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Machine learning models to support reservoir production optimization
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IFAC PapersOnLine 52-1 (2019) 498–501 Machine learning models to support reservoir production optimization Machine learning models to support reservoir production optimization Alexto F. support Teixeira*, Argimiro R. Secchi** Machine reservoir production Machine learning learning models models to support reservoir production optimization optimization
Alex F. Teixeira*, Argimiro R. Secchi** Alex Argimiro R. R. Secchi** Secchi** Alex F. F. Teixeira*, Teixeira*, Argimiro *Petrobras Research Center, Rio de Janeiro, RJ 21949-900, Brazil (e-mail: [email protected]). **Chemical Engineering Program at Rio COPPE, Federal of Brazil Rio de (e-mail: Janeiro,[email protected]). Rio de Janeiro, RJ 21941-972, Brazil (e*Petrobras Research Center, de Janeiro, RJUniversity 21949-900, mail:[email protected]) *Petrobras Research Center, de RJ 21949-900, Federal of Brazil Rio de (e-mail: Janeiro,[email protected]). Rio de Janeiro, RJ 21941-972, Brazil (e**Chemical Engineering Program at Rio COPPE, *Petrobras Research Center, Rio de Janeiro, Janeiro, RJUniversity 21949-900, Brazil (e-mail: [email protected]). **Chemical University mail:[email protected]) **Chemical Engineering Engineering Program Program at at COPPE, COPPE, Federal Federal University of of Rio Rio de de Janeiro, Janeiro, Rio Rio de de Janeiro, Janeiro, RJ RJ 21941-972, 21941-972, Brazil Brazil (e(email:[email protected]) mail:[email protected]) Abstract: Traditionally, numerical simulators are used in combination with an optimization algorithm to determine controls that maximize total production or net present (NPV) over the life Traditionally, numerical simulators areoil used in combination with an value optimization algorithm to Abstract: optimum of the reservoir. These simulators are complex dynamic models that consider geological information, Abstract: Traditionally, numerical simulators are used in combination with an optimization algorithm to determine optimum controls that maximize total production or net present (NPV) over the life Abstract: Traditionally, numerical simulators areoil used in combination with an value optimization algorithm to rock and fluid properties, as well as information about the completion of the wells. This complexity determine optimum controls that maximize total oil production or net present value (NPV) over the life of the reservoir. These simulators are complex models considervalue geological determine optimum controls that maximize total dynamic oil production or that net present (NPV) information, over the life results in fluid a high computational and pose a challenge for application gradient-based of reservoir. These simulators are complex dynamic models that information, rock properties, as well time as about the completion of the geological wells.ofThis complexity of the theand reservoir. These simulators areinformation complex dynamic models thattheconsider consider geological information, optimization algorithms, since calculation of gradients of the objective function with respect to controls rock and fluid properties, as well as information about the completion of the wells. This results in a high computational time and pose a challenge for the application of gradient-based rock and fluid properties, as well as information about the completion of the wells. This complexity complexity may demand several evaluations of the simulation model. This paper proposes the use of a machine results in a high computational time and pose a challenge for the application of gradient-based optimization algorithms, since calculation of gradients of the objective function with respect to controls results in a high computational time and pose a challenge for the application of gradient-based learning model, based on artificial neural networks, to represent the non-linear dynamic behavior of the optimization algorithms, since calculation of gradients of the objective function with respect to may demand several evaluations of the simulation model. This paper proposes the use of a machine optimization algorithms, since calculation of gradients of the objective function with respect to controls controls reservoir. The proposed approach was applied to data generated with a synthetic reservoir simulation may demand several evaluations of the simulation model. This paper proposes the use of a machine learning model, basedevaluations on artificialofneural networks, to represent non-linear dynamic of the may demand several the simulation model. Thisthe paper proposes the usebehavior of a machine model showing promising results. neural learning model, based artificial networks, to non-linear dynamic behavior of reservoir. The proposed was applied to data generatedthe a synthetic reservoir simulation learning model, based on onapproach artificial neural networks, to represent represent thewith non-linear dynamic behavior of the the reservoir. The proposed approach was applied to data generated with a synthetic reservoir simulation model showing promising results. reservoir. The proposed approach was applied to data generated with a synthetic reservoir simulation © 2019, IFAC (International of Automatic Hosting by Elsevier Ltd. All rights reserved. Keywords: machine learning,Federation optimization, artificialControl) neural network, reservoir. model model showing showing promising promising results. results. Keywords: machine learning, optimization, artificial neural network, reservoir. Keywords: network, reservoir. Keywords: machine machine learning, learning, optimization, optimization, artificial artificial neural neural network, reservoir.was tested using data generated with a strategy. The concept 1. INTRODUCTION synthetic reservoir simulation model. strategy. The concept was tested using data generated with a 1. INTRODUCTION When the natural driving mechanism present in the reservoir synthetic strategy. The concept was tested using reservoir simulation model. strategy. The concept was tested using data data generated generated with with aa 1. INTRODUCTION 1. INTRODUCTION is not able to support an efficient and economically attractive synthetic reservoir simulation model. When the natural driving mechanism present in the reservoir synthetic 1.1 Machine Learning reservoir simulation model. oil recovery, secondary recovery method is applied. When the driving mechanism present in reservoir is not able to asupport an efficient and economically When the natural natural driving mechanism present in the the attractive reservoir 1.1 Machine Learning Waterflooding is thean common secondary recovery Exponential increase of the computing performance in is able efficient and economically oilnot recovery, secondary recovery method is applied.attractive is not able to to asupport support anmost efficient and economically attractive 1.1 Machine Machine Learning Learning method used to increase oil production and ultimate 1.1 oil recovery, a secondary recovery method is applied. combination increase with the ofhuge data currently