Hydraulic fracturing optimization is very important for low permeability reservoir stimulation and development. This paper couples the fracturing treatment optimization with fracture geometry optimization in order to maximize the dimensionless productivity index. The optimal fracture dimensions and optimal dimensionless fracture conductivity, given a certain mass or volume of proppant, can be determined by Unified Fracture Design (UFD) method. When solving the optimal propped fracture length and width, the volume and permeability of the propped fracture should be determined first. However, they vary according to the proppant concentration in the fracture and cannot be obtained in advance. This paper proposes an iterative method to obtain the volume and permeability of propped fractures according to a desired proppant concentration. By introducing the desired proppant concentration, this paper proposes a rapid semi-analytical fracture propagation model, which can optimize fracture treatment parameters such as pad fluid volume, injection rate, fluid rheological parameters, and proppant pumping schedule. This is achieved via an interval search method so as to satisfy the optimal fracture conductivity and dimensions. Case study validation is conducted to demonstrate that this method can obtain optimal solutions under various constraints in order to meet different treatment conditions.

The pseudosteady state productivity index is very important for evaluating the production from oil and gas wells. It is usually used as an objective function for the optimization of fractured wells. However, there is no analytical solution for it, especially when the proppant number of the fractured well is greater than 0.1. This paper extends the established fitting solution for proppant numbers less than 0.1 by introducing an explicit expression of the shape factor. It also proposes a new asymptotic solution based on the trilinear-flow model for proppant numbers greater than 0.1. The two solutions are combined to evaluate the pseudosteady state productivity index. The evaluation results are verified by the numerical method. The new solution can be directly used for fracture geometry optimization. The optimization results are consistent with those given by the unified fracture design (UFD) method. Using the analytical solution for the pseudosteady state productivity index, optimization results can be obtained for rectangular drainage areas with arbitrary aspect ratios without requiring any interpolation or extrapolation. Moreover, the new solution provides more rigorous optimization results than the UFD method, especially for fractured horizontal wells.