Non-planar Fracture Research Articles

A Comprehensive Model for Investigation of Carbon Dioxide Enhanced Oil Recovery With Nanopore Confinement in the Bakken Tight Oil Reservoir

Summary Carbon dioxide (CO2) injection is an effective enhanced-oil-recovery (EOR) method in unconventional oil reservoirs. However, investigation of the CO2 huff ’n’ puff process in tight oil reservoirs with nanopore confinement is lacking in the petroleum industry. The conventional models need to be modified to consider nanopore confinement in both phase equilibrium and fluid transport. Hence, we develop an efficient model to fill this gap and apply to the field production of the Bakken tight oil reservoir. Complex-fracture geometries are also handled in this model. First, we revised the phase equilibrium calculation and evaluated the fluid properties with nanopore confinement. An excellent agreement between this proposed model and the experimental data is obtained considering nanopore confinement. Afterward, we verified the calculated minimum miscibility pressure (MMP) using this model against the experimental data from a rising-bubble apparatus (RBA). We analyzed the MMP and well performance of CO2 EOR in the Bakken tight oil reservoir. On the basis of the prediction of the field data, the MMP is 450 psi lower than the MMP with bulk fluid when the pore size reduces to 10 nm. Subsequently, we examined the effects of key parameters such as matrix permeability and CO2 molecular diffusion on the CO2 huff ’n’ puff process. Results show that both CO2-diffusion and capillary pressure effects improve the oil recovery factor from tight oil reservoirs, which should be correctly implemented in the simulation model. Finally, we analyzed well performance of a field-scale horizontal well from the Bakken Formation with nonplanar fractures and natural fractures. Contributions of CO2-diffusion and capillary pressure effects are also examined in depth in field scale with complex-fracture geometries. The oil recovery factor of the CO2 huff ’n’ puff process with both CO2-diffusion and capillary pressure effects increases by as much as 5.1% in the 20-year period compared with the case without these factors. This work efficiently analyzes the CO2 huff ’n’ puff process with complex-fracture geometries considering CO2 diffusion and nanopore confinement in the field production from the Bakken tight oil reservoir. This model can provide a strong basis for accurately predicting the long-term production with complex-fracture geometries in tight oil reservoirs.

Laboratory investigation of shale rock to identify fracture propagation in vertical direction to bedding

Affected by beddings and natural fractures, fracture geometry in the vertical plane is complex in shale formation, which differs from a simple fracture in homogeneous sandstone reservoirs. However, the propagation mechanism of a hydraulic fracture in the vertical plane has not been well understood. In this paper, a true tri-axial pressure machine was deployed for shale horizontal well fracturing simulation experiments of shale outcrops. The effects of multiple factors on hydraulic fracture vertical propagation were studied. The results revealed that hydraulic fracture initiation and propagation displayed four basic patterns in the vertical plane of laminated shale formation. A hydraulic fracture would cross the beddings under the high vertical stress difference between a vertical stress and horizontal minimum stress of 12 MPa, while a hydraulic fracture propagates along the beddings under a low vertical stress difference of 3 MPa. Four kinds of fracture geometry, including a single main fracture, a nonplanar fracture, a complex fracture, and a complex fracture network, were observed due to the combined effects of flow rate and viscosity. Due to the influence of binding strength (or cementing strength) on the fracture communication effects between a hydraulic fracture and the beddings, the opening region of the beddings takes the shape of an ellipse.

