Mathematical Model Simulates Actual Well Conditions In Fracture Acidizing Treatment Design

Abstract

A new mathematical model has been developed which considers more of the variables encountered during fracture acidizing treatments than previous models. In particular the variables include, wellbore cooldown, temperature profile of fluid in the fracture, the fracture geometry created by both non-reactive and reactive fluids the spending of the leading edge of the acid, and the conductivity of the etched fracture faces. Productivity increases calculated by the new program correlate more closely with actual field results than those calculated by previous programs. This paper describes the previous programs. This paper describes the method of handling the variables in setting up the new model and presents the equations used to describe the reaction rate of the acid. Introduction Fracture acidizing has been used for stimulating wells for over 25 years. The techniques used have developed more as an art, than a science, often based on intangible ideas, rather than on predictable facts. Although a mathematical model has been available since the early 1960's, little correlation has been observed between predicted and field results. One reason for this undoubtedly was due to the use of the acid as both the hydraulic fracturing fluid and as the reactive fluid. Another was the inadequacy of the model to describe the rheological and physical properties of the fluids in the fracture. properties of the fluids in the fracture. Only when treating techniques changed, in which better results were obtained by creating the fracture with a non-reactive pad fluid ahead of the acid, was serious effort directed toward describing the conditions or properties of the fluids in the fracture. Equations were developed first to describe the cooldown of the wellbore area, as illustrated by Ramey's "Wellbore Heat Transmission" equations in the Appendix. Then, Whitsett and Dysart, and later Sinclair, proposed methods for describing the proposed methods for describing the temperature profile of fluids within a hydraulic fracture. Hall and Dollarhide provided basic equations for considering the fracture geometry created by more than one fluid within the fracture.

Pumping Schedule Optimization in Acid Fracturing Treatment by Unified Fracture Design

“…An acid transport equation for the one-dimensional steady-state is presented [1,2]. Also, a method was established to describe the matrix acidizing, considering all the variables [3]. Schechter (1992) assumed that all flow entering between the plates uniformly leaks out the channel and calculated velocity profiles with Berman's method [4,5].…”

Pumping Schedule Optimization in Acid Fracturing Treatment by Unified Fracture Design

“…An acid transport equation for the one-dimensional steady-state is presented in [1,2]. Additionally, a method was established to describe the matrix acidizing, considering all the variables [3]. Schechter assumed that all flow entering between the plates leaks out of the channel uniformly and calculated velocity profiles with Berman's method [4,5].…”

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.…”