Proppant Transport Modeling With Effects Of Suspension Yield Stress, Jamming, And Filtration Through The Proppant Pack

We present further development of the 2D two-continua model of proppant transport derived from first principles using the lubrication approximation [1]. The model includes effects associated with presence of the slip velocity between particles and fluid, as well the yield stress of carrying fluid. These features are typically missing in standard, effective-medium models of proppant transport, though power-law rheology is often included. Predictions of model [1] have gone through a thorough validation against a set of carefully selected lab data [2].

It is important to stress the presence of a fundamental issue with standard semi-empirical relationships for suspension rheology, which predict singular behavior near the particle packing limit. One possibility to resolve the issue is to introduce an ad-hoc regularization by stepping out from the singularity at a small epsilon to mimic the transition from flowing suspension to Darcy filtration through the packed bed. Clearly, such a regularization is unable to accurately describe the physics for all possible scenarios since the flux has a different dependence on the channel width for Poiseuille and Darcy flows. Alternatively, one may utilize a recently developed suspension flow model [3], in which the issue of singular behavior is resolved by developing the model from first principles. The latter approach is physics-based, self-consistent, and covers the entire range of variation of the particle volume fraction, from dilute through dense to granular pack, and in particular predicts Darcy filtration at the packing limit.

Here, we will present a proppant transport model that accounts for the combined effects of particle jamming due to bridging, dehydration, and transition to close packing, combined with Bingham rheology of the suspension (induced by cross-linking of the polymer-based fracturing fluid, presence of fibers, and suspension rheology itself near the packing limit). We use a unified closure relation for the suspension rheology proposed recently in [3] to cover the whole range of proppant concentration, from dilute suspension, to dense and close packing. Numerical results are given to illustrate the newly introduced effects.

References:

1. Osiptsov, A.A., 2017. Fluid Mechanics of Hydraulic Fracturing: a Review. J. Petrol. Sci. Eng. V. 156, July 2017, pp. 513–535.
2. Boronin, S.A., Osiptsov, A.A. and Desroches, J., 2015. Displacement of yield-stress fluids in a fracture. International Journal of Multiphase Flow, 76, pp.47–63.
3. Dontsov, E.V., and Peirce, A.P., 2014. Slurry flow, gravitational settling, and a proppant transport model for hydraulic fractures. Journal of Fluid Mechanics , 760, 567–590.