Problem Of Hydraulic Fracture Research Articles

Parameter identification of minifrac numerical tests using a gradient boosting‐based proxy model and genetic algorithm

AbstractIn recent years, the petroleum industry has devoted considerable attention to studying fluid flow inside fracture channels due to the discovery of naturally fractured reservoirs. The behavior prediction of these reservoirs is a well‐known challenging task, in which the initial stage consists of identifying reservoir hydromechanical parameters. This work proposes an artificial intelligence‐based approach to identify hydromechanical parameters from borehole injection pressure curves acquired through minifrac tests. This approach combines proxy modeling with a stochastic optimization algorithm to match observed and predicted borehole pressure curves. Therefore, a gradient boosting‐based proxy model is built to predict borehole pressure curves, considering a proper strategy to develop time series modeling. Moreover, a Bayesian optimization algorithm is applied to compute the gradient boosting hyperparameters. In this optimization scenario, this paper proposes an appropriate objective function established from the assumed time series prediction strategy and the k‐fold cross‐validation. Finally, a genetic algorithm is adopted to identify unknown hydromechanical parameters, solving an inverse problem. Based on the proposed workflow, a study of the importance of the hydromechanical parameters is developed. To assess the methodology applicability, the approach is employed to identify parameters in synthetic and field minifrac tests. The results present how this approach can adequately identify hydromechanical parameters of hydraulic fracturing problems.

Finite domain solution of a KGD hydraulic fracture in the viscosity-dominated regime

This paper describes a numerical algorithm for solving the classic problem of a plane strain (KGD) fracture propagating in an impermeable elastic medium with zero toughness. The method, which takes advantage of the self-similar nature of the solution, combines a domain-based scheme to solve the elasticity equations and a finite volume method to solve the nonlinear lubrication equation. This work represents a first step towards developing a model able to account for pore pressure diffusion in the medium and corresponding poroelastic effects, noting that these processes are more efficiently solved using a domain-based rather than a boundary integral method. To enhance the efficiency and accuracy of the numerical scheme, the far-field crack asymptotics is embedded in the discretized elastic relationship between the fluid pressure and the crack opening, while the coupled fluid-solid tip asymptote is enforced in a weak form when solving the nonlinear lubrication equation. The proposed technique yields results that closely match the analytical solution, even with a coarse mesh. This approach offers potential for addressing more complex hydraulic fracturing problems in the future.

On crack propagation in weak geomaterials: Revisiting the superdislocation model in the context of hydraulic fracture

In this paper the problem of hydraulic fracture in elasto-plastic pressure sensitive material is analyzed. The superdislocation model is used to approximate the plastic deformations in the crack tip area. This model is employed to derive a new crack propagation condition based on the concept of effective fracture toughness. A parametric analysis supported by FEM simulations is conducted to verify the underlying assumptions of the superdislocation model and the resulting crack propagation condition. The results, obtained with the new crack propagation condition for the HF problem, are compared with those produced by a commercial geomechanical FEM package Elfen. The comparison proves the validity of the new crack propagation condition and the proposed modeling approach.

Simulation of fully coupled hydro-mechanical behavior based on an analogy between hydraulic fracturing and heat conduction

The hydraulic fracturing process involves complex coupling problems of the deformation and fracturing of solid and fluid flow in fractures. In this paper, a simple numerical tool for simulating the coupled hydro-mechanical behavior is developed by using an analogy between hydraulic fracturing and heat conduction. Using this analogy, the numerical implementation can be simply realized in the framework of a commercial finite element package ABAQUS with two user material subroutines to fully characterize the complex coupling problems of hydraulic fracturing. It is thus considerably simplified without any new development of user-defined element and fluid–solid solver but directly with the commercial finite element package. The proposed numerical tool along with the virtual crack method for elastic–brittle material is firstly verified by the classical 2D plain strain KGD analytical solution and then applied to several representative hydraulic fracturing problems and laboratory tests to illustrate its advantageous features. The present method is aiming to develop a useful numerical tool to study the coupled hydro-mechanical behavior of hydraulic fracturing. However, it is not limited to any specific materials and can be extended to other constitutive models that featured with the fully coupling problems of fluid and solid due to its simplicity.

