Effective Hydraulic Aperture Research Articles

Impact of fractures with multi-scale aperture variability on production observations of geothermal reservoir units

We incorporated aperture variability considering contact obstacles into an ensemble of fractured geothermal reservoir simulations to quantify how variations in this multi-scale aperture feature could impact flow field organization and heat transport behavior at the fracture scale. This work considered the variability of the correlation length and successfully developed two observational parameters for production prediction. Our calculations demonstrated that the degree of flow tortuosity was increased by the correlation length, which in turn affected heat transport. The results showed that using the traditional parallel plate model could overestimate the production temperature and could underestimate the cumulative heat production, and these two observation parameters exhibited scale dependence on the correlation length. However, the plate model with the effective hydraulic aperture inferred from flow could capture the production trend of fractured geothermal reservoirs, which indicates that considering a correction coefficient related to the correlation length could effectively improve the prediction accuracy. We also found that the cumulative heat production attained a positive logarithmic correlation with the channelized flow area and a linear negative correlation with the flow tortuosity. This study contributes to a greater understanding of the uncertainty in production observations of fractured geothermal fields with heterogeneous aperture characteristics.

Reexamination of the permeability-aperture relationship for rough fractures with mismatched self-affine surfaces

The transport property of natural fissured reservoir is highly related to the fracture permeability. The composite topography of natural fractures is always rough, with self-affine surfaces and non-uniform aperture field. All these would affect the transport properties significantly. Therefore, it is of fundamental importance to clarify the control mechanism on fluid flow through rough fractures with self-affine and mismatched surfaces. In this work, four controlling factors, namely local rough geometry, hydraulic tortuosity, surface tortuosity, and non-uniform aperture distribution were identified for the mismatched and rough fracture flows. Afterwards, the implications of these factors on fluid flow were specified by analytical derivation. Combined with the cubic law and the triple-effect model, a quadruple-effect permeability model was established to characterize the comprehensive effects from the composite topography of rough fractures. Moreover, the semi-empirical coefficient and index in surface roughness factor were determined by Lattice Boltzmann simulations, and provide fundamental support to define the effective hydraulic aperture which is a key parameter in the quadruple-effect model. Theoretical analysis denoted that the quadruple-effect model could generalize other models in the literature, and its performance was approved by numerical validation.

Heat transport by flow through rough rock fractures: a numerical investigation

Fracture surface topography exhibits long-range spatial correlations resulting in a heterogeneous aperture field. This leads to the formation, within fracture planes, of preferential flow channels controlling flow and transport processes. By means of a 3-D heat transport model coupled with a 2-D fracture flow model based on the lubrification approximation (i.e., local cubic law), we investigate how the statistical parameters determining spatial aperture variations in individual fractures control the heat exchange at the fluid/rock interface and heat transport by flow. Ensemble statistics over fracture realizations provide insights into the main hydraulic and geometrical parameters controlling the hydraulic and thermal behaviour of rough fractures. Similarly to the rough fracture’s hydraulic behaviour, we find that its heat transport behaviour deviates from the conventional parallel plate fracture model with increasing fracture closure and/or decreasing correlation length. We demonstrate that the advancement of the thermal front is typically slower in rough fractures compared to smooth fractures having the same mechanical aperture. In contrast with previous studies that neglect temporal and spatial temperature variations in the rock matrix, we find that the thermal behavior of a rough-walled fracture can, under field-relevant conditions, be predicted from a parallel plate model with an aperture equal to the rough fracture’s effective hydraulic aperture. This greatly simplifies the prediction of possible reservoir thermal behavior when using field measurable quantities and hydrological modeling.

Investigation of critical non-linear flow behavior for fractures with different degrees of fractal roughness

Non-linear flow behavior in rough fractures with shear dislocations is numerically investigated in this study with the validated multi-relaxation time lattice Boltzmann method. Fracture flow tests with different degrees of fractal roughness are simulated and the results show that the surface roughness has an inhibiting effect on fracture flow. With increasing roughness parameter, the effective transmissivity decreases accordingly. Deviation of fracture flow from the linear regime appears earlier for fractures with rougher surfaces and the non-linearity of fracture flow is enhanced with the tortuous flow-path and corner eddies during the closure process. The non-linearity of fracture flow was found to be anisotropic when applying the pressure gradient parallel and perpendicular to the shear direction. Though the anisotropic feature shows a non-monotonic trend during the closure process, it is enhanced with the increasing roughness parameter. Evaluation of the Forchheimer law in quantifying the non-linear fracture flow is also conducted. The relative difference between the Forchheimer linear transmissivity and intrinsic linear transmissivity is about 1–3%. Assuming that the Forchheimer linear transmissivity is equal to intrinsic linear transmissivity, the linear pressure drop can be underestimated. Relating the non-linear parameters with the dimensionless effective hydraulic aperture, a new model is proposed to predict the critical hydraulic behavior of rough fractures.

