Elsevier

Computers & Chemical Engineering

Volume 106, 2 November 2017, Pages 339-354
Computers & Chemical Engineering

Real-time management of the waterflooding process using proxy reservoir modeling and data fusion theory

https://doi.org/10.1016/j.compchemeng.2017.06.018Get rights and content

Highlights

  • An adaptive algorithm is introduced for waterflooding management in oil reservoirs using proxy models.

  • Time-varying nature and inherent nonlinearity of the complex process is successfully handled.

  • Variations in market prices or operational costs are compensated such that a desired feasible profit is ensured.

  • Using data fusion technique, the real-time profitability/productivity status of the reservoir is monitored.

  • Fair profit-sharing in different field development contracts can be achieved by applying the proposed method.

Abstract

Waterflooding is the use of water injection to enhance the oil recovery in mature oil reservoirs. In this paper an adaptive algorithm has been introduced for waterflooding management in oil reservoirs based on proxy modeling technique. The presented approach is capable to handle the time-varying nature and the inherent nonlinearity of the complex process. In addition, any variation either in market prices or in operational costs is compensated by the designed adaptive controller to fix the obtained profit (here, the net present value: npv) at a desired achievable value. The observed outcomes on 10th SPE-Model#2 benchmark case study have shown that by using this algorithm, any feasible desired trajectory for the expected benefit can be satisfied during the waterflooding-based production. Since the suggested controller has adaptive structure, it can be re-adjusted continuously in each time-step, using available operational data, to take into account the reservoir dynamical variations as well as the external disturbances to present an acceptable performance. By including a monitoring module in the algorithm structure based on data fusion technique, the updated profitability/productivity status of the reservoir is estimated. By using this information the npv setpoint induced to the closed-loop system can be automatically re-adjusted such that it always remains in an acceptable and reasonable range. In conclusion, the proposed methodology is an applicable solution for fairly profit-sharing in different kinds of contracts. In other words, the gained profit can be appropriately allocated to the shareholders according to the contractual obligations or a defined npv trajectory while considering the current condition of the reservoir. This strategy helps to prevent from ultra-production in a specific period of time by the clients or contractors which may lead to an unexpected reduction in the share of other parties in the reservoir life-cycle.

Introduction

For reducing the gap between demand and sources of hydrocarbon-based energy, an effective solution is increasing the oil recovery factor in existing reservoirs. The average recovery factor may disappointingly come down to about 15% in complex reservoirs (Sarma, 2006, Golder Associates, 2000). However; by using secondary production approaches such as waterflooding- in which water is injected into the reservoir for conducting the oil toward production wells for more efficiency- up to 70% of the hydrocarbon can be recovered theoretically (van den Hof et al., 2009). So, different aspects of waterflooding modeling, control and optimization studies, have recently attracted much attention by the researchers (Sarma et al., 2006, Shirangi and Durlofsky, 2015, Grema and Cao, 2016, Sorek et al., 2017).

Although hydrocarbon production is a complex large-scale dynamical process, the operators in the fields mostly manage it just based on their own experiences. Fortunately, widespread applications of advanced instrument and control devices have increased the opportunity to optimize the oil production using model-based control and optimization techniques (Jansen et al., 2008). Nowadays, intelligent reservoirs are generally equipped with appropriate sensors and actuators to monitor the wells and reservoir conditions as well as to control the fluids flow of the producing and injecting wells. It has been perceived that applying advanced monitoring and control systems in reservoirs can significantly increase the hydrocarbon recovery (Glandt, 2005).

Closed-loop reservoir management (CLRM) is a popular methodology, which take into account the reservoir observed data as well as the information obtained from model-based simulations, to design the suitable optimal control strategies (Foss, 2012). Generally, the manipulated variables in a reservoir are bottom-hole pressures (bhp) or flow-rates of the wells, and the ultimate goal in CLRM is to maximize an objective function which is usually selected as the net present value (npv) of the recovery process subject to the operational constraints. In other words, optimization in oil reservoirs can be performed by adjusting optimum injection and production rate settings for maximizing the npv as a well-known profitability index. In model-based optimization approaches which use open-loop configuration, the reservoir models are supposed to be perfect in presenting all existing dynamics of the system (Asadollahi and Naevdal, 2009). Consequently, open-loop techniques, such as dynamic optimization, suffer from loss of robustness against uncertainties and may deduce suboptimal or even non-optimal results (Brouwer and Jansen, 2004). On the other hand, robust optimization techniques, which use a set of reservoir realizations for considering different types of probable geological models, have been introduced to cope with the uncertainties (van Essen et al., 2009). However, these methods’ principle assumption, which is all existing reservoir characteristics and production behaviors are presented by the developed realizations, is somehow unrealistic (Grema and Cao, 2016). That is to say, the set of various realizations may not be completely successful to reflect the real reservoir dynamic which is needed for an efficient optimization process.