NUMERICAL INVESTIGATION OF HYDRAULIC FRACTURE PROPAGATION IN HETEROGENEOUS ROCKS USING THE DAMAGE MECHANICS MODEL

In this study, we use a three-dimensional damage mechanics-based finite element model to investigate hydraulic fracture propagation in heterogeneous rocks. In the proposed finite element model, the Weibull random distribution function is adopted to characterize the rock mechanical heterogeneity of the elastic modulus. This damage mechanics model can well reflect the damage evolution of hydraulic fracture propagation in heterogeneous rocks under tensile and compression states. The fully coupled fluid-solid system of the hydraulic fracturing problem is numerically solved by the Newton-Raphson iterative method. Our numerical results show that key factors including the degree of mechanical heterogeneity, tensile strength, elastic modulus, and natural fractures have a significant impact on hydraulic fracture propagation in heterogeneous rocks. Both the damage zone and the first principal stress contour present a random distribution due to the mechanical heterogeneity. In a naturally fractured heterogeneous reservoir, the damage zone presents a banded distribution, which has the same dip angle of natural fractures. Some natural fractures away from the injection point are also partially opened under the combined action shear and normal stress field. This investigation provides new insight into the formation mechanisms of complex fracture networks in heterogeneous rocks.

A novel hybrid model for hydraulic fracture simulation based on peridynamic theory and extended finite element method

The development of subsurface hydrocarbon reservoirs is highly dependent on hydraulic fracturing technology, and it is of great significance to use numerical simulation approaches to explore the propagation characteristics of hydraulic fractures. A novel hybrid model for investigating the hydraulic fracturing problem is proposed in this paper, wherein the crack segment is described using the extended finite element method (XFEM), and the region of the crack tip and potential fracture propagation is described using peridynamic (PD) theory. The fluid flow is governed by the continuity equation and the momentum equation, and the permeability in the fracture is calculated by the cubic law. The proposed model takes advantage of the small computational complexity of XFEM, and uses the stretch in the PD theory to determine whether the bond is broken, avoiding the need to obtain the stress intensity factor. The importance of the hybrid model is the coupling strategy for the transition region from XFEM to PD. Then the model is validated against two classic problems with available analytical solutions. The issue of hydraulic fractures intersecting natural fractures is also addressed. Meanwhile, the mesh size and the coupling region size is studied in this work. The model proposed in this paper is of benefit to provide a new perspective for numerical simulation of hydraulic fracture.

On the pressure decline analysis for hydraulic fractures in elasto-plastic materials

In this paper the problem of a plane strain hydraulic fracture in elasto-plastic material is analyzed. The analysis is based on Finite Element Method computations of crack propagation and closure to simulate the Mini-Frac calibration test. The basic trends of fracture evolution are identified for both, the propagation and the closure stage in elasto-plastic materials and compared with the results obtained for purely elastic deformation of rock. Pressure decline analysis is conducted to identify the closure stress and leak-off coefficient. The results show that the standard techniques of pressure decline analysis can be adopted also for the case where the fractured material deforms inelastically.

