Summary A practical mathematical model based on experimental data is presented for calculation of rheological properties of N2 and CO2 foam stimulation fluids. The laminar flow model is a yield pseudoplastic type, with viscosity dependent on foam quality, pseudoplastic type, with viscosity dependent on foam quality, yield point, base liquid consistency index (K'), and flow behavior index (n'). Turbulent foam flow data were analyzed with API RP39 procedures but were modified to include variable density effects procedures but were modified to include variable density effects of foam fluids. Water-based foam apparent viscosities compare closely to Mitchell's Bingham plastic model at high shear rates. The yield pseudoplastic model also includes viscous effects of gelling agents and measurement at much lower shear rates. Comparison of predicted pipe friction was made to actual field wellhead pressures with good agreement. Introduction Foams are being used in a number of petroleum industry applications that exploit their high viscosity and low liquid content. Some of the earliest applications for foam dealt with its use as a displacing agent in porous media and as a drilling fluid. Following these early applications, foam was introduced as a wellbore circulating fluid for cleanout and workover applications. In the mid-1970's, N2-based foams became popular for both hydraulic fracturing and fracture acidizing stimulation treatments. In the late 1970's and early 1980's, foamed cementing became a viable service, as did foamed gravel packing. Most recently, CO2 foams have been found to exhibit their usefulness in hydraulic fracturing stimulation. Regardless of why they are applied, these compressible foams are structured, two-phase fluids that are formed when a large internal phase volume (typically 55 to 95%) is dispersed as small discrete entities through a continuous liquid phase. Under typical formation temperatures of 90F [32.2C] encountered in stimulation work, the internal phases N2 or CO2 exist as a gas and hence are properly termed foams in their end-use application. In this properly termed foams in their end-use application. In this paper, we consider the formations of such fluids at typical paper, we consider the formations of such fluids at typical surface conditions of 75F [23.9C] and 900 psi [6205. kPa] where N2 is a gas but CO2 is a liquid. A liquid/liquid two-phase structured fluid is classically called an emulsion. The end-use application of the two-phase fluid, however, normally is above the critical temperature of CO2 where only a gas can exist, so we have chosen to consider the fluids together as foams. Evidence is presented later to show the similarity of two-phase structured fluids independent of the state of the internal phase. The liquid phase typically contains a surfactant and/or other stabilizers to minimize phase separation (or bubble coalescence). These dispersions of an internal phase within a liquid can be treated as homogeneous fluids, provided bubble size is small in comparison to flow geometry dimensions. Volume percent of the internal phase within a foam is its quality. The degree of internal phase dispersion is its texture. At a fixed quality, foams are commonly referred to as either fine or coarse textured. Fine texture denotes a high level of dispersion characterized by many small bubbles with a narrow size distribution and a high specific surface area, and coarse texture denotes larger bubbles with a broad size distribution and a lower specific surface area.

This paper explains the variables involved in borate chemistry as they affect crosslink formation, stability, and breaking properties. The borate-ion concentration in solution is a function of pH and temperature. A method for calculating borateion equilibria is used to help establish the required final pH value for application of a borate-crosslinked gel at a specific temperature. IntroductionMany of the properties of borate-crosslinked fluids can be explained in terms of the shift in borate-ion equilibria with pH and temperature. Syneresis, the process of forming a dense polymer mass and excluding liquid from the structure, is easily understood as a product of increased borate-ion concentration when a fluid is cooled. Proppantsettling behavior that is pH-dependent also can be explained. As the equilibrium concentration of borate ion increases with increasing pH, the number of network crosslinks increases and hence the proppantsettling rate decreases.Rheological measurements from flow-