Waterflooding is the most common secondary oil recovery, a secondary recovery method is applied.recovery the amounts Exponential computingof performance in hydrocarbon recovery. Injected water helps to maintain Waterflooding is the most common secondary recovery available are responsible for a machine learning in the method used to increase oil production and ultimate Exponential increase increase ofhuge the amounts computingof performance performance in Waterflooding is the most common secondary recovery combination with the of datahype currently Exponential the computing in reservoir pressure time and oil inand the method to increase oil production ultimate industry. Injected water helps to direction maintain combination with the huge amounts of data currently hydrocarbon recovery. method used used to over increase oil displace production and ultimate available are responsible for a machine learning hype in the combination with the huge amounts of data currently of the producer wells, efficiency. hydrocarbon recovery. Injected water to maintain Despite the that manyfor techniques have been available for reservoir pressure overimproving time and sweeping displace oil available are responsible aa machine learning hype in the hydrocarbon recovery. Injected water helps helps to direction maintain industry. arefact responsible for machine learning hype in in the the Traditionally, dynamic simulation models used in available reservoir pressure overimproving time and and sweeping displace oil oil inare the direction direction decades, advances in computing performance are making of the producer wells, efficiency. industry. reservoir pressure over time displace in the Despite industry.the fact that many techniques have been available for combination optimizer tomodels determine of the wells, sweeping efficiency. possible their in severalperformance new solve Traditionally, dynamic simulation are optimum used in Despite fact that many techniques have been for of the producer producerwith wells,animproving improving sweeping efficiency. decades, advances computing are tomaking Despite the the factapplication that in many techniques have problems been available available for controls (water injection rate of the injection Traditionally, dynamic simulation are used in them in a simple and efficient way. combination with an optimizer advances in computing performance are making tomodels determine optimum Traditionally, dynamic simulation models are wells used and in decades, possible their application in several new problems to solve decades, advances in computing performance are making bottom-hole pressure liquid of the producing wells) combination with an to determine optimum Artificial neural networks are computational application in new to controls (water injection rate rate of the injection wells and possible combination with anor optimizer optimizer to determine optimum them in atheir simple and efficient way. possible their application in several several new problems problemsstructures to solve solve that maximize total oil production or the net present value controls (water injection rate of the injection wells and by the functioning of the human nervous system, bottom-hole pressure or liquid rate of the producing them in a simple and efficient way. controls (water injection rate of the injection wellswells) and inspired Artificial neural networks are computational structures them in a simple and efficient way. (NPV) over the life of reservoir. dynamic bottom-hole pressure or liquid rate of the producing wells) ofthesimple processing called structures neurons, that maximize total oil production the presentmodels value consisting Artificial neural networks aretheelements, computational structures bottom-hole pressure orthe liquid rate or ofThese the net producing wells) inspired byneural functioning ofare human nervous system, Artificial networks computational are usually complex numerical reservoir simulators that that maximize total oil production or the net present value connected in a network and used to store experimental (NPV) over the life of the reservoir. These dynamic models inspired by the functioning of the human nervous system, that maximize total oil production or the net present value inspired consistingbyofthesimple processing elements, called neurons, functioning of the human nervous system, consider geological information, rock and fluid properties, as (NPV) over the life of the reservoir. These dynamic models knowledge obtained through application of machine learning consisting of simple processing elements, called neurons, are usually complex numerical reservoir simulators that (NPV) over the life of the reservoir. These dynamic models consisting connected of in simple a network and used to store experimental processing elements, called neurons, well as information about the completion of simulators theproperties, wells. This are usually usually complex numerical reservoir simulators that techniques, as discussed in Haykin (2000). aa network and used to experimental consider geological information, rock and fluid as connected are complex numerical reservoir that knowledge in obtained through application machine learning connected in network and used to ofstore store experimental complexity results in a high computational time to simulation consider geological information, rock and fluid properties, as As explained in Dreyfus (2004), training is the algorithmic obtained through application of machine learning well as information about the completion of theproperties, wells. This consider geological information, rock and fluid as knowledge techniques, as discussed in Haykin (2000). knowledge obtained through application of machine learning run a challenge forthe thecompletion applicationtime of the gradient-based well as information of This procedure whereby the parameters of the neural network are as discussed in Haykin (2000). complexity results inabout a high computational towells. simulation welland as pose information about the completion of the wells. This techniques, As explained in Dreyfus (2004), training is the algorithmic techniques, as discussed in Haykin (2000). optimization algorithms, since of the As complexity in computational time to estimated, in order to allow it to learn, as accurately as explained in Dreyfus (2004), training is the algorithmic run and poseresults a challenge for thecalculation applicationof ofgradients gradient-based complexity results in aa high high computational time to simulation simulation procedure whereby the parameters of the neural network are As explained in Dreyfus (2004), training is the algorithmic objective function with for respect to controls may demand run aa challenge the application gradient-based possible, the task it has been assigned. Within this optimization algorithms, since ofof of the estimated, procedure whereby the parameters of the neural network are run and and pose pose challenge for thecalculation application ofgradients gradient-based to allow it to in order learn, as accurately as procedure whereby the parameters of the neural network are several evaluations of