Non-local continuum damage model for poro-viscoelastic porous media

We present a novel poro-damage-viscoelastic model for predicting the failure response of fluid-saturated porous geomaterials. The Generalized Maxwell model is introduced for the representation of the viscoelastic behavior of the solid skeleton, which is achieved by a standard Prony-series type expansion. Damage regularization is obtained by an non-local integral-type formulation and damage behavior is described by Mazars model with the modified von Mises-type equivalent strain measure. The poromechanics parameters (Biot’s coefficient, Biot’s modulus) are functions of damage, and the fluid flow obeys Darcy’s seepage law in the entire domain, while the permeability is assumed to be anisotropic and strain dependent. The coupled system is discretized in time using a backward Euler scheme. The non-linear system is linearized using a Newton Raphson scheme and solved monolithically every time step. A consistent Jacobian matrix and residual vector are derived analytically. Several numerical examples are studied in order to investigate the performance of the proposed approach, including (i) a column undergoing hysteresis from cyclic loading, stress relaxation, creep and variable strain rate loading tests and (ii) fluid-driven fracturing in a 2D poro-viscoelastic domain. The numerical time-dependent results exhibit mesh insensitivity for all field variables, and confirm the feasibility and applicability of the proposed non-local damage model for simulating hydraulic fracture. • A non-local damage model for poro-viscoelastic saturated porous media is proposed. • Von-Mises strain measure is used to drive the non-local integral type damage growth. • Damage-response includes nonlinear Biot’s coefficients and anisotropic permeability. • A mixed FEM solution is developed, including a monolithic iterative solution. • Analytically derived Jacobian is used to drive the non-linear solution of equations. • Benchmark problems include poro-viscoelastic column and hydraulic fracture problems. • Objective mesh-independent and oscillation free numerical results are presented. • The model has the potential to represent time-dependent damage in several rock types.

Modeling of solids particle diversion to promote uniform growth of multiple hydraulic fractures

Solid particulate additives are sometimes used to promote the uniform growth of multiple hydraulic fractures in horizontal oil and gas wells. The principle is that solid particulates block, accumulate, and form larger porous plugging zones preferentially at entrances of fracture taking in the most fluid volume. These porous zones create fluid flow resistance or additional pressure loss; thereby, inhibiting the growth of these dominant fractures and diverting fluid to suppressed fractures. While this technology is promising, governing design parameters and ramifications of placing solids diverters inside the fracture remain unclear. This paper models the propagation of multi-fractures with diverter pressure losses induced by the porous plugging zones. The resulting non-linear hydraulic fracturing problem is solved numerically with an Implicit Level Set Algorithm (ILSA) for each time step and the mechanisms of diversion are illustrated by comparing and contrasting cases with and without particle diverter. In both cases, during the fluid ramp-up period (pumping rate gradually increases from 0 to fracturing rate (QT)), the injection can be equally distributed among fractures before the stress interference affects the fluid allocation (Phase I). Then, stress interference starts to partition more fluid into outer fractures and suppress the growth of the middle fracture (Phase II). Once the perforation friction loss is sufficient to counteract the stress interaction, injection begins to shift to the middle fracture, but still gives a significantly non-uniform fracture growth (Phase III). At this point, solid diverter particles are introduced, leading to three additional phases of growth. Phase IV introduces solid diverters to the treatment at a reduced pumping rate. Particles bridge, accumulate and create porous plugging zones at the flow entrance. A higher pressure drop in outer fractures diverts injection fluids to the middle fracture. Phase V resumes the treatment rate to QT without diverter. The increased pump rate in turn increases the pressure drop in outer fractures and diverts more fluids to the middle fracture. This results in a rapid extension velocity for the middle fracture, enabling it to have the chance to catch up with the longer outer fractures (in Phase VI). This process is controlled by the interplay among stress interference, perforation friction loss, and diverting pressure drop. These simulations demonstrate that a model-based optimization could improve the effectiveness of the diverter technology and promote a uniform multi-fracture growth.

Analysis of a constant height hydraulic fracture driven by a power-law fluid

The focus of this study is to analyze a parametric space for the problem of a constant height hydraulic fracture driven by a power-law fluid. The interplay of physical mechanisms related to toughness, fluid resistance, and leak-off is considered, but the model is restricted to local elasticity for simplicity. The problem of a semi-infinite constant height fracture is first analyzed: limiting solutions are obtained analytically and their locations inside the dimensionless parametric space are obtained. Then, the problem of a finite constant height fracture is investigated. Similarly, limiting vertex solutions are first outlined and then their locations in the parametric space are quantified. Results demonstrate that the effect of the power-law factor is relatively mild, as it does not significantly distort the parametric spaces. At the same time, there are quantitative differences, which are also determined by the obtained results. Numerical examples highlighting the effect of fracture regime on morphology of multiple fractures are presented at the end.

