| Knowing that determining the geometry of the hydraulic fractures with horizontal wells is demanding yet challenging for petroleum engineers, in this thesis we have developed a computer program to automatically optimize the length, the conductivity as well as the spacing of hydraulic fractures in unconventional reservoirs.;In our program, the cumulative discounted Net Present Value (NPV) is selected as the target function and the gradient descent methodology is adopted as the optimizer. Relying on the gradient information, gradient descent searches for the optimal solution along the steepest decent direction. A comprehensive reservoir simulator, MSFLOW, with gas adsorption/desorption and Klinkenberg effect coupled, is adopted to obtain the production rate and NPV at each searching step. Armijo rule is used to determine the searching step size.;With the developed workflow, we have investigated the optimal geometry of the fractures with single horizontal well as well as zipper type wells. We have observed that gradient descent method is able to quickly converge to the optimal point. Moreover, we have preliminarily studied the sensitivity of the optimization parameters. Our work can be readily adopted by reservoir engineers to guide the fracturing strategies in unconventional formations. |
