Analysis of Short Transient Tests Affected by Changing Wellbore Storage

It is well known that wellbore storage and phase redistribution have a direct influence over well testing data, mainly on those recorded at early times of the test. After this early time period, such influence disappears, and the pressure response is dominated by the reservoir and the skin zone properties. However, sometimes the effects of wellbore dynamics last long enough as to completely disguise the reservoir response. The above situation frequently constrains the use of some analysis procedures such as type curve matching, especially if the test did not last long enough as to reach radial flow conditions. In this way, some tests are uninterpretable because of the duration of these wellbore effects. Using as a basis two classical models related to well test affected by changing wellbore storage, this work introduces a new method of analysis for these tests with insufficient duration to reach radial flow conditions. The use of the methodology proposed in this work is illustrated with synthetic examples and a field case. For some synthetic cases the type curve matching procedure may yield completely erroneous values of the parameters, while with the suggested method reasonable estimates are obtained. Introduction Wellbore storage is recognized as a phenomenom that affects the recorded pressure behavior at early times during a well test. Sometimes, the phenomena related to mass balance and fluid momentum that occur inside the wellbore, constrain the application of some analysis procedures, especially if the test does not show transient radial flow conditions, and can even disguise completely the pressure response. Phase redistribution occurs when a producing well (that contains more than one phase) is closed at the surface, and due to gravitational forces these phases segregate from each other, this causes a distorsion on early time data of the test. In 1981, Fair introduced a model which takes into account the phase redistribution phenomenom in the diffusivity equation solution as applied to buildup analysis. He assumed an exponential increase in wellbore storage. More recently, Hegeman et. al., proposed an extension to Fair's model, obtaining a general solution in Laplace space, which allows to add the changing wellbore storage effect for a variety of analytical well-reservoir models. These authors considered two models of changing wellbore storage, the exponential function and the error function. For the error function, the transition period is more abrupt than with the exponential function. In 1992, Fair presented another study on the influence of a wide range of wellbore phenomena including mass-balance and momentum phenomena. Also, in that work wellbore phenomena such as fluid temperature changes (represented by an exponential function as in the case of wellbore storage), phase changes inside the production tubing and inertial effects were considered. Currently, the only available method to estimate the reservoir permeability and skin factor from insufficient transient data (tests affected by changing wellbore storage and that have not reached radial flow period) is the type-curve matching technique. To apply this procedure it is necessary to identify the function (exponential or error function) that fits best the storage effect. Nevertheless, the absence of data in the infinite acting period difficults the matching procedure, resulting in a match with high uncertainty. With the purpose of modeling in a more rigorous way the reservoir-wellbore system, it is necessary an algorithm that couples the mechanistic behavior of the well with that of the reservoir, such as that of Hasan and Kabir, Winterfeld propose the use of a completely numerical scheme that simulates the transient conditions of the system.