Guest Editorial: Four Real-World Challenges in Hydraulic-Fracture Modeling

The development of theoretical hydraulic-fracturing models started several decades ago, setting a basis for hydraulic-fracture design, optimization, and diagnostics. As a reservoir stimulation technique, the problem of hydraulic fracturing in essence is the prediction of the geometric shape and dimensions (length, width, and height) of the growing fracture as a function of time. This mathematically translates to a set of nonlinear, integro-differential equations with moving boundaries, solved numerically over a number of time-steps (SPE 168600). When it comes to multistage fracture treatments (Fig. 1), where many fractures are being “pumped” simultaneously within each stage, the problem’s complexity increases exponentially. The old adage of four inputs being necessary for optimal fracture design (reservoir permeabilities, in-situ stress distributions, a sound geological model, and a fluid-loss model in naturally fractured rocks) is no longer the case as multiple-fracture (multi-frac) interactions and interference (intra-stage, intra-well, and inter-well) should also be incorporated (SPE 1210-0034-JPT). Classic treatment-design software, although convenient to use, struggle to predict multi-frac growth geometries with sufficient certainty, leading to significant disparities between simulations and field observations. Four real-world challenges associated with multi-frac modeling from horizontal well operations are described below. Although each formation presents its own set of challenges rendering it necessary for operators to learn from experience, the development of computational techniques to facilitate the simulation of these common occurrences will yield more-realistic models. 1. Nonsimultaneous fracture initiation within a stage Fracture-propagation pressures are significantly smaller than fracture-initiation pressures (approximated by the recorded “formation-breakdown” pressures) in the same rock. Hence, earlier fracture initiation from one perforation provides a low-energy pathway for the fracturing fluid, which would “prefer” to enter an existing fracture and propagate it rather than initiating new fractures from nearby perforations. 2. Dominant (or “runaway”) fracture creation Dominant (or runaway) fractures are those whose growth is significantly larger compared to that of the other fractures. Laboratory-scale experiments where more than one fracture was pumped from a single fluid source displayed dominant fracture creation as a consistent observation (Michael). This observation qualitatively agrees with acoustic sensing data from the field-scale operations (Fig. 2). Dominant fractures end up receiving the entire fracturing fluid by the end of a stage (SPE 194334), while the remaining fractures cease propagating. The contribution of these few dominant fractures in the post-stimulation well productivity could be major. 3. Inactive perforation clusters Fracturing fluid can bypass entire perforation clusters, initiating fractures from perforation clusters further downstream along the horizontal lateral (SPE 194334). This occurs both by inactive perforation clusters located between active clusters and by inactive perforation clusters located adjacent (upstream or downstream) of active clusters (Michael). There are many possible causes of a perforation cluster failing to generate fractures, including nonsimultaneous fracture initiation and dominant fracture creation. Limited-entry techniques accomplished by varying perforation numbers and diameters (SPE-530-PA), later proposed for mitigating interference between simultaneously growing fractures from horizontal wells (“stress-shadowing”), can potentially be effective in eliminating inactive perforation clusters if specific patterns are detected.

A continuous fracture front tracking algorithm with multi layer tip elements (MuLTipEl) for a plane strain hydraulic fracture

The problem of a plane strain hydraulic fracture propagating in a layered formation is considered. Fracture toughness, in-situ stress, and leak-off coefficient are assumed to vary by layer, while the elastic properties are kept constant throughout the domain for simplicity. The purpose of this study is to develop a numerical algorithm based on a fixed mesh approach, which is able to solve the above problem accurately using elements which can even be larger than the layer size. In order to do this, the concept of fictitious tip stress is first introduced for determining the fracture front location. In this technique, an additional stress is applied to the tip element to suppress the opening and to mimic the width corresponding to the actual fracture front location. A theoretical basis for this concept has been established and it is further calibrated for piece-wise constant elements. Once the ability to track the crack front location is developed, the effect of layers is included by varying properties as a function of front location. Several numerical examples benchmarking the numerical solution, as well as highlighting capabilities of the algorithm to tackle multiple thin layers accurately are presented.

