An Effective Model for Pipe Friction Estimation in Hydraulic Fracturing Treatments

Abstract

Abstract An adequate model of pipe friction and fluid hydrostatic head is needed to allow understanding of bottomhole treating pressure trends during pumping. Models currently used by service providers appear to be inadequate, based on observation of field bottomhole treating pressure (BHP) plots. A new model is provided which has been extensively tested for gelled fluids, foams, and slick-water fracs. The model predictions are compared to direct measurements of BHP during typical high-rate treatments in various pipe sizes. Use of an adequate pipe friction model improves analysis of stimulation treating pressures and allows better decisions to be made regarding on-the-fly design changes and post-job interpretations of created fracture geometry and resulting conductivity. The paper presents a useful model for the estimation of pipe friction, slurry head, and surface treating pressure during hydraulic fracturing treatments. Introduction Interpretation of bottomhole treating pressure (BHTP) data is often an integral part of real-time and post-job fracture treatment diagnostics. Many people use plots or trend analysis of bottomhole pressure to make on-the-fly decisions regarding job design and execution. Inaccurate estimation of BHTP can lead to bad decisions and incorrect interpretation of fracture geometry or treatment behavior. Calculation of BHTP is comprised of two primary parts: hydrostatic head and pipe friction. The actual fracture treating pressure is further removed from the BHTP inside the wellbore by perforation friction and near-well pressure drop or "tortuosity". This paper does not address calculation of these two factors and focuses on the estimation of BHTP inside the pipe only. Equations are presented for straight water and oil, slick-water, linear polymer aqueous gels, crosslinked gels (both rapid and delayed crosslink systems), and N2 and CO2 foams. The method presented here is not expected to be a final solution to this complex problem. Matching observed bottomhole treating pressure data with the equations presented here points out the amount of variation in fluid properties that may occur during a job. It may not be possible to predict an accurate BHTP "on the fly" but application of a consistent method is expected to give better trend analysis. At worst, changes in calculated BHTP induced by surface input changes can be used to infer errors in the model inputs and improve overall prediction accuracy. Fluid Density and Hydrostatic Head Estimates For N2 and CO2 foam and assist treatments the estimation of "foam" fluid density during the job is a necessary starting point. Data are available from the National Institute of Standards (NIST) and other sources to characterize N2 and CO2 density as functions of temperature and pressure. Complex equations of state are also available that provide accurate estimates of these properties. For hydraulic fracturing operations a simpler method is desirable for rapid estimation of density while pumping. Equations 1 and 2 give useful estimates of CO2 and N2 density, in units of g/cm3, respectively. In the equations the temperature is in units of degrees Fahrenheit and pressure is in lbf/in2 (psi).