thesince simulation model. Inmay somedemand cases, optimization algorithms, calculation of of framework, areto types objective function with respect to controls estimated, the inthere order to allow it of to training: learn, assupervised accurately as optimization algorithms, since calculation of gradients gradients of the the possible, task ittwo has been assigned. Within and this estimated, in order allow it to learn, as accurately as for a grid with a huge number of cells, a single model objective function with respect to controls may demand unsupervised. several evaluations of the simulation model. In some cases, possible, the task it has been assigned. Within this objective function with respect to controls may demand framework, there are ittwohas types of training: supervised and possible, the task been assigned. Within this evaluation may many hours, of as model. pointedaIn in Sarma several evaluations the simulation some cases, Due to its learning ability, artificial neural supervised network canand be framework, there two types of for a grid with take a of huge cells, single model several evaluations of the number simulation model. Inout some cases, unsupervised. framework, there are are two the types of training: training: supervised and (2006). for aa grid grid may with take huge number of cells, single model unsupervised. used to model the dynamics of a nonlinear system based in evaluation manynumber hours, of as cells, pointedaa out in Sarma for with aa huge single model Due to its learning ability, the artificial neural network can be unsupervised. evaluation take many as out Sarma This paper may proposes usehours, of a machine the signals acquired experimentally when the system is to its learning ability, the artificial neural network can be (2006). evaluation may take the many hours, as pointed pointedlearning out in in model, Sarma Due used to model the dynamics of a nonlinear system based in Due to its learning ability, the artificial neural network can be (2006). basedpaper on artificial networks, to represent non- used excited by the variation of its input signals, as discussed to model the dynamics of a nonlinear system based in This proposesneural the use of a machine learningthemodel, (2006). the signals acquired experimentally when the system is used to model the dynamics of a nonlinear system based in linear dynamic behavior of the reservoir. The proposed model Bhat and McAvoy (1990), Wang et al, (1998) and Tehlah, This paper proposes the use of a machine learning model, the signals acquired experimentally when the system excited by the variation of its input signals, as discussed in based on artificial neural networks, to represent the nonThis paper proposes the use of a machine learning model, the signals acquired experimentally when the system is is will enabler to theofimplementation, atproposed an appropriate Kaewpradit andvariation Mujtaba (2016). basedbedynamic onan artificial artificial neural networks, to The represent themodel non- Bhat excited the of its input as in behavior the reservoir. linear andby (1990), Wang al, (1998) and Tehlah, based on neural networks, to represent the nonexcited byMcAvoy the variation of its inputet signals, signals, as discussed discussed in computational cost,tooftheaof dynamic production The benefits of Wang the use of (1998) an artificial neural linear behavior the The model Bhat two and main McAvoy (1990), Wang et al, al, (1998) and Tehlah, Tehlah, anoptimization appropriate will an enabler and Mujtaba (2016). linearbedynamic dynamic behavior ofimplementation, the reservoir. reservoir. Theatproposed proposed model Kaewpradit Bhat and McAvoy (1990), et and network as the model in the optimization strategy to will be an enabler to the implementation, at an appropriate Kaewpradit and Mujtaba (2016). computational cost,toofthea implementation, dynamic production two main benefits (2016). of the use of an artificial neural will be an enabler at anoptimization appropriate The Kaewpradit and Mujtaba computational cost, of a dynamic production optimization The two main benefits of the use of an artificial neural thebenefits model ofin the theuse optimization strategy to computational cost, of a dynamic production optimization network The two as main of an artificial neural network as the model in the optimization strategy to network as the model in the optimization strategy to Copyright © 2019 IFAC 498 2405-8963 © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review©under of International Federation of Automatic 2019 responsibility IFAC 498Control. Copyright 10.1016/j.ifacol.2019.06.111 Copyright © 2019 IFAC 498 Copyright © 2019 IFAC 498
2019 IFAC DYCOPS Florianópolis - SC, Brazil, April 23-26, 2019Alex F. Teixeira et al. / IFAC PapersOnLine 52-1 (2019) 498–501
determine the optimum controls of the reservoir are the reduction of the CPU time and the possibility to faster gradients computing. There are different types of neural networks, and in this work, so-called multilayer perceptrons (MLP) and the backpropagation algorithm were used.
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In order to excite the system to generate data to support the model identification process, variations were generated in the water flow rate of the injection wells, as can be seen in Figure 2. The effect on the oil and water flow rates of the producing wells was analysed. Variations in the bottom-hole pressure of the producing wells were also performed, aiming to represent the effect of variations in the well choke valves opening.
2. CASE STUDY In this section, we will consider a synthetic model, called UNISIM-I-M, to demonstrate the proposed approach. As presented in Avansi and Schiozer (2015), this synthetic model is based on the Namorado Field, located in the Campos Basin. It is implemented in the IMEX® simulator and has a corner point grid (81 x 58 x 20 cells) with 36.739 active cells (Figure 1). Each cell measures 100 x 100 x 8 meters. The Namorado field, discovered in November 1975, is located at 80 km from the Rio de Janeiro coast, in a water depth varying between 130 and 240 meters. Production started in June 1979 and the original oil in place was 100 MM m3 (630 MM STB). The field has been produced by two fixed platforms: PNA-1 e PNA-2.
Fig. 2. Variations in the water rate of the injection wells. In a real scenario, historical production and injection data may be used in the model training and validation process. Simulated data, generated with the numerical reservoir simulator, could be combined with historical data to increase fidelity of the artificial neural network model. 3. NEURAL NETWORKS ARCHITECTURES Two different neural network architectures were tested. As a first attempt, we opted to evaluate a MLP neural network with a hidden layer with neurons using sigmoidal activation functions and an output layer with neurons with a linear activation function. As inputs to the neural network, the water injection rates of the injection wells and past values of oil rates of the producing wells were used, both sampled every 30 days (monthly). The structure of the model can be seen in Figure 3.