From another point of view, in model-based dynamic reservoir optimization using direct methods, it is possible to define the optimal control problem in the framework of nonlinear programming (NLP) (Binder et al., 2001). In this methodology, the optimizer seeks for the solution sequentially. It means that a control profile is computed at each step and then the obtained profile is simulated for investigating the results. This sequential-optimization process is generally known as single shooting (SS) (Jansen, 2011). For instance, generalized reduced gradient (Kraaijevanger et al., 2007), and augmented Lagrangian (Chen et al., 2010) are common gradient-based methods for dealing with NLP’s, specially applied in reservoir optimization. In these techniques, gradients of the objective and function evaluations should be computed. In addition, existence of operational constraints forces some limitations on bhp’s and flow-rates of the wells. Function evaluations is the technical term for presenting the dynamic behavior of the reservoir and can be achieved using valid simulators. Furthermore, objective gradient can be calculated via adjoint techniques. However, existence of nonlinear constraints can dictate additional adjoint simulations and increase the computational load of such techniques. As a result, methods to lump reservoir output constraints, such as limitation on the volume of the produced water, into a single constraint have been developed to evade from extra adjoint computations (Suwartadi et al., 2011, Kourounis et al., 2014). Nevertheless, these approaches may induce extra approximations as well as parameters retuning. To handle the mentioned problem related to the output constraints, direct method for dynamic optimization in oil reservoirs based on multiple shooting (MS) technique, has been proposed in (Codas et al., 2015). But, applying this approach requires an intense interaction between optimizer and simulator, which causes to a huge computational load. In addition, to achieve an efficient MS implementation, parallel-computing facilities and extensive-memory should be available. Moreover, several research on reservoir optimization and production management based on proper orthogonal decomposition (van Doren et al., 2006) and trajectory piecewise linearization (Cardoso and Durlofsky, 2010, Gunnerud and Foss, 2010) have tried to develop methods in which the search-space and also memory requirements decrease.

Obviously, all model-based approaches applicable for the production management in the hydrocarbon reservoirs require accurate reservoir models. A real reservoir can expose totally different behaviors compared to the assumed models. As a result, by just relying on the outcomes of cumbersome model-based optimization techniques, which have been validated in simulation mode while ignoring the real-time production data, the optimization goals may not be achieved in the real applications. This fact has origin in continuous time-varying dynamics of the reservoir as well as the impacts of unknown geological and financial uncertainties during the operation. In other words, in the presence of uncertainties, implementation of appropriate control strategies for optimizing purposes is completely a challenging task. Hence, although many contributions which apply different control techniques use reservoir models to identify the optimal response (Sarma et al., 2005, Jansen et al., 2009), the obtained results are not applicable in practice since the considered models are rarely predictive.

When a batch of new information such as recent production data, up-to-date well logs, and new seismic data are provided during the operation in the oil fields, the utilized reservoir model(s) may be updated by history matching process. Therefore, new optimization calculations would be done based on the updated reservoir models (Foss and Jensen, 2011). Yet, even history-matched models may not be able to forecast the future behavior of reservoirs precisely (Tavassoli et al., 2004). Consequently, instead of periodically updating of the reservoir models via history matching process, closed-loop control strategies based on last measured production data have been introduced (Foss and Jensen, 2011, Jansen et al., 2008).

In other words, besides utilizing complicated model-based methods for optimization objectives, either gradient-based or derivative-free techniques (Chen et al., 2008, van Essen et al., 2011, Ciaurri et al., 2011, Giuliani and Camponogara, 2015, Wang et al., 2016), exploring for more realistic solutions, which profit from simplicity in comparison with fully model-based optimization approaches, is an active research area in this domain (Foss and Jensen, 2011, Shuai et al., 2011, Reynolds and Oliveira, 2013, de Holanda et al., 2015). To this aim, there have been some attempts to consider the CLRM as a regulatory feedback control problem (Grema and Cao, 2016; Güyagüler et al., 2010; Grebenkin and Davies, 2010). Generally, the characteristic of direct feedback-control robustness against unknown reservoir uncertainties is one of the strengths of this approach (Chen et al., 2012). It means that by applying feedback control strategy, the performance becomes less sensitive to model errors and inherent uncertainties of the oil reservoirs. The obtained results in (Dilib and Jackson, 2013, Dilib et al., 2015) demonstrate that closed-loop control methodology which is based on direct feedback between reservoir monitored variables and production flows can lead to near optimal achievements in oil reservoirs. Closed-loop feedback control of the reservoir can also alleviate the effect of existing geological uncertainties on reservoir behavior.

