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Optimization of formation analysis and evaluation protocols using neuro-simulation
Journal of Petroleum Science and Engineering 49 (2005) 97 – 109 www.elsevier.com/locate/petrol
Optimization of formation analysis and evaluation protocols using neuro-simulation T. Ertekin*, N. Silpngarmlers Penn State University, University Park, PA, USA Accepted 20 May 2005
Abstract Neuro-simulation, which conjoins hard computing protocols with soft computing protocols, has been adapted to various applications in petroleum industry. This approach offers the advantage of optimizing number of model/simulation studies that need to be conducted. Simulation/model studies, in this context, refer to various modes of operations through which data are collected and results generated. Thus, experimental protocols followed in laboratories, field tests and operations conducted, and analyses carried using numerical and/or mathematical models are all considered as components of these studies. In this paper, an example implementation of neuro-simulation in the optimization of number of experiments that need to be conducted in measuring relative permeabilities is illustrated. D 2005 Elsevier B.V. All rights reserved. Keywords: Neuro-simulation; Formation characterization; Artificial neural networks; Relative permeability prediction
1. Introduction Artificial neural network technology offers various attractive features including adaptive learning, self-organization, fault tolerance, real-time operation, and ease of adaptation into existing systems. With their adaptive learning capabilities, neural networks learn the existing patterns between the input stimuli and the output without having a prior knowledge of the models or the functional relationships. Neural networks are capable to self-organize or create a distinct representation of the presented data. They are fault-tolerant not only with regard to the noisy, distorted, or incomplete data but also to the damage within the networks. Their ability to process data in parallel, which allows the processing of * Corresponding author. Tel.: +1 814 238 1055; fax: +1 814 863 1875. E-mail address: [email protected] (T. Ertekin). 0920-4105/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2005.05.002
a large number of data in a short period of time, makes them attractive for numerous areas of application. The developed and trained networks can be easily incorporated into the existing analysis systems for specific purposes. These unique features of neural networks make them very attractive in the areas of pattern recognition, signal filtering, database mining and associative search, optimization, scheduling and routing, and mapping of complex phenomena (Maren et al., 1990). Neuro-simulation is a protocol that combines artificial neural network technology with simulation studies. In this context, the term dsimulationT refers to various modes of studies through which data are collected and results generated. Thus, experimental protocols followed in laboratories, field tests and operations conducted, and analyses carried using numerical and/or mathematical models all are considered as components of simulation. Neuro-simulation has been used in petroleum industry in a variety of applications, including well log interpreta-
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tion, well test analysis, phase equilibria analysis, reservoir characterization, reservoir simulation, seismic data interpretation, risk analysis, field development studies and core analysis. The principal objective of neuro-simulation methodology is the optimization of the number of actual model studies that need to be conducted. The data gathered and results generated from the real-time model studies along with their prevailing scenarios are then used to train the neural networks. Upon the completion of the training, the networks become experts as they have already captured the existing relationship between the system properties, imposed conditions and the output generated. Consequently, the successfully trained networks can be used to predict the output for other systems. This approach will offer a fast and reliable means to generate results for systems of interest. For example, by conducting a neuro-simulation study, it is possible to optimize the number of relative permeability experiments that needs to be conducted. This can be achieved by performing only a minimum number of relative permeability experiments. The information generated from the experiments then can be used in training the network. Once the training is successful, the network is ready to function as a predictor. In this way, instead of recovering more core samples and conducting a large number of experiments on the core samples, the trained network can be used as an expert system to predict the relative permeability characteristics to complete the missing entries of the data set. Depending upon the extent of the database utilized in training and the types of input neurons used in structuring the topology of the network, the same expert system can furthermore generate predictions for other core samples with different properties. This paper describes the main ingredients of the neuro-simulation methodology and presents a set of guidelines that can be used in optimizing the number of actual model studies that need to be conducted. In this way, the cost function and energy function associated with the model studies are minimized such that the resulting time, energy and cost savings will permit the engineers and scientists to concentrate more on design of the model and analysis of the data generated.
concept by creating artificial neurons which are highly interconnected simple processing elements to mimic a small portion of the information processing ability of the biological neural network. ANNs are typically organized in layers mainly categorized as input, hidden, and output layers as shown in Fig. 1. These layers are made up of interconnected processors called neurons. Neurons in each layer are connected to neurons in the adjacent layer through connection weights. Patterns will be presented to the networks through input neurons which communicate with neurons of the hidden layer where the actual processing of the information is performed. The output responses are then sent to the output layer where the results are obtained. The training or learning of the ANNs is achieved through the adjustment of the connection weights. ANNs can be characterized as computational systems with particular abilities such as to adopt or to learn, to generalize, to recognize, to classify, and to organize data. There are many different types of ANNs, each of which has different strengths particular to their applications. The abilities of different networks can be related to their structure, dynamics, and learning methods. ANNs offer various attractive features including adaptive learning, self-organization, fault tolerance, real-time operation, and ease of adaptation into existing systems. With their adaptive learning capabilities, neural networks learn the existing patterns between the input stimuli and the output without having a prior knowledge of the models or the functional relationships. Neural networks are capable to self-organize or create a distinct representation of the presented data. They are fault-tolerant not only with regard to the noisy, distorted, or incomplete data but also to the damage within the networks. Therefore, when they degenerate, they do so gracefully. Their ability to process data in parallel, which allows the processing of a large number
2. Overview of Artificial Neural Networks (ANNs) Artificial neural network (ANN) is an emerging technology which is inspired by the capabilities of biological neural networks that consist of massively interconnected neurons such that parallel and serial processing of the incoming information can be achieved rapidly. Artificial neural networks utilize this same
Fig. 1. General structure of ANN.
