of the whole fault, while reservoir geological models, from which flow simulator grids are generated, require information on the 3D characteristics of fault populations. Here, a stochastic model of fault damage zone architecture is generated and used to explore the impact of damage zone architecture on extrapolation from 1D (fault throw) and 2D (fault length) to 3D fault population characteristics. Sampling of the simulated damage zone models shows that clustering of faults causes deviations from simple laws relating particularly 1D samples to 3D population power-law exponents, with differences between expected and observed values of up to 0.25. The stochastic model is used to generate input for a 2D discrete fracture flow model for the case where minor (isotropic) fault permeability is four orders of magnitude lower than that of the host rock and, thus, forms partial barriers to flow. The flow model is used to explore the impact of fault damage zones on bulk fault permeability. The damage zone is shown to be around 50% efficient, i.e. a simple estimate of bulk permeability can be made using the harmonic average of fault rock and host-rock permeability weighted by thickness in 1D traverses (e.g. core, well logs), where only half the observed thickness of fault rock in the fault damage zone is assumed. Considering the contributions of the damage zone and the major slip zone, the fault damage zone is likely to make a significant contribution to the bulk permeability of the fault as a whole when the permeability of minor faults in the damage zone is similar to, or at most, one order of magnitude greater than that of the slip zone fault rocks.

Permeability and degassing of dome lavas undergoing rapid decompression: An experimental determination

The gas permeability of volcanic rocks may influence various eruptive processes. The transition from a quiescent degassing dome to rock failure (fragmentation) may, for example, be controlled by the rock’s permeability, in as much as it affects the speed by which a gas overpressure in vesicles is reduced in response to decompression. Using a modified shock-tube-based fragmentation bomb (Alidibirov and Dingwell 1996a,b; Spieler et al. 2003a), we have measured unsteady-state permeability at a high initial pressure differential. Following sudden decompression above the rock cylinder, pressurized gas flows through the sample. Two pressure transducers record the pressure signals above and below the sample. A transient 1D filtration code has been developed to calculate permeability using the experimental decay curve of the lower pressure transducer. Additionally an analytical steady-state method to achieve permeability is presented as an alternative to swiftly predict the sample permeability in a sufficiently precise manner. Over 100 permeability measurements have been performed on samples covering a wide range of porosity. The results show a general positive relationship between porosity and permeability with a high data scatter. Our preferred interpretation of the results is a combination of two different, but overlapping effects. We propose that at low porosities, gas escape occurs predominantly through microcracks or elongated micropores and therefore could be described by simplified forms of Kozeny–Carman relations (Carman 1956) and fracture flow models. At higher porosities, the influence of vesicles becomes progressively stronger as they form an increasingly connected network. Therefore, a model based on the percolation theory of fully penetrable spheres is used, as a first approximation, to describe the permeability-porosity trend. In the data acquired to date it is evident, that in addition to the porosity control, the sample’s bubble size, shape and distribution strongly influence the permeability. This leads to a range of permeability values up to 2.5 orders of magnitude at a given porosity.

In search of preferential flow paths in structured porous media using a simple genetic algorithm

Fracture network and preferential flow path images from exposed outcrops of geological formations, exposed soil pedon faces, and extracted soil columns and rock cores are often used to conceptualize and construct models to predict the fate and transport of subsurface contaminants. Both the scale resolutions inherent in these observations and the upscaling methods used to obtain macroscopic flow and transport parameters may result in uncertainties in the prediction. We present a mechanistic‐based approach that utilizes a discrete fracture flow and transport model, a distributed and high performance computational architecture, and a genetic‐based search algorithm to invert scale‐ representative, equivalent fracture networks or the preferential flow paths. Synthetic breakthrough curves (BTCs) and exposed structural information from known fracture networks in hypothetical soil columns are presented to the search algorithm. Using three genetic operators, a simple genetic algorithm (SGA) is able to invert the correct pictures of simple but not complex fracture networks. Solute transport experiments using soil columns often assume that the structure of soil columns is laterally uniform with respect to the macroscopic transport direction and the transport process is longitudinally one‐ dimensional. This assumption and the one BTC thus collected for each injection of solutes, even with flow interruptions, are not sufficient to guide the search algorithm toward the global optimum. Additional information (e.g., multiple solute BTCs along a cross section of the soil column) is necessary for the SGA to invert the correct fracture network. Three SGA population statistics, fracture network uncertainty, informatic entropy, and matrix‐fracture contact area, are proposed to measure the uncertainty of SGA near optima. A positive correlation between the reduction of these statistics and the level of relevant information to better confine the SGA search space was found. The SGA search algorithm is then applied to a laboratory solute transport problem. Multiple scenarios of search constraints, derived from visually traced surface features, are examined. The hypothesis that variation in fracture aperture may reduce the uncertainty of SGA near optima is also tested. The results from these applications suggest that there is a certain degree of uncertainty regarding the flowing nature of the exposed fracture segments that are visually traced. The uncertainty of SGA near optima is not improved by incorporating fracture aperture information into the fracture networks. Breakthrough curves thus calculated have marginal improvement, relative to the uniform aperture SGA near optima, in fitting the observations. The lack of improvement may be caused by the relative uniform structure of the soil and the scale of the problem. It is further suggested that in applying the search algorithm to laboratory and field problems, one explores only the search scenarios that relevant information and search constraints may warrant.