Based on the above explanations, transforming the complicated reservoir optimization problem to the regulatory control framework is among the possible solutions which can have acceptable efficiency, simplicity, and potential of being easily implemented in practice. On the other hand, due to the nature of an oil reservoir and different uncertainty sources, field noises and disturbances during the operation, self-optimizing-control (SOC) strategy can be a proper candidate for optimizing the waterflooding process under certain conditions (Grema and Cao, 2016). It has been proved that if the controlled variables are selected appropriately in SOC framework and also regulated such that they remain constant during the operation, the system is near optimal even in the presence of uncertainty and disturbances (Skogestad, 2000, Skogestad, 2004, Halvorsen et al., 2003). As a result, controlled variables (CV’s) determination which can be an appropriate combination of available measurements is an important step in SOC methodology. Clearly, by fixing the selected CV(s) around a specific setpoint through feedback control, the optimality or near-optimality of the whole system can be guaranteed (Girei et al., 2014, Hu et al., 2012, Ye et al., 2013).

Another important issue is that of finding an efficient strategy of water injection in waterflooding process as an efficient oil recovery technique in reservoir management, availability of a valid simulator or a precise mathematical model for estimating the quality of the process performance is a vital prerequisite (Fanchi, 2001). Various simulation and modeling approaches with different levels of complexity exist for presenting the reservoir behavior during the operation. Utilization of each modeling methodology is related to the available information, the level of required accuracy, the calculated time-cost, and the user’s expectation from modeling and simulation (Ertekin et al., 2001). For example, the prevalent and precise but complex and memory-demanding solution for reservoir simulation, generally used by professional simulators, is numerically solving of a set of partial-differential equations by discretizing in time and space (Chen et al., 2006). Furthermore, exploring for fast modeling strategies with acceptable accuracy is a hot topic in reservoir modeling studies which results to proxy/surrogate models (Sayyafzadeh et al., 2011). The surrogate models are appropriate tools for estimating the performance of various control and optimization strategies in oil reservoirs. The models can be categorized based on their applications as linear and nonlinear; or fixed and adaptive. Each of the proposed modeling strategies has different advantages which make them suitable for distinct cases of various reservoir types based on the user expectation (van Essen et al., 2012; Tafti et al., 2013; Bruyelle and Gu&rillot, 2014; Mohaghegh and Abdulla, 2014; Elkamel, 1998).

Due to the time-varying nature of the waterflooding process, applying appropriate adaptive modeling structures for representing the dynamical behavior based on the last observed production data is inevitable. For example, in (Hourfar et al., 2016) an adaptive linear-based approach for proxy modeling of waterflooding process in oil reservoirs has been presented. The developed modeling technique is completely compatible for being utilized by popular adaptive control and optimization strategies to enhance the economic performance of the reservoir while the production is feasible.

In this paper, based on the adaptive modeling technique presented in (Hourfar et al., 2016), by which the defined system outputs can be modeled using the recommended system identification (SI) algorithm, an adaptive control configuration has been developed for production management via waterflooding process. So needless to directly challenge with the reservoir PDE’s to assess the production management algorithm, by utilization of the proxy-model the required information about the appropriate injection/production profiles can be provided not only with low computational cost but also with acceptable accuracy.

