Efficient Optimization and Automated History Matching for Fracture-Stimulated Wells

The interaction between flowing hydrocarbons, water, and the matrix must be understood to determine the limitations of gas production from fractured reservoirs. An efficient numerical model was built using simplified geometry combined with transient analysis of pressure distribution in an extended fracture-stimulated domain of a condensate reservoir with detailed accounting for gas condensation and water flow. The active set method is chosen for multivariable optimization of fracture stage and automated history matching.

Using simplified geometry of fractures in the effective approach to the problem, the computational domain is defined as half of the volume between two parallel fractures and extends from the wellbore to the reservoir boundary. The model solves equations for gas, oil, and water flow, and accounts for gas-oil phase transition. To solve corresponding transient equations, the alternating direction implicit (ADI) method is used. The resulting production decline curve is compared to the field data on well production as a function of time. The automated history matching algorithm is based on minimization of the discrepancy between the predicted and measured production decline curves. For this purpose, the active set method was used for fast multivariable constrained minimization of the discrepancy, which ultimately provides the best matching values for such important parameters as fracture spacing and absolute reservoir permeability.

For the test simulations, the developed numerical model has been realized in a commercial software code and used for sensitivity analysis of reservoir productivity regarding changes of fracture size and spacing, as well as reservoir permeability in the fractured condensate reservoirs, while fully accounting for multiphase reservoir flows and reservoir properties. The condensation/evaporation process is simulated using the pressure/volume/temperature (PVT) tables, which are downloaded before the simulations begin. This solution is dynamically combined with a solution outside of the fractures; consequently, the pressure profile in the fractures is updated at every time step.

Detailed comparison with predictions of two commercial software tools showed that the model accurately predicts transient pressure fields near the fractures, as well as the production decline curve. Applying the model in the fracture stage optimization yields optimal parameters based on various target functions, including total hydrocarbon production and net present value (NPV). By using the discrepancy between the well production log and predicted production curve as the target function, the method is extended to provide automated history matching for available field data. Because of the simplicity of considered fracture geometry, the simulations are fast and usable in the form of application for wellbore solvers, reducing the need for their coupling with 3D reservoir solvers.

 

Because of the geometrical simplicity and detailed accounting for physical/chemical effects, the developed mathematical and numerical model can be used to perform fast production decline analysis with a detailed accounting for condensate properties, including phase transitions. The effectiveness of the model enables running this analysis quickly, which results in efficient fracture optimization and automated history matching.