⚡ electrical engineering

An injection/production-efficiency based surrogate optimization algorithm for optimal well controls in waterflooding reservoirs

This paper proposes a novel streamline-based surrogate optimization algorithm that integrates injection/production efficiency metrics with advanced sampling strategies to efficiently and reliably optimize well controls in heterogeneous waterflooding reservoirs, thereby significantly improving oil recovery and economic benefits while overcoming the limitations of traditional streamline and pure surrogate methods.

Original authors: Lixia Zhang, Yong Li, Dandan Hu, Yang Yu, Chenchao Liu

Published 2026-08-19

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Lixia Zhang, Yong Li, Dandan Hu, Yang Yu, Chenchao Liu

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Deep beneath the Earth's surface, vast networks of porous rock hold the world's oil and gas. To extract this energy, engineers often inject water into these reservoirs to push the oil toward production wells, a process known as waterflooding. However, the underground rock is rarely uniform; it contains hidden channels of high permeability and barriers that cause the injected water to rush through some paths while bypassing oil trapped in others. This uneven flow leads to a frustrating reality: water breaks through to the production wells too quickly, flooding the system and leaving valuable oil behind. For decades, the challenge has been to find the perfect balance of injection and production rates to sweep the reservoir efficiently without wasting time or money on trial and error.

A team of researchers from the CNPC Research Institute of Petroleum Exploration and Development has developed a new method to solve this problem, combining two distinct approaches to create a faster, more reliable way to manage these complex underground systems. Their work, published recently, introduces an algorithm that acts like a smart guide for reservoir engineers. Instead of relying solely on slow, heavy computer simulations or simple rules of thumb, this new system uses a technique called streamline simulation to understand how water moves through the rock, and then applies a sophisticated search strategy to find the best possible settings for every well. The result is a schedule that significantly increases oil recovery while drastically reducing the amount of water produced, offering a clearer path to maximizing the value of a reservoir.

The core of this new method lies in how it measures the success of each injection and production well. The researchers defined a concept they call "injection and production efficiency." Imagine looking at a specific pair of wells—one pumping water in and one pulling oil out. The team calculated how much money the oil produced by that pair is worth compared to the cost of the water injected and the liquid produced. If a well pair is generating more value than the average, the system knows to increase its activity. If it is underperforming, the system reduces its rate. This calculation happens at the level of individual well pairs and also for single wells, creating a detailed map of which parts of the reservoir are working well and which are struggling.

Traditionally, optimizing these rates has been a slow and difficult process. Engineers often had to run complex numerical simulations, which are like detailed 3D models of the underground rock, to test different scenarios. Because these models are so computationally expensive, running them hundreds of times to find the best solution is often impossible within a reasonable timeframe. Alternatively, simpler methods exist that are fast but lack the precision to handle the complex, changing conditions of a real reservoir over many years. The researchers sought a middle ground that could offer the speed of simple methods with the accuracy of complex simulations.

To achieve this, they built a "surrogate optimization" algorithm. In this context, a surrogate is a simplified, fast-running model that stands in for the heavy, slow simulation. The algorithm starts by testing a few different rate settings and using the results to build this simplified model. It then uses a smart sampling strategy to guess where the best solution might be hidden. The algorithm looks for points that are either likely to give a good result based on the current model or are far away from what has already been tested, ensuring it explores new possibilities. By constantly updating its simplified model with new data from the real, heavy simulation only when absolutely necessary, the algorithm finds the optimal solution with far fewer expensive calculations than traditional methods.

The researchers tested this new approach on two different scenarios: a synthetic model designed to mimic a reservoir with specific geological features, and a real-world reservoir in the Middle East. In the synthetic model, the reservoir contained high-permeability streaks that caused water to channel through specific paths, leaving oil behind. The base schedule, which represented the standard way of managing the wells, resulted in a net present value of roughly 43.67 million US dollars. When the new algorithm took over, it adjusted the injection rates, notably increasing the water injection into a specific injector that was surrounded by untapped oil. This change allowed the water to push the remaining oil more effectively. The optimized schedule increased the net present value to about 44.10 million US dollars, a significant improvement. More importantly, it increased total oil production by over 27,000 cubic meters while reducing total water production by nearly 48,000 cubic meters.

The test on the real Middle Eastern reservoir yielded even more dramatic results. This reservoir had been in production for over twelve years, with five injectors and nine producers. The standard management approach, which relied on fixed capacity limits, resulted in a net present value of roughly 11.08 million US dollars for the optimization period. The new algorithm, however, identified that the injection and production rates needed to be shifted away from the dominant wells and toward others that were underutilized. By gradually increasing the injection rate at a specific injector and adjusting the production rates of several wells, the system improved the sweep of the reservoir. The optimized schedule raised the net present value to approximately 13.33 million US dollars, an increase of over 2.2 million dollars. Perhaps most striking was the reduction in water production, which dropped by more than 68,000 cubic meters, and a massive decrease in the water cut, the percentage of water in the total fluid produced, which fell by over 26 percentage points.

