Optimal pumping schedule design to achieve a uniform proppant concentration level in hydraulic fracturing

Yang, Seeyub; Siddhamshetty, Prashanth; Kwon, Joseph

doi:10.1016/j.compchemeng.2017.02.035

Cited by 42 publications

(25 citation statements)

References 24 publications

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“…Additionally, the following assumptions are also considered: (1) the fractures are confined vertically (constant height), (2) the rock properties remain constant with respect to time and space and (3) because the fracture length is much greater than its width (z-axis), the fracture propagation and proppant advection are neglected along the z-axis. In the PKN model, the fracture cross-sectional area is considered to be elliptical and the fracture shape is rectangular [44].…”

Section: Hydraulic Fracturing Processmentioning

confidence: 99%

Data-Driven Model Reduction for Coupled Flow and Geomechanics Based on DMD Methods

Bao

Gildin

Narasingam

et al. 2019

Fluids

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Learning reservoir flow dynamics is of primary importance in creating robust predictive models for reservoir management including hydraulic fracturing processes. Physics-based models are to a certain extent exact, but they entail heavy computational infrastructure for simulating a wide variety of parameters and production scenarios. Reduced-order models offer computational advantages without compromising solution accuracy, especially if they can assimilate large volumes of production data without having to reconstruct the original model (data-driven models). Dynamic mode decomposition (DMD) entails the extraction of relevant spatial structure (modes) based on data (snapshots) that can be used to predict the behavior of reservoir fluid flow in porous media. In this paper, we will further enhance the application of the DMD, by introducing sparse DMD and local DMD. The former is particularly useful when there is a limited number of sparse measurements as in the case of reservoir simulation, and the latter can improve the accuracy of developed DMD models when the process dynamics show a moving boundary behavior like hydraulic fracturing. For demonstration purposes, we first show the methodology applied to (flow only) single- and two-phase reservoir models using the SPE10 benchmark. Both online and offline processes will be used for evaluation. We observe that we only require a few DMD modes, which are determined by the sparse DMD structure, to capture the behavior of the reservoir models. Then, we applied the local DMDc for creating a proxy for application in a hydraulic fracturing process. We also assessed the trade-offs between problem size and computational time for each reservoir model. The novelty of our method is the application of sparse DMD and local DMDc, which is a data-driven technique for fast and accurate simulations.

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Section: Hydraulic Fracturing Processmentioning

confidence: 99%

Data-Driven Model Reduction for Coupled Flow and Geomechanics Based on DMD Methods

Bao

Gildin

Narasingam

et al. 2019

Fluids

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“…. The proppant velocity in the horizontal direction equals the slurry velocity in the horizontal direction . That is

V_{p x} = \frac{H - H_{bed}}{H} \frac{W^{2}}{12 μ} \frac{\partial P}{\partial x}

…”

Section: Model Development and Solutionmentioning

confidence: 99%

“…The rate of proppant bed build‐up can be determined by

\frac{d H_{b}}{d t} = \frac{C V_{s}}{C_{\max}}

where V s is the settling velocity of the proppant at a volume fraction, m/s; C max is saturation concentration, dimensionless, which means the max proppant concentration in the proppant bed. In this article, C max is set as 0.63, which was also used in the investigation by Tong and Mohanty …”

Section: Model Development and Solutionmentioning

confidence: 99%

“…The settling velocity is given by the classical Stokes equation and revised by experimental correlations. The Stokes equation is used to describe single proppant settling in the fluid

V_{normals}_{1} = \frac{g (ρ_{p} - ρ_{f}) D^{2}}{18 μ}

where V s1 is the settling velocity of single proppant, m/s;

ρ_{p}

is proppant density, kg/m 3 ;

ρ_{f}

is fluid density, kg/m 3 ; D is proppant diameter, m;

g

is gravitational acceleration, m/s 2 . The effects of proppant concentration on the terminal settling velocity can be expressed as

\frac{V_{s}}{V_{s}_{1}} = \frac{1 - C}{10^{1.82 C}}

…”

Section: Model Development and Solutionmentioning

confidence: 99%

“…Based on the models above, Gu and Hoo developed a model to calculate the proppant transport in the field scale in high viscosity fluid (0.56 Pa·s) . Yang et al proposed a similar model as the model proposed by Gu and Hoo to optimize the injection schedule to achieve a uniform proppant concentration level in hydraulic fracturing in field scale with high viscosity fluid (0.56 Pa·s) . The limitations of previous investigations are discussed as follows.…”

Section: Introductionmentioning

confidence: 99%

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A new model for simulating particle transport in a low‐viscosity fluid for fluid‐driven fracturing

Song

et al. 2018

AIChE Journal

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Fluid-driven fracture (i.e., Hydraulic fracturing) is an important way to stimulate the well productivity in the development of unconventional reservoirs. A low-viscosity fluid called slickwater is widely used in the unconventional fracturing. It is a big challenge to simulate the particle (or proppant) transport in the low-viscosity fluid in a field-scale fracture. A new model to simulate particle transport in the low-viscosity fluid in a field-scale fracture is developed. First, a new parameter is defined, called the rate of proppant bed wash-out, by which we incorporated the mechanism of proppant bed wash-out into Eulerian-Eulerian proppant transport model. Second, we proposed a novel way to consider the effect of proppant settling on the proppant concentration in the upper layer (or suspending layer) to accurately simulate the proppant transport. Additionally, a dimension reduction strategy was used to make the model quickly solved. Our simulation results were compared with published experimental data and they were consistent. After validation, the effect of fluid viscosity, injection rate, fracture height, and proppant concentration on the proppant distribution in a fracture is investigated. This study provides a new model to simulate particle transport. Meanwhile, it gives critical insights into understanding particle transport in the fieldscale fracture.

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Feedback control of proppant bank heights during hydraulic fracturing for enhanced productivity in shale formations

et al. 2017

Self Cite

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In hydraulic fracturing of shale formations, compared to conventional reservoirs, the fracturing fluid injected is of lowviscosity and hence during pumping the proppant settles significantly, forming a proppant bank. Motivated by this consideration, we initially develop a high-fidelity process model of hydraulic fracturing to describe the dominant proppant settling behavior during hydraulic fracturing process. Second, a novel remeshing strategy is developed to handle the high computational requirement due to moving boundaries. Third, a section-based optimization method is employed to obtain key fracture design parameters for enhanced productivity in shale formations subject to given fracturing resources. Fourth, a reduced-order model is constructed to design a Kalman filter and to synthesize a real-time model-based feedback control system by explicitly taking into account actuator limitations, process safety and economic considerations. We demonstrate that the proposed control scheme can regulate the uniformity of proppant bank heights along the fracture at the end of pumping.

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Optimal pumping schedule design to achieve a uniform proppant concentration level in hydraulic fracturing

Cited by 42 publications

References 24 publications

Data-Driven Model Reduction for Coupled Flow and Geomechanics Based on DMD Methods

Data-Driven Model Reduction for Coupled Flow and Geomechanics Based on DMD Methods

A new model for simulating particle transport in a low‐viscosity fluid for fluid‐driven fracturing

Feedback control of proppant bank heights during hydraulic fracturing for enhanced productivity in shale formations

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