Prediction Model of Rate Decline for Acid-Fracturing Vertical Wells in Pore-Cavity-Fracture Carbonate Reservoirs

In view of the lack of rate decline prediction model of acid-fracturing vertical wells (AFVWs) in pore-cavity-fracture carbonate reservoirs, a prediction model of AFVWs with consideration of wormholes and fractures generated by acid fracturing is established by using the idea of compound reservoir. Acid fracturing significantly increases well productivity in the early period, but in the late period, its impact on instantaneous and cumulative production almost disappears. A higher interzonal diffusivity ratio or a lower interzonal conductivity ratio generated by acid fracturing can bring a better stimulation effect in the early period. Three typical production stages can be observed on the conventional productivity curves under constant wellbore pressure, corresponding to early linear decline stage, middle stable production stage, and late depletion decline stage, respectively. A new productivity function is defined by using a pseudo-steady state constant, and a set of new type rate decline curves of AFVWs in pore-cavity-fracture carbonate reservoirs is plotted and presented. Six typical flow regimes can be identified on these new type curves, including two or three V-shaped segments. The duration of all flow regimes and the depth and amplitude of V-shaped segments are controlled by interzonal diffusivity ratio, interzonal conductivity ratio, elastic storability ratio, crossflow coefficient, and boundary conditions. Reservoir parameter interpretation and future productivity prediction for an oil well in North Truva Oilfield were conducted by using our proposed model. The prediction results are consistent with the actual production, proving our model's accuracy and reliability. Compared with the conventional rate decline curves, these new type rate decline curves have more prominent flow regimes and can improve well-test inversion accuracy, reduce shut-in time, and increase well productivity.