The success of this method comes from its ability to integrate the physical understanding of how water moves through rock with the mathematical power of optimization. The streamline simulation provides a clear picture of the flow paths, allowing the algorithm to make decisions based on the actual physics of the reservoir rather than just statistical guesses. By using the surrogate optimization framework, the researchers avoided the computational bottleneck that usually prevents such detailed optimization from being done in a timely manner. The algorithm proved that it is possible to find a schedule that is both economically superior and physically efficient, extracting more oil while producing less water.

The researchers emphasize that this approach is particularly valuable for the middle and late stages of reservoir development, where the remaining oil is often scattered and difficult to reach. The method is not limited to just adjusting rates; the framework is flexible enough to be extended in the future to optimize the location of new wells or the arrangement of the entire well pattern. For now, the work demonstrates that by combining a deep understanding of fluid flow with modern search algorithms, engineers can make better decisions that extend the life of reservoirs and improve the efficiency of global energy production. The findings suggest that with the right tools, the complex challenge of managing waterflooding can be turned into a precise science, yielding better results with less waste.

Technical Summary: An Injection/Production-Efficiency Based Surrogate Optimization Algorithm for Optimal Well Controls in Waterflooding Reservoirs

Problem Statement

Waterflooding is a primary energy-supplement method for sandstone and carbonate reservoirs, yet reservoir heterogeneity (e.g., high-permeability streaks, faults) often leads to low sweep efficiency, premature water breakthrough, and limited recovery in the middle to late stages of development. Traditional production optimization methods face a trade-off between computational speed and result reliability:

Reservoir Engineering Methods: Fast and practical but rely heavily on empirical knowledge, offering low accuracy and subjective results.
Numerical Simulation Methods: High reliability but computationally expensive, making automatic optimization via iterative simulation prohibitive for large-scale problems.
Surrogate Optimization Methods: Aim to reduce computational costs by using approximate models but often struggle with high-dimensional decision spaces, initial sample sensitivity, and the time-consuming nature of constructing initial surrogates for complex, constrained problems. Specifically, pure surrogate optimization is sensitive to the dimensionality of decision variables and is not recommended for large-scale reservoir production optimization problems where the number of control parameters is high.
Streamline Simulation Methods: Offer fast flow-field diagnosis and clear physical meaning for rate allocation but are often limited to well-control optimization and may lack the robustness of global optimization algorithms when dealing with complex parameter tuning.

The core challenge is to develop a method that balances computational efficiency, optimization accuracy, and reliability for time-consuming, constrained reservoir production optimization problems.

Methodology

The authors propose a streamline-based surrogate optimization algorithm that integrates the physical insights of streamline simulation with the global search capabilities of surrogate optimization. The methodology consists of three main components:

1. Streamline-Derived Injection/Production Efficiency and Rate Optimization Strategy

Efficiency Definitions: Based on streamline simulation, the authors define Injection Efficiency (IE) and Production Efficiency (PE) at both the well-pair and single-well levels. These metrics quantify the economic value of injected water and produced liquid relative to costs and oil prices.
- Well-pair IE/PE: Reflects the effectiveness of specific injector-producer pairs.
- Single-well IE/PE: Aggregates contributions from all connected pairs to evaluate individual well performance.
Rate Updating Strategy: A bounded-weight criterion is introduced to adjust injection and production rates. The update weight ( $W$ $W$ ) is determined by the normalized efficiency ( $\beta$ $β$ ) relative to the average efficiency ( $\beta_{ave}$ $β_{a v e}$ ).
- If a well/pair is more efficient than average, its rate is increased (up to a limit).
- If less efficient, its rate is decreased (potentially to zero).
- The strategy includes parameters for the weight exponent ( $\alpha$ ), calculation range ( $R$ ), and linear scaling coefficients ( $W_{lim,min}, W_{lim,max}$ ) to control the intensity of adjustments.
Workflow: This streamline optimization requires only one forward simulation (including all time steps) to generate a full schedule. Crucially, the streamline optimization method itself is insensitive to the number of injection and production wells, making it efficient for large-scale rate allocation.

2. Surrogate Optimization Framework
To optimize the parameters of the streamline rate-updating criterion (which are otherwise manually tuned), the authors embed the streamline method into a surrogate optimization framework.

