Fractured Porous Rock Research Articles

Seismic wave modeling of fluid-saturated fractured porous rock: including fluid pressure diffusion effects of discretely distributed large-scale fractures

Abstract. The scattered seismic waves of fractured porous rock are strongly affected by the wave-induced fluid pressure diffusion effects between the compliant fractures and the stiffer embedding background. To include these poroelastic effects in seismic modeling, we develop a numerical scheme for discretely distributed large-scale fractures embedded in fluid-saturated porous rock. Using Coates and Schoenberg's local-effective-medium theory and Barbosa's dynamic linear slip model characterized by complex-valued and frequency-dependent fracture compliances, we derive the effective viscoelastic compliances in each spatial discretized cell by superimposing the compliances of the background and the fractures. The effective governing equations for fractured porous rocks are viscoelastic anisotropic and numerically solved by the mixed-grid-stencil frequency-domain finite-difference method. The main advantage of our proposed modeling scheme over poroelastic modeling schemes is that the fractured domain can be modeled using a viscoelastic solid, while the rest of the domain can be modeled using an elastic solid. We have tested the modeling scheme in a single fracture model, a fractured model, and a modified Marmousi model. The good consistency between the scattered waves off a single horizontal fracture calculated using our proposed scheme and the poroelastic modeling validates that our modeling scheme can properly capture the fluid pressure diffusion (FPD) effects. In the case of a set of aligned fractures, the scattered waves from the top and bottom of the fractured reservoir are strongly influenced by the FPD effects, and the reflected waves from the underlying formation can retain the relevant attenuation and dispersion information. The proposed numerical modeling scheme can also be used to improve migration quality and the estimation of fracture mechanical characteristics in inversion.

Hyper-gravity experiment of solute transport in fractured rock and evaluation method for long-term barrier performance

Hyper-gravity experiment enable the acceleration of the long-term transport of contaminants through fractured geological barriers. However, the hyper-gravity effect of the solute transport in fractures are not well understood. In this study, the sealed control apparatus and the 3D printed fracture models were used to carry out 1 ​g and N g hyper-gravity experiments. The results show that the breakthrough curves for the 1 ​g and N g experiments were almost the same. The differences in the flow velocity and the fitted hydrodynamic dispersion coefficient were 0.97–3.12% and 9.09–20.4%, indicating that the internal fractures of the 3D printed fracture models remained stable under hyper-gravity, and the differences in the flow and solute transport characteristics were acceptable. A method for evaluating the long-term barrier performance of low-permeability fractured rocks was proposed based on the hyper-gravity experiment. The solute transport processes in the 1 ​g prototype, 1 ​g scaled model, and N g scaled model were simulated by the OpenGeoSys (OGS) software. The results show that the N g scaled model can reproduce the flow and solute transport processes in the 1 ​g prototype without considering the micro-scale heterogeneity if the Reynolds number (Re) ​≤ ​critical Reynolds number (Recr) and the Peclet number (Pe) ​≤ ​the critical Peclet number (Pecr). This insight is valuable for carrying out hyper-gravity experiments to evaluate the long-term barrier performance of low-permeability fractured porous rock.

An Analytical Model for Water Inflow into a Karst Tunnel in Vuggy and Fractured Porous Rock Aquifers

Vugs and fractures are the main channels within porous rock aquifers and play a dominant role in the water inrush of the karst tunnel. In this paper, a mathematical model of the coupled free-fluid seepage-fluid with second-order accuracy was established to analyze the flow field characteristics of vuggy and fractured porous rock aquifers. The Navier–Stokes equation was used to govern the free fluid flow in vugs and fractures, while the Darcy–Brinkman equation was employed to describe the seepage fluid motion in the porous rock matrix. The analytical solutions for the flow velocity and water discharge were derived under the requirement of continuous velocity and shear stress at the interface between free and seepage fluids. These solutions can be successfully reduced to those of the classical Poiseuille’s law, assuming that the rock matrix is impervious to water. The numerical, experimental, and analytical results were compared to validate the present analytical model, and the results of the analytical model showed greater accuracy compared with the classical Poiseuille’s law and cubic law. Furthermore, the water inrush of the Xiangpingshan karst tunnel was selected as a real engineering case. Perforated bricks were used to stack a vuggy and fractured porous physical tunnel model (1:100) with the same hydraulic conductivity as the Xiangpingshan tunnel. The relative errors between current theoretical and physical tests obtained for the water inflow discharges are within 18%. The current model can provide a reference for predicting the water inflow of karst tunnels in vuggy and fractured porous rock aquifers.