Fig. 1. 3D view of the synthetic simulation model based on the Namorado Field, including wells perforations. The model has eleven horizontal injection wells and fourteen oil producing wells (4 vertical and 10 horizontal wells). A list of the wells can be seen in Table 1. Table 1. Wells from the synthetic model. Injection Wells INJ01 INJ02 INJ03 INJ04 INJ05 INJ06 INJ07 INJ08 INJ09 INJ10 INJ11 -
Producing Wells PROD01 PROD02 PROD03 PROD04 PROD05 PROD06 PROD07 PROD08 PROD09 PROD10 PROD11 PROD12 PROD13
Fig. 3. Structure of the proposed artificial neural network. In Figure 3, M is the number of injection wells, N is the number of producing wells, k is the current time and lagin is the number of time delays. 499
2019 IFAC DYCOPS 500 Florianópolis - SC, Brazil, April 23-26, 2019Alex F. Teixeira et al. / IFAC PapersOnLine 52-1 (2019) 498–501
The proposed neural network was implemented in Matlab® software and the training was performed using backpropagation combined with Levenberg-Marquardt optimization algorithm. As a strategy to support the decision regarding the number of time delays used in the input variables, a sensitivity analysis was performed by varying the number of time delays and comparing the results based on the mean square error (MSE). For the training and evaluation of the networks tested, the data available was divided in three groups as can be seen in Table 2. Table 2. Data groups. Training Validation Test
A second neural network was proposed considering also the bottom-hole pressure of the producing wells. As can be seen in the Figure 6, this network has two hidden layers with 250 and 125 neurons respectively. Fifteen time delays (lagin) were used for each input variable.
70% 15% 15% Fig. 6. Structure of the second proposed artificial neural network, considering bottom-hole pressure of the producing wells.
In Figure 4, we show the results obtained with the sensitivity analysis, where we concluded that the best MSE for the training, validation and test data was obtained for a network with 15 time delays (lagin) for each input variable (water injection rates of the injection wells and past values of oil rates of the producing wells).
4. RESULTS In Figure 7, we can observe a comparison between the oil flow rate values of a new test data set with the estimations obtained for each producing well, using the neural network of the Figure 3.
Fig. 4. Result of the sensitivity analysis in relation to the number time delays considered for each input variable. The same strategy was used to support the decision regarding the number of neurons in the hidden layer. A sensitivity analysis was performed by varying the number of neurons and comparing the results based on the mean square error (MSE). In Figure 5, we show the results obtained with the sensitivity analysis, where we concluded that the best MSE for the training, validation and test data was obtained for a network with 450 neurons in the hidden layer.
Fig. 5. Results of the sensitivity analysis in relation to the number of neurons in the hidden layer.
Fig. 7. Oil flow rate estimated for each well (red lines) over time compared to reservoir simulator results (blue lines).
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2019 IFAC DYCOPS Florianópolis - SC, Brazil, April 23-26, 2019Alex F. Teixeira et al. / IFAC PapersOnLine 52-1 (2019) 498–501
The blue lines were obtained using the commercial simulator and the red lines are estimations performed by the neural network. The proposed neural network was able to follow the variations in the produced oil flow rates from all the wells of the Namorado Field, but presented a noisy behaviour with some high amplitude spikes. Noisy behaviour with small amplitude spikes also appeared in the results obtained with the training data set for all the tested structures (variations in the number of time delays and neurons in the hidden layer), what made us discard the possibility of an overfitting. The determination of the cause of noisy behaviour will demand further investigation. In Figure 8, we can observe a comparison between the oil flow rate values of a new test data set with the estimations obtained for each producing well, using the neural network showed in Figure 6.
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optimized reservoir management, once both control variables are inputs for the model (water flow rate of the injection wells and bottom-hole pressure of the producing wells). 4. CONCLUSIONS Two proposals of artificial neural network architectures were evaluated to model the relationship between oil production and control variables. Both proposals were evaluated using data generated with a synthetic reservoir model based on Namorado Field. The results obtained with the training, validation and test data sets were satisfactory in terms of following variations in the oil flow rates of the producing wells, proving the potential of this modelling strategy. Although, the noisy behaviour displayed in the results obtained with both proposed architectures will demand further investigation, since it can affect the calculation of the gradients for the optimization. 5. REFERENCES Avansi, G. D., and Schiozer, D. J. (2015). UNISIM-I: Synthetic Model for Reservoir Development and Management Applications. International Journal of Modeling and Simulation for the Petroleum Industry, Vol. 9, NO. 1, pages 21-30. Bhat, N., and McAvoy, T. J. (1990). Use of Neural Nets dor Dynamic Modeling and Control of Chemical Process Systems. Computers Chemical Engineering, Vol. 14, pages. Dreyfus, G. (2004). Neural Networks Methodology and Applications (2nd Edition). Springer. Haykin, S. (2000). Neural Networks: A Comprehensive Foundation (2nd Edition). Prentice Hall. Sarma, P. (2006). Efficient Closed-Loop Optimal Control of Petroleum Reservoirs under Uncertainty. Dissertation, Stanford University. Tehlah, N., Kaewpradit, P. and Mujtaba, I. M. (2016). Artificial Neural Network Based Modeling and Optimization of Refined Palm Oil Process. Neurocomputing, Vol. 216, pages. Wang, H., Oh, Y. and Yoon, E. S. (1998). Strategies for Modeling and Control of Nonlinear Chemical Processes Using Neural Networks. Computers Chemical Engineering, Vol. 22, pages.
