Viscoelasticity of Crosslinked Fracturing Fluids and Proppant Transport

Abstract

ABSTRACT In hydraulic fracturing treatments, the success of the treatment strongly depends on the proper placement of the proppant particles in the fracture. By proper placement, one means the packing of the fracture to achieve maximum conductivity of gas/oil through the fracture into the wellbore. The placement of the proppants along the fracture is based on design equations where sand transport velocity is related to the rheological parameters of the fracturing fluid and characteristics of the proppant particle such as size and density. The current design equations consider viscous parameters such as K' and n' of power-law model. In practice, however, there are numerous cross-linked fracturing fluids which are not just viscous, but visco-elastic in nature. At present, there are no design equations for proppant transport that can be incorporated into a hydraulic fracturing program which takes into account linear and non-linear viscoelasticity of cross-linked fluids. The purpose of this paper is three fold. The first part of the paper describes the theoretical transport equations that take into account the elasticity of the fluid in predicting proppant settling rate in the fracture. The second part of the paper presents the experimental data of commonly used fracturing fluids (titanate and borate cross-linked). The rheology data includes both viscous and elastic parameter measurements using Rheometrics Pressure Rheometer and Rheometrics Mechanical Spectrometer. This data shows some important differences between borate cross-linked gels and titanate cross-linked gels. The third part of the paper presents experimental data of proppant settling rates in various fracturing fluids and how these can be correlated with rheological parameters that were obtained in this work. The difference in rheology between borate and titanate gels was correlated with the difference in settling rates of proppants in these two gels. Based on the theoretical and experimental work presented in this paper, it is concluded that the model for proppant placement in a hydraulic fracture should include: (i) proppant characteristics, (ii) viscous rheological parameters (K' and n'), (iii) elastic parameters (complex dynamic viscosity) from linear viscoelastic constitutive equation, and (iv) normal stress difference from non-linear viscoelastic constitutive equation. The influence of cross-linked polymer gel network structure on proppant transport is also discussed.