High-Temperature Rheological Study of Foam Fracturing Fluids
Authors: Harris P.C. , Reidenbach V.G. 
Published: December 2007

Summary.
Two significant observations were made during measurement of N2 foam properties at temperatures up to 300 degrees F [149 degrees C] in a high-temperature, high-pressure recirculating loop viscometer:foam fluids did not thin as rapidly as gel fluids under similar conditions, so foams offer inherent advantages for high-temperature stimulation work, andhigh gelling-agent concentrations do not improve dynamic foam stability; instead, high-temperature dynamic stability depends on surfactant type and concentration.
Mathematical equations have been developed from experimental data to describe foam rheological behavior from 75 to 300 degrees F [24 to 149 degrees C], 0 to 80 quality, containing 0 to 80 lbm hydroxypropyl guar (HPG)/1,000 gal [0 to 9586 g HPG/m3] in the aqueous phase. Basic physical properties previously outlined determined foam rheological physical properties previously outlined determined foam rheological behavior at 75 degrees F [24 degrees C]. Foams were classified as yield-pseudoplastic-type fluids. This paper extends the previous work from 75 to 300 degrees F [24 to 149 degrees C] and covers a broader range of external liquid-phase compositions applicable to foam stimulation work.

Introduction
Reidenbach et al. recently outlined the basic physical properties that determine foam rheological behavior at properties that determine foam rheological behavior at 75 degrees F [24 degrees C]. Important laminar flow parameters included texture (bubble-size distribution), parameters included texture (bubble-size distribution), quality, liquid-phase properties (n and K), and yield point. Foam fluids were classified as yield-pseudoplastic point. Foam fluids were classified as yield-pseudoplastic or Herschel-Bulkley type. Because foams used for stimulation are normally used with bottomhole temperatures above 75 degrees F [24 degrees C], N2 foam properties were measured at temperatures up to 300 degrees F [149 degrees C]. Foam fluids did not thin as rapidly as base gel fluids under similar conditions. We had anticipated using n and K values for base gel fluids at elevated temperatures in the room-temperature foam equations to predict foam properties at elevated temperatures. Such calculated viscosities generally were lower than experimental viscosities at elevated temperatures. To include temperature effects properly, therefore, the original equations had to be modified.

Theory
The basic laminar flow equation for pressure loss of foam fluids in a pipe has been given asThe yield point, sigma yp, is a function of quality, gamma, only. Gamma is the ratio of gas volume to gas plus liquid volume at a specific temperature and pressure. For gamma less than 0.6,and for gamma greater than 0.6,The consistency index of the foam, Kf, depends on the consistency index of the liquid gel phase, KL, its quality, and a tabulated empirical constant, C1, according toIn actual use, C1 varies with liquid-phase gelling-agent concentration.
The flow-behavior index, n, was assumed to be the same for both gel phase and foam. From the initial high-temperature experiments using 70-quality N2 foam and various gelling-agent concentrations, we did not know the functional relationship, if any, between yield point, consistency index, and flow-behavior index vs. temperature. It was apparent that the fluid-behavior index remained nearly constant with increasing temperature, but the consistency index decreased with increasing temperature. The effect of temperature on yield point with various gel concentrations was uncertain. Data are presented that examine the effect of these parameters on foam viscosity.

Experimental Procedure
The recirculating flow-loop viscometer was based on 0.305-in. [7.75-mm]-ID stainless-steel tubing. Valves in the flowline were the full-opening ball type. Fig. 1 is an outline of the flow pattern. The aqueous phase of the fluid to be tested was pumped from a 5-L pressure vessel to the loop by a metering pump. The loop was filled with liquid to a pressure of pump. The loop was filled with liquid to a pressure of 1,000 psi [6.9 MPa], as regulated by a backpressure regulator. During the filling process, fluid flowed through a mass flowmeter. Specific gravity was read to three decimal places with computer averaging. The specific gravity reading allowed foam quality to be adjusted on-line. A glass inspection gauge allowed visual inspection of the fluid.
JPT
p. 613