Fig. 8. Oil flow rate estimated (considering water rate and bottom-hole pressure) for each well (red lines) over time compared to reservoir simulator results (blue lines). The second proposed neural network was also able to estimate produced oil flow rates from all the wells considering variations in the water flow rate of injection wells and bottom-hole pressure of producing wells of the Namorado Field. The results also presented the noisy behaviour with high amplitude spikes, what will demand further investigation. This architecture is an appropriate model for the optimum determination of the controls for an 501
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IFAC PapersOnLine 52-1 (2019) 498–501 Machine learning models to support reservoir production optimization Machine learning models to support reservoir production optimization Alexto F. support Teixeira*, Argimiro R. Secchi** Machine reservoir production Machine learning learning models models to support reservoir production optimization optimization
Alex F. Teixeira*, Argimiro R. Secchi** Alex Argimiro R. R. Secchi** Secchi** Alex F. F. Teixeira*, Teixeira*, Argimiro *Petrobras Research Center, Rio de Janeiro, RJ 21949-900, Brazil (e-mail: [email protected]). **Chemical Engineering Program at Rio COPPE, Federal of Brazil Rio de (e-mail: Janeiro,[email protected]). Rio de Janeiro, RJ 21941-972, Brazil (e*Petrobras Research Center, de Janeiro, RJUniversity 21949-900, mail:[email protected]) *Petrobras Research Center, de RJ 21949-900, Federal of Brazil Rio de (e-mail: Janeiro,[email protected]). Rio de Janeiro, RJ 21941-972, Brazil (e**Chemical Engineering Program at Rio COPPE, *Petrobras Research Center, Rio de Janeiro, Janeiro, RJUniversity 21949-900, Brazil (e-mail: [email protected]). **Chemical University mail:[email protected]) **Chemical Engineering Engineering Program Program at at COPPE, COPPE, Federal Federal University of of Rio Rio de de Janeiro, Janeiro, Rio Rio de de Janeiro, Janeiro, RJ RJ 21941-972, 21941-972, Brazil Brazil (e(email:[email protected]) mail:[email protected]) Abstract: Traditionally, numerical simulators are used in combination with an optimization algorithm to determine controls that maximize total production or net present (NPV) over the life Traditionally, numerical simulators areoil used in combination with an value optimization algorithm to Abstract: optimum of the reservoir. These simulators are complex dynamic models that consider geological information, Abstract: Traditionally, numerical simulators are used in combination with an optimization algorithm to determine optimum controls that maximize total production or net present (NPV) over the life Abstract: Traditionally, numerical simulators areoil used in combination with an value optimization algorithm to rock and fluid properties, as well as information about the completion of the wells. This complexity determine optimum controls that maximize total oil production or net present value (NPV) over the life of the reservoir. These simulators are complex models considervalue geological determine optimum controls that maximize total dynamic oil production or that net present (NPV) information, over the life results in fluid a high computational and pose a challenge for application gradient-based of reservoir. These simulators are complex dynamic models that information, rock properties, as well time as about the completion of the geological wells.ofThis complexity of the theand reservoir. These simulators areinformation complex dynamic models thattheconsider consider geological information, optimization algorithms, since calculation of gradients of the objective function with respect to controls rock and fluid properties, as well as information about the completion of the wells. This results in a high computational time and pose a challenge for the application of gradient-based rock and fluid properties, as well as information about the completion of the wells. This complexity complexity may demand several evaluations of the simulation model. This paper proposes the use of a machine results in a high computational time and pose a challenge for the application of gradient-based optimization algorithms, since calculation of gradients of the objective function with respect to controls results in a high computational time and pose a challenge for the application of gradient-based learning model, based on artificial neural networks, to represent the non-linear dynamic behavior of the optimization algorithms, since calculation of gradients of the objective function with respect to may demand several evaluations of the simulation model. This paper proposes the use of a machine optimization algorithms, since calculation of gradients of the objective function with respect to controls controls reservoir. The proposed approach was applied to data generated with a synthetic reservoir simulation may demand several evaluations of the simulation model. This paper proposes the use of a machine learning model, basedevaluations on artificialofneural networks, to represent non-linear dynamic of the may demand several the simulation model. Thisthe paper proposes the usebehavior of a machine model showing promising results. neural learning model, based artificial networks, to non-linear dynamic behavior of reservoir. The proposed was applied to data generatedthe a synthetic reservoir simulation learning model, based on onapproach artificial neural networks, to represent represent thewith non-linear dynamic behavior of the the reservoir. The proposed approach was applied to data generated with a synthetic reservoir simulation model showing promising results. reservoir. The proposed approach was applied to data generated with a synthetic reservoir simulation © 2019, IFAC (International of Automatic Hosting by Elsevier Ltd. All rights reserved. Keywords: machine learning,Federation optimization, artificialControl) neural network, reservoir. model model showing showing promising promising results. results. Keywords: machine learning, optimization, artificial neural network, reservoir. Keywords: network, reservoir. Keywords: machine machine learning, learning, optimization, optimization, artificial artificial neural neural network, reservoir.was tested using data generated with a strategy. The concept 1. INTRODUCTION synthetic reservoir simulation model. strategy. The concept was tested using data generated with a 1. INTRODUCTION When the natural driving mechanism present in the reservoir synthetic strategy. The concept was tested using reservoir simulation model. strategy. The concept was tested using data data generated generated with with aa 1. INTRODUCTION 1. INTRODUCTION is not able to support an efficient and economically attractive synthetic reservoir simulation model. When the natural driving mechanism present in the reservoir synthetic 1.1 Machine Learning reservoir simulation model. oil recovery, secondary recovery method is applied. When the driving mechanism present in reservoir is not able to asupport an efficient and economically When the natural natural driving mechanism present in the the attractive reservoir 1.1 Machine Learning Waterflooding is thean common secondary recovery Exponential increase of the computing performance in is able efficient and economically oilnot