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of data in a short period of time, makes them attractive for numerous areas of application. The developed and trained networks can be easily incorporated into the existing analysis systems for specific purposes. 3. Neuro-simulation methodology Neuro-simulation methodology couples hard computing protocols with soft computing protocols. Hard computing protocols in this context are computational and experimental models which refer to various modes of studies through which data are collected and results are generated. The hard computing protocols usually provide precise results. However, they are rather demanding in terms of computational overhead, manpower, and instrumentation. Soft computing protocols in this context refer to artificial neural networks through which some pragmatic solutions are generated. In the application of neuro-simulation methodology, simulation models are used to generate some case studies or scenarios while soft computing protocols become instrumental in structuring ANNs. The data gathered and results generated from simulation models along with their prevailing scenarios are then used to train the ANNs. During the training phase, ANNs learn the existing relationships between the input parameters and the output response with the help of the training patterns. If there is any pattern or consistent relationship between the input and output of each data set, the network will be able to eventually create an internal mapping which can accurately produce the corresponding output. Upon completion of the training, networks become experts as they have already captured the existing relationships between the system properties, imposed conditions and output generated. The networks are then ready to be used as a tool to make predictions for other data sets. In this fashion, neuro-simulation provides us with an effective alternative methodology to obtain reliable results while minimizing the cost and energy functions.
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available rock and fluid properties such as phase viscosities, absolute permeability, porosity, irreducible water saturation, critical gas saturation, and residual oil saturation. The structure of the ANN is shown in the Appendix and a detailed description of the model can be found in Silpngarmlers et al., 2001. The ANN model has already been trained with experimental relative permeability data. This information is stored and ready to be used to predict relative permeabilities at various saturations for other systems where some rock and fluid properties are available as input parameters. The implementation of this approach can be realized in two different applications. In the first application, after a core sample is recovered from a reservoir, experimental protocols are conducted to measure its relative permeability characteristics. Instead of recovering more core samples, restoring the reservoir conditions in the laboratory for each core sample, and repeating the similar experimental procedures, the developed relative permeability predictor is used to generate the relative permeability data based on the rock and fluid properties of the system. The results produced by the ANN are then compared against the experimental results. If there is a good agreement between the experimental data and the data generated by the ANN, we can believe, in confidence, that the measured relative permeability data exhibit consistent characteristics with the other experimental relative permeability data utilized during the training of ANN. In this way, multi-repetition of the same experiments to measure relative permeability from different core samples obtained from the same horizon will not be necessary. An example of a relative permeability data set generated by the ANN-based oil/ gas relative permeability predictor compared with the experimental relative permeabilities is shown in Fig. 2.
4. Application of neuro-simulation An example application of neuro-simulation approach in petroleum industry can be illustrated in experimental relative permeability measurements. The objective of using neuro-simulation in this example is to optimize the number of experiments that needs to be conducted to obtain relative permeability characteristics from core samples. In this example, we use the ANN as a relative permeability model capable of predicting oil and gas relative permeability characteristics. The input parameters of the developed model are the readily
Fig. 2. Experimental and predicted relative permeability characteristics.
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It can be seen that the data predicted by the network is in good agreement with the experimental data. It should be emphasized that the network has not been exposed to this experimental data set during the training. However, it is capable of accurately capturing relative permeability behavior using its knowledge on existing relationships between rock and fluid properties and the relative permeability characteristics. It is important to note that there are some precautions in the implementation of this approach. One important aspect of the ANN whose learning is supervised through the examples is that its performance is superior when a given pattern has similar characteristics to those it has learned. In order for the network to respond correctly to a new pattern or correlation existing between input and output, the examples of the new pattern need to be given along with the corresponding outputs to retrain the network. Another cautionary note to remember is that the prediction capabilities of ANN usually become attenuated when it is forced to make predictions for systems with properties outside the range of the original training database. Therefore, the analysis of predicted data for such systems should be carried out with caution. It should be reiterated that a careful analysis is crucial in generating meaningful results using ANN. For instance, if relative permeability data predicted by the ANN are not in good agreement with the experimental data, the characteristics of the given relative permeability data should be examined. If they exhibit significantly different characteristics from other experimental data sets that the network has been exposed to a priori, this new data set should be incorporated into the training database and the network need to be retrained with the current extended database. This procedure is also applicable in the case when properties of a given system fall outside the range of training database. In the second application, ANN can be used in economizing the number of experimental measure-
ments on a given core sample. In the inclusion of the new experimental data sets into the training database of the network, a fixed number of data points are utilized in training the network. Therefore, in this application, on a core sample, a fixed number of experimental measurements will be needed to be performed. These data points are then used in updating the training database in order to retrain the network. If the data is recalled correctly, the quality of the data and the performance of the network are considered as reliable. However, if the network experiences difficulty in reproducing this data set, the ANN practitioner should be suspicious about the quality of the data set. Under such circumstances, an additional relative permeability experiment on another core sample retrieved from the same formation should be conducted in order to confirm the prediction of the ANN. Here, to illustrate the concept of generating an optimum number of experimental data points, we provide an example using an experimental oil/gas relative permeability data set which has different characteristics from the ones used in training the network. In this example, after the recovery of a core sample, we assume that relative permeability measurements are conducted at a fixed number of saturation points. Later, this experimentally generated information is used to train the ANN. The successfully trained network is then used as a tool to produce relative permeability values at various additional saturation points to generate a complete set of relative permeability curves. In this way, we are searching for a minimum number of experimental data points to be used during the training phase that are sufficient for the network to capture the relative permeability characteristics. In this exercise, different numbers of data points are used to train the network and the ability of the network in generating the entire relative permeability curves is examined. Accordingly, we have used progressively
Fig. 3. Experimental and predicted relative permeability values when experimental data points at two saturation values (S o = 0.34; 0.91) are used in training.