Strategies for Effective Stimulation of Multiple Perforation Clusters in Horizontal Wells

Summary Increasing the efficiency of completions in horizontal wells is an important concern in the oil and gas industry. To decrease the number of fracturing stages per well, it is common practice to use multiple clusters per stage. This is done with the hope that most of the clusters in the stage will be effectively stimulated. Diagnostic evidence, however, suggests that in many cases, only one or two out of four or five clusters in a stage are effectively stimulated. In this paper, strategies to maximize the number of effectively stimulated perforation clusters are discussed. A fully 3D poroelastic model that simulates the propagation of nonplanar fractures in heterogeneous media is developed and used to model the propagation of multiple competing fractures. A parametric study is first conducted to demonstrate how important fracture-design variables, such as limited-entry perforations and cluster spacing, and formation parameters, such as permeability and lateral and vertical heterogeneity, affect the growth of competing fractures. The effect of stress shadowing caused by both mechanical and poroelastic effects is accounted for. 3D numerical simulations have been performed to show the effect of some operational and reservoir parameters on simultaneous-competitive-fracture propagation. It was found that an increase in stage spacing decreases the stress interference between propagating fractures and increases the number of propagating fractures in a stage. It was also found that an increase in reservoir permeability can decrease the stress interference between propagating fractures because of poroelastic-stress changes. A modest (approximately 25%) variability in reservoir mechanical properties along the wellbore is shown to be enough to alter the number of fractures created in a hydraulic-fracturing stage and mask the effects of stress shadowing. Interstage fracture simulations show post-shut-in fracture extension induced by stress interference from adjacent propagating fractures. The effect of poroelasticity is highlighted for infill-well-fracture design, and preferential fracture propagation toward depleted regions is clearly observed in multiwell-pad-fracture simulations. The results in this paper attempt to provide practitioners with a better understanding of multicluster-fracturing dynamics. On the basis of these findings, recommendations are made on how best to design fracture treatments that will lead to the successful placement of fluid and proppant in a single fracture, and result in a set of fractures that are competing for growth. The ability to successfully stimulate all perforation clusters is shown to be a function of key fracture-design parameters.

Numerical simulation of simultaneous multiple fractures initiation in unconventional reservoirs through injection control of horizontal well

Simultaneous fracturing stimulations in horizontal well are effective tools for promoting productivity of unconventional reservoirs. However, fracture lengths and widths of some perforation clusters may be restricted due to the stress shadow effects. In this paper, a numerical model to simulate nonplanar fractures simultaneous initiation in porous media is established based on the extended finite element method (XFEM). The amount of fluid flowing into each fracture is dynamically calculated with a total injection volume in this model. Sensitivity studies of formation parameters on fractures geometry of simultaneous fracturing are presented. The in-situ stress contrast is found to be the main factor controlling the fractures propagation. The initiation of interior fracture will be restricted or compressed to be closed in the vicinity of the injection point. The influence of injection rate and perforation friction on fractures initiation is investigated. Strategies to optimize fractures geometry are presented through injection control of each fracture. The method presented in this paper can be used in horizontal well design to achieve reasonable fractures geometry.

Productivity of multiple fractures in a closed rectangular reservoir

It is found that hydraulic fractures always exhibit complex geometry patterns by direct observation on fractured cores, geological evidence and laboratory experiments. The main objectives of this paper are to propose a new uniform-flux solution and analyze the productivity index of the complex fractures in a closed rectangular reservoir.Firstly, we present mathematical models of productivity index for single wing and complex fractures with the principle of superposition based on the new uniform-flux solution with angle β in a closed rectangular reservoir, respectively. Secondly, 3 cases have been used to verify uniform-flux solution and productivity index for a finite-conductivity fracture. It is demonstrated that results from our new method match other solutions very well. Thirdly, the new semi-analytical method is employed to obtain the productivity index for other complex fracture patterns, including asymmetric fracture, non-planar fracture and multi-wing fractures connected to a vertical well or a horizontal well. The effects of the asymmetry, the distribution, the rotation, the number, the azimuth, the penetration ratio and the conductivity of the fractures on the productivity index have been discussed in details. It is shown that the symmetric, evenly-distribution and multi-wing fractures with a high penetration ratio lead to high productivity index for a vertically fractured well. The productivity index of a horizontal well is high when the wings with equal reservoir lay perpendicularly to the well. The effect of the rotation of the fracture can be negligible for both vertical well and horizontal well if the distributions of fractures and the location of the wellbore are fixed in a square reservoir.In addition, the wing model is very flexible and general in the sense that it has not only the ability to generate complex-fracture models but also can be easily incorporated into the effect of non-Darcy flow model.