recovery, secondary recovery method is applied.attractive is not able to to asupport support anmost efficient and economically attractive 1.1 Machine Machine Learning Learning method used to increase oil production and ultimate 1.1 oil recovery, a secondary recovery method is applied. combination increase with the ofhuge data currently Waterflooding is the most common secondary oil recovery, a secondary recovery method is applied.recovery the amounts Exponential computingof performance in hydrocarbon recovery. Injected water helps to maintain Waterflooding is the most common secondary recovery available are responsible for a machine learning in the method used to increase oil production and ultimate Exponential increase increase ofhuge the amounts computingof performance performance in Waterflooding is the most common secondary recovery combination with the of datahype currently Exponential the computing in reservoir pressure time and oil inand the method to increase oil production ultimate industry. Injected water helps to direction maintain combination with the huge amounts of data currently hydrocarbon recovery. method used used to over increase oil displace production and ultimate available are responsible for a machine learning hype in the combination with the huge amounts of data currently of the producer wells, efficiency. hydrocarbon recovery. Injected water to maintain Despite the that manyfor techniques have been available for reservoir pressure overimproving time and sweeping displace oil available are responsible aa machine learning hype in the hydrocarbon recovery. Injected water helps helps to direction maintain industry. arefact responsible for machine learning hype in in the the Traditionally, dynamic simulation models used in available reservoir pressure overimproving time and and sweeping displace oil oil inare the direction direction decades, advances in computing performance are making of the producer wells, efficiency. industry. reservoir pressure over time displace in the Despite industry.the fact that many techniques have been available for combination optimizer tomodels determine of the wells, sweeping efficiency. possible their in severalperformance new solve Traditionally, dynamic simulation are optimum used in Despite fact that many techniques have been for of the producer producerwith wells,animproving improving sweeping efficiency. decades, advances computing are tomaking Despite the the factapplication that in many techniques have problems been available available for controls (water injection rate of the injection Traditionally, dynamic simulation are used in them in a simple and efficient way. combination with an optimizer advances in computing performance are making tomodels determine optimum Traditionally, dynamic simulation models are wells used and in decades, possible their application in several new problems to solve decades, advances in computing performance are making bottom-hole pressure liquid of the producing wells) combination with an to determine optimum Artificial neural networks are computational application in new to controls (water injection rate rate of the injection wells and possible combination with anor optimizer optimizer to determine optimum them in atheir simple and efficient way. possible their application in several several new problems problemsstructures to solve solve that maximize total oil production or the net present value controls (water injection rate of the injection wells and by the functioning of the human nervous system, bottom-hole pressure or liquid rate of the producing them in a simple and efficient way. controls (water injection rate of the injection wellswells) and inspired Artificial neural networks are computational structures them in a simple and efficient way. (NPV) over the life of reservoir. dynamic bottom-hole pressure or liquid rate of the producing wells) ofthesimple processing called structures neurons, that maximize total oil production the presentmodels value consisting Artificial neural networks aretheelements, computational structures bottom-hole pressure orthe liquid rate or ofThese the net producing wells) inspired byneural functioning ofare human nervous system, Artificial networks computational are usually complex numerical reservoir simulators that that maximize total oil production or the net present value connected in a network and used to store experimental (NPV) over the life of the reservoir. These dynamic models inspired by the functioning of the human nervous system, that maximize total oil production or the net present value inspired consistingbyofthesimple processing elements, called neurons, functioning of the human nervous system, consider geological information, rock and fluid properties, as (NPV) over the life of the reservoir. These dynamic models knowledge obtained through application of machine learning consisting of simple processing elements, called neurons, are usually complex numerical reservoir simulators that (NPV) over the life of the reservoir. These dynamic models consisting connected of in simple a network and used to store experimental processing elements, called neurons, well as information about the completion of simulators theproperties, wells. This are usually usually complex numerical reservoir simulators that techniques, as discussed in Haykin (2000). aa network and used to experimental consider geological information, rock and fluid as connected are complex numerical reservoir that knowledge in obtained through application machine learning connected in network and used to ofstore store experimental complexity results in a high computational time to simulation consider geological information, rock and fluid properties, as As explained in Dreyfus (2004), training is the algorithmic obtained through application of machine learning well as information about the completion of theproperties, wells. This consider geological information, rock and fluid as knowledge techniques, as discussed in Haykin (2000). knowledge obtained through application of machine learning run a challenge forthe thecompletion applicationtime of the gradient-based well as information of This procedure whereby the parameters of the neural network are as discussed in Haykin (2000). complexity results inabout a high computational towells. simulation welland as pose information about the completion of the wells. This techniques, As explained in Dreyfus (2004), training is the algorithmic techniques, as discussed in Haykin (2000). optimization algorithms, since of the As complexity in computational time to estimated, in order to allow it to learn, as accurately as explained in Dreyfus (2004), training is the algorithmic run and poseresults a challenge for thecalculation applicationof ofgradients gradient-based complexity results in aa high high computational time to simulation simulation procedure whereby the parameters of the neural network are As explained in Dreyfus (2004), training is the algorithmic objective function with for respect to controls may demand run aa challenge the application gradient-based possible, the task it has been assigned. Within this optimization algorithms, since ofof of the estimated, procedure whereby the parameters of the neural network are run and and pose pose challenge for thecalculation