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Fig. 4. Experimental and predicted relative permeability values when experimental data points at three saturation values (S o = 0.34; 0.64; 0.91) are used in training.
increasing number of relative permeability values measured at 2, 3, 4, 5, and 10 saturation points. The prediction results for each case as compared against the experimental data are shown in Figs. 3–7. It can be seen from this exercise that the quality of the match between the experimental data and the data predicted by the artificial neural network is not significantly improved as number of experimental data points increases from four points to five, and to ten points. In this implementation, in addition to the number of data points utilized, the saturation values at which the experimental data points obtained are important as well. The criticality of the selection of the data points are investigated by using only four data points in the training. The four data points are varied for each training run. The results from four predictions while different four saturation values are used in training the network are shown in Figs. 8–11. In these figures, the asterisks represent the experimental data points used in training the networks. Fig. 8 shows the prediction results from ANN as compared with the experimental results when four experimental data points utilized in training the network are the data points taken at the low oil saturation range. It can be clearly seen that the network can
accurately predict the relative permeability characteristics in the range of saturations that it received during its training. Fig. 9 represents comparison of the results from ANN and the experimental data when only four data points at upper saturation end are used during training phase. Similar to the results observed in Fig. 8, the network can capture relative permeability characteristics of the data points effectively within the high oil saturation range. As expected, when the network is trained with four data points in between the two end points, the network is able to accurately mimic the middle portion of relative permeability curves as shown in Fig. 10. When the network is exposed to the relative permeability data at both end point saturations, the end point relative permeability values are predicted accurately (Fig. 11). In this case, the network exhibits difficulty in capturing the middle portion of the relative permeability curves. It should be noted that the prediction results shown in Fig. 5 is also the case when four experimental relative permeability data points are used to train the networks. The results in Fig. 5 display a good level of agreement between relative permeability values predicted by the networks and the experimental data. This is because the four experimental data points used
Fig. 5. Experimental and predicted relative permeability values when experimental data points at four saturation values (S o = 0.34; 0.54; 0.71; 0.91) are used in training.
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Fig. 6. Experimental and predicted relative permeability values when experimental data points at five saturation values (S o = 0.34; 0.41; 0.58; 0.78; 0.91) are used in training.
in the training include the two end point data, and another two points equally spaced in between the two end points. This shows the importance of end point characteristics in controlling the overall behavior of the relative permeability curves. Through these exercises, we have shown that ANN can be used to optimize the number of experiments that need to be performed in acquiring the relative permeability data. Obviously, this will result in minimizing the cost, energy and time associated with the recovery of the core samples, the experimental measurement of relative permeability characteristics, and the computational overhead necessary in the analysis of the data collected. A generic flowchart for this approach is shown in Fig. 12. 5. Cost analysis One of the primary motivations in optimizing number of simulation studies is to minimize the cost function associated with the studies. An example of the possible alternatives to obtain relative permeability data from a reservoir and the associated costintensive work involved are schematically shown in Fig. 13. Note that scenario 1 involves only the implementation of a pure experimental protocol, while
scenarios 2 through 5 include the use of neuro-simulation protocols. The total cost involved for each scenario consists of three main components as shown in Fig. 14. These cost components are associated with the recovery of core sample, experimental measurement of relative permeability at each saturation point, and use and development of ANN model. Fig. 13 shows five scenarios in obtaining n sets of relative permeability data from a reservoir. Scenario 1 represents the case when n core samples are recovered from the reservoir and a full range of experiments is performed to obtain m data points for each core sample. The cost associated with this procedure includes the total cost to recover n core samples and the experimental cost to obtain m data points for each core sample and can be expressed as follows: Total Cost ¼ ðn CoreÞn ðm expÞ
ð1Þ
where: Core = total cost to recover a core sample Exp = cost to measure relative permeability at one saturation point. Scenario 2 represents the situation when n core samples are recovered from the reservoir. However, only m 1 relative permeability data points are obtained from the experiment for each core sample. In this
Fig. 7. Experimental and predicted relative permeability values when experimental data points at ten saturation values (S o = 0.34; 0.40; 0.48; 0.58; 0.64; 0.71; 0.76; 0.80; 0.85; 0.91) are used in training.
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Fig. 8. Experimental and predicted relative permeability values when experimental data measured at four lower-bound oil saturation points are used in training.
scenario, ANN-based relative permeability models are used to generate the complete relative permeability curves. The associated cost for this protocol is as follows:
Scenario 4 is similar to Scenario 3 except that only m 1 data points for each core sample will be obtained from experiment. The associated cost is as follows:
Total Cost ¼ ðn CoreÞ þ n ðm1 expÞ
Total Cost ¼ ðn1 CoreÞ þ n1 ðm1 expÞ
þ ðm m1 Þ ANN
ð2Þ
where: ANN = total cost in generating relative permeability curve for each core sample using ANN and it should be noted that 0 V m 1 b m. The cost associated with scenario 3, in which only n 1 core samples are recovered from the reservoir, m data points are obtained through experimental measurements for each core sample, and ANN is used to generate the remaining (n n 1) relative permeability curves. Cost associated with this scenario is shown below. Total Cost ¼ ðn1 CoreÞ þ n1 ðm expÞ þ ðn n1 Þ ANN with 0 V n 1 b n.
ð3Þ
þ n ANN
ð4Þ
Last scenario is the one in which no core samples will be recovered. All of the relative permeability data are generated by ANN and the cost associated with this approach is: Total Cost ¼ n ANN
ð5Þ
The comparison of the expected cost functions of all of the five scenarios is shown in Fig. 15. The total cost decreases as the number of cores recovered and the number of experiments performed decrease. In this qualitative representation it is assumed that the principal cost originates from the recovery of the core sample. While analyzing the cost associated with each protocol, it is crucial not to overlook the importance of
Fig. 9. Experimental and predicted relative permeability values when experimental data measured at four upper-bound oil saturation points are used in training.