Decision Variables: The parameters of the bounded-weight criterion ( $\alpha, R, W_{lim,min}, W_{lim,max}$ ) serve as the decision variables. By optimizing these few parameters rather than individual well rates, the method significantly reduces the dimensionality of the problem.
Surrogate Model: A Radial Basis Function Interpolation Model (RBF-IM) is used due to its low computational cost and ability to guarantee exact values at known sample points.
Sampling Strategies: Three strategies are employed to select potential candidate points for the next simulation:
1. Minimum Surrogate Response (RS_Min): Focuses on local exploitation (minimizing the surrogate objective).
2. Maximum Search Ability (SA_Max): Focuses on global exploration (selecting points farthest from existing samples).
3. Maximum Integrated Value (IV_Max): Balances exploitation and exploration by combining the normalized surrogate response and distance metrics.
Constraint Handling: Constraints are managed via penalty functions or screening of feasible points generated by random sampling or optimization algorithms.

3. Integrated Algorithm
The proposed algorithm runs the streamline optimization procedure within the surrogate optimization loop. The surrogate algorithm iteratively updates the parameters of the streamline rate-updating criterion to maximize the Net Present Value (NPV). This approach reduces the dimensionality of the problem (optimizing a few criterion parameters rather than thousands of well rates directly) and minimizes the number of expensive numerical simulations required. While pure surrogate optimization is sensitive to the dimensionality of decision variables and not recommended for large-scale problems where decision variables are numerous, this hybrid approach mitigates that issue by limiting the decision variables to the streamline criterion parameters.

Key Contributions

Novel Algorithm: The development of a streamline-based surrogate optimization algorithm that couples flow-field diagnostics with surrogate optimization. This hybrid approach leverages the speed of streamline simulation and the global search capability of surrogate methods.
Efficiency Metrics: The formal definition of injection/production efficiencies at well-pair and single-well levels, providing a physically grounded basis for rate allocation.
Bounded-Weight Criterion: A flexible rate-updating mechanism that allows for controlled rate adjustments based on efficiency diagnostics, preventing extreme or unstable changes.
Dimensionality Reduction: By treating the streamline optimization parameters as decision variables rather than individual well rates, the method reduces the dimensionality of the problem, thereby avoiding the "curse of dimensionality" that typically limits pure surrogate optimization in large-scale reservoirs where decision variables are numerous.

Results

The algorithm was validated using two numerical models: a synthetic 5-injector/4-producer model and a real-world low-permeability carbonate reservoir (Reservoir A) with 5 injectors and 9 producers.

Synthetic Model Results:

Compared to a base schedule (historical rates) and a standard streamline optimization (Opt_IE), the proposed Opt_IE_Sur method achieved the highest Net Present Value (NPV).
Improvements: Cumulative oil production increased by 26.06%, cumulative water production decreased by 9.24%, and the final water cut was reduced by 2.75 percentage points.
The optimized schedule effectively targeted remaining oil around Injector INJ3 by increasing its injection rate and reducing production from Producer PRO4, demonstrating the algorithm's ability to adapt to heterogeneity.

Real Reservoir (Reservoir A) Results:

The Opt_IE_Sur schedule significantly outperformed both the base schedule and the standard streamline optimization.
Improvements: Cumulative oil production increased by 22.12%, while cumulative water production decreased by a substantial 80.52%. The final water cut dropped by 26.23 percentage points.
The NPV increased by 22.55% compared to the base schedule.
Flow-field analysis showed that the optimized schedule successfully altered the injection sweep pattern, shifting focus from the over-performing AI3 to under-swept areas near AI1 and AI4, thereby improving drainage efficiency.

Significance and Claims

The paper claims that the proposed streamline-based surrogate optimization algorithm successfully addresses the limitations of existing methods:

Speed vs. Accuracy: It overcomes the time-consuming nature of pure surrogate optimization (which requires many simulations for high-dimensional problems) and the low accuracy of pure streamline methods (which rely on fixed parameter settings).
Applicability: The method is suitable for large-scale, time-consuming, constrained optimization problems. The underlying streamline optimization component is insensitive to the number of wells, while the surrogate component effectively manages the reduced dimensionality of the criterion parameters, making the overall approach scalable.
Synergy: By integrating streamline simulation into the surrogate framework, the method retains the physical interpretability of flow-field diagnostics while benefiting from the robustness of global optimization.
Future Potential: The authors state that this framework has strong scalability and can be extended to joint optimization of well patterns, well locations, and well-control parameters in future work.

The study concludes that this integrated approach provides a reliable, fast, and accurate tool for optimizing waterflooding operations, offering significant economic benefits and improved recovery factors in heterogeneous reservoirs.