The Effect of Viscous Fluid Properties on Excess Friction Pressures Measured During Hydraulic Fracture Treatments Stephen A. Holdltch, SPE, Brad M. Robinson, SPE, .lohn W. Ely, SPE, and Zillur Rahim, SPE, SA Holditch & Assocs. Inc. Summary. A plot of excess pressure vs. time can be used to predict fracture-growth patterns only when both the viscosity of the fluid in the fracture and the stress at the fracture tip remain constant. This paper uses laboratory data and field examples to explain how increased friction owing to viscous slurries affects the interpretation of fracturing pressures. Introduction Currently, no simple, affordable technique directly measures hy- draulic fracture dimensions. However, one can estimate values of fracture length and fracture conductivity by history matching field data with numerical simulators. Two types of simulators can be used: a fracture-propagation model for analyzing fracture treatment pressures and a reservoir simulator for history matching the post, fracture production performance. Both analysis techniques have been described in the literature 1-5 and are generally accepted in the in- dustry. Unfortunately, most engineers do not use numerical models to analyze field data because (1) the models are not available to the practicing engineer, (2) the input data needed to run the model are not available, and (3) most companies do not assign the manpower needed to solve the problem. As a result, more simplified analysis techniques are needed to evaluate hydraulically fractured reservoirs. In 1979, Nolte and Smith 6 presented a theoretical basis for understanding fracture-growth patterns and for estimating fracture dimensions on the basis of the interpretation of pressures measured during a fracture treatment. Specifically, by analyzing the excess pressure above closure pressure as a function of time, one could estimate the amount of fracture-height growth and/or the leakoff characteristics of the fluid in the fracture. Since Nolte and Smith's paper was first published, the methods proposed have been widely accepted and practiced within the pe- troleum industry. In many situations, the interpretation of excess pressure has led to a better understanding of hydraulic fracturing and improvements in the stimulation process. In certain situations, however, the interpretation of excess pressure is more complex than assumed in Nolte and Smith's work. In this paper, data from actual fracture treatments and from laboratory measurements are used to extend Nolte and Smith's observations. The information and data presented here were developed during work done over the past several years under contract to the Gas Research Inst. (GRI). Explanation of Original Concept Nolte and Smith presented "a basis for interpreting fracture-treating pressures that permits identification of periods of confined-height extension, uncontrolled height growth, and, more importantly, a critical pressure." They used Eq. 1 to explain the relationship among fracture length, fracture height, fluid leakoff, and excess pressure in the fracture: i=A.+LPeh(M. + dp + de + . ............... (1) L P e h dt See Ref. 6 for the derivation of this equation. Fig. 1 shows the various modes of pressure behavior observed in the original work. Mode 1 refers to the excess-pressure behavior expected on the basis of Nordgren's theories 7 when a fracture is propagating. Nordgren's work assumed that the injection rate, injection-fluid viscosity, stress at the fracture tip, fracture height, Copyright 1991 Society of Petroleum Engineers SPE Production Engineering, February 1991 and leakoff rate were all constant. Therefore, as the fracture length extended, the pressure in the fracture should increase with time. According to Nordgren's theories, during Mode 1 growth, frac- ture height is contained and the fracture grows normally. As Nolte and Smith began to analyze field data, they recognized that after a certain period of Mode 1 growth, many wells exhibited other behaviors, called Mode 2, Mode 3, and Mode 4 in Fig. 1. Mode 2 occurs when the change in excess pressure is essentially zero. To interpret this behavior, Nolte and Smith again assumed that the injection rate, fluid viscosity, and stress at the fracture tip were all constant. Therefore, to keep Eq. 1 balanced, either frac- ture height or fluid leakoff must increase during Mode 2. Both ex- planations are possible during an actual fracture treatment. Mode 2 represents the case where the excess pressure levels off at the critical pressure. The critical pressure is where "leaks" be- gin to develop either along the fracture walls or at the top and bottom fracture edges. If excess leakoff occurs during Mode 2, then one would expect the pad fluid to deplete eventually and the proppant to begin bridging in the fracture. When that occurs, fracture length and fracture height quit growing and a screenout occurs (Mode 3). Again, to interpret Mode 3 as the screenout mode, one must as- sume that the fluid viscosity in the fracture, injection rate, and stress at the fracture tip are constant. Mode 4 represents the case where pressure decreases rapidly in the fracture. The only logical explanation for such a decrease is a rapid increase in fracture-height growth. Factors That Affect Excess Pressure In Fig. I, P represents the excess pressure in the fracture. To de- velop a plot like that in Fig. 1, one must accurately measure or calculate the excess pressure. Eq. 2 shows that the excess pressure is a function of fracture width, fracture-fluid viscosity, fluid-leakoff characteristics, injection rate, fracture height, and rock compliance. p= f(b'Pf,A.,i,h,e). . ............................... (2) In the original Nolte-Smith paper, the values of viscosity, leakoff, injection rate, and compliance were all considered to be constant. The Nolte-Smith interpretation method relates the change in ex- cess pressure to changes in fluid loss and fracture height. When the fluid viscosity, injection rate, and stress at the fracture tip re- main constant, the Nolte-Smith interpretation method is accurate. However, if the fluid viscosity or stress at the fracture tip changes substantially, the interpretation of excess-pressure data becomes more complex. For example, the assumption of a constant-viscosity fluid during the treatment is not always valid. Eq. 3 illustrates that the viscosity of a sandlfluid slurry is a function of fluid viscosity, proppant con- centration, and shear rate in the fracture: Jl. s = f(Jl.f,Cp,t) . .................................. (3) When Nolte and Smith published their paper, most large frac- ture treatments were pumped with a rapid-crosslinked hydroxy- propyl guar (HPG) fluid. This fluid exhibits severe shear degradation when exposed to high shear rates in tubulars. By the time such a 9