The use of an inverse injectivity versus superposition time plot to diagnose the changing skin factor in a matrix acidizing treatment has been presented previously by Hill and Zhu1. The model has been extended to calculate skin factor as a function of injection time or injected volume directly to help the operator monitor and optimize the treatment. A Windows program based on the theory has been developed to provide a pretreatment test to evaluate the permeability and the initial skin factor of the formation when they are not available before the acid treatment, to calculate and plot the evolving skin during the treatment in real-time, and to evaluate treatments afterwards. It converts surface pressure, when measured, to the bottomhole pressure for the calculation, and handles fluid density and viscosity changes in real time. Several field examples showed that the technique can be used conveniently to monitor skin changes and diversion effects during matrix acidizing treatments. The program is reliable and flexible in acquiring and processing data, calculating skin, and diagnosing matrix acidizing treatments.
To monitor changing skin during a matrix acidizing treatment, the theory for a standard injectivity test using the approximate line source solution for transient flow during injection has been adopted1,2. The pressure transient response to injection for multiple injection rates is
Equations 2 and 3
and the superposition time function, ?tsup, is defined as
According to Eq. 1, a plot of inverse injectivity, (pi-pw)/qN, versus the superposition time function, ?tsup, will yield a straight line with a slope of m and an intercept of b. During an acid treatment, all of the parameters defining the slope, m, do not change, leaving m a constant. Among the parameters defining the intercept, b, the only one that changes as acid is injected is the skin factor, s. As a result, each inverse injectivity/superposition time point will l ie on a straight line having a slope, m, with its intercept depending on the skin factor at the moment. Thus, a family of constant skin curves can be calculated and plotted on a diagnostic chart of inverse injectivity versus superposition time function before the treatment, and the skin change can be monitored by locating the inverse injectivity as a function of superposition time on the chart.
This method is easy to apply in the field and the result is comparable with other more complicated methods developed before3,4,5, but it requires the user to read from the diagnostic chart and interpolate between lines of constant skin to obtain the skin factor in real time. The model has been extended so that the evolving skin is calculated directly in real time as the treatment proceeds, allowing the operator to monitor and optimize the treatment more conveniently.