(333f) Optimal Proppant Pumping Schedule Design for Hydraulic Fracturing Operation Using a Eulerian-Lagrangian Model
Motivated by this, in this work, a computationally efficient three-dimensional multiphase particle-in-cell (MP-PIC) model has been employed to simulate the multi-size proppant transport in a field-scale geometry using the Lagrangian description for the proppant particles, and the Eulerian continuum description for the fracturing fluid [6, 7]. Instead of tracking each particle, groups of particles (called parcel) are tracked, which allows to simulate the proppant transport in field-scale geometries at an affordable computational cost. The MP-PIC model was simulated using the Ada and Terra clusters provided by Texas A&M high performance research computing facility. The MP-PIC method required around 96 hours of calculation of 28 CPUs to simulate proppant transport in the described field-scale fracture geometry. In the literature, available CFD simulations only considered the fracture length of up to 10 m, which is much smaller than field-scale fracture geometries, and fracturing fluid injection times of up to 200 s, which is also not a field-scale injection time . Because of the gain in computational efficiency by the use of the MP-PIC method, we are able to simulate proppant transport in the field-scale fracture geometry; in particular, a fracture of 180 m in half length, 30 m in height, and 0.00762 m in width is considered with 1 hour operation time for hydraulic fracturing. From these simulation results, we found that shale gas production from unconventional reservoirs depends on the propped fracture surface area (PFSA) and average fracture conductivity (AFC) values at the end of hydraulic fracturing. We also found that a smaller size proppant results in a larger PFSA because proppants can penetrate deeper inside the fracture due to less gravitational settling. On the other hand, using large proppant particles results in a high AFC due to their high permeability.
Motivated by these sensitivity studies, we used the MP-PIC model for optimal operation of hydraulic fracturing. The reservoir simulation software from Computer Modeling Group Ltd. (CMG) is used to simulate shale gas production from an unconventional reservoir. To reduce the computational requirement of using the MP-PIC model and CMG within the optimization framework, a reduced order model (ROM) was developed to describe proppant transport during hydraulic fracturing, and a map was developed to predict the cumulative shale gas production volume as a function of PFSA and AFC at the end of hydraulic fracturing. Then, we used the ROM and map in an optimization framework to design an optimal multi-size proppant pumping schedule. Simulation results presented in this work show that the AFC and PFSA values obtained by the proposed pumping schedule were able to maximize the cumulative shale gas production volume from an unconventional reservoir for given fracturing resources.
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