Numerical modeling of frequency-dependent velocity and attenuation in a fractured-porous rock saturated with two immiscible fluids

The dispersion and attenuation of seismic-wave propagation induced by ‘squirt flow’ effects in hydrocarbon-saturated reservoirs are significantly affected by their rock properties and fluid content. In this study, we analyse the frequency-dependent velocity, attenuation, and seismic responses when fractured porous rock is saturated with two immiscible fluids. First, when considering reservoir wettability, we calculate the effective fluid viscosity using a stable parameter, the capillary pressure, and a lattice Boltzmann model (LBM)-based relative permeability equation, which is a function of the saturation and viscosity ratio of the immiscible two-phase fluid. Then, we explore the frequency-dependent effects of fractured porous rocks saturated with two immiscible fluids under different cases of viscosity ratios and capillary pressure parameters by employing the Chapman model from the dynamic equivalent-medium theory. Then, we use a four-layer model to analyse the frequency-dependent seismic responses. The results show that the characteristics of frequency-dependent velocity and attenuation are both affected by the wettability, capillary pressure parameter, saturation, and viscosity ratio. The frequency-dependent features are greatly influenced by the capillary pressure parameter and viscosity ratio. For a larger viscosity ratio and lower capillary parameter, a dispersive effect can occur in the seismic frequency band. This indicates that the velocity dispersion anomalies are sensitive to wettability, capillary pressure parameter and viscosity ratio and should not be neglected. Synthetic seismic records demonstrate that the seismic reflection signatures, such as the waveform, amplitude, and reflective travel time, at the interfaces for saturated reservoirs are significantly affected by wettability and saturation. The numerical modeling helps to improve the wave propagation in rocks saturated by two immiscible fluids.

Analysis of Coupled Seepage and Temperature Fields of Fractured Porous Rock Mass under Brine–Liquid Nitrogen Freezing

The existence of fracture flow has an undesirable effect on the creation of the frozen wall. Brine and liquid nitrogen combined freezing technology can ensure the safety of freezing engineering, reduce the construction period and save cost. Considering the permeability of the rock matrix, fluid exchange and Darcy–Stokes coupling effect between the rock matrix and fracture, a thermo-hydraulic model of the fractured porous rock mass under water seepage is herein established. The interfacial seepage field characteristics of fractured rock mass under different fluid flow models and interface conditions are compared. The numerical simulations of the initial brine freezing and liquid nitrogen reinforcement freezing are carried out. The results show that the overall permeability of fractured rock mass computed by free flow considering the Darcy–Stokes effect is greater than that computed by the Cubic law. The limit seepage velocity of the intact rock mass in brine freezing is 2.5 m/d, and that of fractured rock mass decreases to 1 m/d. The fracture aperture and groundwater seepage velocity are directly proportional to the closure time of the frozen wall. Liquid nitrogen freezing can seal water quickly and shorten the closure time of the frozen wall when the seepage velocity of the fractured rock mass is greater than the limit seepage velocity, and the rapid cooling of the upstream region plays an important role in the formation of the frozen wall in fractured rock mass.

