A new method is presented to calculate the total inflow and associated productivity index (PI) under two-phase conditions by a sum of contributions from matrix and N multiple fractures using semi-analytical methods. Maximizing the net Present present value (NPV), the new inflow performance relationship (IPR) models can determine the optimal fracture stage number. Furthermore, the deliverable PI is used as an input to a network model to calculate the operating rate, taking into account the network constraints such as the node pressure, allowed flowrate, or choke in place. Through this analysis, one may determine that the horizontal well of interest may not flow at the maximum PI-it suggests that the network constraints dissipate the contribution from m stage(s) fractures. The number of fracture stages is then reset to (N-m), the IPR model is rerun, and an updated PI is imported into the network model. This process is iterated until the final optimization is achieved.This method can quickly optimize the number of fracture stages for horizontal wells under two-phase solution-gas conditions, assisting operating companies in planning field development.* Guoqing Han currently holds the faculty position at China University of Petroleum Beijing

Reservoir and well simulations are often coupled to allow more realistic production forecasts. Proxy functions are typically generated by a well simulator as a preprocessing step to characterize the response from the production system when the reservoir condition changes. With proxy functions, a reservoir simulator can take into account the response from the well without simultaneously performing the well simulation, which can be time prohibitive. This indirect coupling is effective only when the interpolated values from the proxy function closely match the results from the surface simulation. Typical implementations of proxy functions require characterizations at each grid point, which can be expensive to compute for a fine grid. Due to the intrinsic curvilinearity of well performance curves, the accuracy of proxy functions highly depends on the number of sampling points. In this paper, we discuss a new method for generating proxy functions that improves accuracy without sacrificing performance. We propose to use kriging to enhance the efficiency and accuracy of characterization of the surface simulation. Kriging interpolation provides a grid-free representation of the proxy function, which allows the flexibility of choosing the sampling points for well simulations. We propose to put more sampling points where the rate of change of the proxy function is relatively large. Our numerical results show that the grid-free method reduces the interpolation error by over 40%, without increasing the number of sampling points. Furthermore, with a comparable level of accuracy, simulation time for generating the proxy function is reduced by 50%.

A progressive cavity pump (PCP) characterization model is developed to predict flow characteristics under varying multiphase flowing conditions. This paper presents a procedure for modeling PCPs and its integration to grid-based network solvers including successively accelerated substitution (SAS) and Newton-based. Our numerical study shows the latter leads to a much lower computing cost than that of its counterparts. This PCP model also provides calibration capacity on the performance curve at in-situ PVT properties.This modeling work will assist production engineers in PCP related jobs, including: PCP surveillance, well planning, nodal analysis, and network optimization.