A weak fluid supply model for transient pressure analysis in vertically fractured wells from tight gas reservoirs: A case study

An interesting phenomenon of weak fluid supply (WFS) has been observed in tight gas reservoirs from the Ordos Basin. To facilitate parameters evaluation and productivity estimations of those well, this paper presents a new WFS model for transient pressure analysis in vertically fractured wells from tight gas reservoirs. In the new model, a WFS pressure and a WFS index are first introduced to describe the weak fluid supply boundary. Based on that, a mathematical model is developed with considering WFS, finite-conductivity fractures, and stress-sensitive effect. Using perturbation transformation method and semianalytical method, the proposed mathematical model is solved with effects of wellbore storage and skin factor. Following that, the model verification, sensitivity study, and field application are performed. Results shows that the WFS causes a rapid drop after "hump" at the late stage in the pressure curves. The start time of "hump" decreases as the WFS index increases. When the WFS pressure is bigger than zero, the pressure derivative curves exhibit a significant "hump", and it is more obvious with the increase in the WFS pressure. When the WFS pressure is equal to zero, the pressure derivative curves directly drop, which is assemble to the effect of constant pressure boundary. When the WFS index is zero, the pressure derivative curve in the late period is a unit-slope line, demonstrating a closed boundary effect. The field application in the well Z1 from the Ordos Basin shows that a "hump" caused by WFS does appears at the late stage in the pressure curves. By using the WFS model, the estimated reservoir permeability and drainage radius are 0.524 mD and 451.68 m. The WFS pressure and WFS index are respectively estimated as 0.13 and 0.022 by the WFS model. It demonstrates the applicability of the new proposed WFS model, which also provides a good understanding of transient pressure behaviors and accurate estimation of reservoir parameters for fractured wells with WFS.