Abstract

Despite the existence of many correlations to predict the friction pressures of fracturing predict the friction pressures of fracturing fluids, there is little understanding of the effects of viscoelastic properties on this behavior. One reason for the relative lack of understanding of this problem is that the interactions between the turbulent velocity fluctuations and the viscoelastic fluid properties that cause the observed friction pressures are extremely complex. As a result, there are no theoretically-based methods for either pipe diameter scale-up or friction pressure predictions for fracturing fluids.

This paper presents an attempt to predict turbulent friction pressures of fracturing fluids by extending results of a numerical simulation for viscoelastic fluids found in the literature. The literature work provides near-wall velocity profiles for two viscoelastic fluid models. These profiles for two viscoelastic fluid models. These profiles are integrated to generate friction factor profiles are integrated to generate friction factor versus Reynolds number expressions with the Deborah number as a parameter. Comparison to available data shows good agreement but requires an independent calculation for the Deborah number. Calculations using three Deborah number correlations yield inconsistent results. The lack of agreement between the theory and the data suggests increased modeling sophistication is needed to predict friction pressures of fracturing fluids in turbulent pipe flow.

Introduction

Most fracturing fluids are rheologically characterized as power-law fluids, which are described with the power law index (n') and consistency index (K'). While the power-law model accurately describes the viscosity of fracturing fluids, it fails to predict the friction pressure behavior of these fluids pumped in pressure behavior of these fluids pumped in turbulent pipe flows. The measured turbulent friction pressures of water-based polymeric fracturing fluids are typical of viscoelastic fluid systems and do not match data or theories for power-law fluids. To accurately predict friction power-law fluids. To accurately predict friction pressure behavior of fracturing fluids one must pressure behavior of fracturing fluids one must account for the viscoelastic properties of the fluid system. Unfortunately, there are no analytical methods available to predict friction pressures of viscoelastic fluids in turbulent flow, and predictions are based on correlations to available predictions are based on correlations to available data.

Drag reduction in turbulent flow was first reported in 1948 by Toms who found that small amounts of polymer dissolved in water would significantly reduce the turbulent friction pressures. pressures. P. 563

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