Fracture Compliance Research Articles

Identification of Nearly Pure Leakoff Phase from Pressure Falloff Curve and Its Interpretation on Stimulated Fracture Areas

Summary Evaluation of fractures post-hydraulic fracturing is crucial for optimizing fracturing designs. Pressure falloff analysis methods, due to their cost-effectiveness and ease of data acquisition, have been widely used in oil fields. However, traditional pressure falloff analysis methods are based on the assumption of simple double-wing fractures and often overlook the impact of early-time abnormal leakoff behaviors. While some scholars have proposed pressure falloff equations for individual abnormal leakoff behavior, establishing pressure falloff models that consider the coupling of multiple abnormal leakoff behaviors is challenging, making the assessment of complex fracture networks difficult. This paper proposes a method that identifies the phase of nearly pure leakoff pressure falloff through continuous wavelet transform (CWT) and utilizes this phase for fracture inversion. Additionally, the fracture inversion model considers the differences in closure pressure and fracture compliance between main and secondary fractures. This method is applied to a shale horizontal well, and the results show that the inversion fracture areas are 20.3% smaller on average than the traditional method after removing the disturbance of abnormal leakoff behaviors. The new method is verified by the production data of each stage. The correlation between the main fracture area of new method and the production of each stage is better than that of the traditional method, and the correlation coefficient is 0.767. It is also found that the development degree of natural fractures affects the proportion of main and secondary fractures. In addition, it is found from the time-frequency diagram after CWT that the stages with higher secondary fracture proportions have more high-frequency components in the time-frequency diagram.

Non-stationary inversion of seismic data for fracture compliances in azimuthally anisotropic mediag

Fractures and tectonic settings cause azimuthal anisotropy in reservoirs. Recognizing the fracture model from the seismic data is a useful tool for identifying the productive zone in the reservoirs. We applied azimuthal velocity analysis in seismic processing to improve image quality and to estimate anisotropic model parameters. Using azimuthal residual moveout analysis, we predicted the direction of azimuthal anisotropy in the reservoir, and found that the results are consistent with fracture orientations obtained from the image logs in the reservoirs. Bayes’ theorem, and a cascaded procedure in least-squares inversion, matching observed amplitudes to linearized Zoeppritz equations, were used to estimate the elastic moduli in a first step and normal and tangential fracture weaknesses in a second step. We used laboratory experiments on core samples to validate the first step inversion results. We found that the propagation wavelet varied in space and reflection time, and so a library of extracted wavelets in the time-frequency domain was used for seismic inversion. Maps of computed fracture fluid index and the estimated fracture weaknesses help to visualize the role of fractures in reservoir productivity and revealed a consistency with the seismic peak frequency attribute in identifying zones of highly compliant fracture fill. The estimated fracture model demonstrates a good fit with the fractures seen in the available core samples and implies that the fracture fluid index is a useful attribute for determining the productive zones in the reservoir.

Effects of background elastic and permeability anisotropy on dynamic seismic signatures of a fluid-saturated porous rock with aligned fractures

Seismic dispersion, attenuation, and frequency-dependent anisotropy due to wave-induced fluid flow (WIFF) in fluid-saturated porous and fractured rocks have been widely studied. However, most of these studies do not consider the effects of background elastic and permeability anisotropy. In this work, we study such effects by considering a fluid-saturated porous rock with penny-shaped fractures embedded in the isotropic plane of a transversely isotropic (TI) background. Starting with P-waves propagating perpendicularly to the fracture plane, we obtain the wavefields in the fluid-saturated porous TI background scattered from a single fracture. This allows for the calculation of effective P-wavenumber through the Foldy approximation and the derivation of a frequency-dependent fracture compliance matrix. The angle-dependent seismic dispersion and attenuation, as well as frequency-dependent anisotropy, can thus be calculated. Using this model, we study a fractured tight sandstone with a TI background. The results show that the background elastic anisotropy primarily affects the seismic frequency-dependent anisotropy, while the background permeability anisotropy not only affects seismic frequency-dependent anisotropy but also influences seismic dispersion and attenuation. In particular, the background permeability anisotropy alters the rate of change in seismic velocities and velocity anisotropy parameters with frequencies and the peaks of seismic attenuation and attenuation anisotropy parameters. By comparing the theoretical predictions of our model to other theories and also to two sets of experimental data, our model is validated. Our model can be applied to characterize the fractured, layered earth.

