History Matching, Prediction and Production Optimization with a Physics-Based Data-Driven Mode

Assisted history matching and life-cycle production optimization are the two key components of closed-loop reservoir management, which are traditionally performed based on a multitude of runs of full-scale reservoir simulation models which incur high computational costs for large-scale problems. To reduce the computational cost spent on full-scale simulation runs when performing history matching and production optimization, we focus on developing a new data-driven model, Interwell Numerical Simulation Model with Front Tracking (INSIM-FT). INSIM-FT can be built without any prior knowledge of geological information of the target reservoir. Although the INSIM-FT model is developed from production data and requires no prior knowledge of rock property fields, it incorporates far more fundamental physics than that of the popular Capacitance-Resistance Model (CRM). INSIM-FT also represents a substantial improvement on an interwell numerical simulation model (INSIM) developed by Zhao et al. (2016). Specifically, we introduce a theoretically correct procedure to compute water saturation in INSIM-FT that generally gives more robust and accurate solutions than are obtained with INSIM where saturations are computed with an ad hoc method. In addition, unlike INSIM, INSIM-FT incorporates the parameters defining power-law relative permeability curves as additional history-matching parameters so that prior knowledge of relative permeabilities is no longer required as is the case with INSIM. Also, we introduce imaginary wells and their associated interwell connections (stream tubes) to enable more potential flow paths in the INSIM-FT model than are used in INSIM. These additional flow paths enable INSIM-FT to honor more correctly the physics than is done with the original INSIM model. With these modifications, one expects that INSIM-FT will be more robust than INSIM, and via computational examples, we show that this is the case.;After developing INSIM-FT for a two-dimensional reservoir model, we extend INSIM-FT to full three-dimensional multi-layered reservoirs, where it is necessary to consider gravitational effects. The extended model, which is referred to as INSIM-FT-3D, can be used for history matching, prediction and production optimization for a three-dimensional reservoir under waterflooding. Compared to the original INSIM-FT model, INSIM-FT-3D replaces the original Riemann solver in INSIM-FT by a new Riemann solver based on a convex-hull method that enables the solution of the Buckley-Leverett problem with gravity, where a fractional flow function may have more than one inflection point. Secondly, unlike the original INSIM-FT model, which assumes all wells are vertical, the INSIM-FT-3D model allows for the inclusion of wells with arbitrary trajectories with multiple perforations. Third, INSIM-FT-3D applies Mitchell's best-candidate algorithm to automatically generate the imaginary wells that are evenly distributed in the reservoir given a set of prefixed actual well nodes and fourth INSIM-FT-3D utilizes our own modification of Delaunay triangulation to build the 3D connection map necessary to use the general INSIM-FT-3D formulation.;The ensemble-smoother with multiple data assimilation (ES-MDA) is used for history matching with INSIM-FT or INSIM-FT-3D. The history matching parameters for INSIM-FT and INSIM-FT-3D are similar and include the connection-based parameters and the parameters that define power-law permeabilities. In addition to the common parameters included with the two methods, the parameters that define the well indices for the wells with multiple perforations are included in the INSIM-FT-3D model. For production optimization with INSIM-FT and INSIM-FT-3D, ensemble-based optimization (EnOpt) is used. Because initially the developed data-driven models only allow rate controls, pressure controls cannot be used for production optimization. We provide a procedure to estimate the values of well indices via the history matching process if bottom-hole pressure (BHP) data are available. Then, BHP can be specified at each control step in the INSIM-FT(-3D) model to allow optimization of the life-cycle net present value (NPV) of production, where the producer's BHPs at control steps are included in the optimization variables.;Computational results show that, history matching and production optimization performed with INSIM-FT two- and three-dimensional models are far more computationally efficient than are those performed with full-scale reservoir simulation models but still give a characterization of a reservoir under waterflooding, future predictions and estimates of the optimal NPV of production, that are similar to those obtained using computationally expensive full-scale reservoir simulation models.