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Fig. 10. Experimental and predicted relative permeability values when experimental data measured at four mid-range oil saturation points are used in training.
the accuracy of the data. The desired protocol is the one that minimizes the cost while maintaining an acceptable level of accuracy for the data generated. It is known that the accuracy of the data generated is increased as number of experiments and number of recovered core samples increase. Similarly, the associated cost also increases as number of recovered core samples and number of experimental measurements increase. These relationships are qualitatively shown in Fig. 16. It can be stated that the accuracy of the data generated and the cost function are not expected to increase in a linear fashion with the number of measurements conducted and/or with the number of core samples recovered. In other words, the increase of the cost as number of core samples recovered and number of experiments conducted increase is not constant. As the level of intensity of experimental work increases, the incremental cost will become smaller due to the fact that the principal portion of the cost is expended in setting up the experimental facility. Afterwards, the incremental cost to perform more number of experiments depends mainly on the number of measurements conducted. This is repre-
sented by a smaller and constant slope of cost function as volume of experimental work increases. Similar to the cost function, the increase in the accuracy of data generated as number of experiments or number of core samples increases is not constant. The function representing the accuracy of data generated has a continuously decreasing slope. As shown in Fig. 16, gain in accuracy becomes less significant indicating that the accuracy gained at the expense of increased cost is possibly not justifiable. Therefore, the gradient of accuracy gained with respect to the number of experiments or number of core samples and its associated cost determines the optimum number of experiments or optimum number of core samples that need to be obtained. Obviously, such an optimization process depends on the desired level of accuracy of data generated and the budget allocated to the project. 6. Extension to other applications Conceptually similar methodologies can be adopted for other applications in petroleum industry. For instance, neuro-simulation approach can be used to
Fig. 11. Experimental and predicted relative permeability values when experimental data measured at end point saturations are used in training.
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Fig. 12. A generic flowchart for the implementation of neuro-simulation towards the optimization of number of experimental measurements conducted.
optimize the number of simulation runs in field development studies and history matching applications. In this type of study, only some limited number of field development scenarios or history matching runs need to be performed. These simulation runs must be carefully organized such that they provide the critical information needed and cover a
wide spectrum of situations which can be encountered. The prevailing scenarios and system properties along with the results from these simulation runs will be utilized to train the ANNs. Upon the successful training of the ANNs, they can be used as a tool to predict the results for a wide-range of other cases of interest.
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Fig. 13. Possible protocols in obtaining relative permeability data.
Neuro-simulation methodology can also be used in reservoir characterization with applications in the areas of well test analysis, well log interpretation,
PVT analysis, and seismic interpretation in which certain specific patterns exist and are looked for. For example, classical well test analysis can be
Fig. 14. Principal components of the total cost expended in generating relative permeability data.
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Fig. 15. Cost associated with different scenarios in obtaining relative permeability data.
used to identify the existence of fault plane in the reservoir by investigating particular signature of the pressure transient data. In this application, the classical well test analysis can be used to generate some scenarios which will be used to train the ANN. In other words, pressure transient data for systems with variations in fault characteristics can be generated and analyzed using classical well test analysis. These analyses provide information such as distance to the fault, configuration of the fault systems with respect to each other, and transmissibility characteristics across the fault plane (sealing or non-sealing). The ANN can be trained to learn the existing relationships and characteristics between the pressure transient signature and the system properties. After the training is completed, the networks can be used as analytical tools to predict the existence of fault plane and its characteristics when exposed to the pressure transient data collected. This similar approach can also be
applied to provide inverse solutions for other complex systems such as naturally fractured and layered reservoirs. 7. Summary and conclusions Neuro-simulation protocol provides an alternative methodology in performing simulation studies which refers to various modes of studies through which data are collected and results generated. These studies include experimental laboratory protocols, field tests and operations conducted, and computational analyses carried using numerical and/or mathematical models. The following observations and conclusions are offered in the light of the material discussed in this paper. 1. Neuro-simulation can be used in optimizing number of actual model studies that need to be conducted. In
Fig. 16. Relationship between cost and accuracy of data with number of samples and number of experimental measurements.
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this way, the cost and energy functions associated with the model studies can be minimized. The resulting time, energy and cost savings are expected to allow engineers and scientists to concentrate more on the design of the simulation studies and analysis of the data generated. 2. Neuro-simulation approach utilizes the experiential capabilities of the ANN to generate results for the system of interest based on its learning from other systems. Therefore, the quality of the data used in the training of ANN is very critical. 3. Scenarios used to train the ANN must be carefully designed such that they provide useful information to the network and cover various situations that can be encountered in the simulation studies. This will enhance the capability of the networks to learn and make accurate predictions. 4. Due to the adaptive learning, self-organizing, and fault-tolerant features of ANNs, the networks are capable to learn the existing relationships between input stimuli and output, and to create a distinct pattern recognition from an incomplete
data set. This offers advantage in optimizing the range of data necessary in training the networks. Acknowledgments We acknowledge the partial financial support provided by the Petroleum and Natural Gas Engineering program of the Department of Energy and Geo-Environmental Engineering at the Pennsylvania State University, and the Consortium for Virtual Operations Research (CVOR). We extend our gratitude to Saudi Aramco Research and Development Center for providing experimental relative permeability data sets which are used in training and testing of the relative permeability model developed. Appendix A ANN topologies for oil/gas relative permeability predictions are shown below. Figs. A-1 and A-2.
Fig. A-1. Schematic diagram of the k ro model of the oil/gas relative permeability predictor (Silpngarmlers et al., 2001).
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Fig. A-2. Schematic diagram of the k rg model of the oil/gas relative permeability predictor (Silpngarmlers et al., 2001).
References Maren, A.J., Harston, C.T., Pap, R.M, 1990. Handbook of Neural Computing Applications. Academic Press, Inc., San Diego.
Silpngarmlers, N., Guler, B., Ertekin, T., Grader, A.S., 2001. Development and testing of two-phase relative permeability predictors using artificial networks. SPE 69392 Presented at the SPE Latin American and Caribbean Petroleum Engineering Conference Buenos Aires, Argentina, March 25–28, 2001.