Dynamic response and sound radiation of cracked asphalt pavements under moving loads and variable thermal profiles

ABSTRACT This study investigates the acoustic performance and dynamic response of cracked, viscoelastic porous asphalt pavements under moving loads and variable thermal conditions. Realistic pavement cracks are modelled using an advanced line spring model with fracture compliance coefficients. The novelty lies in the synergistic integration of a heterogeneous triple-porosity media model, a non-uniform depth-dependent temperature profile, and an advanced fracture mechanics-based line spring model with arbitrary crack orientation. Variations in temperature that are uniform, linear, and nonlinear with respect to the thickness layer axis are taken into account. The governing equations are derived by Hamilton’s principle and solved analytically via Fourier-Laplace transforms. The acoustic pressure is first-time predicted through Rayleigh integral analysis. Durbin’s numerical inversion validates the model’s accuracy versus sophisticated finite element simulations. Parametric analysis offers new insights into the effects of crack length, pore size distribution, loading frequency, and thermal gradients on noise pollution and fatigue cracking. The integrated chemo-thermo-mechanical modelling enables optimal structural design and accelerated pavement testing to limit acoustic radiation and premature failure in porous asphalt pavements. It allows for the development of noise-reducing porous asphalt mixtures by modifying aggregate gradation, binder content, and air void distribution.

Precise three dimensions reconstruction closure experiment and a new apparent compliance model for self-propped fractures

Fracture compliance, an essential indicator of fracture deformation, is also a key parameter for post-fracturing network diagnosis and inversion. However, current research lacks detailed experimental studies to acquire this vital parameter of fracture compliance, and the influence of fracture roughness and rock Young’s modulus on fracture compliance remains unclear, leading to a deficiency in models for the evolution of fracture compliance. Therefore, based on 3D reconstruction technology of fracture surfaces, an experiment was designed to observe the deformation of self-propped fractures, obtaining experimental data on fracture deformation. Utilizing this data, a new apparent compliance model for fractures was proposed. The results indicate that closure pressure is the decisive factor affecting the apparent compliance of fractures, regardless of their roughness. The influence of fracture roughness and rock Young’s modulus on apparent compliance shifts under varying closure pressures. At lower closure pressures, apparent compliance is primarily governed by fracture roughness—the greater the roughness, the higher the compliance. At higher closure pressures, the apparent compliance are mainly controlled by the rock’s Young’s modulus—the higher the modulus, the lower the compliance. This phenomenon is attributed to the elastic-plastic damage cycle during the compressive deformation of fractures.

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.

Comparison of elastic anisotropy in the Middle and Upper Wolfcamp Shale, Midland Basin

AbstractOrganic‐rich shales contain large amounts of oil and gas and are anisotropic because of fine‐scale layering and the partial alignment of organic matter and anisotropic clay minerals with the bedding. An example is the Wolfcamp Shale in the Permian Basin. Elastic anisotropy needs to be accounted for in the characterization of such formations using seismic data and plays a role in hydraulic fracturing and in the evaluation of stress changes and geomechanical effects resulting from production. Using extensive well log data acquired in the Midland Basin, the eastern sub‐basin of the Permian Basin, we estimate and compare the elastic anisotropy in the Middle and Upper Wolfcamp Shale by combining data from a vertical pilot well with two lateral wells, one (6SM) drilled in the Middle Wolfcamp and one (6SU) drilled in the Upper Wolfcamp. The data used were acquired at the Hydraulic Fracture Test Site 1, located in the eastern part of the Midland Basin. Thomsen's anisotropy parameter calculated from the fast and slow shear sonic is higher on average for the 6SM lateral than for 6SU, consistent with there being less carbonate content in 6SM than in 6SU. However, the anisotropy parameter in some regions with higher carbonate content in well 6SU is higher than in well 6SM. This may indicate the influence of natural fractures. The primary set of steeply dipping fractures observed in the lateral wells at Hydraulic Fracture Test Site 1 acts to increase if the ratio of the normal‐to‐shear fracture compliance is less than about 0.5. Sub‐horizontal fractures may also increase and could affect the vertical extent of hydraulic fractures. Relations between elastic moduli C33 and C55 in the Upper and Lower Wolfcamp in a vertical pilot well allow C33 to be predicted in a lateral well using measurements of C55 in that well. Comparison of Thomsen's anisotropy parameters and , with calculated from the measured values of C55 and C66 and calculated from the measured values of C11 and predicted values of C33, show that is mostly greater than .

