A semi-analytical pressure and rate transient analysis model for inner boundary and propped fractures exhibiting dynamic behavior under long-term production conditions

The loss of hydrocarbon production caused by the dynamic behavior of the inner boundary and propped fractures under long-term production conditions has been widely reported in recent studies. However, the quantitative relationships for the variations of the inner boundary and propped fractures have not been determined and incorporated in the semi-analytical models for the pressure and rate transient analysis. This work focuses on describing the variations of the inner boundary and propped fractures and capturing the typical characteristics from the pressure transient curves.A generalized semi-analytical model was developed to characterize the dynamic behavior of the inner boundary and propped fractures under long-term production conditions. The pressure-dependent length shrinkage coefficients, which quantify the length changes of the inner zone and propped fractures, are modified and incorporated into this multi-zone semi-analytical model. With simultaneous numerical iterations and numerical inversions in Laplace and real-time space, the transient solutions to pressure and rate behavior are determined in just a few seconds. The dynamic behavior of the inner boundary and propped fractures on transient pressure curves is divided into five periods: fracture bilinear flow (FR1), dynamic PFs flow (FR2), inner-area linear flow (FR3), dynamic inner boundary flow (FR4), and outer-area dominated linear flow (FR5). The early hump during FR2 period and a positive upward shift during FR4 period are captured on the log-log pressure transient curves, reflecting the dynamic behavior of the inner boundary and propped fractures during the long-term production period.The transient pressure behavior will exhibit greater positive upward trend and the flow rate will be lower with the shrinkage of the inner boundary. The pressure derivative curve will be upward earlier as the inner boundary shrinks more rapidly. The lower permeability caused by the closure of un-propped fractures in the inner zone results in greater upward in pressure derivative curves. If the permeability loss for the dynamic behavior of the inner boundary caused by the closure of un-propped fractures is neglected, the flow rate will be overestimated in the later production period.