Effects of multiscale heterogeneity on transport in three-dimensional fractured porous rock with a rough-walled fracture network

This study numerically analyzed the effect of multiscale heterogeneity on flow and transport response of a three-dimensional (3D) fractured porous rock with rough-walled fracture network. 3D discrete fracture matrix (DFM) models with different heterogeneity scales (network-scale, fracture-to-fracture-scale, and individual fracture-scale) were generated. The results showed that the velocity and concentration distributions among the different DFMs were highly variable due to multiscale heterogeneity. The cumulative distribution function curves (CDFs) of the concentration disctribution indicated that fracture-to-fracture-scale heterogeneity led to an earlier breakthrough time than network-scale heterogeneity, and this behavior was further enhanced by individual fracture-scale heterogeneity, suggesting that transport was accelerated by enhanced local channeling flow with increasing fracture roughness. The complementary cumulative distribution function curves (CCDFs) showed obvious long tailing as heterogeneity increased from fracture-to-fracture-scale to individual fracture-scale. Compared with the case where only network-scale heterogeneity was considered, the calculated downstream concentration with fracture-to-fracture-scale heterogeneity increased first from 0.670 to 0.709. However, the downstream concentration then decreased from 0.684 to 0.618 as the roughness increased from σ = 0.03 mm to σ = 0.07 mm. These results can help predict the migration behavior of radioactive nuclides in far-field areas and assess the long-term performance of deep geological repositories.

The Impact of Fracture Geometries on Heterogeneity and Accuracy of Upscaled Equivalent Fracture Models

Abstract Fractures are widely distributed in the upper crust, which is important to transport processes in groundwater, geothermal, and hydrocarbon reservoirs. Little attention has been paid to the heterogeneity and accuracy of upscaled equivalent fracture models (EFMs) regarding the complex fracture geometries during numerical reservoir simulation. This paper investigates how fracture geometric properties affect the accuracy of highly heterogeneous EFMs. An ensemble of synthetic fractured porous rocks is generated stochastically with varied fracture length, fracture density, and aperture-length correlation. Each realization is upscaled to EFM with the recently developed multiple boundary method. Flow problems are solved for EFMs and discrete fracture models (DFMs) simultaneously, and their flow rates are compared. The results demonstrate that the heterogeneity of EFMs decreases with the number and length of fractures and increases with the aperture-length correlation component. The flow rates calculated by EFMs fit well with those by DFMs with a slope around 1.08 and R2 coefficient above 0.98. The accuracy of the upscaled EFM decreases when the aperture-length correlation changes from sublinear to linear. The uncertainty of upscaling accuracy decreases with dimensionless fracture density. The findings of this study can help for a better understanding of the effect of the discrete fracture geometries on the performance of upscaled EFMs and choosing the appropriate models for different kinds of fractured reservoirs.

A Porothermoelastic Model Considering the Dynamic Temperature-Perturbation Boundary Effect for Borehole Stability in Fractured Porous Rocks

Summary Conventional drilling design tends to inappropriately predict the mud density required for borehole stability of deep fractured porous rocks, such as shale, tight sandstone, and hot dry rock, because it is treated as a single-porosity case and even introduces the influence of weak plane to cover the effect on the fracture system. When the external loadings are applied, fractured porous rocks naturally display two different poromechanical responses of the matrix system and the fracture system considering respective hydraulic and mechanical properties. Besides, the constant temperature difference between the drilling mud and formation rock is often chosen as a boundary condition to solve the temperature balance equation, and thus the incorrect prediction of temperature variations of fractured rock further leads to inappropriate evaluation of the pore pressure and stress fields considering the thermo-hydromechanical (THM) coupling (porothermoelastic model), since a dynamic temperature-perturbation boundary condition related to the temperature at the borehole wall actually accounts for the circulating effect of the drilling mud. Therefore, this paper first uses the API RP 13D (1995) model in combination with the circulating temperature-fields model of Raymond (Raymond 1969) to obtain a set of fully transient analytical solutions to circulating temperature fields, including the four types of temperature inside the drilling pipe, borehole annulus, at the borehole wall, and formation. Furthermore, under local thermal equilibrium (LTE) condition, one considers the dynamic temperature-perturbation boundary condition and provides semianalytical porothermoelastic solutions to the field variables around a vertical borehole subjected to nonhydrostatic stresses in fractured porous rock with dual porosity and dual permeability. The solutions for field variables are obtained in line with the plane strain assumption. The variables include displacements, stresses, and two pore pressures of the matrix system and fracture system. The model is verified by the analytical solutions in the case of a porous medium with a single-porosity one under LTE condition. The main results show that the dual-porosity medium displays a higher borehole instability potential than the single-porosity one. This increasingly cooling effect increases the higher risk of the tensile transverse fracturing when the constant temperature-perturbation boundary condition chooses a smaller temperature difference than that of the dynamic case at a later time. The drilling mud-pressure window narrows with increasing time when the coupled porothermoelastic model is considered. It suggests that the drilling engineer takes into consideration the dynamic temperature-perturbation boundary effect, fracture spacing, and fracture width into the predrilling design of the time-dependent safe mud-pressure window (SMPW).