Horizontal transverse isotropy anisotropic parameter inversion via azimuthal seismic velocity anisotropy and its application to anisotropic 3D in-situ stress estimation

Anisotropic parameter inversion in horizontal transverse isotropy (HTI) media plays an important role in predicting the fracture density and the anisotropic in-situ stress for unconventional reservoirs. The current industry practice is to use the azimuthal PP-wave reflection coefficient to estimate the HTI anisotropic parameters. Based on the linear slip theory, we develop an innovative approach that uses azimuthal P-wave phase velocity to calculate HTI anisotropic parameters, which presents superiority over the conventional azimuthal PP-wave reflection coefficient inversion. Specifically, we first verify that the azimuthal P-wave phase velocity is for the HTI elliptical fitting than the azimuthal PP-wave reflection coefficient using the analytical formulations. Second, we sort the prestack wide-azimuth data into offset vector tile sectors and perform amplitude-variation-with-offset inversion at each azimuth. Third, we apply an elliptical fitting to the obtained azimuthal P-wave phase velocities to estimate the HTI anisotropic parameters, fracture density, and fracture direction. Fourth, based on the HTI mechanical earth model, we formulate a cost-effective 3D in-situ stress estimation method using the obtained elastic parameters and fracture compliance. Finally, field examples from the Zhaotong area, China, demonstrate that the estimated fracture density and anisotropic in-situ stress are more accurate and have higher resolution compared with conventional methods. The dominant stress regime in the study area is a strike-slip faulting regime with a governing orientation of northeast–southwest and presents good alignments with well logs, which demonstrates the reliability and accuracy of our method for predicting fracture density and anisotropic in-situ stress.

Sensitivity of shear wave splitting to fracture connectivity

SUMMARY Shear wave splitting (SWS) is currently considered to be the most robust seismic attribute to characterize fractures in geological formations. Despite its importance, the influence of fluid pressure communication between connected fractures on SWS remains largely unexplored. Using a 3-D numerical upscaling procedure based on the theory of poroelasticity, we show that fracture connectivity has a significant impact on SWS magnitude and can produce a 90° rotation in the polarization of the fast quasi-shear wave. The simulations also indicate that SWS can become insensitive to the type of fluid located within connected fractures. These effects are due to changes of fracture compliance in response to wave-induced fluid pressure diffusion. Our results improve the understanding of SWS in fractured formations and have important implications for the detection and monitoring of fracture connectivity in hydrocarbon and geothermal reservoirs as well as for the use of SWS as a forecasting tool for earthquakes and volcanic eruptions.

Wave reflection and transmission coefficients for layered transversely isotropic media with vertical symmetry axis under initial stress