Optimization of formation analysis and evaluation protocols using neuro-simulation T. Ertekin*, N. Silpngarmlers Penn State University, University Park, PA, USA Accepted 20 May 2005
Abstract Neuro-simulation, which conjoins hard computing protocols with soft computing protocols, has been adapted to various applications in petroleum industry. This approach offers the advantage of optimizing number of model/simulation studies that need to be conducted. Simulation/model studies, in this context, refer to various modes of operations through which data are collected and results generated. Thus, experimental protocols followed in laboratories, field tests and operations conducted, and analyses carried using numerical and/or mathematical models are all considered as components of these studies. In this paper, an example implementation of neuro-simulation in the optimization of number of experiments that need to be conducted in measuring relative permeabilities is illustrated. D 2005 Elsevier B.V. All rights reserved. Keywords: Neuro-simulation; Formation characterization; Artificial neural networks; Relative permeability prediction
1. Introduction Artificial neural network technology offers various attractive features including adaptive learning, self-organization, fault tolerance, real-time operation, and ease of adaptation into existing systems. With their adaptive learning capabilities, neural networks learn the existing patterns between the input stimuli and the output without having a prior knowledge of the models or the functional relationships. Neural networks are capable to self-organize or create a distinct representation of the presented data. They are fault-tolerant not only with regard to the noisy, distorted, or incomplete data but also to the damage within the networks. Their ability to process data in parallel, which allows the processing of * Corresponding author. Tel.: +1 814 238 1055; fax: +1 814 863 1875. E-mail address: [email protected] (T. Ertekin). 0920-4105/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2005.05.002
a large number of data in a short period of time, makes them attractive for numerous areas of application. The developed and trained networks can be easily incorporated into the existing analysis systems for specific purposes. These unique features of neural networks make them very attractive in the areas of pattern recognition, signal filtering, database mining and associative search, optimization, scheduling and routing, and mapping of complex phenomena (Maren et al., 1990). Neuro-simulation is a protocol that combines artificial neural network technology with simulation studies. In this context, the term dsimulationT refers to various modes of studies through which data are collected and results generated. Thus, experimental protocols followed in laboratories, field tests and operations conducted, and analyses carried using numerical and/or mathematical models all are considered as components of simulation. Neuro-simulation has been used in petroleum industry in a variety of applications, including well log interpreta-
98
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tion, well test analysis, phase equilibria analysis, reservoir characterization, reservoir simulation, seismic data interpretation, risk analysis, field development studies and core analysis. The principal objective of neuro-simulation methodology is the optimization of the number of actual model studies that need to be conducted. The data gathered and results generated from the real-time model studies along with their prevailing scenarios are then used to train the neural networks. Upon the completion of the training, the networks become experts as they have already captured the existing relationship between the system properties, imposed conditions and the output generated. Consequently, the successfully trained networks can be used to predict the output for other systems. This approach will offer a fast and reliable means to generate results for systems of interest. For example, by conducting a neuro-simulation study, it is possible to optimize the number of relative permeability experiments that needs to be conducted. This can be achieved by performing only a minimum number of relative permeability experiments. The information generated from the experiments then can be used in training the network. Once the training is successful, the network is ready to function as a predictor. In this way, instead of recovering more core samples and conducting a large number of experiments on the core samples, the trained network can be used as an expert system to predict the relative permeability characteristics to complete the missing entries of the data set. Depending upon the extent of the database utilized in training and the types of input neurons used in structuring the topology of the network, the same expert system can furthermore generate predictions for other core samples with different properties. This paper describes the main ingredients of the neuro-simulation methodology and presents a set of guidelines that can be used in optimizing the number of actual model studies that need to be conducted. In this way, the cost function and energy function associated with the model studies are minimized such that the resulting time, energy and cost savings will permit the engineers and scientists to concentrate more on design of the model and analysis of the data generated.
concept by creating artificial neurons which are highly interconnected simple processing elements to mimic a small portion of the information processing ability of the biological neural network. ANNs are typically organized in layers mainly categorized as input, hidden, and output layers as shown in Fig. 1. These layers are made up of interconnected processors called neurons. Neurons in each layer are connected to neurons in the adjacent layer through connection weights. Patterns will be presented to the networks through input neurons which communicate with neurons of the hidden layer where the actual processing of the information is performed. The output responses are then sent to the output layer where the results are obtained. The training or learning of the ANNs is achieved through the adjustment of the connection weights. ANNs can be characterized as computational systems with particular abilities such as to adopt or to learn, to generalize, to recognize, to classify, and to organize data. There are many different types of ANNs, each of which has different strengths particular to their applications. The abilities of different networks can be related to their structure, dynamics, and learning methods. ANNs offer various attractive features including adaptive learning, self-organization, fault tolerance, real-time operation, and ease of adaptation into existing systems. With their adaptive learning capabilities, neural networks learn the existing patterns between the input stimuli and the output without having a prior knowledge of the models or the functional relationships. Neural networks are capable to self-organize or create a distinct representation of the presented data. They are fault-tolerant not only with regard to the noisy, distorted, or incomplete data but also to the damage within the networks. Therefore, when they degenerate, they do so gracefully. Their ability to process data in parallel, which allows the processing of a large number
2. Overview of Artificial Neural Networks (ANNs) Artificial neural network (ANN) is an emerging technology which is inspired by the capabilities of biological neural networks that consist of massively interconnected neurons such that parallel and serial processing of the incoming information can be achieved rapidly. Artificial neural networks utilize this same
Fig. 1. General structure of ANN.
