Pressure Buildup in Reservoir Limit Testing of Stratified Systems
Authors: Kazemi Hossein 
Published: December 2007

If a reservoir is characterized by a special type of heterogeneity such as stratification with no crossflow, the usual methods of determining reservoir limits are either not applicable or not practical. Proposed here is a way of estimating the drainage radius from pressure buildup data - a method especially useful whenever the drawdown data are not reliable.

Introduction
The reservoir limit test is a method of determining either the proximity of the boundaries of a reservoir to a flowing well or the size of drainage volume associated with the well. This method makes use of the usual equations for pressure drawdown and was first introduced by Park J. Jones. Other types of flow and pressure buildup tests that yield similar results, or pressure buildup tests that yield similar results, or additional improvements, can also be considered as reservoir limit tests; this is a natural extension of the basic ideas stated by Jones and others. If the reservoir is either homogeneous or heterogeneous with crossflow between various components, it has been shown that almost identical sets of pressure drawdown equations can be used for reservoir pressure drawdown equations can be used for reservoir limit calculations. Examples should be found in stratified reservoirs with crossflow and in some naturally fractured reservoirs. If, on the contrary, there prevail special types of heterogeneity such as stratification with no crossflow, then the usual methods are either not applicable or impractical. This latter type of reservoir is the subject of this work. The basic principles of the reservoir limit calculations can be summarized as follows. 1. During the early transient period of a drawdown or a buildup test, the wellbore pressure is linear with the logarithm of time, and the onset of non-linearity is related to the proximity of the reservoir boundaries. The distance to the nearest boundary can be approximated by Eq. 1 for drawdown and by Eq. 2 for buildup:
(1)
(2)
For an ideal circular reservoir with a centrally located well, Odeh and Nabor reported to be about 0.4, and to be about 0.25. Their work was based on an RC analyzer. Our approach, based on a numerical finite difference solution, yielded a value of 0.214 for, which will be used as a norm in this paper. The value of will be taken as 0.25. In paper. The value of will be taken as 0.25. In fact, no precise value can be assigned to and . Their value depends mostly on the nature of the reservoir and the accuracy of the pressure measurement.2. During the semisteady period the wellbore pressure of a drawdown test is linear with time, and the pressure of a drawdown test is linear with time, and the onset of this linearity is given by Eq. 3:
(3)
where for an ideal circular reservoir is about 0.1. Nonsymmetrical drainage boundaries give rise to larger values of . For instance, its value is 0.7 for a well in the center of a 4 × 1 rectangular reservoir. For a crossflow system is still about the same as that of its equivalent homogeneous reservoir of the same geometry. For no-crossflow stratified systems is much larger than the aforementioned figures.
JPT
P. 503