Влияние толщины стенок обсадных труб на распределение напряжений в приствольных зонах добывающих скважин

The influence of the thickness of casing walls in oil and gas producing wells on the values of effective radial, angular (tangential) and vertical stresses caused by the existence of a depression funnel around these wells and affecting the filtration characteristics of the formation in the bottomhole zones of wells has been studied by mathematical modeling methods. It is established that the sum of radial and angular stresses near the borehole does not depend on the thickness of the casing walls, which affects only the ratio of the values of these stresses. It is shownthat this ratio significantly affects the filtration conductivity of bottom-hole zones of producing wells, especiallyin the development of carbonate reservoirs belonging to the type of fractured-porous rocks. Based on the conducted studies, it was concluded, in particular, that for rocks with a high value of the Poisson’s ratio, it is most rational to use casing pipes with a large wall thickness. This will contribute both to reducing the magnitude of angular compressive stresses in the rock and to reducing the intensity of rock creep processes in the bottomhole zones of wells.To reduce radial compressive stresses, it is rational to use casing pipes with a small thickness of their walls.Keywords: producing wells, depression funnel, carbonate rocks, casing pipes.

Equivalent Permeability Distribution for Fractured Porous Rocks: Correlating Fracture Aperture and Length

Estimating equivalent permeability at grid block scale of numerical models is a critical issue for large-scale fractured porous rocks. However, it is difficult to constrain the permeability distributions for equivalent fracture models as these are strongly influenced by complex fracture properties. This study quantitatively investigated equivalent permeability distributions for fractured porous rocks, considering the impact of the correlated fracture aperture and length model. Two-dimensional discrete fracture models are generated with varied correlation exponent ranges from 0.5 to 1, which indicates different geomechanical properties of fractured porous rock. The equivalent fracture models are built by the multiple boundary upscaling method. Results indicate that the spatial distribution of equivalent permeability varied with the correlation exponent. When the minimum fracture length and the number of fractures increase, the process that the diagonal equivalent permeability tensor components change from a power law like to a lognormal like and to a normal-like distribution slows down as the correlation exponent increases. The average dimensionless equivalent permeability for the equivalent fracture models is well described by an exponential relationship with the correlation exponent. A power law model is built between the equivalent permeability of equivalent fracture models and fracture density of discrete fracture models for the correlated aperture-length models. The results demonstrate that both the fracture density and length-aperture model influence the equivalent permeability of equivalent fracture models interactively.

Deformation characteristics of high-porosity rock mass with a single flaw under axial loading and lateral restraint

