A production-based model for a fractured well in unconventional reservoirs

Due to the depletion of conventional reservoirs and the high demand of energy, unconventional reservoirs will be relied on to supply the world's energy for the foreseeable future. Unfortunately, because of their complex storage and flow mechanisms, modelling and analysis of unconventional reservoirs have been very challenging. Although semi-analytical and numerical models have been proposed, these models rely on somewhat simplifying assumptions and require several input parameters. In this paper, a production-based model is proposed to analyze and predict a fractured-well performance in unconventional reservoirs (specifically, tight and shale reservoirs). The model assumes a power law with a stretched exponential cut-off. While the power-law term governs the transient-state period, the stretched exponential term, which is a superposition of exponential decays, governs the boundary-dominated flow period. As a result, the model is capable of matching both the transient state and boundary-dominated flow portions of the data. The model has been validated with a numerical data and applied to several field data. Results of the model have been compared with other existing models. The findings show that the proposed model yields relatively good estimates, and matches both the transient and boundary-dominated flow periods. The proposed model may contribute to the ongoing efforts to improve the analysis and forecasting of fractured-well performance in unconventional reservoirs.