NanoSIMS study of seismically deformed zircon: Evidence of Y, Yb, Ce, and P redistribution and resetting of radiogenic Pb

Lattice defects in zircon can cause trace elements redistribution and disturbance of isotopic systems. This study investigates in detail how seismically induced deformation microstructures in zircon correlate with trace element and isotope re-equilibration. Felsic mylonites with pseudotachylyte veins from the Ivrea-Verbano Zone in Northern Italy were studied with special focus on deformed zircon. We have revealed the following post-growth deformation microstructures: planar deformation bands (PDBs), planar fractures (PFs), non-planar fractures (both healed and open), and finite strain patterns. PDBs are planar portions of crystal lattice that are strictly parallel to {100} crystallographic planes, and are rotated to up to 3° with respect to the host grain. They are from 0.5 to 1 μm wide and have average spacing of 5 μm. PDBs originate in seismically active environment at elevated differential stress, strain rate and temperature. Several grains, in which PDBs are observed, were analyzed with ion microprobe. Ion maps indicate redistribution of radiogenic Pb isotopes associated with PDB formation. Isotopic redistribution preferably occurs in PDBs with larger crystallographic misorientation. Profiling demonstrated clear spatial correlation of PDBs with variations of REE abundances (both gain and loss), and possible correlations with increased and decreased Hf, Ti, and P abundances. Trace elements can be depleted or enriched (compared to the abundance in surrounding matrix) in deformed domains, depending on the spacing of PDBs and the proximity of the analyzed volume to grain boundary or to detrital core. 207 Pb/ 206 Pb ratio demonstrates systematic Pb-loss in the PDB-bearing lattice domains with respect to PDB-free domains; in some cases Pb-gain is observed, where the PDBs source radiogenic Pb from older detrital cores. Our study has important implications for geochronology and microchemistry of zircon from seismically deformed sections of Ivrea-Verbano Zone and from other paleo-seismic zones of the world. Zircon found in seismically deformed rocks near pseudotachylyte veins may demonstrate distorted and even reset isotopic ages, and altered trace element abundances. Enhanced trace element exchange between deformed zircon and host mylonite can influence mass-balance calculations for the bulk rock.

A Comprehensive Model for Simulation of Gas Transport in Shale Formation With Complex Hydraulic-Fracture Geometry

Summary A comprehensive model for simulating gas transport in shale formation with complex fracture geometry is still lacking in the petroleum industry. First, the current models are challenging to efficiently handle the complex nonplanar fractures with varying fracture width and fracture permeability along fracture length caused by very-complicated gridding issues, a high computational cost, and complexities in development of computational codes. Second, the conventional gas-diffusivity equation needs to be revised to include all important gas-transport mechanisms such as gas slippage, gas diffusion, and gas desorption. Hence, the goal of this study was to develop a new model to fill this gap. We present an efficient semianalytical model by dividing fractures into several fracture segments to represent the complex nonplanar-fracture geometry and present a revised diffusivity equation to consider all the important gas-transport mechanisms for shale-gas reservoirs. We verified this model against a numerical reservoir simulator and an analytical solution for a single planar fracture. Transient-flow behavior between planar fractures and nonplanar fractures with and without considering the natural fractures was compared. Furthermore, a well with actual production data from the Marcellus Shale was analyzed. First, we use a complex hydraulic-fracture-propagation model to generate nonplanar-fracture geometry. Then, we apply the fracture geometry in the semianalytical model to evaluate well performance. Contributions of each mechanism to gas recovery are examined. By use of history matching and production forecasting, the difference of cumulative gas production between the nonplanar fractures and the converted planar fractures with equal fracture length is approximately 12% at 30 years of production. In addition, the contribution of gas diffusion, gas slippage, and gas desorption to gas recovery at 30 years of production compared with that without considering them is approximately 11, 16, and 25%, respectively. In total, the contribution of these three important mechanisms is approximately 56%. Hence, modeling of gas production from the nonplanar fractures and modeling the important gas-transport mechanisms in shale-gas reservoirs are significant.