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of data in a short period of time, makes them attractive for numerous areas of application. The developed and trained networks can be easily incorporated into the existing analysis systems for specific purposes. 3. Neuro-simulation methodology Neuro-simulation methodology couples hard computing protocols with soft computing protocols. Hard computing protocols in this context are computational and experimental models which refer to various modes of studies through which data are collected and results are generated. The hard computing protocols usually provide precise results. However, they are rather demanding in terms of computational overhead, manpower, and instrumentation. Soft computing protocols in this context refer to artificial neural networks through which some pragmatic solutions are generated. In the application of neuro-simulation methodology, simulation models are used to generate some case studies or scenarios while soft computing protocols become instrumental in structuring ANNs. The data gathered and results generated from simulation models along with their prevailing scenarios are then used to train the ANNs. During the training phase, ANNs learn the existing relationships between the input parameters and the output response with the help of the training patterns. If there is any pattern or consistent relationship between the input and output of each data set, the network will be able to eventually create an internal mapping which can accurately produce the corresponding output. Upon completion of the training, networks become experts as they have already captured the existing relationships between the system properties, imposed conditions and output generated. The networks are then ready to be used as a tool to make predictions for other data sets. In this fashion, neuro-simulation provides us with an effective alternative methodology to obtain reliable results while minimizing the cost and energy functions.
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available rock and fluid properties such as phase viscosities, absolute permeability, porosity, irreducible water saturation, critical gas saturation, and residual oil saturation. The structure of the ANN is shown in the Appendix and a detailed description of the model can be found in Silpngarmlers et al., 2001. The ANN model has already been trained with experimental relative permeability data. This information is stored and ready to be used to predict relative permeabilities at various saturations for other systems where some rock and fluid properties are available as input parameters. The implementation of this approach can be realized in two different applications. In the first application, after a core sample is recovered from a reservoir, experimental protocols are conducted to measure its relative permeability characteristics. Instead of recovering more core samples, restoring the reservoir conditions in the laboratory for each core sample, and repeating the similar experimental procedures, the developed relative permeability predictor is used to generate the relative permeability data based on the rock and fluid properties of the system. The results produced by the ANN are then compared against the experimental results. If there is a good agreement between the experimental data and the data generated by the ANN, we can believe, in confidence, that the measured relative permeability data exhibit consistent characteristics with the other experimental relative permeability data utilized during the training of ANN. In this way, multi-repetition of the same experiments to measure relative permeability from different core samples obtained from the same horizon will not be necessary. An example of a relative permeability data set generated by the ANN-based oil/ gas relative permeability predictor compared with the experimental relative permeabilities is shown in Fig. 2.
4. Application of neuro-simulation An example application of neuro-simulation approach in petroleum industry can be illustrated in experimental relative permeability measurements. The objective of using neuro-simulation in this example is to optimize the number of experiments that needs to be conducted to obtain relative permeability characteristics from core samples. In this example, we use the ANN as a relative permeability model capable of predicting oil and gas relative permeability characteristics. The input parameters of the developed model are the readily
Fig. 2. Experimental and predicted relative permeability characteristics.
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It can be seen that the data predicted by the network is in good agreement with the experimental data. It should be emphasized that the network has not been exposed to this experimental data set during the training. However, it is capable of accurately capturing relative permeability behavior using its knowledge on existing relationships between rock and fluid properties and the relative permeability characteristics. It is important to note that there are some precautions in the implementation of this approach. One important aspect of the ANN whose learning is supervised through the examples is that its performance is superior when a given pattern has similar characteristics to those it has learned. In order for the network to respond correctly to a new pattern or correlation existing between input and output, the examples of the new pattern need to be given along with the corresponding outputs to retrain the network. Another cautionary note to remember is that the prediction capabilities of ANN usually become attenuated when it is forced to make predictions for systems with properties outside the range of the original training database. Therefore, the analysis of predicted data for such systems should be carried out with caution. It should be reiterated that a careful analysis is crucial in generating meaningful results using ANN. For instance, if relative permeability data predicted by the ANN are not in good agreement with the experimental data, the characteristics of the given relative permeability data should be examined. If they exhibit significantly different characteristics from other experimental data sets that the network has been exposed to a priori, this new data set should be incorporated into the training database and the network need to be retrained with the current extended database. This procedure is also applicable in the case when properties of a given system fall outside the range of training database. In the second application, ANN can be used in economizing the number of experimental measure-
ments on a given core sample. In the inclusion of the new experimental data sets into the training database of the network, a fixed number of data points are utilized in training the network. Therefore, in this application, on a core sample, a fixed number of experimental measurements will be needed to be performed. These data points are then used in updating the training database in order to retrain the network. If the data is recalled correctly, the quality of the data and the performance of the network are considered as reliable. However, if the network experiences difficulty in reproducing this data set, the ANN practitioner should be suspicious about the quality of the data set. Under such circumstances, an additional relative permeability experiment on another core sample retrieved from the same formation should be conducted in order to confirm the prediction of the ANN. Here, to illustrate the concept of generating an optimum number of experimental data points, we provide an example using an experimental oil/gas relative permeability data set which has different characteristics from the ones used in training the network. In this example, after the recovery of a core sample, we assume that relative permeability measurements are conducted at a fixed number of saturation points. Later, this experimentally generated information is used to train the ANN. The successfully trained network is then used as a tool to produce relative permeability values at various additional saturation points to generate a complete set of relative permeability curves. In this way, we are searching for a minimum number of experimental data points to be used during the training phase that are sufficient for the network to capture the relative permeability characteristics. In this exercise, different numbers of data points are used to train the network and the ability of the network in generating the entire relative permeability curves is examined. Accordingly, we have used progressively
Fig. 3. Experimental and predicted relative permeability values when experimental data points at two saturation values (S o = 0.34; 0.91) are used in training.
