An Analysis of the Acidizing Process in Acid Fracturing

Abstract

The theoretical analysis of the acid-fracturing process for turbulent-flow conditions has been process for turbulent-flow conditions has been reconsidered taking fluid losses into account. For a simple fracture model and an idealized acidizing process, the acid concentration in the fracture process, the acid concentration in the fracture during acid injection and the fracture width have been determined as functions of time and place for three loss conditions:no fluid loss,fluid loss proportional to time, andfluid loss proportional to the square root of time. proportional to the square root of time. From the results of the analysis, it is concluded that even under the unfavorable conditions of turbulent flow in the fracture and fluid loss, acid penetration is, in general, not a limiting factor in penetration is, in general, not a limiting factor in the application of the acid-fracturing process. However, it will not be possible to predict the productivity increase resulting from a given productivity increase resulting from a given treatment until more experimental data on the conductivity of etched fractures and on certain aspects of the reaction kinetics have been gathered. Introduction Acid-fracturing treatments are frequently applied to improve well productivity in limestone formations. In this process, hydrochloric acid is injected into a hydraulically induced fracture, which extends diametrically from the wellbore into the formation. During injection, the limestone faces of the fracture are dissolved. As a result, acid is consumed and its concentration decreases in the direction of flow. The width of the fracture increases, and the fracture faces may become irregularly etched as a result of the natural anisotropies of the formation. The etching pattern produced may contribute to an improvement in fracture conductivity after the fracture is allowed to close. The extent of this etching into the fracture and its final fluid conductivity determine the increase in productivity. Barron et al. have presented an empirical formulation of the acid-fracturing process for laminar flow conditions without fluid loss. When a theoretical description given by Prins et al. concerning the heat-transfer in laminar flow between parallel plates, is applied to the acid-fracturing parallel plates, is applied to the acid-fracturing process, the acid concentration in a fracture for process, the acid concentration in a fracture for steady-state laminar flow can be exactly described, provided that the fracture width is constant and no provided that the fracture width is constant and no fluid loss occurs. A comparison of the acid concentrations calculated from the empirical reaction-rate data of Barron with those theoretically derived according to Prins shows that these values are of the same order of magnitude and can be made equal for acceptable values of the diffusion rate only in the range of low velocities. Judging from the experimental set-up of Barron, we believe that for higher velocities the entrance transition length for fully developed laminar flow should be longer. For this reason, no agreement in the higher velocity ranges can be expected. This view is supported by Williams et al., who compared theoretically derived reaction rates in the heterogeneous calcium-carbonate /hydrochloric-acid system with those of Barron et al., who also conclude that entry effects may be responsible for the discrepancies in the higher velocity range. Nierode and Williams determined a kinetic model for the heterogeneous reaction of hydrochloric acid with limestone. The reaction order and rate constant used in their model were obtained from experiments. On the basis of this model, they derived an acid-fracturing design for laminar flow conditions including fluid loss. In the study described below, the acid-fracturing process has been reconsidered for turbulent-flow process has been reconsidered for turbulent-flow conditions in which both fluid loss and change in fracture width have been taken into account. We feel that the study provides a more realistic description of the process for both a vertical and horizontal fracture and that it may be used as a bask for designing acid-fracturing treatments. MATHEMATICAL DESCRIPTION OF THE ACIDIZING PROCESS FOR A RECTILINEAR FRACTURE A vertical rectangular fracture (rectilinear) with initially plan-parallel and flat fracture faces was adopted as a fracture model. SPEJ P. 239

Dynamic Etching Tests Aid Fracture-Acidizing Treatment Design

“…It has been shown that increased turbulence generally increases the rate of dissolution of the fracture face. 16,23,25 After the face of the test sample is turned flat, a hole is drilled through the axis of the sample and the lead mounting. The sample is then placed in the etching test cell with the turned face of the sample touching an ampcoloy plate, which acts as the opposite fracture face.…”

“…7,[12][13][14] Fracture geometry relating to carbonate stimulation by fracture acidizing has also been researched. [15][16][17] With regard to fracture conductivity, however, more emphasis has been placed on the volume of rock removed and the length of etched fracture than on the actual conductivity generated. Most etched-fracture-conductivity calculations are based on an ideal fracture conductivity.…”

New Correlations of Acid-Fracture Conductivity at Low Closure Stress Based on the Spatial Distributions of Formation Properties

“…Generally, effective fracture length is shorter than dynamic fracture length and liveacid-penetration distance because the fracture may be closed under closure stress. In early acid-fracture designs Nierode et al 1972;van Domselaar et al 1973;Roberts and Guin 1974;Coulter et al 1974), fracture conductivity was assumed to be infinite to a distance from the wellbore where the acid is 10% of its initial concentration.…”

A New Acid Fracture Conductivity Model Based on the Spatial Distributions of Formation Properties

“…Acid fracturing design models date back to the early 1970's. In early acid fracture designs Nierode et al, 1972;van Domselaar et al, 1973;Roberts and Guin, 1975;Coulter et al, 1974), fracture conductivity was assumed to be infinite to a distance from the wellbore to where the acid is 10% of its initial concentration. Of course, acid fracture conductivity is not infinite.…”