SUMMARYThe stress-dependent wave reflection and transmission (R/T) coefficients for the layered transversely isotropic media with a vertical symmetry axis (VTI) are seldom investigated in the published literature. To fill this gap, we propose the exact formulas for the plane wave R/T coefficients on the welded and non-welded boundaries between two distinct VTI half-spaces under the effect of initial stress. The theory of acoustoelasticity is used to describe the influence of initial applied stress on the overall elastic properties of VTI media and to represent two different boundary conditions. The normal and tangential compliances are used to characterize the discontinuity of non-welded boundary based on the linear-slip model, and their stress dependences are ideally considered according to the effect of stress on fracture aperture. Then the plane-wave displacement equations are substituted into the boundary conditions to yield the analytic formulas for frequency-independent R/T coefficients for the welded interface and frequency-dependent R/T coefficients for the non-welded interface. The stress-dependent wave slowness vector and polarization vector embedded in R/T coefficients can be directly computed with the Christoffel equation given by the acoustoelastic equation. Modelling results graphically show the effects of initial stress on the angle-dependent wave velocities, Thomsen elastic anisotropy parameters, fracture compliances, the R/T coefficients and seismic reflection responses for welded and non-welded interfaces in detail. The R/T coefficients are more sensitive to initial stress at relatively large incidence angles for the designed two-layer model with welded or non-welded boundary. The proposed R/T coefficient formulas and modelling results are relevant to in situ stress detection, fracture characterization, and exploration for oil and gas in shale reservoirs in high-stress fields.

The hydromechanical behavior of opalinus clay fractures: Combining roughness measurements with computer simulations

The role of surface roughness of fractures in Opalinus Clay and in rocks in general is relevant in understanding the hydromechanical behavior of fractures. Two different fracture surfaces of shear fractures in the Opalinus Clay were investigated. The fracture surfaces were characterized based on their roughness power spectrum. It was found that slickensides fracture surfaces are near fractal-like up to the longest scale with a fractal dimension Df ∼ 2.1 and in the absence of a roll-off region at long wavelengths. In contrast, the glassy fracture surfaces show a roll-off region, which is characteristic of a flat surface with rather small and local topographic height variations. The glassy fracture surface is near fractal like with Df ∼ 2.0. The measured roughness power spectra were used to create fracture models to study the behavior of different fracture closure mechanism: 1) increasing congruence (matedness), 2) closure by compression and 3) closure by swelling. It turned out that the relationship between permeability and mean aperture depends on the fracture closure mechanism. Concerning closure by compression, the root mean square (rms) value of the aperture (aper) distribution aperrms influences the contact formation behavior, which in turn controls the hydromechanical properties. The lower aperrms is, the lower the fracture compliance. Apart from aperrms, the simulations show that in clay rocks, plastic deformation plays an important role in the closure of fractures by compression. In agreement with the experiments, the simulations predict that the permeability falls below 10% of the initial value at a compressive stress of 5 MPa. The simulations predict that fracture closure by swelling is rather ineffective for confining pressures exceeding ∼1 MPa.

Mechanical Compliance of Individual Fractures in a Heterogeneous Rock Mass From Production‐Type Full‐Waveform Sonic Data

AbstractThe mechanical fracture compliance is of interest in a number of geoscientific applications. Seismic borehole methods, especially full‐waveform sonic (FWS) data, have indicated their potential to infer the compliance of macroscopic fractures under in situ conditions. These approaches rely on the assumption of a homogeneous background embedding the fractures and, as of yet, compliance estimates for individual fractures are limited to static FWS measurements. In this work, we assess the potential of inferring the compliance of individual fractures from standard, production‐type FWS data in the presence of background heterogeneity. We first perform a comparative test on synthetic data to evaluate three approaches known as the transmission, phase, and group time delay methods. The results indicate that the former two produce adequate compliance estimates for scenarios with a strongly heterogeneous background or a damage zone around the fracture. These two methods are then applied to two FWS data sets acquired before and after a hydraulic stimulation campaign in a crystalline rock, which allows to test them on natural and man‐made fractures. The transmission method turned out to be unsuitable for the considered data due to its reliance on amplitudes. Conversely, the travel time behavior remained stable and the phase time delay method produced robust and consistent estimates. The results for a newly created hydro‐fracture imply the capability of resolving remarkably small compliance values of the order of 10−14 m/Pa. This estimate is one order‐of‐magnitude smaller than that for the natural fracture, which may help to distinguish between these two fracture types.

