Hydraulic fracturing: New uncertainty based modeling approach for process design using Monte Carlo simulation technique

Hydraulic fracturing is a key method used in completion of shale gas wells as well as in well stimulation. There are a lot of factors affecting the hydraulic fracturing treatment; i.e. formation in-situ stresses, fracturing fluid properties, proppant, pumping rate, reservoir fluid and rock properties…etc. For predictive modeling, these factors are associated with a lot of uncertainties, since most of them are laboratory measured, calculated or subjectively estimated. Moreover, the precise contribution of each factor on the final fracturing result is unknown for each individual case. Therefore, for better treatment performance and in order to find the best range of designing parameters, a hydraulic fracturing predictive model that involves these uncertainties is required specially for newly exploited shale gas reservoir. In this paper a new uncertainty-based approach is described for hydraulic fracturing processes. It is based on assigning probability distribution for some variables and parameters used in the designing process. These probability distributions are used as input data for analytical equations that describe the fracturing processes. Monte Carlo Simulation technique is used to apply uncertainty-based values on the designing analytical formulas. A hypothetical hydraulic fracturing example is used to simulate the effect of different variables and designing parameters on the entire fracturing process. The simulation results are illustrated into probability distribution curves and variance-based sensitivity analysis is performed to assess the contribution and the correlation between different variables and outcomes. Fracture geometry is almost controlled by the injection fluid’s viscosity, in case of constant injection rate; while rock properties have insignificant effect on the fracture width compares to fracturing fluid’s effect. Therefore more emphases shall be directed to rheological modeling of the fracturing fluid. It is found also that fracture height, which is difficult to be estimated, is the most crucial parameter in the calculation of treatment size or the injected fluid’s volume. Proppant porosity, injected fluid viscosity and formation strength are slightly affecting propped fracture width, while proppant final concentration plays the main role of determining the calculated propped fracture width. It is observed from the simulation results that the initial formation permeability will extremely affect the post fracturing skin factor while other formation rock properties have almost no effect on the skin factor. Throughout the implementation of the uncertainty-based modeling approach for hydraulic fracturing process design, it is found that uncertainties in the value of many variables and parameters are slightly affecting the process outcomes. However, injected fluid viscosity, shale formation permeability and proppant final concentration are found to be the most influencing factors in the entire process. Therefore, it is highly recommended to perform in-depth study for these factors prior conducting any designing process of hydraulic fracturing.