A novel well test model for fractured vuggy carbonate reservoirs with the vertical bead-on-a-string structure

Abstract

The bead-on-a-string structure has been widely observed in many fractured vuggy carbonate reservoirs, especially in Shunbei oilfield, northwestern China. To date, there are still no appropriate well test methods for analyzing these reservoirs with the vertical bead-on-a-string structure. This paper proposes a new theoretical well test model, which considers the gravity effect and the natural fractures connecting the vuggs, to analyze this kind of reservoirs. First, we establish the mathematical model of fractured vuggy reservoirs with the vertical bead-on-a-string structure. With the different outer boundary conditions, Laplace transform and inversion are employed to solve the well test model. Then, the type curves for the well test model are plotted and discussed. It is found that the gravity effect can be equivalent to a type of constant pressure boundary condition. Take the three-region-two-cave as an example, type curves can be divided into nine distinct flow regimes, including wellbore storage, skin, linear flow I and II, transition flow I and II, vug storage I and II, and boundary flow. The transition flow and vug storage period are named as the vug storage effect. Subsequently, the effects of relevant parameters are studied. It is concluded that the depth of the drop during vug storage effect increases with increasing dimensionless vug storage constant CvD and dimensionless vug height zD2-zD1; the greater dimensionless gravity effect coefficient GD leads to the smaller equivalent boundary distance of the constant pressure boundary condition; the smaller the mobility ratio M12, the earlier the appearance of the second linear flow regime; the larger the storage ratio ω12, the more distinct the vug storage effect. Finally, two field case studies are carried out by using the proposed method. The locations and volumes of the caves are estimated, which shows that the proposed theoretical well test model has a great potential of obtaining the formation and cave parameters accurately. However, there is not available data that enable an accurate description of the locations and volumes of the caves by now, the proposed model still needs further field verifications.