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Accurate estimation of fracture width is necessary for successful hydraulic fracturing or FracPac treatments. This information becomes even more critical when most of the fluid leakoff is forced through the proppant pack and out through the tip of the fracture during hydraulic fracturing or FracPac treatments. With the development of new, low-leakoff fluid systems, the coupling of fluid flow through porous media and subsequent pressure responses must be incorporated in predicting fracture-width profile. The generalized width equations, although well-known, are seldom solved for cases other than constant pressure throughout the fracture or for simple pressure distributions. This paper demonstrates how these complex fracture-width equations can be solved for an arbitrary pressure distribution in a simplified approach. The generalized width equations for fracturing calculate a fracture’s width along its length or radius, w(x) or w(r), given a pressure profile, p(x) or p(r). Two main width techniques are discussed, one based on a modified Perkins-Krech approach and the other on a corrected Valko-Economides approach. A comparison to the Jaeger-Cook deflection equation is made. In the Perkins-Krech and the Jaeger-Cook cases, the method of superposition is used. In the Valko-Economides case, the pressure is fit with a polynomial equation, and the integration is carried out term by term. The results are comparable with a finite element analysis (FEA) model, and good agreement has been observed. Examples are presented on how these techniques can be set up in spreadsheets, allowing the engineer to investigate concepts like "dry tip" and stresses around a fracture perimeter.

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Summary During acidizing stimulation or cleanup operations, metal tubulars, downhole tools/valves, and surface lines are exposed to acidic fluids and are prone to corrosion. Because corrosion rates drastically increase in high-temperature wells, controlling corrosion is critical and must be dealt with carefully. In addition, corrosion protection is important for maintaining the integrity and long life of downhole tools installed in a well. Several corrosion inhibitors, such as quaternary ammonium compounds and propargyl alcohol-based compounds, have been effectively used in the industry. However, because of stringent environmental regulations, attention has focused on the development of new corrosion inhibitors that are environmentally benign. Food-grade products that are considered "green" chemicals have significant potential as corrosion inhibitors in the oil and gas industry. In this paper, application of chicory as a corrosion inhibitor for high-temperature and strong-acidic conditions is discussed. Chicory is a perennial bush plant available in many parts of the world. The root of the chicory plant can be roasted and ground for use as a coffee substitute or additive. Chicory is environmentally acceptable and, being of plant origin, is widely recognized as biodegradable in nature. This study shows that chicory can provide corrosion protection for alloys such as N-80, 13Cr-L80, and 1010 steel in the presence of either inorganic or organic acids at temperatures up to 250°F (121°C). Considering its performance and lack of toxicity issues, chicory has significant potential for acid corrosion-inhibition applications. The mixing procedure for preparing the blend, experimental setup and test procedure, and laboratory results of high-pressure/high-temperature (HP/HT) corrosion tests are discussed.