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Fig. 4. Experimental and predicted relative permeability values when experimental data points at three saturation values (S o = 0.34; 0.64; 0.91) are used in training.
increasing number of relative permeability values measured at 2, 3, 4, 5, and 10 saturation points. The prediction results for each case as compared against the experimental data are shown in Figs. 3–7. It can be seen from this exercise that the quality of the match between the experimental data and the data predicted by the artificial neural network is not significantly improved as number of experimental data points increases from four points to five, and to ten points. In this implementation, in addition to the number of data points utilized, the saturation values at which the experimental data points obtained are important as well. The criticality of the selection of the data points are investigated by using only four data points in the training. The four data points are varied for each training run. The results from four predictions while different four saturation values are used in training the network are shown in Figs. 8–11. In these figures, the asterisks represent the experimental data points used in training the networks. Fig. 8 shows the prediction results from ANN as compared with the experimental results when four experimental data points utilized in training the network are the data points taken at the low oil saturation range. It can be clearly seen that the network can
accurately predict the relative permeability characteristics in the range of saturations that it received during its training. Fig. 9 represents comparison of the results from ANN and the experimental data when only four data points at upper saturation end are used during training phase. Similar to the results observed in Fig. 8, the network can capture relative permeability characteristics of the data points effectively within the high oil saturation range. As expected, when the network is trained with four data points in between the two end points, the network is able to accurately mimic the middle portion of relative permeability curves as shown in Fig. 10. When the network is exposed to the relative permeability data at both end point saturations, the end point relative permeability values are predicted accurately (Fig. 11). In this case, the network exhibits difficulty in capturing the middle portion of the relative permeability curves. It should be noted that the prediction results shown in Fig. 5 is also the case when four experimental relative permeability data points are used to train the networks. The results in Fig. 5 display a good level of agreement between relative permeability values predicted by the networks and the experimental data. This is because the four experimental data points used
Fig. 5. Experimental and predicted relative permeability values when experimental data points at four saturation values (S o = 0.34; 0.54; 0.71; 0.91) are used in training.
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Fig. 6. Experimental and predicted relative permeability values when experimental data points at five saturation values (S o = 0.34; 0.41; 0.58; 0.78; 0.91) are used in training.
in the training include the two end point data, and another two points equally spaced in between the two end points. This shows the importance of end point characteristics in controlling the overall behavior of the relative permeability curves. Through these exercises, we have shown that ANN can be used to optimize the number of experiments that need to be performed in acquiring the relative permeability data. Obviously, this will result in minimizing the cost, energy and time associated with the recovery of the core samples, the experimental measurement of relative permeability characteristics, and the computational overhead necessary in the analysis of the data collected. A generic flowchart for this approach is shown in Fig. 12. 5. Cost analysis One of the primary motivations in optimizing number of simulation studies is to minimize the cost function associated with the studies. An example of the possible alternatives to obtain relative permeability data from a reservoir and the associated costintensive work involved are schematically shown in Fig. 13. Note that scenario 1 involves only the implementation of a pure experimental protocol, while
scenarios 2 through 5 include the use of neuro-simulation protocols. The total cost involved for each scenario consists of three main components as shown in Fig. 14. These cost components are associated with the recovery of core sample, experimental measurement of relative permeability at each saturation point, and use and development of ANN model. Fig. 13 shows five scenarios in obtaining n sets of relative permeability data from a reservoir. Scenario 1 represents the case when n core samples are recovered from the reservoir and a full range of experiments is performed to obtain m data points for each core sample. The cost associated with this procedure includes the total cost to recover n core samples and the experimental cost to obtain m data points for each core sample and can be expressed as follows: Total Cost ¼ ðn CoreÞn ðm expÞ
ð1Þ
where: Core = total cost to recover a core sample Exp = cost to measure relative permeability at one saturation point. Scenario 2 represents the situation when n core samples are recovered from the reservoir. However, only m 1 relative permeability data points are obtained from the experiment for each core sample. In this
Fig. 7. Experimental and predicted relative permeability values when experimental data points at ten saturation values (S o = 0.34; 0.40; 0.48; 0.58; 0.64; 0.71; 0.76; 0.80; 0.85; 0.91) are used in training.
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Fig. 8. Experimental and predicted relative permeability values when experimental data measured at four lower-bound oil saturation points are used in training.
scenario, ANN-based relative permeability models are used to generate the complete relative permeability curves. The associated cost for this protocol is as follows:
Scenario 4 is similar to Scenario 3 except that only m 1 data points for each core sample will be obtained from experiment. The associated cost is as follows:
Total Cost ¼ ðn CoreÞ þ n ðm1 expÞ
Total Cost ¼ ðn1 CoreÞ þ n1 ðm1 expÞ
þ ðm m1 Þ ANN
ð2Þ
where: ANN = total cost in generating relative permeability curve for each core sample using ANN and it should be noted that 0 V m 1 b m. The cost associated with scenario 3, in which only n 1 core samples are recovered from the reservoir, m data points are obtained through experimental measurements for each core sample, and ANN is used to generate the remaining (n n 1) relative permeability curves. Cost associated with this scenario is shown below. Total Cost ¼ ðn1 CoreÞ þ n1 ðm expÞ þ ðn n1 Þ ANN with 0 V n 1 b n.
ð3Þ
þ n ANN
ð4Þ
Last scenario is the one in which no core samples will be recovered. All of the relative permeability data are generated by ANN and the cost associated with this approach is: Total Cost ¼ n ANN
ð5Þ
The comparison of the expected cost functions of all of the five scenarios is shown in Fig. 15. The total cost decreases as the number of cores recovered and the number of experiments performed decrease. In this qualitative representation it is assumed that the principal cost originates from the recovery of the core sample. While analyzing the cost associated with each protocol, it is crucial not to overlook the importance of
Fig. 9. Experimental and predicted relative permeability values when experimental data measured at four upper-bound oil saturation points are used in training.
