Analytical investigation of boundaries in naturally fractured unconventional reservoirs, An

Abstract

This research presents a heuristic approach to develop an analytical model to study the effects of a stimulated zone in a fractured unconventional reservoir and the inherent boundaries that are observed. To simulate a stimulated reservoir volume (SRV) around the fractured horizontal well surrounded by a virgin outer reservoir, three separate solutions are generated and superimposed: Solution 1 - a multiply fractured, horizontal-well in an infinite-acting, homogeneous reservoir with the properties of the outer zone; Solution 2 - a multiply fractured, horizontal-well in a bounded, homogeneous (un-fractured) reservoir with the properties of the outer reservoir; and Solution 3 - a multiply fractured, horizontal-well in a bounded, naturally fractured reservoir with the properties of the stimulated zone. The solution for the composite reservoir consisting of a stimulated (naturally fractured) reservoir surrounded by an infinite acting, un-fractured (virgin) reservoir is obtained by subtracting Solution 2 from Solution 1 and then adding Solution 3. The same approach is also applied to develop a solution for the case where there is an additional transition zone between the SRV and the outer (virgin) reservoir. This method creates an approximate solution for the composite-reservoir system. Although the model is derived analytically, computations require numerical methods and the model is therefore referred to as semi-analytical. The model is verified against literature models and an industry numerical simulator to find its limitations. This verification shows that the accuracy of the model is dependent on the size of the stimulated zone. For a large stimulated zone, because the flux profiles along the boundaries of the fractured (Solution 3) and un-fractured (Solution 2) reservoirs are not equal, the model over-predicts the drawdown pressure. However in real-world examples of multiply fractured horizontal wells, the stimulated zone is much smaller and the model closely matches the drawdown pressures calculated in the numerical simulator. Therefore, the heuristic approach used in this work leads to an ad-hoc solution for the common configurations of fractured horizontal wells in shale reservoirs. Several synthetic examples are considered to show that the solution developed in this work can be used to identify the flow regimes after the effect of the stimulated reservoir boundary (that is, the fracture tip effects) are felt. This is an advantage over the commonly used trilinear model when the diffusivities of the stimulated and virgin reservoirs are comparable. Although not explored in this research, the ultimate utility of the proposed approach is in modeling multiple fractured-horizontal-wells to study the interference among SRVs. The fracture enhancement and extent influence the productivity of the well more than any other parameter and should be of utmost importance to characterize. And last, this model can be used with other tools to identify optimal full field development.