Experimental Reproducibility and Natural Variability of Hydraulic Transport Properties of Fractured Sandstone Samples

Flow and transport processes in fractured systems are not yet fully understood, and it is challenging to determine the respective parameters experimentally. Studies on 10 samples of 2 different sandstones were used to evaluate the reproducibility of tracer tests and the calculation of hydraulic transport properties under identical boundary conditions. The transport parameters were determined using the advection–dispersion equation (ADE) and the continuous time random walk (CTRW) method. In addition, the fracture surface morphology and the effective fracture aperture width was quantified. The hydraulic parameters and their variations were studied for samples within one rock type and between both rock types to quantify the natural variability of transport parameters as well as their experimental reproducibility. Transport processes dominated by the influence of fracture surface morphology experienced a larger spread in the determined transport parameters between repeated measurements. Grain size, effective hydraulic aperture and dispersivity were identified as the most important parameters to evaluate this effect, as with increasing fracture aperture the effect of surface roughness vanishes and the experimental reproducibility increases. Increasing roughness is often associated with the larger effective hydraulic aperture canceling out the expected increased influence of the fracture surface morphology.

Bayesian full-waveform inversion of tube waves to estimate fracture aperture and compliance

Abstract. The hydraulic and mechanical characterization of fractures is crucial for a wide range of pertinent applications, such as geothermal energy production, hydrocarbon exploration, CO2 sequestration, and nuclear waste disposal. Direct hydraulic and mechanical testing of individual fractures along boreholes does, however, tend to be slow and cumbersome. To alleviate this problem, we propose to estimate the effective hydraulic aperture and the mechanical compliance of isolated fractures intersecting a borehole through a Bayesian Markov chain Monte Carlo (MCMC) inversion of full-waveform tube-wave data recorded in a vertical seismic profiling (VSP) setting. The solution of the corresponding forward problem is based on a recently developed semi-analytical solution. This inversion approach has been tested for and verified on a wide range of synthetic scenarios. Here, we present the results of its application to observed hydrophone VSP data acquired along a borehole in the underground Grimsel Test Site in the central Swiss Alps. While the results are consistent with the corresponding evidence from televiewer data and exemplarily illustrate the advantages of using a computationally expensive stochastic, instead of a deterministic inversion approach, they also reveal the inherent limitation of the underlying semi-analytical forward solver.

Impact of normal stress-induced closure on laboratory-scale solute transport in a natural rock fracture

The impact of normal stress-induced closure on fluid flow and solute transport in a single rock fracture is demonstrated in this study. The fracture is created from a measured surface of a granite rock sample. The Bandis model is used to calculate the fracture closure due to normal stress, and the fluid flow is simulated by solving the Reynold equation. The Lagrangian particle tracking method is applied to modeling the advective transport in the fracture. The results show that the normal stress significantly affects fluid flow and solute transport in rock fractures. It causes fracture closure and creates asperity contact areas, which significantly reduces the effective hydraulic aperture and enhances flow channeling. Consequently, the reduced aperture and enhanced channeling affect travel time distributions. In particular, the enhanced channeling results in enhanced first arriving and tailing behaviors for solute transport. The fracture normal stiffness correlates linearly with the 5th and 95th percentiles of the normalized travel time. The finding from this study may help to better understand the stress-dependent solute transport processes in natural rock fractures.

