Abstract:

In view of partial penetration in fractured-vuggy carbonate reservoirs,this paper establishes an unsta-ble mathematical percolation model with wellbore storage and skin effects incorporated under various combina-tions of sealing top boundary,sealing bottom boundary,constant top boundary and constant bottom boundary.La-place transform and variable separation methods are used to obtain solutions of the model,which are turned to real space solutions through Stehfest numerical inversion.Pressure and pressure derivative log-log type curves are drawn up based upon these real space solutions.Flow regime is divided after the characteristic analysis of the type curves based on percolation mechanism.The results show that parameters related to partial penetration affect early-stage shapes of derivative type curves only.When a full-penetration percolation model is applied to well test analysis in a partial penetration well,a bigger skin factor and thus a false image of severe wellbore damage might be generated,leading to inaccurate conclusion or errors.For a relatively low partial penetration well,well test analysis with a complete penetration model may have large error.The results obtained from the model can be used in the study of the flow pattern and the analysis of pressure transient and well testing of partial-penetration wells in triple-porosity fractured-vuggy carbonate reservoirs.

Key words: Laplace transform, variable separation method, mathematic model, partial penetration, triple-porosity, fractured-vuggy reservoir