Modeling Permeability and Fluid Flow Through Packed Particles: From a Unitary System to Binary Mixture

Abstract

Solid particles have been widely used in the petroleum industry for applications including fluid diversion, wellbore strengthening and hydraulic fracturing. The corresponding permeability and fluid flow through packed particles (diverting agents or proppant sands) dictate the effectiveness of such operations. However, to account for the complexity of binary particle mixtures, a more generalized model is required to accurately predict the porosity and permeability, and hence fluid flow.

Conventional Kozeny-Carman equation is well accepted to describe the permeability of a particle system composed of mono-sized grains. However, for a particle system with two distinct sized grains, its porosity and fluid path are a complex function of small grains. An analytical model is introduced to analyze the porosity and permeability of a binary particle system. A modified Ergun correlation models fluid flow through packed solid grains. These models have been calibrated with experiments and verified with field data.

The impact of particle composition on fluid flow with regard to permeability and associated pressure drop is investigated through sensitivity analysis. The sensitivity results show that the resulting pressure drop through a packed particle system is dominantly influenced by particle size and ratio, which are the keys for determining the porosity and permeability of a binary mixture. The presence of small particles can significantly impact the porosity and fluid path. From both model predictions and field data analyses, it confirms that a minimal of porosity and permeability can be obtained by adjusting the particle ratio, which is the ultimate goal of fluid diversion and wellbore strengthening applications. Through a field case study, our analyses show that the diverter design can be optimized to enhance fluid diversion efficiency.

The proposed model can simulate the grain-packing and fluid-flow phenomena through the packed particle system. In this model, the porosity and permeability are predicted based on the particle size and ratio. This model is applicable for estimating permeability and fluid flow through both unitary and binary systems. Our analysis shows that the composition and utilization of binary particle systems can be customized to reach the expected goals for different field applications.