## Production Optimization in Waterfloods: A New Approach to Interwell-Connectivity Modeling

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In the complete paper, the authors present a novel methodology to model interwell connectivity in mature waterfloods and achieve an improved reservoir-energy distribution and sweep pattern to maximize production performance by adjusting injection and production strategy on the well-control level. The method involves a reduced-physics-based fast numerical tracer test on each well, which yields interwell connection strength or well-allocation factors (WAFs), and then a data-driven efficiency model on each interwell connection calibrated automatically from the injection and production history of the reservoir.

## Introduction

The approach combines and balances the advantages of both simulation and data-driven techniques. The approach models interwell connections based on a relatively mature waterflood history and performs fast forecast and waterflood optimization on the basis of the interwell-connection analysis. Injector/producer connections are identified by computing WAFs with a numerical tracer method. Then, a data-driven empirical efficiency model is adopted that defines the profile of the oil cut of each interwell connection, and reservoir-production history is used to calibrate the model. Therefore, each interwell connection is quantified with two critical parameters: WAF and connection efficiency. The reservoir model is simplified into a connection-based network model that can be used to predict oil and water production without use of rigorous time-dependent numerical simulation. A production-optimization algorithm is then implemented. The optimization objective is to minimize water production while maintaining oil-production rate, subject to a range of practical constraints. The production optimization is integrated into a numerical-simulation model, and a blind test is run for 6 months. A significant decrease in water production is observed.

## Methodology

**Waterflood Surveillance. WAF.** In the process of waterflooding, water is injected into injectors to displace remaining oil. In this water/oil communication system, incompressibility is assumed in fluid dynamics and reservoir rock. This assumption is equivalent to assuming that pressure communication between any two points in the reservoir is essentially instantaneous. The WAF quantifies the strength of connection between two wells of different types.

WAF is often computed by tracing streamlines and counting the number of streamlines between wells. However, the streamline-based method is incompatible with a dual-porosity system, and in general has poor performance in unstructured grids. The authors adopt a stationary numerical tracer method to compute WAF. The equations used in this process are presented in the complete paper.

The numerical tracer method provides WAF results identical to those provided by the streamline-based method. However, the numerical tracer method does not need to trace numerous streamlines and can obtain WAF directly by solving a single partial-differential equation (PDE). Moreover, thanks to the finite-volume nature of the tracer method, it can be applied easily to unstructured grids or dual-porosity, dual-permeability problems.

* Data-Driven Well-Connection Efficiency Model. *To describe the waterflood pattern correctly and to optimize production by waterflood properly, it is critical to understand the efficiency (EFF) of each interwell-connection pair.

In practice, computing EFF with water/oil saturation from numerical simulation requires special caution. A carefully history-matched simulation model is needed, and the process of history matching often involves many human biases and large degrees of uncertainty and suffers from an overfitting issue because of the large freedom of the parameter space. The robustness of a history-match result is usually questionable, and the uncertainty is difficult to quantify. The problem becomes even more challenging for mature-waterflood fields because of their long history.

To resolve this problem, the authors propose a data-driven connection-efficiency model, described in detail in the complete paper, that can be automatically calibrated fully by historical production and injection data. The efficiency model is an ensemble of decline functions, and each function describes the EFF of each injector/producer pair. Thanks to the nature of the data-driven model, the longer the reservoir history is, the better the calibration results (with lower uncertainties) that can be obtained.

**Production Forecast and Optimization. **With interwell-connectivity strength (WAF) and EFF, the subsurface flow dynamics of the reservoir has been simplified into a connection-based network model. One can now perform short-term production forecasting by performing simple linear algebra by use of only WAF and EFF. To run a production forecast given a set of well-control configurations, first, the pressure is solved and the velocity field computed with Darcy’s law; then, the tracer PDE is solved for each producer, injector, and aquifer. This gives the WAF of each interwell pair. EFF of each connection, calibrated by the production history, is forwarded one timestep for the future step. With new WAF and EFF, the predicted oil- and water-production rate of each producer is obtained.

Because there is no finite-volume time evolution involved, the forecast process is very fast. This further enables high-speed production optimization. The objective of production optimization is to decrease the water-production rate while maintaining the oil-production rate by simply adjusting the liquid rate of producers and the injection rate of injectors so that the resulting flow pattern has high WAF for high-efficiency connections and weak WAF for low-efficiency connections. To avoid unphysical optimization results, various constraints are applied. The uncertainty of the empirical efficiency model is considered in the optimization process to prevent high-risk adjustment to the well-control configuration, which relies on connections with highly uncertain efficiency.