A Comprehensive Model for Real Gas Transport in Shale Formations with Complex Non-planar Fracture Networks.

A complex fracture network is generally generated during the hydraulic fracturing treatment in shale gas reservoirs. Numerous efforts have been made to model the flow behavior of such fracture networks. However, it is still challenging to predict the impacts of various gas transport mechanisms on well performance with arbitrary fracture geometry in a computationally efficient manner. We develop a robust and comprehensive model for real gas transport in shales with complex non-planar fracture network. Contributions of gas transport mechanisms and fracture complexity to well productivity and rate transient behavior are systematically analyzed. The major findings are: simple planar fracture can overestimate gas production than non-planar fracture due to less fracture interference. A “hump” that occurs in the transition period and formation linear flow with a slope less than 1/2 can infer the appearance of natural fractures. The sharpness of the “hump” can indicate the complexity and irregularity of the fracture networks. Gas flow mechanisms can extend the transition flow period. The gas desorption could make the “hump” more profound. The Knudsen diffusion and slippage effect play a dominant role in the later production time. Maximizing the fracture complexity through generating large connected networks is an effective way to increase shale gas production.

Experimental investigation on non-planar fractures mechanisms in hydraulic fracturing

The deflection of initial fractures and the formation of new fractures as non-planar fractures were investigated, which both are possible mechanisms for production improvement in refracturing or SRV(Stimulated reservoir volume). Firstly, initial fractures were formed under initial tri-axial stresses loading. Secondly, the formation and development of new fractures from refracturing were stimulated with changing horizontal stresses. The results show that (1) During refracturing new fractures were formed, and the initial fractures were re-opened, initiated and deflected. Whlie most of the deflection was identified as tensile and shear failure. (2) New fractures do not always result from the stress field change. This implied the smaller horizontal stress difference was, the easier the initial fractures were deflected, and the larger horizontal stress difference was, the easier the new single-wing fractures were formed on the walls of the initial fractures; (3) Deflection of initial fractures was more easier than formation of new fractures. The study indicated that, the injection pressure of deflection was lower than the initial breakdown pressure, while the formation of new fractures required higher pressure than initial breakdown pressure. (4) The injection rate contributed to a significant effect on the formation of new fractures. When injection rate was low, the formation of new fractures on the walls of the initial fractures was difficult. But when injection rate was high, new single-wing fractures formation was easily occurred on the walls of the initial fractures.

Effective Flow Properties for Cells Containing Fractures of Arbitrary Geometry

Summary Hydrocarbon production from unconventional resources such as shale usually entails stimulation by hydraulic fracturing, which results in nonplanar (curved) fractures. However, most reservoir models assume that the induced fractures are planar for the sake of simplicity. Considering the growing interest of the petroleum industry in better understanding production from these resources, we develop a fracture-cell model to capture the effects of fracture nonplanarity on transport properties. To build a realistic reservoir model for a fractured formation, we must account for three types of interactions: matrix-matrix (M-M), matrix-fracture (M-F), and fracture-fracture (F-F). The transport properties of the M-M interaction are based on laboratory measurements. In this study, we analytically determine the transport properties of the two other types of interactions (M-F and F-F). For this purpose, we account for the aperture size and spatial location of the fracture. As a result, we provide effective porosity and effective anisotropic permeabilities for a reservoir cell that contains a fracture inside it. The reservoir cell with transport properties that are modified is a fracture cell. We implement the fracture-cell model in a reservoir simulator and perform analyses for a single fracture and for multiple intersecting fractures; these fractures are nonplanar. The analyses include both single- and multiphase flow models and show that the hydrocarbon pressure inside the reservoir is strongly dependent on the fracture geometry when the matrix permeability is smaller than 1 µd. Thus, it is crucial to model the fracture geometry more accurately in unconventional reservoirs with ultralow permeabilities such as shale. One can easily implement the developed fracture-cell model in reservoir simulators, and there is no local refinement around the fracture. The main advantage of the proposed model is its simplicity, conjoined with its ability to capture the nonplanarity of the fracture. The developed model has major applications for understanding production from formations that are heavily fractured.

