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Fractures are ubiquitous through out the Earth's upper crust and dominate the mechanical and hydraulic properties of the affected rock masses. Indeed, open fractures act as fluid conduits and, commonly, flow is controlled by larger fractures, which are, in turn, likely to be connected to smaller ones. Therefore, fracture characterization is of paramount importance for many pertinent applications, such as geothermal energy production, CO2 sequestration, nuclear waste storage, and hydrocarbon exploration. Seismic reflection methods are useful tools for fracture characterization due to the generally high reflectivity that large fractures exhibit as a consequence of their strong mechanical contrast with the embedding intact background. The magnitude of this mechanical contrast is known to be strongly affected by fracture-to-background wave-induced fluid pressure diffusion (FPD). Conversely, the FPD effects associated with secondary connected fractures remain so far unexplored. We investigate the influence of FPD on the normal compliance and on the vertical incidence PP reflectivity of a large fracture that is hydraulically connected to smaller fractures. To this end, we use several models that consist of an infinite horizontal main fracture connected to multiple vertical secondary fractures of finite length. This fracture system is embedded in impermeable background. The individual models differ only with regard to the geometrical (e.g., length and aperture), and physical properties (e.g., permeability and bulk modulus) of the secondary fractures. For comparison, we also calculate the normal compliance and the reflectivity of an isolated infinite horizontal fracture. To assess the changes of fracture compliance due to FPD, we perform a vertical compressional oscillatory test over samples of the aforementioned models that include part of the fracture system and the embedding background. This test simulates the FPD effects that a vertically propagating P-wave generates between the main and secondary fractures. Specifically, the wave produces a pressure increase in the horizontal fracture that equilibrates as fluid flows into the secondary vertical fractures. Based on this oscillatory test, we compute the average of the vertical components of strain and stress over the main fracture, which we use to estimate its normal compliance. We then proceed to calculate the PP reflectivity at normal incidence using its inferred P-wave modulus. Our results show that both the compliance and the PP reflectivity of the main fracture increase as much as two-orders of magnitude in response to the presence of secondary fractures. We also find that the physical and geometrical properties of the secondary connected fractures have an influence on the normal compliance and reflectivity of the main fracture.

The generalized finite-element method (GFEM) has been applied frequently to solve harmonic wave equations, but its use in the simulation of transient wave propagation is still limited. We have applied GFEM for the simulation of the acoustic wave equation in models relevant to exploration seismology. We also perform an assessment of its accuracy and efficiency. The main advantage of GFEM is that it provides an enhanced solution accuracy compared to the standard finite-element method (FEM). This is attained by adding user-defined enrichment functions to standard FEM approximations. For the acoustic wave equation, we consider plane waves oriented in different directions as the enrichments, whose argument includes the largest wavenumber of the wavefield. We combine GFEM with an unconditionally stable time integration scheme with a constant time step. To assess the accuracy and efficiency of GFEM, we compare the GFEM simulation results against those obtained with the spectral-element method (SEM). We use SEM because it is the method of choice for wave propagation simulation due to its proven accuracy and efficiency. In the numerical examples, we first perform a convergence study in space and time, evaluating the accuracy of both methods against a semianalytical solution. Then, we consider simulations of relevant models in exploration seismology that include low-velocity features, an inclusion with a complex geometric boundary and topography. Results using these models indicate that GFEM presents comparable accuracy and efficiency to those based on SEM. For the given examples, the GFEM efficiency stems from the combined effect of local mesh refinement, nonconforming or unstructured, and the unconditionally stable time integration scheme with a constant time step. Moreover, these features provide great flexibility to the GFEM implementations, proving advantageous when using, for example, unstructured grids that impose severe time step size restrictions in SEM.