3D fluid–structure interaction with fracturing: A new method with applications

This paper presents a methodology for simulating general, three-dimensional fluid–structure interaction problems involving fracturing. Ordinary state-based peridynamics is used to describe the mechanical behaviour of the solid phase in a Lagrangian framework. The governing equations of peridynamics are coupled via a multi-direct immersed boundary method with the incompressible formulation of the Navier–Stokes equations, which are used to govern the dynamics of the fluid phase. The synchronization of the solution is achieved via a fully explicit, weak-coupling strategy that allows for fast and efficient computations. A detailed description of the methodology is provided, together with the results of several validation benchmarks. The qualitative results of the unsteady hydraulic fracture of a porous medium are also presented to show the potential of the proposed approach. The authors believe that the numerical technique described in this paper contributes to advance the capability of models in reproducing complex fluid–structure interaction and hydraulic fracture problems, providing a very detailed description of both the fluid and solid mechanics of the processes involved.

A FDEM based 3D discrete mixed seepage model for simulating fluid driven fracturing

This paper presents a 3D discrete mixed seepage model that considers the effect of fracture on pore seepage. We unify the 3D fracture-pore mixed seepage model and finite-discrete element method (FDEM) to build a coupled hydro-mechanical model to simulate the fluid-driven deformation and fracturing, which can also consider the influence of fracture propagation on fracture seepage and pore seepage. The model has been implemented in a GPU parallel multiphysics finite-discrete element software MultiFracS. For the continuum seepage problem, we conduct a parameter sensitivity analysis for the fluid exchange coefficient and propose the criterion for selecting the coefficient. Then, we verify the model to deal with 3D pore seepage in a continuum media, fracture-pore seepage in discontinuous media with a single fracture, and fracture-pore seepage in discontinuous media with multi-fractures. Finally, the coupled hydro-mechanical model is employed to study a one-dimensional consolidation and a hydraulic fracturing problem. The research shows that the simulation results are in good agreement with the analytical solutions and the experimental results, which verifies the effectiveness of the method for solving the 3D fracture-pore mixed seepage and the coupled hydro-mechanical model for dealing with seepage problems in fractured porous media and fluid-driven fracturing.

A simplified modelling of hydraulic fractures in elasto-plastic materials

In this paper the problem of a plane strain hydraulic fracture propagating in an elasto-plastic material is analyzed. A new stress redistribution model for the proximity of the fracture tip is formulated and a resulting plasticity-dependent crack propagation condition is introduced. A modified variant of the KGD problem that accounts for the plastic deformations in the near-tip zone only is proposed. It is demonstrated that this model can be a credible substitute for the full elasto-plastic hydraulic fracture problem in the case of moderate plastic deformation. The crack-tip shielding effect introduced by the plastic deformation is quantified.

Failure Patterns and Mechanisms of Hydraulic Fracture Propagation Behavior in the Presence of Naturally Cemented Fractures

In this study, we use the extended finite element method (XFEM) with a consideration of junction enrichment functions to investigate the mechanics of hydraulic fractures related to naturally cemented fractures. In the proposed numerical model, the lubrication equation is adopted to describe the fluid flow within fractures. The fluid-solid coupling systems of the hydraulic fracturing problem are solved using the Newton-Raphson method. The energy release rate criterion is used to determine the cross/arrest behavior between a hydraulic fracture (HF) and a cemented natural fracture (NF). The failure patterns and mechanisms of crack propagation at the intersection of natural fractures are discussed. Simulation results show that after crossing an NF, the failure mode along the cemented NF path may change from the tensile regime to the shear or mixed-mode regime. When an advancing HF kinks back toward the matrix, the failure mode may gradually switch back to the tensile-dominated regime. Key factors, including the length of the upper/lower portion of the cemented NF, horizontal stress anisotropy, and the intersection angle of the crack propagation are investigated in detail. An uncemented or partially cemented NF will form a more complex fracture network than a cemented NF. This study provides insight into the formation mechanism of fracture networks in formations that contain cemented NF.

