Designed Simulations for Optimization of Hydraulic Fracture Design and Production Well Constraints in Shale Gas Reservoirs with Reduced-Physics Metamodeling
Authors: Al-Mudhafar Watheq J. , Sepehrnoori Kamy 
Published: April 2018

Abstract
Tremendous amount of oil and gas left behind in unconventional reservoirs, especially in the United States. Therefore, it is necessary to economically recover these shale-based energy resources by the effective hydraulic fracturing technology. In this paper, a pseudo-component black oil reservoir simulator was used to evaluate the gas production from a synthetic shale gas reservoir through hydraulic fracturing (HF).
In that reservoir, one horizontal well was placed with 11 hydraulic fractures to predict the future reservoir performance within 22-year prediction period. The base case of HF simulation was set with a default values for the hydraulic fracturing parameters along with default production well constraints. The HF design parameters included are fracture conductivity and permeability, fracture width and half length, layers up and down, and minimum fracture spacing. The production well constraints were minimum bottom hole pressure and maximum gas production rate. Next, Design of Experiments (DoE) and proxy modeling were adopted for the optimization of hydraulic fracturing design through the shale gas production. In particular, these operational controllable parameters were manipulated using the Latin Hypercube Design (LHD-DoE) approach to obtain the optimal gas production and to build the proxy models. Two successive sets of experiments (running cycles) were designed by mixing the levels of these operational parameters using the LHD-DoE.
The optimization approach significantly increased the cumulative gas production about 1.3734E9 SCF in the 1st running cycle and 3.6583E9 in the 2nd running cycle over the base case of default parameter setting. The 2nd running cycles (640 runs) were successively implemented after refining the range of each parameter based on the outcome of the first running cycle (550 runs). After that, two proxy models were constructed to obtain a simplified reduced-physics metamodel alternative to the complex (full-physics) reservoir simulator: 2nd degree polynomial equation and RBF Neural Network. The two proxy approaches led to accurate matching between the simulator- and proxy-based cumulative gas production. However, RBF-NN was more accurate prediction of cumulative gas production than the polynomial regression.
Finally, Sobol sensitivity analysis was adopted to determine the most influencing hydraulic fracture parameters and well constraints that impact the shale gas production performance. Sobol analysis was adopted based on the RBF-NN and polynomial proxy models. In descending order, the most influencing parameters are the fracture half-length, layers up, layers down, and the minimum bottom hole pressure in the production well. The other HF had essentially negligible impact on the cumulative gas production performance. The fracture half-length was by far the most influential factor affecting the shale reservoir performance because this parameter is directly related to the total fracture area in which the gas produced.