Rock-like replicas with different dip-angle flaws were tested in an apparatus with axial loading and lateral restraint to study the stress-strain characteristics of high-porosity rock with a single flaw. The results showed that a coefficient of the lateral stress could be calculated using a coefficient of the lateral frictional resistance and frictional coefficient. It was determined that the lateral stress increases linearly with axial loading. The relationship between the flaw aperture and loading can be described by an exponential function. The high-porosity rock mass with a single flaw exhibited a creep deformation, which was practically no creep deformation during an initial loading stage and then increased remarkably when the loading pressure exceeded the uniaxial compressive strength. The internal flaw affected a lateral deformation of the porous space for a high-porosity rock replica, which was limited to outside lateral deformation, and the porosity structure collapse was the main reason for the flaw closure. Elastic-plastic stage, collapse stage, and strain-hardening stage were investigated in the rock replica stress-strain process, and the strain-hardening process was generated after the flaw closure. The volumetric ratio of fracture volume to porosity was kept constant in the first loading process, and after the porosity structure collapsed, the ratio decreased quickly, and porosity deformation played a dominant role in the overall strain. This study provided a new understanding related to research of stress-strain characteristics of fractured-porous rock.

Stress induced permeability changes in brittle fractured porous rock

This paper aims at deriving an approximate model of stress-induced permeability enhancement for brittle cracked porous rock, based on the linear fracture mechanic theory. A recently proposed model of the effective permeability of a porous rock containing an anisotropic distribution of several crack families is used. In such a model, the fluid flow is modelled by Poiseuille's law within the crack and Darcy's law for the porous matrix. The presence of this effective permeability model coupled to an analytical expression of crack growth under shear loading enables the modelling of the permeability variation due to stress-induced cracking in a porous rock. The model is applicable for any initial crack density (i.e. lower, around or upper to percolation threshold). Comparisons with experimental results and existing models show the validation and the advantage of the present model. All stages of fluid flow through a cracked porous medium are also reproduced. The proposed model can be easily implemented in a hydromechanical formulation with application to fractured geological formations.

Linearized amplitude variation with offset and azimuth and anisotropic poroelasticity

ABSTRACTThe normal‐to‐shear weakness ratio is commonly used as a fracture fluid indicator, but it depends not only on the fluid types but also on the fracture intensity and internal architecture. Amplitude variation with offset and azimuth is commonly used to perform the fluid identification and fracture characterization in fractured porous rocks. We demonstrate a direct inversion approach to utilize the observable azimuthal data to estimate the decoupled fluid (fluid/porosity term) and fracture (normal and shear weaknesses) parameters instead of the calculation of normal‐to‐shear weakness ratio to help reduce the uncertainties in fracture characterization and fluid identification of a gas‐saturated porous medium permeated by a single set of parallel vertical fractures. Based on the anisotropic poroelasticity and perturbation theory, we first derive a linearized amplitude versus offset and azimuth approximation using the scattering function to decouple the fluid indicator and fracture parameters. Incorporating Bayes formula and convolution theory, we propose a feasible direct inversion approach in a Bayesian framework to obtain the direct estimations of model parameters, in which Cauchy and Gaussian distribution are used for the a priori information of model parameters and the likelihood function, respectively. We finally use the non‐linear iteratively reweighted least squares to solve the maximum a posteriori solutions of model parameters. The synthetic examples containing a moderate noise demonstrate the feasibility of the proposed approach, and the real data illustrates the stabilities of estimated fluid indicator and dry fracture parameters in gas‐saturated fractured porous rocks.

Experimental Investigation on the Law of Grout Diffusion in Fractured Porous Rock Mass and Its Application

Because of the limitation of mining techniques and economic conditions, large amounts of residual coal resources have been left in underground coal mines around the world. Currently, with mining technology gradually developing, residual coal can possibly be remined. However, when residual coal is remined, caving areas might form, which can seriously affect the safety of coal mining. Hence, grouting technology is put forward as one of the most effective technologies to solve this problem. To study the grouting diffusion in fractured rock mass, this paper developed a visualization platform of grouting diffusion and a three-dimensional grouting experimental system that can monitor the grout diffusion range, diffusion time and grout pressure; then, a grouting experiment is conducted based on this system. After that, the pattern of the grouting pressure variation, grout flow and grout diffusion surface are analyzed. The relationship among some factors, such as the grouting diffusion radius, compressive strength of the grouted gravel, porosity, water-cement ratio, grouting pressure, grouting time, permeability coefficient and level of grout, is quantitatively analyzed by using MATLAB. The study results show that the flow pattern of the grout in fractured porous rock mass has a parabolic shape from the grouting hole to the bottom. The lower the level is, the larger the diffusion range of the grout is. The grouting pressure has the greatest influence on the grouting diffusion radius, followed by the grouting horizon and water-cement ratio. The grouting permeability coefficient has the least influence on the grouting diffusion radius. The grout water-cement ratio has the greatest influence on the strength of the grouted gravel, followed by the grouting permeability. The grouting pressure coefficient has the least amount of influence on the grouting diffusion radius. According to the results, the grouting parameters are designed, and a layered progressive grouting method is proposed. Finally, borehole observation and a core mechanical property test are conducted to verify the application effect. This grouting technology can contribute to the redevelopment and efficient utilization of wasted underground coal resources.