Perspectives for development of ice drilling technology: continuation of the discussion

AbstractRecently, innovations in ice drilling have yielded considerable improvements to existing drilling techniques, as well as innovative drilling technologies that can be used in new types of applications. However, some specific challenges have to be addressed for improving existing drilling methods and developing new ones: (1) combination and unification of different drilling systems; (2) facilitating ice core breaking; (3) improving existing systems and developing new rapid-access ice drilling systems; (4) reliable elimination of ice hydraulic fracturing problems; (5) developing new environment-friendly methods of drilling in the sub-glacial lake sediments; and (6) design of unconventional ice drilling systems. Possible solutions to these problems are presented herein.

The numerical asymptotic solution to initial condition problem of preexisting plane-strain hydraulic fracture with fluid lag

The numerical asymptotic solution to the initial condition problem (early-time solution) of the pre-existing plane-strain hydraulic fracture with a fluid lag is obtained under different levels of in-situ stress. This solution can provide a more accurate initial condition for simulation of hydraulic modelling. The perturbation method is applied to calculate time-derivative terms of the governing equations based on the derivative definition, and the double-iteration method is used to seek more accurate values of these time-derivative terms. Besides, the profiles of dimensionless fracture opening and dimensionless net pressure are obtained under different levels of in-situ stress, and a simplified self-similar model with no time derivative terms is put forward, because time-derivative terms can be neglected under the large in-situ stress.

Multi-physics flux coupling for hydraulic fracturing modelling within INMOST platform

AbstractThis work presents an overview of techniques that enable the construction of collocated finite volume method for complex multi-physics models in multiple domains. Each domain is characterized by the properties of heterogeneous media and features a distinctive multi-physics model. Coupling together systems of equations, corresponding to multiple unknowns, results in a vector flux. The finite volume method requires continuity of intradomain and interdomain vector fluxes. The continuous flux is derived using an extension of the harmonic averaging point concept. Often, the collocated coupling of the equations results in a saddle-point problem subject to inf-sup stability issues. These issues are addressed by the eigen-splitting of indefinite matrix coefficients encountered in the flux expression. The application of the techniques implemented within INMOST platform to hydraulic fracturing problem is demonstrated.

A Novel Approach for Direct Numerical Simulation of Hydraulic Fracture Problems

Hydraulic fracturing is a non-linear and multi-physics problem involving the break up of a solid medium due to the action of hydrodynamic forces. Fluid and solid mechanics are involved at the same time together with fracture mechanics. Despite its relevance in many scientific and engineering fields, the theoretical and numerical description of hydraulic fracturing remains a challenging matter and the capabilities of existing models for applications are still limited. In this context, we propose a novel numerical approach to the Direct Numerical Simulation of hydraulic fracturing based on the Navier–Stokes equations coupled with peridynamic theory of solid mechanics through a multi-direct Immersed Boundary Method. The main advantage of this approach consists in the reliable crack-detection and tracking capabilities of peridynamics together with the capability of the Immersed Boundary Method of managing no-slip and no-penetration boundary conditions on complex and time-evolving interfaces. A massive-parallel solver based on this model has been implemented. We present a detailed theoretical description of the proposed methodology as well as the results of an extensive validation campaign for the new solver. Different benchmarking tests are provided together with the qualitative results of a simulation reproducing the fracture of a solid structure in a laminar, unsteady flow.