In addition, considering SOC concepts allows to transform the challenging and complicated task of reservoir optimization to a popular regulatory control problem by properly defining the controlled variable. In other words, by maintaining the suitable considered controlled variable at a constant value, the system can present near optimal behavior with minimum sensitivity to the existing disturbances under certain circumstances. Another advantage of the developed algorithm is providing the capability of controlling the waterflooding process while coping with the inherent time-varying nature of the oil reservoir and also the hydrocarbon market. Adding the adaptation characteristics to the designed controller enables the procedure to track the reservoir dynamic variations and re-adjust the controller parameters for effectively regulating the specified controlled variable. Furthermore, design of a condition monitoring module for the reservoir, using ordered weighted averaging (OWA) method which is known as one of the popular data fusion techniques, helps to modify the setpoint of the controller by taking into account the last productivity status of the reservoir. Embedding this unit in the general configuration of the algorithm assists to prevent ultra-expectation of the closed-loop system performance. That means whenever the reservoir is impotent to produce the sufficient hydrocarbon due to the production history and the amount of total extracted hydrocarbon, the condition will be detected and consequently a new rational controller setpoint will be substituted. Online monitoring of the reservoir condition also facilitates applying the developed methodology in practical applications especially for different types of field development international or multilateral contracts in which a compromise between short-term and long-term production plans is necessary during the operation. Since the produced hydrocarbon and the gained profit are mostly the challenging concerns between the host governments (known as the clients) and the international oil companies (IOC’s) (known as the contractors), precisely controlling and managing the obtained profit by appropriately regulating the production regime in various operational phases are important issues. Hopefully, the presented technique helps to monitor and control the expected npv based on reservoir and market conditions. This fact makes the algorithm applicable for different types of contracts such as buyback or production sharing (Ghandi and Lin, 2012, Ghandi and Lin, 2014, Feng et al., 2014, Zhao et al., 2012, Shakhsi-Niaei et al., 2014). Based on the highlighted characteristics, it can be easily deduced that the developed methodology is perfectly suitable for being implemented in real-time reservoir closed-loop management during the waterflooding process.

Section snippets

Comprehensive modeling of oil reservoir dynamics

As explained in Section 1, availability of a valid model is one the most important prerequisites for design and development of a useful controlling strategy during waterflooding operation.

Conservation of mass and momentum equations are commonly applied for representing the fluid flow behavior in oil reservoirs and the dynamics of waterflooding process may be simulated based on the reservoir partial differential equations. By ignoring gas phase existence and just focusing on oil and gas, the

Data driven proxy-modeling of oil reservoir

A real oil reservoir can be considered as a Multi-Input-Multi-Output system since it may contain 10–1000 injection and production wells on which the system inputs and outputs are defined. The candidate models should be able to reflect the nonlinearity as well as the time-varying nature of the reservoir. Generally, in SI framework applied to a reservoir, the inputs are considered as flow rate or bhp of the wells and variables such as oil and water production rates of producing wells are supposed

General formulation of waterflooding performance assessment

The performance of waterflooding process in a certain period of time can be evaluated by calculation of an index which is normally the accumulative npv. The accumulative npv is defined as the summation of instant npv’s of each time step. As mentioned in section 1, in the waterflooding process, water is injected in the reservoir to augment the produced oil or maximize an objective function. In general, the accumulative npv is mathematically formulated for a reservoir including Nprd production

Controlling of the gained profit

Although the instant npv is a function of several variables, in this section we demonstrate that under certain conditions, it is possible to fix the npv value at a feasible setpoint, just by controlling the total injection rate.

By ignoring the time-varying dynamics of the reservoir and also linearizing the waterflooding process around a specific setpoint, Gp(s) which is the reservoir transfer function from total injected water, U, to the total produced oil, Yo, can be expressed as:Yo(s)=Gp(s)U(s

Relaxing the limiting assumptions

In the previous section we exposed that fixing the value of npv at a desired value is possible just by manipulating the total injection rate. In addition, this action may lead to even optimal solution under certain conditions. However; since the dynamics of a real reservoir and consequently the waterflooding process is completely nonlinear and time-varying and also the values of oil prices and production costs are not constant during the life-cycle of the reservoir, replacing the fix-structured

Developed algorithm for production management

In this section, the developed methodology for production management in hydrocarbon reservoirs via adaptive control of npv based on the productivity/profitability condition of the considered system is summarized. The proposed algorithm is divided into three steps as explained below:

Algorithm implementation and results

The developed waterflooding profit management algorithm has been implemented, using Matlab Reservoir Simulation Toolbox (MRST) environment (Lie, 2014). Without loss of generality, it is assumed that the producing wells are being operated in the fixed bhp’s according to operational recommendations. In addition, the annual discount rate in accumulative npv formula, is supposed to be zero. Furthermore, the voidage assumption is valid which implies: for over-pressurization prevention, the total

Conclusion

Although many optimization algorithms have been developed in recent years for achieving an efficient waterflooding strategy, most of the solutions encounter with unpredicted problems in practical applications due to the time-varying nature of hydrocarbon reservoirs and also the existence of geological and hydrocarbon market uncertainties. On the other hand, the profit sharing between the clients and contractors in different stages of field development projects dictated by various types of

Acknowledgement

We appreciate the assistance of Ms. Ladan Khoshnevisan for her useful technical comments, as well as her collaboration in finalizing this manuscript.

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    Present address: Department of Chemical Engineering, University of Waterloo, Ontario, Canada.

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