Abstract
In a fracture acidizing treatment the acid reacts with the fracture faces. This acid/rock reaction generates heat that causes the acid temperature itself to increase. To predict accurately the temperature profile and acid spending rate of acid traveling down a hydraulically created fracture, this heat must be considered.Since the heat generated by reaction depends on the reaction rate, the thermal energy equation must be coupled with the acid spending equation. A model has been developed that, for the first time, examines the effect of the heat of reaction on fluid temperature and acid penetration in a fracture. Some sample calculations have also been made to illustrate the effects of the most important parameters on acid penetration in a fracture.
Introduction
Acid hydraulic fracturing is a common method of stimulating a reservoir. Acid selectively reacts with, and dissolves, portions of the fracture wall so that a finite fluid conductivity remains when the well is returned to production. An important aim in designing such fracturing treatments is determining the distance that live acid will penetrate down the hydraulically induced fracture. This distance is usually called the acid penetration distance and is essential to estimate the production improvement from a given treatment.Because of its importance in predicting stimulation ratio, acid penetration in fractures has been studied by numerous investigators. They assumed the temperature in the fracture was uniform. In real fractures, however, the temperature will vary from the wellbore to the tip of the fracture. Therefore, the assumption of constant temperature seems to be an oversimplification.Whitsitt and Dysart were among the first to study the temperature distribution in a fracture. They constructed a model but it could be applied only to a nonreacting fluid flowing in a fracture because the heat generated by an acid/rock reaction was not considered. In a fracture acidizing treatment, the acid is reacting with the rock walls. This acid/rock reaction generates heat, which causes the acid temperature itself to increase. To predict accurately the temperature profile along the fracture, this heat also must be considered. A model has been developed that, for the first time, examines the effect of the heat of reaction on fluid temperature and acid penetration distance.
Mathematical Development
The mathematical model is a modification of that introduced by Whitsitt and Dysart to allow for the heat of reaction in the energy-balance equation. Since the heat generated by the acid reaction also depends on the reaction rate, the thermal-energy equation is coupled with the mass-balance equation. These two equations must be solved simultaneously .The model for acid spending in a fractures is illustrated in Fig. 1. The fluid leakoff velocity Vw is assumed constant over the fracture length. Assuming steady-state flow in a vertical fracture and constant fluid properties, the mass-balance equation for acid flowing in a fracture is
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SPEJ
P. 501＾
Analysis of Selected Methods Use for Calculation of the Coefficients of Adsorption Isotherms and Simplified Equations of Adsorption Dynamics with the Use of IZO Application
