It is common for a multi-fractured horizontal well (MFHW) to experience changes in operational conditions during its life, such as choke setting changes and shut-ins. This work provides a rigorous semi-analytical model for analyzing MFHWs experiencing a series of operational changes.
Prior to model derivation, the nature of multiple pressure transients, induced by operational upsets and propagating into a reservoir, was investigated using numerical simulation. Simulation of the reservoir pressure distribution at each timestep leads to the observation that additional pressure transients are initiated in the reservoir after each upset, and occur along with the continuation of transients started by previous cycles. A multiple dynamic-drainage-area (m-DDA) model is therefore proposed to reproduce the multiple pressure transients. Productivity-index equations are solved for each drawdown/buildup cycle. Material-balance equations, combined with the concept of m-DDA, are developed to calculate the average pressure in the m-DDAs at each timestep. Moreover, both matrix reservoir and hydraulic fracture (HF) conductivity stress-sensitivity and hysteresis corresponding to loading/unloading paths, quantified in our laboratory, are incorporated into the modeling of each drawdown/buildup cycle.
Verification of the new m-DDA model is performed using fully numerical simulation. The pitfalls of both the method of re-initialization, and the conventional DDA model, are revealed through analysis of simulated data. The method of re-initialization after each operational upset leads to errors because this method only accounts for the latest induced transient and ignores the previously initiated transients. The conventional DDA model is also not accurate when operational upsets result in large fluctuations in flow rates, because of an inaccurate estimate of average reservoir pressure over drawdown/buildup cycles. The new m-DDA model provides a reasonable history-match of well/reservoir performance during a series of drawdown/buildup periods by reproducing multiple moving flowing boundaries.
The practicality of the new model is demonstrated using a field example with three production cycles (including a downhole choke removal/ and a shut-in); importantly the "transient spike" after each operational upset is reproduced accurately. Moreover, the incorporation of permeability/porosity hysteresis, along with an accurate estimate of average pressure, provides the basis for reservoir/fracture characterization performed over multiple drawdown/buildup cycles. In short, the model is conceptually simple, efficient to compute, and is able to reproduce multiple drawdown/buildup cycles of a well.