A Semianalytical Model for Production Simulation From Nonplanar Hydraulic-Fracture Geometry in Tight Oil Reservoirs

SummaryTwo key technologies such as horizontal drilling and hydraulic fracturing have led to the economic production of unconventional resources such as shale gas and tight oil. In reality, a nonplanar hydraulic-fracture geometry with varying fracture width and fracture permeability is created during the hydraulic-fracturing process. However, it is challenging to simulate well performance from the nonplanar fracture geometry. For the sake of simplicity, the nonplanar fracture geometry is often represented by ideal planar fracture geometry with constant fracture width, which one can easily handle analytically, semianalytically, and numerically. However, such ideal fracture geometry is inadequate to capture the physics of the transient flow behavior of the nonplanar fracture geometry. Although significant efforts were made in recent years to numerically model well performance from the complex fracture geometry, these approaches are still challenging to model the nonplanar fracture geometry with varying width because of a large considerable fracture-gridding issues and an expensive computation cost. In addition, the effect of nonplanar fracture geometry on well productivity and transient flow behavior was not reported in the literature. Hence, a model to handle the nonplanar fracture geometry by considering varying fracture width and fracture permeability is still lacking in the petroleum industry. Zhou et al. (2014) proposed a semianalytical model to handle the complex fracture geometry with constant fracture width. However, the semianalytical model did not consider the effects of stress-dependent fracture conductivity and the nonplanar fracture geometry as well as planar fracture geometry with varying fracture width along the fracture. In this work, we extended the semianalytical model to simulate production from the nonplanar fracture geometry as well as planar fracture geometry with varying width. In addition, the effect of stress-dependent fracture conductivity was implemented in the model. We verified the semianalytical model against a numerical reservoir simulator for single planar fracture with constant width. We performed two case studies. The first case contains a comparison of two planar fractures, one with constant fracture width and another with varying fracture width. In the second study, we compared two fractures with different fracture geometries such as planar fracture geometry and nonplanar fracture geometry, which were generated from the fracture-propagation model. In addition, transient flow regimes were investigated on the basis of a log-log graph of the dimensionless pressure drop and pressure-drop derivative vs. the dimensionless time. This work can provide critical insights into understanding the well performance from tight oil reservoirs with the nonplanar hydraulic-fracture geometry.

From Streamlines to Fast Marching: Rapid Simulation and Performance Assessment of Shale-Gas Reservoirs by Use of Diffusive Time of Flight as a Spatial Coordinate

