Multiphase Non-Darcy Pressure Drop In Hydraulic Fracturing

Valhall, an offshore field in Norway, is a black oil reservoir producing mainly through multi-fractured (with proppant) horizontal wells.  The bottom hole flowing pressure is well below the bubble point and hence the fracture conductivity is significantly constrained by multiphase non-Darcy pressure drop losses.

Geertsma in 1974 was the first to propose a multiphase Beta (non-Darcy constant) correlation as a function of permeability, porosity (size) and saturation.  Recent testing to measure the non-Darcy pressure drop for multiphase flow in proppant packs was successful in verifying a strong relationship to saturation.

Three different proppant types with three different resins were tested in a conductivity cell under field conditions, for a proppant loading of 4 lb/ft².  The proppant was placed in the cell using a 30 lb borate X-link fluid with encapsulated breaker for 24 hours to allow fluid break prior to conducting the flow tests.

The Geertsma type equation was used to match the laboratory data.  The equation constants (for permeability, porosity and saturation) for each proppant/resin type were delivered.  The non-Darcy correlations for each proppant were used in a numerical simulator to determine the pressure drop in the fracture and to quantify the effects on production rates.  This presentation highlights the importance of proppant size for optimizing fracture design for wells producing under multiphase flow.