A novel method for determining the binomial deliverability equation of fractured caved carbonate reservoirs

The binomial deliverability equation is one of the essential parameters that control the fluid production/injection rate from wells. The presence of caves and fractures introduces many difficulties related to the determination of the binomial deliverability equation of fractured caved carbonate reservoirs. In this work, a novel method for determining the binomial deliverability equation of fractured caved carbonate reservoirs is proposed for the first time. First, the detailed procedure of our method is illustrated. More specifically, the superposition principle is used to derive the expressions of (Δp/Q). The pressure buildup data and type curve matching are employed to induce the dimensionless bottom-hole pressure solution. Sequentially, the binomial deliverability equation can be obtained through the least square method. Then, we employ our method to a simple case and compare the calculation results with the literature data to calibrate the accuracy of our method. Next, we present the applications of our method to two example wells from the Shunbei Oilfield, western China. The results show that our method is reliable. Moreover, the results also indicate that our method is more suitable for fractured caved carbonate reservoirs than the deliverability test. Meanwhile, through the calculations of massive field data and theoretical analysis, we conclude three constraints on the input parameters. They are as follows: (i) the flow rate of each production system must be incremental; (ii) the production time must satisfy tp1 = tp2 – tp1 = tp3 – tp2 = tp4 – tp3; and (iii) the flow rate must satisfy Q2 = 2Q1, Q3 = 3Q1, Q4 = 4Q1. Finally, we prove the necessity of these constraints.