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Fig. 10. Experimental and predicted relative permeability values when experimental data measured at four mid-range oil saturation points are used in training.
the accuracy of the data. The desired protocol is the one that minimizes the cost while maintaining an acceptable level of accuracy for the data generated. It is known that the accuracy of the data generated is increased as number of experiments and number of recovered core samples increase. Similarly, the associated cost also increases as number of recovered core samples and number of experimental measurements increase. These relationships are qualitatively shown in Fig. 16. It can be stated that the accuracy of the data generated and the cost function are not expected to increase in a linear fashion with the number of measurements conducted and/or with the number of core samples recovered. In other words, the increase of the cost as number of core samples recovered and number of experiments conducted increase is not constant. As the level of intensity of experimental work increases, the incremental cost will become smaller due to the fact that the principal portion of the cost is expended in setting up the experimental facility. Afterwards, the incremental cost to perform more number of experiments depends mainly on the number of measurements conducted. This is repre-
sented by a smaller and constant slope of cost function as volume of experimental work increases. Similar to the cost function, the increase in the accuracy of data generated as number of experiments or number of core samples increases is not constant. The function representing the accuracy of data generated has a continuously decreasing slope. As shown in Fig. 16, gain in accuracy becomes less significant indicating that the accuracy gained at the expense of increased cost is possibly not justifiable. Therefore, the gradient of accuracy gained with respect to the number of experiments or number of core samples and its associated cost determines the optimum number of experiments or optimum number of core samples that need to be obtained. Obviously, such an optimization process depends on the desired level of accuracy of data generated and the budget allocated to the project. 6. Extension to other applications Conceptually similar methodologies can be adopted for other applications in petroleum industry. For instance, neuro-simulation approach can be used to
Fig. 11. Experimental and predicted relative permeability values when experimental data measured at end point saturations are used in training.
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Fig. 12. A generic flowchart for the implementation of neuro-simulation towards the optimization of number of experimental measurements conducted.
optimize the number of simulation runs in field development studies and history matching applications. In this type of study, only some limited number of field development scenarios or history matching runs need to be performed. These simulation runs must be carefully organized such that they provide the critical information needed and cover a
wide spectrum of situations which can be encountered. The prevailing scenarios and system properties along with the results from these simulation runs will be utilized to train the ANNs. Upon the successful training of the ANNs, they can be used as a tool to predict the results for a wide-range of other cases of interest.
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Fig. 13. Possible protocols in obtaining relative permeability data.
Neuro-simulation methodology can also be used in reservoir characterization with applications in the areas of well test analysis, well log interpretation,
PVT analysis, and seismic interpretation in which certain specific patterns exist and are looked for. For example, classical well test analysis can be
Fig. 14. Principal components of the total cost expended in generating relative permeability data.
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Fig. 15. Cost associated with different scenarios in obtaining relative permeability data.
used to identify the existence of fault plane in the reservoir by investigating particular signature of the pressure transient data. In this application, the classical well test analysis can be used to generate some scenarios which will be used to train the ANN. In other words, pressure transient data for systems with variations in fault characteristics can be generated and analyzed using classical well test analysis. These analyses provide information such as distance to the fault, configuration of the fault systems with respect to each other, and transmissibility characteristics across the fault plane (sealing or non-sealing). The ANN can be trained to learn the existing relationships and characteristics between the pressure transient signature and the system properties. After the training is completed, the networks can be used as analytical tools to predict the existence of fault plane and its characteristics when exposed to the pressure transient data collected. This similar approach can also be
applied to provide inverse solutions for other complex systems such as naturally fractured and layered reservoirs. 7. Summary and conclusions Neuro-simulation protocol provides an alternative methodology in performing simulation studies which refers to various modes of studies through which data are collected and results generated. These studies include experimental laboratory protocols, field tests and operations conducted, and computational analyses carried using numerical and/or mathematical models. The following observations and conclusions are offered in the light of the material discussed in this paper. 1. Neuro-simulation can be used in optimizing number of actual model studies that need to be conducted. In
Fig. 16. Relationship between cost and accuracy of data with number of samples and number of experimental measurements.
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this way, the cost and energy functions associated with the model studies can be minimized. The resulting time, energy and cost savings are expected to allow engineers and scientists to concentrate more on the design of the simulation studies and analysis of the data generated. 2. Neuro-simulation approach utilizes the experiential capabilities of the ANN to generate results for the system of interest based on its learning from other systems. Therefore, the quality of the data used in the training of ANN is very critical. 3. Scenarios used to train the ANN must be carefully designed such that they provide useful information to the network and cover various situations that can be encountered in the simulation studies. This will enhance the capability of the networks to learn and make accurate predictions. 4. Due to the adaptive learning, self-organizing, and fault-tolerant features of ANNs, the networks are capable to learn the existing relationships between input stimuli and output, and to create a distinct pattern recognition from an incomplete
data set. This offers advantage in optimizing the range of data necessary in training the networks. Acknowledgments We acknowledge the partial financial support provided by the Petroleum and Natural Gas Engineering program of the Department of Energy and Geo-Environmental Engineering at the Pennsylvania State University, and the Consortium for Virtual Operations Research (CVOR). We extend our gratitude to Saudi Aramco Research and Development Center for providing experimental relative permeability data sets which are used in training and testing of the relative permeability model developed. Appendix A ANN topologies for oil/gas relative permeability predictions are shown below. Figs. A-1 and A-2.
Fig. A-1. Schematic diagram of the k ro model of the oil/gas relative permeability predictor (Silpngarmlers et al., 2001).
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Fig. A-2. Schematic diagram of the k rg model of the oil/gas relative permeability predictor (Silpngarmlers et al., 2001).
References Maren, A.J., Harston, C.T., Pap, R.M, 1990. Handbook of Neural Computing Applications. Academic Press, Inc., San Diego.
Silpngarmlers, N., Guler, B., Ertekin, T., Grader, A.S., 2001. Development and testing of two-phase relative permeability predictors using artificial networks. SPE 69392 Presented at the SPE Latin American and Caribbean Petroleum Engineering Conference Buenos Aires, Argentina, March 25–28, 2001.