This paper presents the results of a study regarding multiphase flow within proppant cells. Immobile liquid saturations (such as gel residue) were shown to increase the pressure drop by 3-fold compared to non-Darcy flow of dry gas. However, additions of minute quantities of mobile liquid increased the pressure drop by nearly an order of magnitude. The authors state:
“The increase in magnitude of the non-Darcy flow coefficient in the presence of a mobile liquid saturation is of too great a magnitude to be attributed solely to the decrease in available crosssectional flow area.”
This increase is apparently due to increased complexity of the flow regime and interaction between the two phases. Three-phase production models which merely account for changes in fluid saturation and relative permeability changes will have a difficult time matching the observed data.
The authors also found a relationship between proppant quality and beta:
“…the relationship between the non-Darcy flow coefficient and the permeability of a proppant depends on the manner in which the proppant reacts to a varying closure stress. The dependence of a proppant’s permeability upon application of closure stress is determined by the shape and strength of the proppant; therefore, if the proppant is of low quality (angular in shape and low in compressive strength), it will be broken into smaller pieces more easily than a high-quality (highly spherical and higher-compressive strength) proppant. This fracturing of the proppant under stress results in an increase in the number of particles and angularity of the particles and a decrease in the size of the particles, thus increasing the heterogeneity of the proppant, which will increase the non-Darcy flow coefficient.”
Author(s): E.V. Evans, Mississippi State U., and R.D. Evans, U. of Oklahoma
Paper Number: SPE 15066