Estimating the Least Principal Stress in a Granitic Rock Mass: Systematic Mini-Frac Tests and Elaborated Pressure Transient Analysis.

The hydraulic fracturing technique (also termed mini-frac test) is commonly used to estimate the in situ stress field. We recently conducted a mini-frac stress measurement campaign in the newly-established Bedretto Underground Laboratory (BedrettoLab) in the Swiss Alps. Four vertical boreholes, dedicated for stress characterization of the granitic rock mass, hosted a total of 19 mini-frac test intervals. Systematic pressure transient analysis was performed to carefully estimate the magnitude of the least principal stress (S_mathrm {3}). We compared five different methods (inflection point, bilinear pressure decay rate, tangent, fracture compliance, and jacking pressure) to identify an adequate approach best suited for our test scale and the host rock mass. We found that the methods used to determine the fracture closure pressure underestimate the magnitude of S_mathrm {3}, presumably due to the rapid closure of the hydraulic fracture after shut-in. The most consistent results were found using the inflection point and bilinear pressure decay rate method, which both determine the (instantaneous) shut-in pressure as the proxy for the S_mathrm {3} magnitude. The determined shut-in pressure, or S_mathrm {3} magnitude, is 14.6pm 1.4 MPa from the inflection point method. This allowed us to further estimate the stress environment around the BedrettoLab, which is transitional between normal and strike-slip faulting. The measured local pore pressures from extended shut-in periods are between 2.0 and 5.6 MPa, significantly below hydrostatic. A combination of drainage, cooling, and the excavation damage zone of the tunnel may have significantly perturbed the in situ stress field in the vicinity of the BedrettoLab.

Guest Editorial: Want To Learn Something New About DFITs? Start With an Old Book

Early in the development of unconventional reservoirs, the industry had little choice but to rely on the toolsets handed down from decades of conventional engineering practices. Later, new tools would be crafted in the hopes of better fitting the unconventional paradigm. This presents a choice to the technical community—rely on a traditional and proven method, or one designed for the unconventional system but less tested? Recently, many hydraulic fracturing engineers have been asking themselves this question when it comes to the diagnostic fracture injection test (DFIT). That includes myself, and the journey I took to find an answer culminated in a technical paper (SPE 206239) that was presented at the 2021 SPE Annual Technical Conference and Exhibition. What follows are some of that paper’s key findings which are being shared with the intent to further the discussion on best practices for those challenged with interpreting unconventional diagnostics. The paper utilizes the concept of permeability to validate traditional minimum stress interpretations across multiple reservoir conditions by comparing DFIT fracture closure time permeability estimates with core, pressure buildup, after-closure pressure, and rate transient analysis. This author was able to further support the results by the integration of a wide range of diagnostic technologies such as fiber optics, microseismic, and, among others, DFIT numerical inversions shared through eight case histories. Diagnostic Injections, a Long History Made Short One of the few ways to begin a conversation with a reservoir is by pumping treated fluid at fracturing rates and analyzing how the pressure falls off with time after the injection is stopped. The language for such dialogue and information exchange is formed by the dimensionless time function called “G-function” and was introduced by Ken Nolte in 1979. Nolte’s innovative postulations allowed our industry to determine the expected frac geometry, its conductivity, the formation flow capacity, and the optimum hydraulic fracture design as well as the means necessary to place the treatment. Recently introduced into industry literature is the proposed fracture closure pressure interpretation based on the fracture compliance method, interpreting an earlier, higher-stress estimation than estimates from well‑established methodologies. The practitioner is now faced with the dilemma of finding out which fracture closure interpretation technique is correct since this has a profound impact on how fracture geometry is modeled and optimized. To answer this question, a multibasin analysis of pre-frac tests from the Russia, North Sea, Europe, North Africa, and South America regions was undertaken.

