Model-Based Closed-Loop Control of the Hydraulic Fracturing Process

Gu, Qiuying; Hoo, Karlene A.

doi:10.1021/ie5024782

Cited by 40 publications

(21 citation statements)

References 32 publications

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“…In the respect of the irreversibility of damage, the damage variable may only increment monotonically from zero during loading (dF 1 > 0 or dF 2 > 0) and remain unchanged during unloading (dF 1 < 0 or dF 2 < 0). In this respect, the damage, defined by Equation (20), reduces the elastic modulus E and the shear modulus G of the rock, via to Equations (20) and (21).…”

Section: Governing Equations Accommodating Rock Heterogeneity and Dammentioning

confidence: 99%

“…This means that the fractures formed by hydraulic fracturing from orientated perforations may be very complex. With regard to moving boundary problems in hydraulic fracturing, many model reduction techniques have been proposed to achieve the desired accuracy and computational efficiency [18][19][20]. Recently, several efforts have been made to determine an optimal perforation condition utilizing the integrated reduced-order model [21] and 3D fracture-propagation model [22].…”

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confidence: 99%

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The Impact of Oriented Perforations on Fracture Propagation and Complexity in Hydraulic Fracturing

Liu

Elsworth

et al. 2018

Processes

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To better understand the interaction between hydraulic fracture and oriented perforation, a fully coupled finite element method (FEM)-based hydraulic-geomechanical fracture model accommodating gas sorption and damage has been developed. Damage conforms to a maximum stress criterion in tension and to Mohr-Coulomb limits in shear with heterogeneity represented by a Weibull distribution. Fracturing fluid flow, rock deformation and damage, and fracture propagation are collectively represented to study the complexity of hydraulic fracture initiation with perforations present in the near-wellbore region. The model is rigorously validated against experimental observations replicating failure stresses and styles during uniaxial compression and then hydraulic fracturing. The influences of perforation angle, in situ stress state, initial pore pressure, and properties of the fracturing fluid are fully explored. The numerical results show good agreement with experimental observations and the main features of the hydraulic fracturing process in heterogeneous rock are successfully captured. A larger perforation azimuth (angle) from the direction of the maximum principal stress induces a relatively larger curvature of the fracture during hydraulic fracture reorientation. Hydraulic fractures do not always initiate at the oriented perforations and the fractures induced in hydraulic fracturing are not always even and regular. Hydraulic fractures would initiate both around the wellbore and the oriented perforations when the perforation angle is >75 • . For the liquid-based hydraulic fracturing, the critical perforation angle increases from 70 • to 80 • , with an increase in liquid viscosity from 10 −3 Pa·s to 1 Pa·s. While for the gas fracturing, the critical perforation angle remains 62 • to 63 • . This study is of great significance in further understanding the near-wellbore impacts on hydraulic fracture propagation and complexity. failure [3][4][5]. Implicit in this is understanding fracture initiation and propagation in the near-wellbore region as of great significance for hydraulic fracture treatment and injectivity test interpretation [6][7][8].Since most wells are cased and require to be perforated to access the reservoir, the majority of hydraulic fracturing treatments are conducted through perforations. Perforations play a vital role in the origin of complex fracture geometries [6,[9][10][11][12]. In fractured reservoirs, perforations are often the sole hydraulic connection between the fractured reservoir and the wellbore. Hydraulic fractures initiated from preexisting perforations will reorient themselves normal to the direction of the minimum far-field stress as they propagate out from the wellbore [2,4,[13][14][15][16]. Near the wellbore, multiple sub-parallel fractures may be generated due to fracture initiation processes such as perforations and natural flaws located at the open-hole wellbore wall. Hydraulic fractures commonly initiate either from perforations located at the cased wellbore or from preexisting natural ...

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Section: Governing Equations Accommodating Rock Heterogeneity and Dammentioning

confidence: 99%

mentioning

confidence: 99%

The Impact of Oriented Perforations on Fracture Propagation and Complexity in Hydraulic Fracturing

Liu

Elsworth

et al. 2018

Processes

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“…At the wellbore, the flow rate q z is specified, and at the fracture tip, L ( t ), the common condition is that the net pressure is zero. These lead to the two boundary conditions

\begin{matrix} left & q_{z} (0, t) = Q_{0} & W (L (t), t) = 0, \end{matrix}

where Q 0 is the fluid injection rate at the wellbore (i.e., the manipulated input). Initially, the fracture is closed leading to

\begin{matrix} left & W (z, 0) = 0 \end{matrix}

…”

