Comparison of Eulerian-Granular and Discrete Element Models for Simulation of Proppant Flows in Fractured Reservoirs

Numerical simulations provide an effective technique to understand the proppant behavior within hydraulic fractures and determine fracking efficiency. Numerical techniques currently available for simulating particulate flow include a range of methods, from resolved direct numerical simulation (DNS) to Eulerian-Eulerian models. Employing high fidelity techniques, such as DNS, that fully resolve the physics are most often impractical for regular engineering applications due to exorbitant computational resource requirements. Hence, alternative simplified methods with reasonable computing power are generally used in regular engineering practice and design. In the present study, the Eulerian-Granular method, which is based on a simplified continuum approximation of the particulate phase, is compared with a relatively more detailed discrete element method (DEM), where individual particles are tracked in a Lagrangian sense. Numerical simulation of proppant flow through a representative fracture has been carried out to understand the relative suitability of these two different multiphase flow simulation techniques. Simulations are carried out for an idealized fracture geometry with a specified leak-off rate along the fracture wall. Computed results for the spreading rate of the proppant obtained from the Eulerian-Granular method are found to be marginally higher than the spreading rate of the proppant obtained from the DEM simulations. As DEM explicitly simulates particle movement; it is expected to provide results that are closer to the actual physical processes. The computational time required to perform the DEM simulations, however, is almost an order of magnitude greater than for the Eulerian-Eulerian technique. Hence, the efficiency of the Eulerian-Granular method probably offsets some modeling shortcomings in resolving particle setting characteristics for regular engineering applications.