application ofgradients gradient-based to allow it to in order learn, as accurately as procedure whereby the parameters of the neural network are several evaluations of thesince simulation model. Inmay somedemand cases, optimization algorithms, calculation of of framework, areto types objective function with respect to controls estimated, the inthere order to allow it of to training: learn, assupervised accurately as optimization algorithms, since calculation of gradients gradients of the the possible, task ittwo has been assigned. Within and this estimated, in order allow it to learn, as accurately as for a grid with a huge number of cells, a single model objective function with respect to controls may demand unsupervised. several evaluations of the simulation model. In some cases, possible, the task it has been assigned. Within this objective function with respect to controls may demand framework, there are ittwohas types of training: supervised and possible, the task been assigned. Within this evaluation may many hours, of as model. pointedaIn in Sarma several evaluations the simulation some cases, Due to its learning ability, artificial neural supervised network canand be framework, there two types of for a grid with take a of huge cells, single model several evaluations of the number simulation model. Inout some cases, unsupervised. framework, there are are two the types of training: training: supervised and (2006). for aa grid grid may with take huge number of cells, single model unsupervised. used to model the dynamics of a nonlinear system based in evaluation manynumber hours, of as cells, pointedaa out in Sarma for with aa huge single model Due to its learning ability, the artificial neural network can be unsupervised. evaluation take many as out Sarma This paper may proposes usehours, of a machine the signals acquired experimentally when the system is to its learning ability, the artificial neural network can be (2006). evaluation may take the many hours, as pointed pointedlearning out in in model, Sarma Due used to model the dynamics of a nonlinear system based in Due to its learning ability, the artificial neural network can be (2006). basedpaper on artificial networks, to represent non- used excited by the variation of its input signals, as discussed to model the dynamics of a nonlinear system based in This proposesneural the use of a machine learningthemodel, (2006). the signals acquired experimentally when the system is used to model the dynamics of a nonlinear system based in linear dynamic behavior of the reservoir. The proposed model Bhat and McAvoy (1990), Wang et al, (1998) and Tehlah, This paper proposes the use of a machine learning model, the signals acquired experimentally when the system excited by the variation of its input signals, as discussed in based on artificial neural networks, to represent the nonThis paper proposes the use of a machine learning model, the signals acquired experimentally when the system is is will enabler to theofimplementation, atproposed an appropriate Kaewpradit andvariation Mujtaba (2016). basedbedynamic onan artificial artificial neural networks, to The represent themodel non- Bhat excited the of its input as in behavior the reservoir. linear andby (1990), Wang al, (1998) and Tehlah, based on neural networks, to represent the nonexcited byMcAvoy the variation of its inputet signals, signals, as discussed discussed in computational cost,tooftheaof dynamic production The benefits of Wang the use of (1998) an artificial neural linear behavior the The model Bhat two and main McAvoy (1990), Wang et al, al, (1998) and Tehlah, Tehlah, anoptimization appropriate will an enabler and Mujtaba (2016). linearbedynamic dynamic behavior ofimplementation, the reservoir. reservoir. Theatproposed proposed model Kaewpradit Bhat and McAvoy (1990), et and network as the model in the optimization strategy to will be an enabler to the implementation, at an appropriate Kaewpradit and Mujtaba (2016). computational cost,toofthea implementation, dynamic production two main benefits (2016). of the use of an artificial neural will be an enabler at anoptimization appropriate The Kaewpradit and Mujtaba computational cost, of a dynamic production optimization The two main benefits of the use of an artificial neural thebenefits model ofin the theuse optimization strategy to computational cost, of a dynamic production optimization network The two as main of an artificial neural network as the model in the optimization strategy to network as the model in the optimization strategy to Copyright © 2019 IFAC 498 2405-8963 © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review©under of International Federation of Automatic 2019 responsibility IFAC 498Control. Copyright 10.1016/j.ifacol.2019.06.111 Copyright © 2019 IFAC 498 Copyright © 2019 IFAC 498
2019 IFAC DYCOPS Florianópolis - SC, Brazil, April 23-26, 2019Alex F. Teixeira et al. / IFAC PapersOnLine 52-1 (2019) 498–501
determine the optimum controls of the reservoir are the reduction of the CPU time and the possibility to faster gradients computing. There are different types of neural networks, and in this work, so-called multilayer perceptrons (MLP) and the backpropagation algorithm were used.
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In order to excite the system to generate data to support the model identification process, variations were generated in the water flow rate of the injection wells, as can be seen in Figure 2. The effect on the oil and water flow rates of the producing wells was analysed. Variations in the bottom-hole pressure of the producing wells were also performed, aiming to represent the effect of variations in the well choke valves opening.
2. CASE STUDY In this section, we will consider a synthetic model, called UNISIM-I-M, to demonstrate the proposed approach. As presented in Avansi and Schiozer (2015), this synthetic model is based on the Namorado Field, located in the Campos Basin. It is implemented in the IMEX® simulator and has a corner point grid (81 x 58 x 20 cells) with 36.739 active cells (Figure 1). Each cell measures 100 x 100 x 8 meters. The Namorado field, discovered in November 1975, is located at 80 km from the Rio de Janeiro coast, in a water depth varying between 130 and 240 meters. Production started in June 1979 and the original oil in place was 100 MM m3 (630 MM STB). The field has been produced by two fixed platforms: PNA-1 e PNA-2.
Fig. 2. Variations in the water rate of the injection wells. In a real scenario, historical production and injection data may be used in the model training and validation process. Simulated data, generated with the numerical reservoir simulator, could be combined with historical data to increase fidelity of the artificial neural network model. 3. NEURAL NETWORKS ARCHITECTURES Two different neural network architectures were tested. As a first attempt, we opted to evaluate a MLP neural network with a hidden layer with neurons using sigmoidal activation functions and an output layer with neurons with a linear activation function. As inputs to the neural network, the water injection rates of the injection wells and past values of oil rates of the producing wells were used, both sampled every 30 days (monthly). The structure of the model can be seen in Figure 3.