Upscaling permeability for three-dimensional fractured porous rocks with the multiple boundary method

Upscaling permeability of grid blocks is crucial for groundwater models. A novel upscaling method for three-dimensional fractured porous rocks is presented. The objective of the study was to compare this method with the commonly used Oda upscaling method and the volume averaging method. First, the multiple boundary method and its computational framework were defined for three-dimensional stochastic fracture networks. Then, the different upscaling methods were compared for a set of rotated fractures, for tortuous fractures, and for two discrete fracture networks. The results computed by the multiple boundary method are comparable with those of the other two methods and fit best the analytical solution for a set of rotated fractures. The errors in flow rate of the equivalent fracture model decrease when using the multiple boundary method. Furthermore, the errors of the equivalent fracture models increase from well-connected fracture networks to poorly connected ones. Finally, the diagonal components of the equivalent permeability tensors tend to follow a normal or log-normal distribution for the well-connected fracture network model with infinite fracture size. By contrast, they exhibit a power-law distribution for the poorly connected fracture network with multiple scale fractures. The study demonstrates the accuracy and the flexibility of the multiple boundary upscaling concept. This makes it attractive for being incorporated into any existing flow-based upscaling procedures, which helps in reducing the uncertainty of groundwater models.

Sensitivity of Seismic Attenuation and Phase Velocity to Intrinsic Background Anisotropy in Fractured Porous Rocks: A Numerical Study

AbstractMany researchers have analyzed seismic attenuation and velocity dispersion due to wave‐induced fluid flow (WIFF) related to the presence of fluid‐saturated fractures embedded in an isotropic porous background. Most fractured formations do, however, exhibit some degree of intrinsic elastic and hydraulic anisotropy of the background, and the impact of which on the effective seismic properties remains largely unexplored. In this work, we extend a numerical upscaling procedure to account for the potential intrinsic elastic and hydraulic anisotropy of the background. To do this, we represent the background of a representative sample of the fractured formation of interest with an anisotropic poroelastic medium and apply a set of relaxation experiments to compute the effective anisotropic seismic properties. A comprehensive numerical analysis allows us to observe that, for samples containing hydraulically connected fractures, the anisotropic behavior of both P and S waves differs significantly from that observed for an isotropic background. The anisotropy of the stiffness of the background plays a fundamental role for WIFF between the fractures and the background as well as for WIFF between connected fractures. Conversely, the anisotropy of the background permeability affects the characteristic frequency, the angle dependence, and the magnitude of the effects related to WIFF between fractures and background. In addition, different correlations between hydraulic and elastic background anisotropy lead to different degrees of effective seismic anisotropy. Our results therefore indicate that accounting for the effects of intrinsic background anisotropy on WIFF is crucial for a quantitative interpretation of seismic anisotropy measurements in fluid‐saturated fractured formations.

Is the permeability of naturally fractured rocks scale dependent?