The authors use a commercial optimizer to search for a local optimal well-control configuration that gives the lowest water-production rate subject to all the constraints. Then, a rigorous forecast is performed by recomputing pressure, tracer, and WAF with the well-control configuration. When the step size from one iteration to another iteration is sufficiently small, the forecast result is very close to the zero-order approximation.

A sparsity constraint is also included in the optimization. In real-project operation, it is sometimes requested that adjustments to well rate can be made only to a certain number of unspecified wells.

## Field Applications

The entire work flow has been applied successfully to dozens of mature-waterflood reservoirs with well counts ranging from 100 to 1,000 and waterflooding history ranging from 5 to 70 years. The example presented here is based on a real giant carbonate reservoir with more than 200 wells (70% are producers and 30% are injectors) and a 5-year waterflooding history. The current water cut of the entire reservoir is approximately 35% and is climbing rapidly.

First, a 2.5D Voronoi perpendicular-bisector (PEBI) unstructured grid is generated that conforms to geological surfaces and has special local mesh refinement for wells and faults. The total number of cells is approximately 500,000. The volume of a typical well cell is 10–3 to 10–2 times the volume of nonwell cells. This can significantly increase numerical accuracy near wells without dramatically increasing the total number of cells. The upper-left panel of **Fig. 1** shows a conceptual view of the grid local refinement for vertical wells and horizontal wells.

Because stationary pressure equations and tracer equations are used and no compressibility is involved, the choice of timestep is essentially arbitrary. The authors choose 1 month as one time interval. They solved pressure and numerical tracers 60 times on the unstructured grid using an ordinary personal computer. Fig. 1 provides some examples of the pressure solution, tracer solution, and sweep partition on the basis of tracer solutions. Efficiency functions are then calibrated for all significant interwell connections with WAF greater than 10% for at least one timestep. A typical producer primarily connects to three or four injectors/aquifer over the entire 5-year period. Therefore, up to eight parameters of four efficiency functions need to be calibrated for one producer. The history-matching results are exceptional: the time-average mismatch in the oil-production rate of all producers is only 1.8%, and the worst history-matched producer has a time-average mismatch of 4.9%.

To verify the performance of production forecasting and optimization, the authors use a history-matched full-physics numerical-simulation model of part of the reservoir to perform a blind test. The simulation model is assumed to be the real reservoir and is run until the 46th month. Then, different simulations (A and B) are begun from this point and each of them is run for 6 more months.

Simulation A neither alters anything from the current well-control configuration, nor drills new wells, nor converts producers to injectors. It simply keeps the existing configuration.

Simulation B does not add new wells or convert producers. However, the well-control configuration is adjusted every month on the basis of the production-optimization recommendation. The objective is to minimize the total water-production rate subject to the constraint of maintaining the current total oil-production rate and injection rate. Each production-optimization process performs 30 internal iterations and takes less than 5 minutes.

It is found that Simulation B yields much better results than Simulation A. In Simulation B, the total oil-production rate is kept stable successfully for 6 months without adding new producers or increasing injection; moreover, the water-production rate was decreased dramatically at the first future step. This current well-control configuration is far from the optimal strategy; thus, after optimization, a sudden decrease of water production is observed. Nevertheless, starting from the second “future” timestep, water production begins to increase because there is little room for optimization. In Simulation A, within 6 months, the water cut increases from approximately 16 to 25%. In Simulation B, water cut first decreases to 8% and then climbs to 15% after 6 months. The authors point out that, in real-field application, because of finite fluid compressibility, the reservoir response to changes of well-control configuration is not instantaneous.

*JPT*Technology Editor Chris Carpenter, contains highlights of paper SPE 182450, “Production Optimization in Waterfloods With a New Approach to Interwell-Connectivity Modeling,” by

**Xiang Zhai, Tailai Wen,**and

**Sebastien Matringe,**Quantum Reservoir Impact, prepared for the 2016 SPE Asia Pacific Oil and Gas Conference and Exhibition, Perth, Australia, 25–27 October. The paper has not been peer reviewed.

Production Optimization in Waterfloods: A New Approach to Interwell-Connectivity Modeling

01 December 2017

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