Mechanical-Chemical-Mineralogical Controls on Permeability Evolution of Shale Fractures

We report experimental observations of permeation of CO2-rich aqueous fluids of varied acidic potential (pH) on three different shales to investigate mechanical, chemical, and mineralogical effects on fracture permeability evolution. Surface profilometry and SEM-EDS (scanning electron microscopy with energy-dispersive X-ray spectroscopy) methods are employed to quantify the evolution in both roughness on and chemical constituents within the fracture surface. Results indicate that, after 12 hours of fluid flow, fracture effective hydraulic apertures evolve distinctly under different combinations of shale mineralogy, effective stress, and fluid acidity. The evolution of roughness and transformation of chemical elements on the fracture surface are in accordance with the evolution of permeability. The experimental observations imply that (1) CO2-rich aqueous fluids have significant impact on the evolution of fracture permeability and may influence (and increase) shale gas production; (2) shale mineralogy, especially calcite mineral, decides the chemical reaction and permeability increasing when CO2-rich aqueous fluids flow through fractures by free-face dissolution effect; (3) clay mineral swelling reduces fracture aperture and additively calcite pressure solution removes the bridging asperities, which are the main reasons for fracture permeability decrease; (4) competition roles among clay mineral swelling, mineral pressure solution, and free-face dissolution determine how fracture permeability changes. Furthermore, a multiple parameter model is built to analyze effective hydraulic aperture evolution in considering above three mechanisms, which provide a reference to forecast fracture permeability evolution in shale formations.

Numerical modeling of the effects of roughness on flow and eddy formation in fractures

The effect of roughness on flow in fractures was investigated using lattice Boltzmann method (LBM). Simulations were conducted for both statistically generated hypothetical fractures and a natural dolomite fracture. The effect of increasing roughness on effective hydraulic aperture, Izbash and Forchheimer parameters with increasing Reynolds number (Re) ranging from 0.01 to 500 was examined. The growth of complex flow features, such as eddies arising near the fracture surface, was directly associated with changes in surface roughness. Rapid eddy growth above Re values of 1, followed by less rapid growth at higher Re values, suggested a three-zone nonlinear model for flow in rough fractures. This three-zone model, relating effective hydraulic conductivity to Re, was also found to be appropriate for the simulation of water flow in the natural dolomite fracture. Increasing fracture roughness led to greater eddy volumes and lower effective hydraulic conductivities for the same Re values.

The characteristics and estimation of flow through a single rough-walled fracture

The flow through a single fracture is numerically studied by means of the Fluent Software. The results show that the roughness of the fracture significantly affects the hydraulic conductivity in the fracture as compared with the cubic law model widely used to describe the flow between two smooth parallel plates. A new model is proposed in this paper, the non-symmetric sinusoidal fracture model, to simulate the flow in a real fracture. This model involves two sinusoidal-varying walls with different phases to replace the flat planes in the cubic law model. The relationships between the effective hydraulic apertures and the phase retardation for different relative amplitudes and wavelengths are numerically investigated. A simple expression of the effective hydraulic aperture of the fracture is obtained, together with the law of the effective hydraulic aperture against the amplitude, the phase retardation and the wavelength of two sinusoidal-varying walls.

The scaling of hydraulic conductivity in rock fracture zones

Beyond the scale of a few meters, fracture traces as viewed on aerial photographs represent fracture zones. Thus for bulk fractured rock permeability, the hydraulic properties of fracture zones are important. Here, observations on joint zones in sandstones from western Norway are used to build a quantitative model relating joint zone length and effective hydraulic conductivity. Using simple rules for hydraulic conductors in series and parallel applied to joint zone geometry, the ‘effective’ hydraulic aperture (the aperture of a single parallel‐walled channel that conducts the same flow) is estimated for 72 joint zones of known length. A power law relation between trace length, l, and effective hydraulic aperture, be, with an effective exponent of around 0.27 is found which may extend to km scales. This exponent contrasts with values of 0.5 to 2.0 reported for veins.

Hydraulic conductivity of rock fractures

The flow of a single-phase fluid through a rough-walled rock fracture is discussed within the context of fluid mechanics. The derivation of the ‘cubic law’ is given as the solution to the Navier-Stokes equations for flow between smooth, parallel plates - the only fracture geometry that is amenable to exact treatment. The various geometric and kinematic conditions that are necessary in order for the Navier-Stokes equations to be replaced by the more tractable lubrication or Hele-Shaw equations are studied and quantified. In general, this requires a sufficiently low flow rate, and some restrictions on the spatial rate of change of the aperture profile. Various analytical and numerical results are reviewed pertaining to the problem of relating the effective hydraulic aperture to the statistics of the aperture distribution. These studies all lead to the conclusion that the effective hydraulic aperture is less than the mean aperture, by a factor that depends on the ratio of the mean value of the aperture to its standard deviation. The tortuosity effect caused by regions where the rock walls are in contact with each other is studied using the Hele-Shaw equations, leading to a simple correction factor that depends on the area fraction occupied by the contact regions. Finally, the predicted hydraulic apertures are compared to measured values for eight data sets from the literature for which aperture and conductivity data were available on the same fracture. It is found that reasonably accurate predictions of hydraulic conductivity can be made based solely on the first two moments of the aperture distribution function, and the proportion of contact area.

