Unconventional gas production from hydraulically fractured well-an application of direct search based optimization algorithm

Unconventional gas reservoirs are now the targets for meeting the demand for gas. These reservoirs are at the depth of more than 10,000 ft (even over 15000 depth as well) and are difficult to be exploited by conventional methods. For the last decades hydraulic fracturing has become the tool to develop these resources. Mathematical models (2D and pseudo-3D) have been developed for fracture geometry, which should be realistically created at the depth by surface controllable treatment parameters. If the reservoir rock is sandstone, then proppant fracturing is suitable and if the rock is carbonates, then acid fracturing is applicable. In both cases, proper design of controllable treatment parameters within constraints is essential. This needs proper optimization model which gives real controllable parametric vales. The model needs the most important analyses from geomechanical study and linear elastic fracture mechanics of rock containing unconventional gas so that fracture geometry makes maximum contact with the reservoirs for maximum recovery. Currently available software may lack proper optimization scheme containing geomechanical stress model, fracture geometry, natural fracture interactions, real field constraints and proper reservoir engineering model of unconventional gas resources, that is, production model from hydraulically fractured well (vertical and horizontal). An optimization algorithm has been developed to integrate all the modules, as mentioned above, controllable parameters, field constraints and production model with an objective function of maximum production (with or without minimization of treatment cost). Optimization is basically developed based on Direct Search Genetic and Polytope algorithm, which can handle dual objective function, non-differentiable equations, discontinuity and non-linearity. A dual objective function will meet operator’s economic requirements and investigate conflict between two objectives. The integrated model can be applied to a vertical or horizontal well in tight gas or ultra-tight shale gas deeper than over 10,000 ft. A simulation (with industrial simulators) was conducted to investigate and analyse fracture propagation behavior, under varying parameters with respect to the fracture design process, for tight gas reservoirs. Results indicate that hydraulic fracture propagation behavior is not uninhibited in deep reservoirs as some may believe that minor variations of variables such as in-situ stress, fluid properties etc. are often detrimental to fracture propagation in some conditions. Application of this model to a hypothetical tight and ultra-tight unconventional gas formations indicates a significant gas production at lower treatment cost; whereas the resources do not flow without any stimulation (hydraulic fracturing).