Summary Current industry practice for characterization and assessment of unconventional reservoirs mostly uses empirical decline-curve analysis or analytic rate- and pressure-transient analysis. High-resolution numerical simulation with local perpendicular bisector (PEBI) grids and global corner-point grids has also been used to examine complex nonplanar fracture geometry, interaction between hydraulic and natural fractures, and implications for the well performance. Although the analytic tools require many simplified assumptions, numerical-simulation techniques are computationally expensive and do not provide the more-geometric understanding derived from the depth-of-investigation (DOI) and drainage-volume calculations. We propose a novel approach for rapid field-scale performance assessment of shale-gas reservoirs. Our proposed approach is dependent on a high-frequency asymptotic solution of the diffusivity equation in heterogeneous reservoirs and serves as a bridge between simplified analytical tools and complex numerical simulation. The high-frequency solution leads to the Eikonal equation (Paris and Hurd 1969), which is solved for a “diffusive time of flight” (DTOF) that governs the propagation of the “pressure front” in the reservoir. The Eikonal equation can be solved by use of the fast-marching method (FMM) to determine the DTOF, which generalizes the concept of DOI to heterogeneous and fractured reservoirs. It provides an efficient means to calculate drainage volume, pressure depletion, and well performance and can be significantly faster than conventional numerical simulation. More importantly, in a manner analogous to streamline simulation, the DTOF can also be used as a spatial coordinate to reduce the 3D diffusivity equation to a 1D equation, leading to a comprehensive simulator for rapid performance prediction of shale-gas reservoirs. The speed and versatility of our proposed method makes it ideally suited for high-resolution reservoir characterization through integration of static and dynamic data. The major advantages of our proposed approach are its simplicity, intuitive appeal, and computational efficiency. We demonstrate the power and utility of our method by use of a field example that involves history matching, uncertainty analysis, and performance assessment of a shale-gas reservoir in east Texas. A sensitivity study is first performed to systematically identify the “heavy hitters” affecting the well performance. This is followed by history matching and an uncertainty analysis to identify the fracture parameters and the stimulated-reservoir volume. A comparison of model predictions with the actual well performance shows that our approach is able to reliably predict the pressure depletion and rate decline.

2D coupled HM-XFEM modeling with cohesive zone model and applications to fluid-driven fracture network

The present work focuses on a new numerical model for the fully coupled hydro-mechanical analysis of groundwater flows through poroelastic saturated media. In particular, the presence and eventual propagation of fluid-driven fractures is accounted for within a non-regularized cohesive zone model. In this paper, the fracture propagation is considered as a reactivation process: the fracture already exists and evolves (i.e. opens or closes) on a pre-defined path initially constrained. The Talon-Curnier constitutive law is considered for the fracture interfaces and its expression has been adapted to the hydro-mechanical coupling related to the fracture evolution. The fluid pressure inside the fracture is governed by the lubrication equation. The momentum-stress balance equations involving fluid flow and deformation of the solid porous matrix are derived within the framework of the generalized Biot theory. The extended finite element method (XFEM) is preferred to a standard finite element spatial discretization in order to easily handle the presence and evolution of discontinuities in the porous medium. A set of four Lagrange multipliers is introduced to prevent spurious oscillations of the numerical solution at the interface. Comparisons between numerical results and theoretical solution assess the validity of the model presented in this paper. In addition, the hydro-mechanical interactions between neighboring fractures and the effects of the permeability of the porous medium are investigated. We also demonstrate the capability of our model to handle non-planar fracture paths.

Optimal spacing of sequential and simultaneous fracturing in horizontal well

Sequential and simultaneous fracturing are two main fracturing methods for creating multiple hydraulic fractures in horizontal wells. The fracture spacing of these two fracturing scenarios is critical for creating fracture network to improve unconventional gas or oil reservoirs production. In this paper, a fully coupled (flow and mechanics) hydraulic fracture propagation model based on extended finite element method (XFEM) is established to account for the sequential and simultaneous propagation of nonplanar fractures. By mapping the distribution of in-situ stress contrast during fracturing process, we calculate the fracture network area that is the extent of low in-situ stress contrast zones. The fracture spacing that satisfies the requirement of preventing sand plug as well as creating large field of fracture network is optimal. Sensitivity studies have been conducted for optimal spacing. It is shown that optimal spacing will decrease with in-situ stress contrast, and is not sensitive to varying Young's modulus of the rock matrix. The method presented in this paper can be used in horizontal well design to estimate reasonable fracture spacing.