Fig. 1. 3D view of the synthetic simulation model based on the Namorado Field, including wells perforations. The model has eleven horizontal injection wells and fourteen oil producing wells (4 vertical and 10 horizontal wells). A list of the wells can be seen in Table 1. Table 1. Wells from the synthetic model. Injection Wells INJ01 INJ02 INJ03 INJ04 INJ05 INJ06 INJ07 INJ08 INJ09 INJ10 INJ11 -
Producing Wells PROD01 PROD02 PROD03 PROD04 PROD05 PROD06 PROD07 PROD08 PROD09 PROD10 PROD11 PROD12 PROD13
Fig. 3. Structure of the proposed artificial neural network. In Figure 3, M is the number of injection wells, N is the number of producing wells, k is the current time and lagin is the number of time delays. 499
2019 IFAC DYCOPS 500 Florianópolis - SC, Brazil, April 23-26, 2019Alex F. Teixeira et al. / IFAC PapersOnLine 52-1 (2019) 498–501
The proposed neural network was implemented in Matlab® software and the training was performed using backpropagation combined with Levenberg-Marquardt optimization algorithm. As a strategy to support the decision regarding the number of time delays used in the input variables, a sensitivity analysis was performed by varying the number of time delays and comparing the results based on the mean square error (MSE). For the training and evaluation of the networks tested, the data available was divided in three groups as can be seen in Table 2. Table 2. Data groups. Training Validation Test
A second neural network was proposed considering also the bottom-hole pressure of the producing wells. As can be seen in the Figure 6, this network has two hidden layers with 250 and 125 neurons respectively. Fifteen time delays (lagin) were used for each input variable.
70% 15% 15% Fig. 6. Structure of the second proposed artificial neural network, considering bottom-hole pressure of the producing wells.
In Figure 4, we show the results obtained with the sensitivity analysis, where we concluded that the best MSE for the training, validation and test data was obtained for a network with 15 time delays (lagin) for each input variable (water injection rates of the injection wells and past values of oil rates of the producing wells).
4. RESULTS In Figure 7, we can observe a comparison between the oil flow rate values of a new test data set with the estimations obtained for each producing well, using the neural network of the Figure 3.
Fig. 4. Result of the sensitivity analysis in relation to the number time delays considered for each input variable. The same strategy was used to support the decision regarding the number of neurons in the hidden layer. A sensitivity analysis was performed by varying the number of neurons and comparing the results based on the mean square error (MSE). In Figure 5, we show the results obtained with the sensitivity analysis, where we concluded that the best MSE for the training, validation and test data was obtained for a network with 450 neurons in the hidden layer.
Fig. 5. Results of the sensitivity analysis in relation to the number of neurons in the hidden layer.
Fig. 7. Oil flow rate estimated for each well (red lines) over time compared to reservoir simulator results (blue lines).
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The blue lines were obtained using the commercial simulator and the red lines are estimations performed by the neural network. The proposed neural network was able to follow the variations in the produced oil flow rates from all the wells of the Namorado Field, but presented a noisy behaviour with some high amplitude spikes. Noisy behaviour with small amplitude spikes also appeared in the results obtained with the training data set for all the tested structures (variations in the number of time delays and neurons in the hidden layer), what made us discard the possibility of an overfitting. The determination of the cause of noisy behaviour will demand further investigation. In Figure 8, we can observe a comparison between the oil flow rate values of a new test data set with the estimations obtained for each producing well, using the neural network showed in Figure 6.
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optimized reservoir management, once both control variables are inputs for the model (water flow rate of the injection wells and bottom-hole pressure of the producing wells). 4. CONCLUSIONS Two proposals of artificial neural network architectures were evaluated to model the relationship between oil production and control variables. Both proposals were evaluated using data generated with a synthetic reservoir model based on Namorado Field. The results obtained with the training, validation and test data sets were satisfactory in terms of following variations in the oil flow rates of the producing wells, proving the potential of this modelling strategy. Although, the noisy behaviour displayed in the results obtained with both proposed architectures will demand further investigation, since it can affect the calculation of the gradients for the optimization. 5. REFERENCES Avansi, G. D., and Schiozer, D. J. (2015). UNISIM-I: Synthetic Model for Reservoir Development and Management Applications. International Journal of Modeling and Simulation for the Petroleum Industry, Vol. 9, NO. 1, pages 21-30. Bhat, N., and McAvoy, T. J. (1990). Use of Neural Nets dor Dynamic Modeling and Control of Chemical Process Systems. Computers Chemical Engineering, Vol. 14, pages. Dreyfus, G. (2004). Neural Networks Methodology and Applications (2nd Edition). Springer. Haykin, S. (2000). Neural Networks: A Comprehensive Foundation (2nd Edition). Prentice Hall. Sarma, P. (2006). Efficient Closed-Loop Optimal Control of Petroleum Reservoirs under Uncertainty. Dissertation, Stanford University. Tehlah, N., Kaewpradit, P. and Mujtaba, I. M. (2016). Artificial Neural Network Based Modeling and Optimization of Refined Palm Oil Process. Neurocomputing, Vol. 216, pages. Wang, H., Oh, Y. and Yoon, E. S. (1998). Strategies for Modeling and Control of Nonlinear Chemical Processes Using Neural Networks. Computers Chemical Engineering, Vol. 22, pages.
Fig. 8. Oil flow rate estimated (considering water rate and bottom-hole pressure) for each well (red lines) over time compared to reservoir simulator results (blue lines). The second proposed neural network was also able to estimate produced oil flow rates from all the wells considering variations in the water flow rate of injection wells and bottom-hole pressure of producing wells of the Namorado Field. The results also presented the noisy behaviour with high amplitude spikes, what will demand further investigation. This architecture is an appropriate model for the optimum determination of the controls for an 501