Coupled 3-D numerical simulation of proppant distribution and hydraulic fracturing performance optimization in Marcellus shale reservoirs

Abstract Effective hydraulic fracturing stimulation is highly reliant on the flow area and proppant pack permeability of the induced hydraulic fractures. The flow area is largely determined by proppant distribution while fracture permeability is mainly governed by proppant sizes. To create a fracture with a large flow area, small proppants are essential to maintain a minimum proppant settling velocity; on the other hand, large proppant sizes provide higher proppant pack permeability. Therefore, an optimum operational procedure, i.e., scheduling of injection rate, proppant size and volume, is required to achieve maximum well productivity index. This, however, requires both field experiments (e.g., small volume pre-job tests) and an advanced numerical simulator that couples solid and fluid transport with fracture propagation model including mass exchange between reservoir matrix and hydraulic fracture, i.e., leak-off rate. In this study, we focused on developing new modules for our in-house 3-D numerical simulator where proppant transport and reservoir performance optimization is considered. In new module Navier–Stokes equation describing fluid flow in the fracture and leak-off in the formation is coupled with mass conservation equation governing the proppant transport, and solved using finite difference approach. Fracture propagation is also one-way coupled with proppant transport and fluid flow using in-house 3D hydraulic fracturing simulator “HFWVU”. During the simulation Proppant slippage velocity is considered over wide range of hydraulic fracturing propagation regimes, i.e., toughness-dominated to viscosity-dominated cases, with small and large leak-offs. The simulation results predict that reservoir matrix permeability highly impacts the proppant size selection and pumping scheduling to achieve the optimum reservoir stimulation performance. Ignoring the fluid–solid interaction, i.e., proppant settling velocity, in hydraulic fracturing simulation leads to overestimating the efficiency of the process in wide range of operation conditions. It has also been predicted that the optimum combination of proppant size and their volume portion exists for specific reservoir and treatment conditions that can optimize fracture performance. Uncertainty analysis of the reservoir behavior using experimental design technique shows that hydraulic fracturing efficiency on production performance can be highly influenced by reservoir matrix permeability, i.e., uncontrollable variable. This implies that the same hydraulic fracturing procedure applied in conventional reservoirs might not be as efficient in unconventional reservoir and special attention to reservoir characteristics needs to be made while designing the hydraulic fracturing procedure. Followed by reservoir matrix permeability, proppant volume and relative proppant/fluid density have the highest impact on hydraulic fracturing efficiency. This study couples hydraulic fracturing simulation with reservoir simulation and is a unique approach for the further understanding of proppant transport and settling, fracture geometry variation and fracture production performance. It also provides foundation for the development of sound numerical models for hydraulic fracturing design.