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In hydraulic fracturing of shale formations, compared to conventional reservoirs, the fracturing fluid injected is of low‐viscosity 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.
In hydraulic fracturing of shale formations, compared to conventional reservoirs, the fracturing fluid injected is of low-viscosity 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.
In this work, we present a temporally-local model order-reduction technique for nonlinear parabolic partial differential equation (PDE) systems with time-dependent spatial domains. In lieu of approximating the solution of interest using global (with respect to the time domain) empirical eigenfunctions, we derive low-dimensional models by constructing appropriate temporally-local eigenfunctions.
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