The substitution of a heterogeneous poroelastic medium by its homogenized viscoelastic representation is an effective technique to study its seismic response. This homogenization procedure reproduces the dispersive behaviour of the original fast P- and S-waves. This dispersive nature results from energy dissipation that occurs when a wave induces pressure gradients between the heterogenous parts of a poroelastic medium that are equilibrated by fluid exchange. The underlying homogenization approach is to apply oscillatory tests on a representative elementary volume (REV) of the poroelastic medium to find the equivalent moduli. The REV is a sample that is typical of the entire medium under consideration and that ensures results independent of boundary conditions. This is, the REV should be larger than the heterogeneities but much smaller than the medium size. Additionally, in poroelastodynamics, the size of the heterogeneities in the REV is dictated by the scale at which the wave-induced fluid exchange takes place. We focus on the mesoscale. At this scale, fluid exchange occurs between heterogeneities that are larger than the grain size but smaller than the wavelength. However, there are poroelastic media of interest that present heterogeneities of comparable size to that of the domain. Here, the REV concept does no longer apply since the poroelastic sample under examination is affected by the boundaries of the domain. For such scenarios, we propose a novel homogenization method that incorporates the boundary effects produced by the surrounding medium. In this method, we take a sample that consist of the affected poroelastic heterogeneity together with part of the embedding medium. Then, we perform the classical oscillatory tests over this ensemble. Finally, to obtain the homogenized moduli of the poroelastic medium, we perform the averaging of strain and stress only over this domain of interest. As examples, we present a poroelastic system of a single sand layer saturated with gas at the top and water at the bottom that is embedded in impermeable background. We also study a water-saturated poroelastic set consisting of a permeable fracture surrounded by a less permeable damage zone that is also embedded in impermeable background. We idealize these cases as 2D media, assuming that the poroelastic system is infinite along the layering plane but bounded perpendicular to it by impermeable half-spaces. The samples subjected to oscillatory tests consist of a piece of the semi-infinite poroelastic domain together with the corresponding bounding half-spaces. To test the viability and accuracy of the method, we compare reflectivities at the top interface of the half-space and homogenized medium against those obtained at the top interface of the half-space and the original poroelastic system. Results show that errors are of the order of 1 %. The proposed method can be readily extended to 3D and more complex models.

The presence of fractures has a predominant influence on the hydraulic and mechanical behavior of rocks. These effects are particularly pronounced and relevant for otherwise largely impermeable and stiff formations. There is widespread evidence pointing to the ubiquitous presence of damaged zones surrounding fractures and faults. The enhanced permeability associated with these zones can promote fluid pressure diffusion in the vicinity of fractures when seismic waves travel through the corresponding subsurface volume. This process, together with the inherent mechanical weakness of damaged zones, is expected to affect the seismic reflectivity of fractures and faults. We investigate these effects based on Biot’s theory of poroelasticity. To this end, we consider a 1D layered representation of the fracture and the associated damaged zone in conjunction with embedding elastic and impermeable half-spaces. We compare a fully elastic fracture-background reference model with a model consisting of a poroelastic fracture and damaged zone enclosed within an elastic background. For these two models, we compute the normal incidence seismic P-wave reflectivities at the background-fracture and at background-damaged zone interfaces, respectively. We also include a model that represents the fracture-damaged zone poroelastic system as an equivalent viscoelastic layer. We aim to test the validity of this representation since it would imply that a similar correspondence is possible to establish when more realistic descriptions of the damaged zone are considered. For this additional model, the viscoelastic layer is characterized by its frequency-dependent P-wave modulus, estimated by applying White’s classical upscaling procedure for 1D poroelastic media composed of alternating layers. We test the validity of the elastic-viscolastic model by comparing its reflectivity against the corresponding results from the elastic-poroelastic model. In doing so, we find that the simplified elastic-viscoelastic model faithfully reproduces the reflectivity of its elastic-poroelastic counterpart up to a threshold frequency, at which resonances produced within the viscoelastic layer become dominant. Overall, our results show that, in the seismic frequency range, there is a substantial increase in seismic fracture reflectivity resulting from the combined effects of fluid pressure diffusion and mechanical weakening associated with the surrounding damaged zone. This, in turn, indicates that the seismic reflectivity of a fracture may indeed be dominated by the thickness and physical properties of its surrounding damaged zone rather than by the properties of the fracture sensu stricto.

Hydraulic fracture treatments may induce complex network geometries that are challenging to incorporate in numerical flow simulators. To capture this complexity, we propose a workflow that integrates a semi-stochastic Discrete Fracture Network (DFN) generator constrained by Microseismic events and core data and an efficient Perpendicular Bisector (PEBI) grid generator for the explicit discretization of the network. We applied this workflow to evaluate the effect of DFN related uncertainties on production performance. We developed a DFN model that constrains the location of natural fractures by microseismic events and samples fracture characteristics from core-data-based Probability Density Functions (PDFs). The model also interconnects natural and hydraulic fractures through a geomechanics-based algorithm. For an efficient fracture discretization, we developed a PEBI meshing technique capable to conform to low-angle intersections of extensively clustered network, incorporating optimization algorithms that reduce highly skewed cells, and ensure good mesh quality. Finally, to evaluate the impact of DFN related uncertainties on production, we implemented an efficient Monte Carlo (MC) methodology that minimizes flow simulations. Our integrated workflow provides a methodology to efficiently model and mesh explicitly complex DFN systems for numerical fluid simulations, incorporating microseismic and core data. Furthermore, this methodology, together with the implementation of an efficient MC technique, allows to evaluate quantitatively the impact on production forecast of DFN related uncertainties, which come from the inherent randomness of the DFN modeling and the lack of accurate knowledge of PDF parameters due to incomplete fracture characterization.

