(65g) Proppant Transport Efficiency Simulation in a Wellbore-Fracture System

Controlling proppant transport in the field is essential to a successful hydraulic-fracturing job. Proppant particles must be delivered to the right fracture locations to prevent their closing. The flow conditions in the wellbore around each of the perforations connected to the fractures vary, and proper delivery of proppants to each perforation is critical. This presentation focuses on the development of a method for predicting particle flow rates to individual perforations, accounting for the effect of the non-Newtonian fluid property on particle transportation. Two dimensionless numbers were generated that dominate the transport efficiency in non-Newtonian fluids.

The interaction of the particle-liquid interphase was modeled using a specific drag-force correlation for non-Newtonian fluid. The analysis of particle-laden fluid flow near an individual perforation showed that the efficiency of particle transport to the fracture (ratio of the particle concentration in the fracture to the particle concentration in the wellbore) depends on two dimensionless parameters: the particle stokes number in a non-Newtonian fluid (St) and the ratio of the flow velocity in the wellbore to the flow velocity in the fracture channel (Λ). Using a detailed 3-D CFD model of fluid-particle flow to the fracture (built with commercial software), the efficiency of particle transport to the fracture was calculated for various combinations of parameters, St and Λ. The tables generated by the model were used to accurately calculate the efficiency of proppant delivery through the linear interpolation of tabulated data. Different particle flow behaviors in Newtonian and non-Newtonian fluids were compared.

The results showed that proppant particle distribution is more homogeneous in non-Newtonian fluid than in Newtonian fluid under the same operating condition. The CFD analysis of fluid and particle motion showed that because the flow conditions around each of the perforations connected to the fractures are different, the amount of proppant carried to each fracture varies. The particle inertia in non-Newtonian fluid was analyzed. The efficiency of particle delivery was calculated for a sequence of parameters, St and Λ, and the results were tabulated. In the case of relatively low particle-volume fractions, using these tables enables a quick and accurate calculation of delivery efficiency in non-Newtonian fluid systems. The proppant-mass flow rate, which is the product of particle mass, particle concentration, and flow velocity in the fracture, can be then calculated for flow to the fracture.