Analytical and Semi-Analytical Models for Composite Reservoirs with Complex Well Completions

Abstract

With the current increasing productivity and the proliferation of shale and tight sand resource plays in Canada, and North America in general, the need to understand and characterize these resource plays, for the purpose of recovery optimization, has taken center stage in reservoir management. It is, however, important to note that these hydrocarbon environments are fundamentally different from conventional reservoirs for which there is an abundance of high-yield technical know-how. In a technical sense, these plays are not reservoirs but source rocks; their permeabilities are in the micro- to nano-darcy range. Hence, they cannot sustain economic hydrocarbon production unless they are engineered using unconventional stimulation methods like multi-stage hydraulic fracturing, for instance. As a result, traditional reservoir modeling methods fail, or give misleading results at best, when used to study these hydrocarbon plays. The objective of this research work is to develop rigorous (and yet) practical analytical and semi-analytical models for multi-well performance in petroleum reservoirs, with a view to simulating and forecasting production from unconventional resources. The models will address flow in different reservoir systems (homogeneous reservoirs and composite reservoirs) produced by various well completion types, including vertical, horizontal, fractured vertical and multiply fractured horizontal wells. It is also worth mentioning that most reservoir studies ultimately dwell on numerical simulation because of the flexibility and ease with which geological features can be incorporated in numerical simulation models. However, field-wide simulation studies are resource intensive and time consuming. In addition, the results obtained are heavily dependent on the quantity and quality of data available. It is therefore advisable and much more affordable to carry out simulations of this magnitude only when an initial performance study has been conducted and initial estimates of reservoir parameters have been obtained from the more tractable analytical and semi-analytical models. The models presented in this research work are practicable for reliable investigation of flow behavior in both conventional and unconventional reservoirs, and also provide results that can be used to seed the more involving numerical simulation.