Parameters affecting the distribution of pulsed proppant in hydraulic fractures

Abstract

Intermittent proppant injection into hydraulic fractures is a newly-developing technology in well stimulation. It is designed to form voids inside proppant packs which serve as highly conductive channels for oil and gas transport. However, it remains unclear the extent to which this non-homogeneous, pulse-like proppant concentration persists over the extent of the fracture. This paper models proppant transport in a PKN (Perkins–Kern–Nordgren) fracture in which the proppant-laden and proppant-free fluids are pumped intermittently. Simulations are performed to investigate proppant transport and final distribution under the influence of various factors. It can be observed that several parameters such as Young's modulus and fluid injection rate have significant influence on proppant transport, particularly the spatial period and attenuation of the resulting waves of proppant concentration as they move into the growing fracture. In contrast, when fluid viscosity is high, some parameters such as density difference, particle size do not strongly affect spatial period and attenuation of the proppant waves. The simulations show when the proppant is injected intermittently using high viscosity fracturing fluid, proppant concentration inside a hydraulic fracture from wellbore bottom hole to fracture tip is non-uniform and appears like a damped wave. An equation which is similar to damped wave solution is used to describe this proppant concentration characteristic, thus enabling a dimensional analysis to identify the key parameters affecting proppant distribution and specifically the attenuation of the concentration waves. Two characteristic lengths can be associated with attenuation of these proppant waves prior to severe screen-out and settlement– one for cases with leakoff and one for cases without leakoff. After scaling the horizontal coordinate by the appropriate characteristic length, the relationship between concentration amplitude and dimensionless distance for all cases can be depicted in a uniform way.