Transport of fluid and electric current through a single fracture

One expects the hydraulic and electrical conductivities of rock to be related, since there is an analogy between the differential equations describing each process. Fractures in rock are commonly described by the parallel plate model, where the fracture surfaces are smooth and parallel with a separation or aperture of d. For this model the hydraulic conductivity is proportional to d3, whereas the electrical conductivity is proportional to d. Deviations from the parallel plate model are expected, since real fracture surfaces are rough and in partial contact. Computer simulations of fluid flow and conduction of electricity were performed on simulated fractures composed of rough surfaces generated with a fractal algorithm. The finite difference method was used to calculate the volume flow rate and electric current. This solution was used in the parallel plate model to get an effective hydraulic aperture dh and electric aperture de. The electric and hydraulic apertures are nearly the same when the surfaces are widely separated. However, de is always smaller than dh, with the difference increasing as the fracture closes. Additionally, the local directions of fluid flow and electric current are not the same. Thus contrary to the common assumption, the actual path length of a fluid particle as measured by the tortuosity is different for each process. The results of these simulations are consistent with the “equivalent channel model,” which shows that by introducing the tortuosity of the fluid flow or electric current paths, one can relate the microscopic physics of the transport properties to the macroscopic behaviors described by Darcy's and Ohm's laws.

Saturated permeability measurements on pumice and welded-tuffaceous materials

Fluid flows in consolidated porous media of volcanic origin are being investigated to support such diverse efforts as the modeling of thermal/outgassing phenomena at Mount St. Helens and the hydrological modeling of tuffaceous rocks in support of the Department of Energy’s (DOE) Nevada Nuclear Waste Storage Investigations Project An experimental apparatus was designed and built to allow water-saturated permeabilities as low as 10−18 m2 to be measured on cores of diameter 5 cm and length 10 cm under steady-state flow conditions. This same apparatus can also be utilized in a transient (pressure-decay) mode in order to measure permeabilities several orders of magnitude lower than the steady-state limit. Tests were conducted on samples of pumice, fractured welded tuff, and welded tuff, representing a permeability range of seven orders of magnitude Pumice was found to have a permeability of ∼3×10−12 m2, sufficiently high to allow the complete Darcy-to-Ergun regime to be investigated Welded (unfractured) tuff was tested in the transient mode, yielding a permeability of ∼5×10−19 m2. Two, long-time-scale, steady-flow experiments were conducted on a core of welded tuff containing a single, through-going fracture. For the first experiment, the core was an integral cylinder containing a naturally occurring fracture. For the second experiment, the core was separated into two pieces along the existing fracture plane, then rejoined. Effects of essentially constant, as well as rapidly varied, circumferential stress were studied in both tests. Results showed core permeability to decay to 2×10−18 m2 in both cases, independent of the initial fracture state (closed versus open). With a naturally occurring fracture, core permeability decreased by a factor of 2 over a 200-h test period. With an initially open fracture, core permeability decreased by a factor of 4 under the influence of a comparable 200-h load-time history, after 700 h of testing, core permeability was reduced by an order of magnitude from its initial level. Final effective hydraulic fracture aperture was calculated to be 10−6 m, corresponding to a calculated effective fracture permeability of 10−13 m2 Fracture flow was thus estimated to account for 80% of the total flow rate through this core under final test conditions.

Hydrogeological investigations at an experimental site in granite, south west England, in relation to the transport of radionuclides through fractured rock

Constant head injection tests and radioactive tracer experiments at an experimental site in the Carnmenellis granite in Cornwall have revealed a fracture permeability in which water movement is confined to discrete fractures separated by rock of low permeability. Data on flow path frequency, orientation, and effective hydraulic aperture, required for network modelling, have been obtained for a 700-m borehole, with additional hydraulic data from three other boreholes. In addition to fractures of “average” hydraulic conductivity, a small number of major hydraulic features (“main drains”) with major implications for radionuclide migration have been identified. A mean hydraulic conductivity for the granite investigated of 1.57 x 10 −7 msec −1 has been obtained, 2.08 x 10 −8 msec −1 if the major hydraulic features (with hydraulic conductivities as high as 10 −5 msec −1) are excluded.