Reactivation mechanism of natural fractures by hydraulic fracturing in naturally fractured shale reservoirs

Hydraulic fracturing technique has been commonly used in the development of shale reservoir aiming to produce from complex network of fractures. One of the key parameters that affects the hydraulic fracture complexity is the natural fracture in the shale reservoir. Hydraulic fractures being trapped by natural fractures propagate non-planar fracture in three dimensions. Therefore, conventional hydraulic fracture model cannot include the non-planar characteristics of these fractures. In case a hydraulic fracture crosses a natural fracture, the dependence of the natural fracture reactivation on injection rate remains poorly understood. A non-planar propagation model for hydraulic fracturing in naturally fractured shale reservoirs was developed based on PKN model. A dynamic model was derived to calculate the stress intensity factor for a natural fracture being crossed by a hydraulic fracture based on the theory of rock fracture mechanics. Based on the experimental data from Longmaxi shale reservoir, the fluid pressure threshold to activate the natural fractures was obtained for different approaching angles. The effects of fluid pressure on the propagation angle of natural fracture were discussed. According to different initial injection rates and approaching angles, the time and minimum injection rate were determined to adjust the pump, which can improve the complexity of hydraulic fracture. True tri-axial hydraulic fracturing test with rapidly variable injection rate was conducted on the shale outcrop from Longmaxi formation. Experimental results proved that increasing the injection rate at the right time can reactivate the natural fractures, which can induce a network of fractures in shale reservoirs.

Overview of numerical models for interactions between hydraulic fractures and natural fractures: Challenges and limitations

The intersection of natural fractures with hydraulic fractures results in formation of complex fracture networks, including non-planar fractures or multi-stranded fractures. On one hand, opening of these natural fractures improves productivity of the formation; on the other hand, coalescence of these fractures into a hydraulic fracture makes pressure analysis and prediction of fracture growth very complicated. Overall, interactions between natural fractures and hydraulic fractures pose more challenges in the fracturing design and its execution. Investigation and understanding of their interaction are crucial in achieving successful fracture treatments in formations with pre-existing natural fracture network. In this paper, we will review the numerical works that have been done in the last decade to model opening of natural fractures during hydraulic fracturing, focusing especially on mechanical models that address propagation of hydraulic fractures in naturally fractures reservoirs. Linear elastic fracture mechanics, cohesive element methods and continuum damage mechanics techniques utilized to understand interaction of hydraulic fractures with natural fractures are discussed here based on their capability to reproduce experimental results and field observations.

Poro-elasto-plastic modeling of complex hydraulic fracture propagation: simultaneous multi-fracturing and producing well interference

With the increasing wide use of hydraulic fractures in the petroleum industry, it is essential to accurately predict the behavior of fractures based on the understanding of fundamental mechanisms governing the process. For effective reservoir exploration and development, hydraulic fracture pattern, geometry and associated dimensions are critical in determining well stimulation efficiency. In shale formations, non-planar, complex hydraulic fractures are often observed, due to the activation of preexisting natural fractures and the interaction between multiple, simultaneously propagating hydraulic fractures. The propagation of turning non-planar fractures due to the interference of nearby producing wells has also been reported. Current numerical simulation of hydraulic fracturing generally assumes planar crack geometry and weak coupling behavior, which severely limits the applicability of these methods in predicting fracture propagation under complex subsurface conditions. In addition, the prevailing approach for hydraulic fracture modeling also relies on linear elastic fracture mechanics (LEFM) by assuming the rock behaves purely elastically until complete failure. LEFM can predict hard rock hydraulic fracturing processes reasonably, but often fails to give accurate predictions of fracture geometry and propagation pressure in ductile and quasi-brittle rocks, such as poorly consolidated/unconsolidated sands and ductile shales, even in the form of simple planar geometry. In this study, we present a fully coupled poro-elasto-plastic model for hydraulic fracture propagation based on the theories of extend finite element, cohesive zone method and Mohr–Coulomb plasticity, which is able to capture complex hydraulic fracture geometry and plastic deformations in reservoir rocks explicitly. To illustrate the capabilities of the model, example simulations are presented including ones involving simultaneously propagating multiple hydraulic fractures and producing well interference. The results indicate that both stress shadow effects and producing well interference can alter hydraulic fracture propagation behavior substantially, and shear failure in ductile reservoir rocks can indeed make a significant difference in fracturing pressure and final fracture geometry.