CRAFIT: A Computer Program for Calibrating Breakthrough Curves of CRAFLUSH, a One‐Dimensional Fracture Flow and Transport Model

AbstractThis Computer note presents a program called CRAFIT, which automates trial and error curve fitting of breakthrough curves for CRAFLUSH, a one‐dimensional fracture flow and transport code. CRAFIT is useful for modeling column experiments where the source function is well‐known but fracture geometry and matrix are to be characterized. CRAFIT is demonstrated for curve fitting with three unknowns and five unknowns, and found a single best‐fit solution for each case.

An Analysis of Gas Tightness Around Unlined Storage Cavern Using a Discrete Fracture Flow FEM Model

ABSTRACT Water curtain method has been utilized to prevent the escape of gas from storage caverns excavated in the rock. The water curtain method appears to be increasingly used in various forms of storage caverns. Fluid flow in crystalline fractured rock where most of water curtains are constructed is basically controlled by the geometry of fracture network and the properties of the individual fracture. The concept of discrete fracture flow is more appropriate approach for analyzing the stability of water curtain system. In order to analyze the groundwater flow in fracture network, we have developed an unsteady state discrete fracture flowing FEM simulator and have applied it to underground LPG storage facilities at Ulsan, Korea. In this site the hydraulic head of observation well Y was monitored as −7.5 m. With the continuum model concept for the fractured rock the hydraulic head of well Y was calculated as −18.62 m, whereas −4 m was estimated with discrete fracture flow model. The result showed that the discrete fracture flow model was more reasonable for the analysis of groundwater flow in fractured rock than the continuum model concept.

Quantifying diffusive mass transfer in fractured shale bedrock

A significant limitation in defining remediation needs at contaminated sites often results from an insufficient understanding of the transport processes that control contaminant migration. The objectives of this research were to help resolve this dilemma by providing an improved understanding of contaminant transport processes in highly structured, heterogeneous subsurface environments that are complicated by fracture flow and matrix diffusion. Our approach involved a unique long‐term, steady state natural gradient injection of multiple tracers with different diffusion coefficients (Br, He, Ne) into a fracture zone of a contaminated shale bedrock. The spatial and temporal distribution of the tracers was monitored for 550 days using an array of groundwater sampling wells instrumented within a fast flowing fracture regime and a slow flowing matrix regime. The tracers were transported preferentially along strike‐parallel fractures, with a significant portion of the tracer plumes migrating slowly into the bedrock matrix. Movement into the matrix was controlled by concentration gradients established between preferential flow paths and the adjacent rock matrix. Observed differences in tracer mobility into the matrix were found to be a function of their free‐water molecular diffusion coefficients. The multiple tracer technique confirmed that matrix diffusion was a significant process that contributed to the overall physical nonequilibrium that controlled contaminant transport in the shale bedrock. The experimental observations were consistent with numerical simulations of the multitracer breakthrough curves using a simple fracture flow model. The simulated results also demonstrated the significance of contaminant diffusion into the bedrock matrix. The multiple tracer technique and ability to monitor the fracture and matrix regimes provided the necessary experimental constraints for the accurate numerical quantification of the diffusive mass transfer process. The experimental and numerical results of the tracer study were also consistent with indigenous contaminant discharge concentrations within the fracture and matrix regimes of the field site. These findings suggest that the secondary source contribution of the bedrock matrix to the total off‐site transport of contaminants is relatively large and potentially long‐lived.

