PRESSURE DERIVATIVE METHOD – WELL TESTING

The type curve approach for the analysis of well testing data was developed to allow for the identification of flow regimes during the wellbore storage-dominated period and the infinite-acting radial flow. It can be used to estimate the reservoir properties and wellbore condition. However, because of the similarity of curves shapes for high values of Cdë2S which lead to the problem of finding a unique match by a simple comparison of shapes and determining the correct values of K, S and C. Tiab and Kumar (1980) and Bourdet et al. (1983)

addressed the problem of identifying the correct flow regime and selecting the proper interpretation model. Bourdet and his co-authors proposed that flow regimes can have clear characteristic shapes if the “pressure derivative” rather than pressure is plotted versus time on the log–log coordinates.

Since the introduction of the pressure derivative type curve, well testing analysis has been greatly enhanced by its use. The use of this pressure derivative type curve offers the following advantages:

• Heterogeneities hardly visible on the conventional plot of  well testing data are amplified on the derivative plot.
• Flow regimes have clear characteristic shapes on the  derivative plot.
• The derivative plot is able to display in a single graph many  separate characteristics that would otherwise require different plots.
• The derivative approach improves the definition of the analysis plots and therefore the quality of the interpretation.

The fundamental basis for the pressure derivative approach is essentially based on identifying these two straight lines that can be used as reference lines when selecting the proper well test data interpreting model.

That picture  illustrates that the effect of skin is only manifested in the curvature between the straight line due to wellbore storage flow and the horizontal straight line due to the infinite-acting radial flow.

The derivative pressure data provides, without ambiguity, the pressure match and the time match, while the Cdë2S value is obtained by comparing the label of the match curves for the derivative pressure data and pressure drop data.

The theory which describes the unsteady-state flow data is based on the ideal radial flow of fluids in a homogeneous

reservoir system of uniform thickness, porosity, and permeability. Any deviation from this ideal concept can cause the predicted pressure to behave differently fromthe actual measured pressure. In addition, a well test responsemayhave different behavior at different times during the test. In general, the following four different time periods can be identified on a log–log plot of P vs. T as shown in that picture:

1. The wellbore storage effect is always the first flow regime to appear.
2. Evidence of the well and reservoir heterigeneities effect wll then appear  in the pressure behavior response. This behavior may be a result of multilayered formation, skin, hydraulic fractures, or fissured formation.
3. The pressure response exhibits the radial infinite-active behavior and represents an equivalent homogeneous system.
4. The last period represents the boundary effects that may occur at late time.