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

Summary A new laboratory technique was developed to measure changes in foam texture (bubble-size distribution) vs. foam viscosity in a recirculating pipeline viscometer. Fluid variables studied included foam quality, surfactant type and concentration, gelling-agent concentration, shear history, system pressure, and liquid-phase chemical type. The viscous properties of foam fluids are determined primarily by quality (internal-phase volume) and liquid-phase properties. The viscosity of an equilibrated foam is influenced by texture to a lesser extent. Foams are shear-history-dependent fluids. The bubble size and degree of dispersion will adjust to an equilibrium state that depends on time at a given shear rate. Finer-texture foams are produced by higher shear rates, higher surfactant concentrations, and higher pressures. Viscosity measurements at low pressure may not adequately simulate field use at high pressure. The liquid-phase chemical type influences texture. The structure of methanol and hydrocarbon foams may result in sensitivity to degradation at high shear rates. Introduction in a number of theoretical and experimental studies of foam behavior, the influence of bubble-size distribution or texture has been recognized. Although polydisperse distributions have been recognized as a more general case than monodisperse distributions, there has been no agreement on how various degrees of dispersion relate to dynamic properties. For this reason, an empirical approach was undertaken to determine the effect of real bubble-size distributions on the rheological properties of foam. Results are limited only by the ability to generate various types of distributions that retain their identities long enough to be measured. To assess the influence of bubble size on the behavior of foam fluids, one must gain an appreciation of the bubble sizes that actually exist in real foams. It is common to speak of either coarse or fine-texture foams, referring to relatively large or small bubble sizes, respectively. Different samples are readily compared by reference to the average diameter, or mean, of each sample. But the real samples considered here have a range of sizes in each sample. How broad the range of sizes is in each bubble-size distribution may be equally as important as the mean size of the distribution. The particular type of mean (volume, surface volume, surface area, or number) used for comparison may also be important. Several opposing factors influence the eventual bubble-size distribution at equilibrium. Shear forces reduce large bubbles to smalr sizes. Sufficient surfactant must be present to stabilize the newly created surfaces. The smallest mean bubble-size distributions are created by high shear rates. There is probably a limiting upper shear rate for a given quality and liquid-phase chemical system beyond which the foam structure will collapse. At low shear rates, the bubbles tend to grow larger and coalesce as a result of gas diffusion between bubbles. At very low shear rates, liquid drainage also becomes significant. A proper balance of all factors must be considered in the determination of the physical properties of such a dynamic fluid as foam. Experimental Foams were prepared and circulated through a foam pipeline loop viscometer as described previously. Foaming surfactant and any viscositying agent [hydroxypropyl guar (HPG)] were added to the liquid phase of the fluid before introduction to the loop. N, gas was added through a small orifice to liquid circulating in the loop. When the specific gravity for the desired foam quality was attained, N2 addition was stopped. Foam fluids were recirculated by a Zenith QM BLB pump, having 22 teeth per gear. Spacing between teeth was much larger than the bubble diameters. Experiments with different sizes of tubing in the flow loop indicated that shear effects were attributable to shear rates in the pipe and not to the pump. Wail slippage effects were considered negligible. A new instrument developed for measuring foam texture sampled the entire foam contents within a shown length of tubing, rather than looking at a possibly skewed sample near the surface of a glass Bubble-size-distribution measurements were made by taking foam samples from the recirculating loop and then conditioning and counting the separated bubbles. The apparatus is shown in Fig. 1. The valving arrangement (Fig. la) allowed a fresh foam sample to be taken from a flowing stream in the loop. Foam flowed through two plug valves and a specially built three-way valve to fill the sample plug valves and a specially built three-way valve to fill the sample tube. Once the sample valves were fined with fresh fluid, valves were switched, as shown in Fig. lb, to isolate approximately 2.8 mL of foam. A bubble-separator chamber, an HIAC (Ref. 17) E-2500 particle-detector cell, and a liquid-phase reservoir were placed particle-detector cell, and a liquid-phase reservoir were placed vertically in line above the three-way sampling valve. A continuous column of the liquid phase was necessary in the HIAC detector cell at all times for proper counting. A liquid-equalizing tube around the detector cell helped maintain this liquid column. As soon as the three-way valve was positioned as shown on the right side of Fig. 1, liquid began to displace foam from between the two valves. Foam separated into individual bubbles, with the largest bubbles rising fastest through the bubble-separator chamber. It is assumed that diluting a foam with a fluid identical to its liquid phase does not alter the volume or size distribution of the discrete, internal-phase bubbles. This assumption requires that the liquid phase in the counter be saturated with N2 before introduction of the foam sample. Separated bubbles were columnated, rose into the detector cell, and were counted photoelectrically. Electrical impulses were separated into six size ranges by a multichannel analyzer. These partitioned sizes were converted mathematically to volumes, and geometric standard deviations and volume means were calculated. Immediately after the sample was taken for texture determination, rheograin measurements were made on foam circulating in the loop. Next, static drain time was measured by closing valves immediately before and after a 10-in. [25.4-cm] -high visual cell and observing the liquid/foam interface rise from the bottom. The time required for one-half of the liquid in the sample to drain to the bottom was recorded.

Dynamic fluid-loss measurements were conducted on core samples ranging in permeability from 0.02 to 140 md to measure the effect of several parameters on the foam fluidloss coefficients. The parameters tested were core permeability, gel concentration in the liquid phase, foam quality, temperature, core length, and differential test pressure. Realistic fluid-loss coefficients are necessary for proper design of foam fracturing treatments.The type of foam used in most conventional fracturing treatments is a wall-building fluid. Although this foam has excellent inherent fluid-loss properties, the fluid-loss values reported in this paper resemble those of conventional fracturing fluids more closely than reported earlier. These values have been used in the successful design of field fracturing treatments.These data support the mechanism of two-phase flow in porous media suggested by Holm. 1 The fluid passing through the cores was rich in liquid phase with composition proportional to the viscosity of the liquid phase.The broad range of fluid-loss coefficients for foam calculated in these tests is intermediate in value to those reported in similar tests by Blauer and Kohlhaas,2 who obtained lower values, and King, 3 who obtained higher values.