Reactivation mechanism of natural fractures by hydraulic fracturing in naturally fractured shale reservoirs

Hydraulic fracturing technique has been commonly used in the development of shale reservoir aiming to produce from complex network of fractures. One of the key parameters that affects the hydraulic fracture complexity is the natural fracture in the shale reservoir. Hydraulic fractures being trapped by natural fractures propagate non-planar fracture in three dimensions. Therefore, conventional hydraulic fracture model cannot include the non-planar characteristics of these fractures. In case a hydraulic fracture crosses a natural fracture, the dependence of the natural fracture reactivation on injection rate remains poorly understood. A non-planar propagation model for hydraulic fracturing in naturally fractured shale reservoirs was developed based on PKN model. A dynamic model was derived to calculate the stress intensity factor for a natural fracture being crossed by a hydraulic fracture based on the theory of rock fracture mechanics. Based on the experimental data from Longmaxi shale reservoir, the fluid pressure threshold to activate the natural fractures was obtained for different approaching angles. The effects of fluid pressure on the propagation angle of natural fracture were discussed. According to different initial injection rates and approaching angles, the time and minimum injection rate were determined to adjust the pump, which can improve the complexity of hydraulic fracture. True tri-axial hydraulic fracturing test with rapidly variable injection rate was conducted on the shale outcrop from Longmaxi formation. Experimental results proved that increasing the injection rate at the right time can reactivate the natural fractures, which can induce a network of fractures in shale reservoirs.

A lubrication fracture model in a poro-elastic medium

We present a non-planar fracture model in a poro-elastic medium. The medium in which the fracture is embedded is governed by the standard Biot equations of linear poro-elasticity and the flow of the fluid within the fracture is governed by the lubrication equation. We establish existence and uniqueness of the linearized coupled system under weak assumptions on the data. Two discretizations of the problem are formulated: one with a continuous Galerkin method and one with a mixed method for the flow in the reservoir and in the fracture. We perform the numerical analysis of the former and we provide an algorithm and numerical experiments for the latter.

Pressure transient analysis of a horizontal well intercepted by multiple non-planar vertical fractures

The principal focus of this work is on pressure behaviors of a horizontal well intercepted by multiple non-planar fractures. The non-planar fractures can be obtained by combinations of multiple wings with varied non-planar angle (NPA) and length. In theory, the bilinear flow regime, first linear flow, first radial, biradial flow and the pseudo radial flow regime can be identified for coplanar multi-fractured well. However, in practice, the shorter fracture spacing makes the biradial flow absent. The results of our investigation indicated that NPA mainly affects the first linear flow when CfD>1 and the bilinear flow when CfD≤1. As the NPA increases, the pressure depletion enlarges. However, the impact of NPA on pressure depletion is not linear relation. When NPA<50°, the change of relative derivative pressure (RDPC) is less than 5%. The characteristic straight line corresponding to the flow regimes can be identified approximately. When NPA=70° and 80°, it reaches 10% and 20%, respectively. In this case, the NPA exerts strong influence on the pressure derivative curve and the formation linear flow cannot be observed even at high fracture conductivities. It is shown that for small value of the wellbore storage CD, it will not affect the existence of flow regimes just delay the occurring time of characteristic flow regimes. For bigger value of the CD, the wellbore storage may conceal the early flow regimes and the bilinear flow and first linear flow may be no longer observed. Meanwhile, the effect of NPA on pressure weakens.