Section: Application To a Hydraulic Fracturing Processmentioning

confidence: 99%

“…At the wellbore, the flow rate q z is specified, and at the fracture tip, L(t), the common condition is that the net pressure is zero. These lead to the two boundary conditions 69,70 q z ð0; tÞ5Q 0 WðLðtÞ; tÞ50;…”

Section: Continuity Equationmentioning

confidence: 99%

Temporal clustering for order reduction of nonlinear parabolic PDE systems with time‐dependent spatial domains: Application to a hydraulic fracturing process

2017

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A temporally‐local model order‐reduction technique for nonlinear parabolic partial differential equation (PDE) systems with time‐dependent spatial domains is presented. In lieu of approximating the solution of interest using global (with respect to the time domain) empirical eigenfunctions, low‐dimensional models are derived by constructing appropriate temporally‐local eigenfunctions. Within this context, first of all, the time domain is partitioned into multiple clusters (i.e., subdomains) by using the framework known as global optimum search. This approach, a variant of Generalized Benders Decomposition, formulates clustering as a Mixed‐Integer Nonlinear Programming problem and involves the iterative solution of a Linear Programming problem (primal problem) and a Mixed‐Integer Linear Programming problem (master problem). Following the cluster generation, local (with respect to time) eigenfunctions are constructed by applying the proper orthogonal decomposition method to the snapshots contained within each cluster. Then, the Galerkin's projection method is employed to derive low‐dimensional ordinary differential equation (ODE) systems for each cluster. The local ODE systems are subsequently used to compute approximate solutions to the original PDE system. The proposed local model order‐reduction technique is applied to a hydraulic fracturing process described by a nonlinear parabolic PDE system with the time‐dependent spatial domain. It is shown to be more accurate and computationally efficient in approximating the original nonlinear system with fewer eigenfunctions, compared to the model order‐reduction technique with temporally‐global eigenfunctions. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3818–3831, 2017

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“…Motivated by some advances in real-time measurement techniques such as downhole pressure analysis and microseismic monitoring, several attempts have recently been made to employ model predictive control (MPC) theory to regulate the fracture geometry and proppant concentration. Specifically, the limited availability of real-time measurements has been addressed by utilizing state estimators [7][8][9], and several model order-reduction (MOR) techniques [10][11][12] have been developed to handle the large computational requirements due to dynamic simulation of multiple highly-coupled partial differential equations (PDEs) defined over moving boundaries to describe the hydraulic fracturing process. However, there are two unresolved issues with the MPC approach.…”

Section: Introductionmentioning

confidence: 99%

Approximate Dynamic Programming Based Control of Proppant Concentration in Hydraulic Fracturing

2018

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Abstract:Hydraulic fracturing has played a crucial role in enhancing the extraction of oil and gas from deep underground sources. The two main objectives of hydraulic fracturing are to produce fractures with a desired fracture geometry and to achieve the target proppant concentration inside the fracture. Recently, some efforts have been made to accomplish these objectives by the model predictive control (MPC) theory based on the assumption that the rock mechanical properties such as the Young's modulus are known and spatially homogenous. However, this approach may not be optimal if there is an uncertainty in the rock mechanical properties. Furthermore, the computational requirements associated with the MPC approach to calculate the control moves at each sampling time can be significantly high when the underlying process dynamics is described by a nonlinear large-scale system. To address these issues, the current work proposes an approximate dynamic programming (ADP) based approach for the closed-loop control of hydraulic fracturing to achieve the target proppant concentration at the end of pumping. ADP is a model-based control technique which combines a high-fidelity simulation and function approximator to alleviate the "curse-of-dimensionality" associated with the traditional dynamic programming (DP) approach. A series of simulations results is provided to demonstrate the performance of the ADP-based controller in achieving the target proppant concentration at the end of pumping at a fraction of the computational cost required by MPC while handling the uncertainty in the Young's modulus of the rock formation.

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Model-Based Closed-Loop Control of the Hydraulic Fracturing Process

Cited by 40 publications

References 32 publications

The Impact of Oriented Perforations on Fracture Propagation and Complexity in Hydraulic Fracturing

The Impact of Oriented Perforations on Fracture Propagation and Complexity in Hydraulic Fracturing

Temporal clustering for order reduction of nonlinear parabolic PDE systems with time‐dependent spatial domains: Application to a hydraulic fracturing process

Approximate Dynamic Programming Based Control of Proppant Concentration in Hydraulic Fracturing

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