Horizontal drilling and hydraulic fracturing produce Unconventional Liquid Reservoirs (ULRs) economically. One of the characteristics of the ULRs is high production declining rate, and thus enhanced oil recovery techniques such as Huff-n-Puff will ensue. In addition, the existence of complex fracture network has been proven by both field and simulation work. This study investigated the potential of CO 2 huff-n-puff in ULRs with complex fracture networks. Two fracture characterization techniques for complex fracture network such as fractal-based, and microseismic-based were applied to reduce uncertainties of fracture networks and thus improve the accuracy of simulation input. In order to study complex CO 2 recovery mechanism, lab-measured data was upscaled to the field-scale, and then used for evaluating production performance of a simple fracture network. Detailed sensitivity analysis showed that diffusion in the field scale is negligible compared with other recovery mechanisms such as oil swelling, gas expansion, viscosity reduction, etc. The following comparison between dual continuum and the explicit fracture modeling approaches highlights the importance of heterogeneity due to the explicit fractures. Dual continuum models yields less accurate pressure behavior than explicit discrete fracture models even though production behavior could be history matched.

Hydraulic fracturing is a common stimulation technique in unconventional reservoirs to create fractures systems and allow hydrocarbon production. Proppant (granular material) is normally injected during hydraulic fracturing to keep open the fracture network and enhance hydrocarbon production performance. Proppant has a strong influence on fracture compliance and therefore will affect the characteristics of the generated seismic wavefield. To account for the effect of proppant in fracture compliance, we have developed new analytical formulations to obtain normal and tangential compliance for the case of dry and fluid-saturated fractures. We derive these expressions based on Hertz-Mindlin contact theory. Results from the compliance sensitivity analyses provide insights into the effects of proppant distribution and mechanical properties on fracture compliance. We also applied the innovative generalized multiscale finite-element method (GMsFEM) to simulate wave propagation through discrete hydraulic fractures filled with proppant. The GMsFEM approach represents individual fractures on a finely discretized mesh; this fine mesh is used to capture fracture properties by generating quantities (basis functions) that are used for modeling wave propagation on a much coarser grid. This methodology reduces the size of the computational problem, allowing faster results. Simulation results indicate the changes of the scattered wavefield as the proppant placement varies in different parts of the fractures and as the number of fracture stages increases.

Hydraulic fracture treatments may induce complex network geometries that are challenging to incorporate in numerical flow simulators. To capture this complexity, we propose a workflow that integrates a semi-stochastic Discrete Fracture Network (DFN) generator constrained by Microseismic events, core data and an efficient Perpendicular Bisector (PEBI) grid generator for the explicit discretization of the network. We applied this workflow to evaluate the effect of DFN related uncertainties on production performance. We developed a DFN model that constrains the location of natural fractures by microseismic events and samples fracture characteristics from core-data-based Probability Density Functions (PDFs). The model also interconnects natural and hydraulic fractures through a geomechanics-based algorithm. For an efficient fracture discretization, we developed a PEBI meshing technique capable to conform to low-angle intersections of extensively clustered network, incorporating optimization algorithms that reduce highly skewed cells, and ensure good mesh quality. Finally, to evaluate the impact of DFN related uncertainties on production, we implemented an efficient Monte Carlo (MC) methodology that minimizes flow simulations. We implemented the workflow in a stage of a hydraulic fracture treatment to evaluate the impact of two type of DFN related uncertainties on production: those coming from the randomness of DFN modeling and those coming from the lack of accurate knowledge of PDF parameters. We show that the proposed DFN modeling approach can be applied to calculate the "Fluid-Producing DFN (FP-DFN)," which is the network area connected to the well and able to produce, to minimize flow simulations for the MC runs. After performing efficient-based MC simulations with our DFN model, we were able to generate the FP-DFN Cumulative Density Function (CDF) incorporating the aforementioned uncertainties. From this CDF, different percentiles were selected with the respective DFN realizations for fluid simulations. We show that the developed PEBI meshing algorithm is capable to grid efficiently these complex DFN geometries with good mesh quality. Finally, 20-year production simulations suggest that a difference of several MSTB between the lowest and highest percentiles may exist revealing the effect of the DFN related uncertainties on production. Our integrated workflow provides a methodology to efficiently model and mesh explicitly complex DFN systems for numerical fluid simulations, incorporating microseismic and core data. Furthermore, this methodology, together with the implementation of an efficient MC technique, allows a quantitative evaluation of the impact on production forecast of DFN related uncertainties.