Optimization of Plug-and-Perforate Completions for Balanced Treatment Distribution and Improved Reservoir Contact

Summary Heel-dominated treatment distribution among multiple perforation clusters is frequently observed in plug-and-perforate (plug-and-perf) stages, causing small propped surface areas, suboptimal production, and unexpected fracture hits. A multifracture simulator with a novel wellbore-fluid and proppant-transport model is applied to quantify treatment distribution among multiple perforation clusters in a plug-and-perf operation. A simulation base case is set up on the basis of a field treatment design with four clusters. Simulation results show that the two toe-side clusters screened out early in the treatment and the two heel-side clusters were dominant. The simulated proppant placement is consistent with distributed-acoustic-sensing observations. The impact of different perforating strategies and pumping schedules on final treatment distribution is investigated. Two criteria are defined that quantify the proppant distribution and fracture area: the weighted average (WA) and standard deviation (SD) of the final fluid and proppant distribution, as well as the hydraulic surface area (HSA) and propped surface area (PSA) of the created fractures. An optimal plug-and-perf design is defined as one that minimizes the SD of the treatment distribution among perforation clusters, and maximizes the PSA. Both perforating strategy and pumping schedule are found to affect the final treatment distribution significantly, and uniform treatment distribution is shown to create more PSA. Having fewer perforations per cluster was found to promote uniform fluid and proppant placement. Other helpful strategies include reducing the number of perforations near the heel and using small, lightweight proppant. The stress shadow effect is accounted for using the displacement discontinuity method (DDM) and was found to play a smaller role than perforation friction and proppant inertia in most cases. An automated process is developed to optimize plug-and-perf completion design with multiple decision variables using a genetic algorithm (GA). Thirteen parameters are optimized simultaneously. The optimal design solution creates an almost even treatment distribution and more than doubles the PSA compared with the base case. The multifracture model presented in this paper provides a way to quantify fluid and proppant distribution for any perforating strategy and pumping schedule, and provides more insight into the physics relevant to plug-and-perf treatment distribution. The perforation and pumping schedule recommendations presented in this paper provide directional guidance for the design of fracturing jobs with balanced treatment distribution and large PSA.

Speed factors computed for pumping schedules in Water Distribution Networks: DDA versus PDA formulations

This paper focuses on a methodology allowing to derive the pumping schedule in Water Distribution Networks (WDN), upon a time dependent water demand. The selected test case is a previously studied WDN. Two pumping algorithms give different pumping rules. By solving the nonlinear system of equations, consisting of energy balance equations, mass balance equations and pumping rules, one gets the pumps speed factors. Solutions attached to the Pressure Driven Analysis (PDA) correspond to energy and cost savings, with respect to the solutions given by the Demand Driven Analysis (DDA). The methodology described in this paper is simple and rapid, but the iterative numerical method used to solve the system of equations is highly dependent on the starting guess.

Optimization of Pumping Schedules Using the Genealogical Decision Tree Approach

This paper examines the application of a particle filtering-based optimization technique, the genealogical decision trees (GDT), to a finite horizon pump scheduling problem in a water distribution network. The GDT approach for trajectory tracking is first introduced, and a modified algorithm for minimization of costs during pump sequence optimization is then presented. Several variants of the algorithm are suggested, using the extended end constraint and neutrality. The performance of the optimization in various algorithm and parameter settings is examined in extensive simulations. It was observed that both the extended end constraint and neutrality improved the performance, however the deviation between solutions within a population and between different runs remained uncomfortably large. Finally, a comparison with a number of alternative up-to-date optimization techniques is provided. It was observed that the performance of GDT was adequate, compared with the best available approaches.

Optimization of the energy management in water supply systems

Water supply systems frequently present high-energy consumption, which correspond to the major expenses of these systems. Energy costs are a function of real consumption and the daily energy tariff. This paper presents a model of optimization to guarantee the delivery of enough water to populations, for each day. Although, in order to achieve that, energy for pumping is needed, representing the main cost for the companies that operate the systems. The model, developed in MATLAB®, provides the best solution to take in each time step. Simultaneously the population water consumption must be guaranteed, and the hydraulic system restrictions fulfilled. The definition of optimal pumping schedules allows the reduction of operation and maintenance costs associated with pumping energy, as well as the increase of global hydraulic system efficiency. The rules are subsequently introduced into a hydraulic simulator (EPANET), to verify the system behaviour along the simulation period. In addiction, a water turbine is introduced in one of the system's branches. The economical benefits from the generated energy from the water turbine can not be neglected and the wind complementary turbine for pumping supply provides also significant economical savings.