Mechanistic and probabilistic rate-time analysis of unconventional reservoirs
Rate-time analysis is a widely used technique to forecast production in oil and gas production. The geological complexity of shale formations and their ultra-low permeability creates significant uncertainty on the behavior of these wells and their production forecast. This work is divided into two parts. The first, develops simple physics-based models to further understand the underlaying mechanisms of unconventional production. The second, introduces a probability approach that attempts to address the uncertainty in the production forecasts. The first part of this work presents mechanistic modeling of unconventional resources to estimate the ultimate recovery (EUR), drainage volumes and recovery factors of wells. Using dimensional analysis, we cast the dimensionless groups of the one-dimensional compressible and slightly compressible single-phase and single porosity diffusivity equation (constant well pressure case). The solutions present the driving force for oil and gas production (drainage mechanism) and its parameters as two desired physical quantities: stimulated volume and characteristic time. Furthermore, we show that this equation is general for the three-dimensional case when there are no-flow boundaries in the other directions. Using this approach, we introduce a rigorous solution for two-phase flow of the slightly compressible diffusivity equation. Moreover, we propose an approximate solution of the single-phase and double-porosity cases of the slightly compressible diffusivity equation. In addition, we develop a modification of the Unconventional CRM equation reducing its parameters to the ones present in the solution of the diffusivity equation. Finally, we present application examples of the discussed models to wells from the Bakken/Three Forks, Wolfcamp/Spraberry and Haynesville Formations. The second part of this thesis displays the application of a probability approach to forecast the production of unconventional wells. The procedure involves sampling the production data, then matching these realizations with different rate-time relations to get EUR distributions for each model. Finally, the method assesses the performance of each rate-time relation with a probability to output a weighted EUR distribution for a given well. A weighted EUR distribution comes closer to acknowledging the uncertainty present in the production forecast. Finally, the procedure is applied to forecast production of wells of the Bakken, Wolfcamp and Haynesville Formations.