Chemical Model for the Rheological Behavior of Crosslinked Fluid Systems
Authors: Conway Michael W. , Almond Stephen W. , Briscoe James Earl , Harris Lawrence E. 
Published: December 2007

Summary
The use of crosslinking agents to improve viscosity in polysaccharide polymer fluids is a widespread practice in hydraulic fracturing. The viscosity obtained from the use of a particular crosslinking agent depends entirely on the parameters of the in-situ chemical reaction to be performed at the wellsite. The major parameters encountered, such as concentration of polymer and crosslinking agent, pH, temperature, and shear regimen, will dictate the apparent viscosity of the product generated by the reaction. A mechanistic model for this crosslinking reaction is presented along with a description of the general effects of concentration, pH, temperature, and shear levels. Macroscopic observation of an ideal "complexed" gel is discussed using the most significant reaction parameters. Data show that the rheological properties of a crosslinked fracturing fluid are time-dependent and vary widely, depending on the reaction parameters to be encountered at the wellsite during a fracture treatment.

Introduction
Since their introduction as stimulation fluids to the industry in 1968, the use of crosslinked fracturing fluids has grown steadily. Today, they account for approximately 35% of the total volume of aqueous gels used in stimulation treatments. These fluids provide several advantages over non-crosslinked gels:greater viscosity per pound of polymer,friction reduction,wider fractures,better sand transport,more viscosity in high-temperature applications, andversatility and adaptability to a wide variety of treatment conditions.
Before a comparison between various crosslinked fluids can be made, it should be recognized that the rheological data are highly dependent on the experimental conditions under which they were obtained. One of our primary objectives is to emphasize the importance of some of the experimental conditions. There are many water-soluble polymers that can be crosslinked with a variety of crosslinking agents to form fracturing fluids. However, only a rather limited number of polysaccharide gelling agents have found extensive commercial application in fracturing fluids. Table 1 shows the many chemical elements that have been used successfully to crosslink polysaccharides materials. Each element has its own unique pH. oxidation state, and concentration range for optimal crosslink formation. Although many metals require specific salt and/or chelated derivatives as the delivery form, the resulting crosslinked gels exhibit many common properties. This paper is restricted to the natural polysaccharides (cellulose and guar gum) and their nonionic derivatives (Fig. 1). We use examples of crosslinking agents from Table 1 to illustrate the effect of shear, pH. temperature, and type of coordination on the general properties exhibited by crosslinked fluids.

Experimental Procedure
Viscosity measurements were made on a Model 50 or Model 39 Fann viscometer using a variety of bob and sleeve combinations as described in Ref. 10. The crosslinking reactions were performed by first prehydrating a 0.48 to 0.72 wt% solution of the base polymer (40 to 60 lbm/1,000 gal) in a blender for 30 minutes in the presence of an adequate buffer concentration to control pH. The ph-control agents used as buffers include fumaric acid, hydrochloric acid, acetic acid, formic acid, sodium bicarbonate, sodium carbonate, and sodium hydroxide.
JPT
P. 315^