AbstractThe equivalent permeability, of stratified fractured porous rocks and its anisotropy is important for hydrocarbon reservoir engineering, groundwater hydrology, and subsurface contaminant transport. However, it is difficult to constrain this tensor property as it is strongly influenced by infrequent large fractures. Boreholes miss them and their directional sampling bias affects the collected geostatistical data. Samples taken at any scale smaller than that of interest truncate distributions and this bias leads to an incorrect characterization and property upscaling. To better understand this sampling problem, we have investigated a collection of outcrop‐data‐based Discrete Fracture and Matrix (DFM) models with mechanically constrained fracture aperture distributions, trying to establish a useful Representative Elementary Volume (REV). Finite‐element analysis and flow‐based upscaling have been used to determine eigenvalues and anisotropy. While our results indicate a convergence toward a scale‐invariant REV with increasing sample size, magnitude can have multi‐modal distributions. REV size relates to the length of dilated fracture segments as opposed to overall fracture length. Tensor orientation and degree of anisotropy also converge with sample size. However, the REV for anisotropy is larger than that for magnitude. Across scales, tensor orientation varies spatially, reflecting inhomogeneity of the fracture patterns. Inhomogeneity is particularly pronounced where the ambient stress selectively activates late‐ as opposed to early (through‐going) fractures. While we cannot detect any increase of with sample size as postulated in some earlier studies, our results highlight a strong anisotropy that influences scale dependence.

Numerical investigation of seismic attenuation in fluid‐saturated fractured media: An extended view of the Skempton coefficient

AbstractThe interpretation of data from seismic exploration gains from consideration of hydro‐mechanical processes in particular when the waves propagate through fluid‐filled fractured porous rocks. We specifically investigate attenuation processes in porous rock containing complex fracture networks with the main objective to identify effective hydro‐mechanical material properties by computational homogenization. To this end, we generate stochastic fracture ensembles and approximate fractures as ellipses with low aspect ratio (1/100). In other words, the fractures constitute thin and long hydraulic conduits with high permeability. Full periodic boundary conditions are employed on the small scale. We observe a strongly heterogeneous pressure propagation in the fracture network and the surrounding rock. The properties of the macroscopic substitute model are derived by means of a volume averaging technique. We identify a dependence of effective properties on fluid saturation and amount of fractures. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Determination of the thermal conductivity of sandstones from laboratory to field scale

For an optimum design of borehole heat exchangers (BHE) of ground-source heat pump systems, the thermal properties of the ground have to be determined. Thermal properties are typically estimated or measured in the laboratory or in the field. However, the determined values might deviate depending on the scale of observation. Thus, it is important to investigate scale effects. This study determines the thermal conductivity determination of silty sandstone from laboratory to field scale. Thermal conductivity and thermal capacity varying with water saturation are initially investigated in the laboratory. Results show that thermal conductivity increases obviously with increasing water saturation. In addition, effective thermal conductivity of the ground is estimated by a thermal response test in field resulting in a thermal conductivity (λ) of 1.84 W/m K. By comparison with the laboratory results (λ = 2.23 W/m K), the field-derived thermal conductivity shows lower values indicating a scale effect. Microscope image and wave velocity are also studied to investigate the structure of the sandstone. These results indicate that there exist a large numbers of fractures in the silty sandstone, implying that the thermal response test is largely affected by these fractures. Hence, the scale effects should be carefully considered in evaluation of thermal conductivity in particular for fractured porous rocks.

Numerical Study of Contaminant Transport in Fractured Porous Rock with Distance Dependent Dispersivity

This paper presents solute concentration profiles with constant, linear and exponential distance-dependent dispersion models for solute transport through fractured porous rock matrices. A numerical analysis has been developed for solution of the equations governing the dispersion model using the hybrid finite volume method. The results of the numerical analysis have been used to investigate the effect of the matrix diffusion coefficient, fracture velocity, and matrix and fracture retardation factors on concentration profiles. It is found that in the presence of higher matrix diffusion coefficients, the behaviour of concentration profiles is different for constant and distance-dependent dispersion models. However, the behaviour of concentration profiles is observed to be nonlinear during the small transport time period, and the matrix diffusion is found to control the spreading of solute in the fracture in the presence of constant and distance-dependent dispersion models.