3D seismic characterization of fractures using elastic P-to-S double beams

Knowledge of the spatial distribution of subsurface fractures is critical for improving the production of geothermal and oil/gas. The double-beam (DB) method using acoustic waves is capable of characterizing the irregularly distributed fractures, including multiple coexisting fracture sets. We have extended the DB method to elastic waves, in particular for P-to-S waves scattered by fractures, using 3C seismic data. This elastic double-beam (EDB) method can add additional information to cross-validate the DB images of P-P waves and increase our confidence in the final fracture characterization results. To test the EDB method, we use a 3D layered reservoir model with multiple nonorthogonal coexisting fracture sets, which captures a wide range of geologic scenarios. Based on this model, we model 3C data using an elastic full-wave finite-difference method. For each subsurface target, the EDB method outputs DB images of P-P, P-Sin, and P-Santi waves, where Sin and Santi represent the in-plane (polarized perpendicular to the fracture plane strike) and antiplane (polarized parallel to the fracture plane strike) scattered vector S-waves, respectively. Numerical results indicate that EDB is a reliable tool to detect fracture distribution using the self-verification feature. In other words, P-P, P-Sin, and P-Santi should all give the same fracture parameters for truly existing fractures. Using EDB, the existence and orientation of fractures are more reliably estimated than fracture compliance for irregular fracture sets. EDB is not sensitive to random noise in data up to high noise levels. EDB can work accurately when velocity models have mild deviations from the true models. The EDB amplitude is large where fractures are dense or the compliance value is large, or both; these can be important in the interpretation of the fluid transport properties of a reservoir.

Laboratory Measurements of the Impact of Fracture and Fluid Properties on the Propagation of Krauklis Waves

AbstractThe Krauklis wave is a slow dispersive wave, generated in fluid‐filled fractures. By analyzing the resonant frequency and quality factor of the Krauklis wave, the fracture dimension and fluid properties can be estimated. However, the accuracy of the estimation of fracture dimension and fluid properties depends on deciphering factors affecting the Krauklis wave such as fluid viscosity, fracture geometry, fracture compliance, and stiffness ratio, some of which have not been experimentally studied yet. We have developed an experimental apparatus to study the Krauklis wave within a trilayer model consisting of a pair of aluminum plates and a mediating viscous fluid layer. We utilize a piezoelectric source and miniature pressure transducers in our measurements. To evaluating the effects of the fracture aperture and fluid viscosity, we examine the impact of complex and realistic fracture geometry by introducing spatially varying aperture, surface roughness, and compliant partial surface contact provided by springs. The phase velocity, resonant frequencies, and quality factors (a) increase with the expansion of fracture aperture and (b) decrease with the increase of the fluid viscosity. Additionally, (c) phase velocity, resonant frequencies, and attenuation decrease with the increase of mechanical compliance. Furthermore, rough and wedge‐shaped fracture surfaces tend to slow down the Krauklis wave. Since the Krauklis wave is used by different disciplines such as volcanology, glaciology, and the petroleum industry to characterize fracture dimensions and properties of the fluids involved, our experimental findings can be used as a benchmark to develop comprehensive theoretical models to better interpret the Krauklis waves.

Full waveform inversion in fractured media based on velocity–stress wave equations in the time domain

SUMMARY In the process of seismic wave propagation, the presence of fractures will cause a seismic wave response associated with fracture compliance. Full waveform inversion (FWI) is an effective way to quantitatively obtain fracture compliance values, which can simulate seismic wave propagation in a fractured medium and compute the gradient expression of the fracture compliance parameters. To obtain the fracture compliance parameters quantitatively, a new technique based on FWI needs to be proposed. Based on linear slip theory, a new finite-difference scheme using a rotated grid has been developed to simulate the propagation of seismic waves in fractured media. The corresponding adjoint equation for FWI and the gradient of fracture parameter expression are presented. The crosstalk between normal compliance and tangential compliance is analysed in a homogeneous background medium. Numerical simulations in double-layer media show that the new gradient equation is effective.