An integrated approach for characterizing fractured reservoirs

Abstract Experience has shown that fractures and faults within a given array are not all equally conductive or well-connected. To investigate new techniques for locating conductive fracture flow paths, a series of high resolution (1 to 10 kHz) crosswell and single well seismic surveys and interference tests were conducted in a shallow five spot well array penetrating a fractured limestone formation. Two inverse approaches for constructing fracture flow models were applied to the interference test data. Both approaches successfully reproduced the transient pressure behaviour at the pumping and observation wells and indicated a preferential fracture flow path between two wells aligned in an east-northeast direction, the dominant direction of fracturing mapped in the area. Crosswell and single well seismic experiments were performed before and after air injection designed to displace water from the fracture flow path and increase seismic visibility. The crosswell experiments showed that replacement of water with gas produces significant changes in the seismic signal. The single well reflection surveys were able to precisely locate the position of the fracture flow path. This location was confirmed by core from a slant well which intersected a single open fracture at the targeted depth.

A numerical model for thermo-hydro-mechanical coupling in fractured rock

Coupled thermo-hydro-mechanical codes with the ability to model fractured materials are used for predicting groundwater flow behavior in fractured aquifers containing thermal sources. The potential applications of such a code include the analysis of groundwater behavior within a geothermal reservoir. The capability of modeling hydro-thermo systems with a dual porosity, fracture flow model has been previously developed in the finite element code, FEHM. FEHM has been modified to include stress coupling with the dual porosity feature. FEHM has been further developed to couple the dependence of fracture hydraulic conductivity on effective stress within two-dimensional, saturated aquifers containing fracture systems. The cubic law for flow between parallel plates was used to model fracture permeability. The Barton-Bandis relation was used to determine the fracture aperture within the cubic law. The code used a Newton-Raphson iteration to implicitly solve for six unknowns at each node. Results from a model of heat flow from a reservoir to the moving fluid in a single fracture compared well with analytic results. Results of a model showing the increase in fracture flow due to a single fracture opening under fluid pressure compared well with analytic results. A hot dry rock, geothermal reservoir was modeled with realistic time steps indicating that the modified FEHM code does successfully model coupled flow problems with no convergence problems.

A numerical model for thermo-hydro-mechanical coupling in fractured rock

Coupled thermo-hydro-mechanical codes with the ability to model fractured materials are used for predicting groundwater flow behavior in fractured aquifers containing thermal sources. The potential applications of such a code include the analysis of groundwater behavior within a geothermal reservoir. The capability of modeling hydro-thermo systems with a dual porosity, fracture flow model has been previously developed in the finite element code, FEHM. FEHM has been modified to include stress coupling with the dual porosity feature. FEHM has been further developed to couple the dependence of fracture hydraulic conductivity on effective stress within two-dimensional, saturated aquifers containing fracture systems. The cubic law for flow between parallel plates was used to model fracture permeability. The Barton-Bandis relation was used to determine the fracture aperture within the cubic law. The code used a Newton-Raphson iteration to implicitly solve for six unknowns at each node. Results from a model of heat flow from a reservoir to the moving fluid in a single fracture compared well with analytic results. Results of a model showing the increase in fracture flow due to a single fracture opening under fluid pressure compared well with analytic results. A hot dry rock, geothermal reservoir was modeled with realistic time steps indicating that the modified FEHM code does successfully model coupled flow problems with no convergence problems.

Joint inversion of tracer tests using reversed flow fields

Two successive dipole tracer experiments were performed in a fractured rock at the Grimsel Test Site in February/March 1993. In both experiments NaCl was used as a tracer and the extraction rate was twice the injection rate. In the second experiment injection and extraction were interchanged (‘reverse experiment’). The withdrawal rate remained twice the injection rate. Long tailing was characteristic for the breakthrough curves in both experiments. The tests were interpreted using a single fracture flow model. Tracer transport is described by advection/dispersion along the fracture allowing for diffusion into an immobile matrix. We were able to interpret the breakthrough curves for both experiments by one unique set of parameters, describing transport and baseflow. Uniqueness could only be achieved when using the information from both experiments. We conclude that performing a reverse experiment is an indispensable tool for parameter identification in dipole tracer tests. A sensitivity analysis proved that not only the exchange of tracer between the mobile zone and the immobile matrix but also transversal dispersivity is responsible for the tailing in the breakthrough curves. Further, the typical exchange time between mobile and immobile media was too small to be attributed to mere molecular diffusion into the matrix. The interpretation of the estimated parameters allows us to conclude that we did not observe matrix diffusion but a fast exchange of tracer between the mobile zone and both the adjacent rock and less pervious zones within the fracture. Analysis of the joint covariance matrices showed that the estimated transport parameters have small errors.