Estimates of Individual Fracture Compliances Along Boreholes From Full‐Waveform Sonic Log Data

AbstractAn important seismic attenuation mechanism in fractured environments is related to energy conversion into reflected and transmitted waves at fracture interfaces. Using full‐waveform sonic (FWS) log data, we show that it is possible to quantify transmission losses across a set of fractures from time delays and amplitude differences of the critically refracted P‐wave as compared to intact sections along the borehole. In the presence of fractures, the transmission coefficient associated with a given fracture is obtained by combining information on transmission losses from multiple receivers and source positions into a linear system of equations for all fractures intersecting the borehole. Fracture compliance is computed from the inferred transmission coefficient based on a linear slip model. For validation, we use synthetic FWS log data obtained from numerical simulations of wave propagation in a water‐filled borehole surrounded by low‐permeability rocks with discrete fractures. The methodology is then applied to field data acquired along boreholes penetrating multiple fractures in a granodioritic host rock. We show that our estimations of mechanical compliance are consistent with previously reported values, which were estimated for individual fractures intersecting one of the boreholes with a related method valid only for isolated single fractures. Comparison between our estimates of fracture compliance and transmissivity profiles from previous hydraulic characterizations of the fractures suggests that the proposed method may also allow to locate the most permeable fractures along a borehole, which, in turn, opens the perspective of enhancing the design and effectiveness of subsequent hydraulic testing and fracturing experiments.

Fractures in Low‐Permeability Rocks: Can Poroelastic Effects Associated With Damage Zones Enhance Their Seismic Visibility?

AbstractFluid pressure diffusion (FPD) between a fracture and a porous permeable background can increase the normal compliance of the fracture and, thus, its reflectivity. However, many fractured environments of interest are associated with background rocks that can be regarded as largely impermeable for the the typical frequencies employed in seismic surveys. Nonetheless, there is evidence to suggest that the seemingly ubiquitous presence of damaged zones (DZs) associated with fractures may provide the necessary hydraulic communication between fractures and their immediate surroundings for FPD to occur. Here, we assess the pertinence of this phenomenon. To this end, we consider a 1D elastic‐poroelastic model, which comprises a poroelastic system consisting of a fracture embedded in adjacent DZ layers. This system is enclosed in an impermeable background represented by two elastic half‐spaces. We calculate the frequency‐dependent P‐wave reflectivity at normal incidence at the background‐DZ interface for different permeabilities, thicknesses, and porosities of the DZ. We also evaluate the corresponding normal fracture compliance. Our results show that, when accounting for the presence of a DZ surrounding an individual fracture, FPD effects between these regions induce a higher seismic reflectivity and a higher normal compliance compared to that of a hydraulically isolated fracture. This, in turn, implies that, even in largely impermeable environments, the seismic visibility of fractures can be enhanced through FPD enabled by the presence of DZs.

Estimation of weak anisotropy parameters and fracture density of asymmetric fractures in monoclinic medium

Abstract One of the typical anisotropic media is the monoclinic anisotropy (MA) medium, which is formed by embedding two sets of non-orthogonal fracture sets into an isotropic or vertical transverse isotropic (VTI) background medium. Weak anisotropy (WA) parameters and fracture density provide important in situ stress and high-porosity zone information. Estimation of WA parameters and fracture density of MA medium by prestack seismic amplitude inversion is important for shale reservoir characterisation. We derive the expression of generalised WA parameters in a basic reflection coefficients formula of MA medium by incorporating a stiffness matrix of VTI background and disturbance compliance matrix of asymmetric fracture. We then re-express the P-wave reflection coefficients in terms of WA parameters and fracture compliance tensors. To achieve the direct inversion of fracture density, we rewrite the linearised expression of P-wave reflection coefficients related to WA parameters and fracture density. Finally, under the Bayesian framework, the WA parameters and fracture density are estimated by using the amplitude versus offset and azimuth (AVOA) inversion parameters. We use a Monte Carlo simulation to test the effect of uncertainties in the priori information about fracture property parameters. The application of synthetic seismic gathers show that the proposed inversion strategy is reliable within moderate noise. Compared with the results obtained by using inversion based on a rotationally invariant fracture, the test indicates that a fracture model with a simplified shape or wrong assumption will increase calculation error and reduce the inversion accuracy.