This article was downloaded by: [University of Waterloo] On: 10 November 2014, At: 09:57 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Petroleum Science and Technology Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/lpet20 Evaluating the Unloading Gradient Pressure in Continuous Gas-lift Systems During Petroleum Production Operations A. Kamari a , A. Bahadori b , A. H. Mohammadi ac & S. Zendehboudi d a Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, Howard College Campus, Durban, South Africa b School of Environment, Science & Engineering, Southern Cross University, Lismore, Australia c Institut de Recherche en Génie Chimique et Pétrolier (IRGCP), Paris, France d Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, MA, USA Published online: 10 Nov 2014. To cite this article: A. Kamari, A. Bahadori, A. H. Mohammadi & S. Zendehboudi (2014) Evaluating the Unloading Gradient Pressure in Continuous Gas-lift Systems During Petroleum Production Operations, Petroleum Science and Technology, 32:24, 2961-2968 To link to this article: http://dx.doi.org/10.1080/10916466.2014.936455 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &
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This article was downloaded by: [University of Waterloo]On: 10 November 2014, At: 09:57Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registeredoffice: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
Petroleum Science and TechnologyPublication details, including instructions for authors andsubscription information:http://www.tandfonline.com/loi/lpet20
Evaluating the Unloading GradientPressure in Continuous Gas-lift SystemsDuring Petroleum Production OperationsA. Kamaria, A. Bahadorib, A. H. Mohammadiac & S. Zendehboudida Thermodynamics Research Unit, School of Engineering, Universityof KwaZulu-Natal, Howard College Campus, Durban, South Africab School of Environment, Science & Engineering, Southern CrossUniversity, Lismore, Australiac Institut de Recherche en Génie Chimique et Pétrolier (IRGCP),Paris, Franced Department of Chemical Engineering, Massachusetts Institute ofTechnology (MIT), Cambridge, MA, USAPublished online: 10 Nov 2014.
To cite this article: A. Kamari, A. Bahadori, A. H. Mohammadi & S. Zendehboudi (2014) Evaluating theUnloading Gradient Pressure in Continuous Gas-lift Systems During Petroleum Production Operations,Petroleum Science and Technology, 32:24, 2961-2968
To link to this article: http://dx.doi.org/10.1080/10916466.2014.936455
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (the“Content”) contained in the publications on our platform. However, Taylor & Francis,our agents, and our licensors make no representations or warranties whatsoever as tothe accuracy, completeness, or suitability for any purpose of the Content. Any opinionsand views expressed in this publication are the opinions and views of the authors,and are not the views of or endorsed by Taylor & Francis. The accuracy of the Contentshould not be relied upon and should be independently verified with primary sourcesof information. Taylor and Francis shall not be liable for any losses, actions, claims,proceedings, demands, costs, expenses, damages, and other liabilities whatsoever orhowsoever caused arising directly or indirectly in connection with, in relation to or arisingout of the use of the Content.
This article may be used for research, teaching, and private study purposes. Anysubstantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &
Evaluating the Unloading Gradient Pressure in ContinuousGas-lift Systems During Petroleum Production Operations
A. Kamari,1 A. Bahadori,2 A. H. Mohammadi,1,3 and S. Zendehboudi4
1Thermodynamics Research Unit, School of Engineering, University of KwaZulu-Natal, HowardCollege Campus, Durban, South Africa
2School of Environment, Science & Engineering, Southern Cross University, Lismore, Australia3Institut de Recherche en Genie Chimique et Petrolier (IRGCP), Paris, France
4Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge,MA, USA
Evaluating the performance, applicability, and field testing of various artificial lift methods, in particularcontinued gas-lift, can be time consuming and costly. To overcome these drawbacks, it is needed topropose a reliable model to estimate gas-lift applicability in advance of the installation under specificwell operational conditions such as tubing size and design oil rate. In this study, the robust least squaremodification of support vector machine (LSSVM) methodology is implemented to propose a computerprogram, by which the unloading pressure gradient region can be determined in various design oilproduction rates and also tubing sizes. The developed LSSVM model results indicate 1.084% averageabsolute relative deviation from the corresponding unloading pressure gradient literature values, andsquared correlation coefficient of 0.9994.
Gas-lift operation is the injection of compressed gas into the upward flow of oil in a productionwell to increase production of oil rate, which is conducted through the casing and injected bygas-lift into the lower section of the tubing (Behbahani et al., 2012). In other words, injectionof gas lead to decrease the density of the oil column, therefore the mix of oil, gas, and/or waterelevates to the upward of the oil production well. The gas-lift technology of oil fields is one ofmany production operation techniques whose performance can be enhanced because of the internalpressure in depleted reservoirs or high depth can force the flow of only a fraction of its oil to thesurface, and by using artificial means becomes necessary to lift the oil, particularly so for deepreservoirs found offshore (Camponogara and Nakashima, 2006). The artificial gas-lift operation canbe designed as two widely used methods including the intermittent (periodical) injection of gas,called intermittent gas-lift (IGL), becomes the more economical alternative, and the continuousgas-lift (CGL), is not efficient (Santos et al., 2001).
Address correspondence to A. Bahadori, School of Environment, Science & Engineering, Southern Cross University,Lismore, NSW, Australia. E-mail: [email protected]
Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lpet.
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Major factors associated with oil and gas properties as well as operational facilities that have animpact on designing the most economical gas-lift operation are pressure-volume-temperature (PVT)properties of the crude oil, density related to the gas injected, wellhead backpressure, water cut ofthe producing stream, pressure rating of the equipment, bubble size distribution, injector geometry,tubing diameter, and oil production amount. For instance, oils with high density (heavy oil) requiremore gas to inject into the wells in order to lift. Moreover, the injection-gas pressure at depth mustbe greater than the flowing producing pressure at the same depth. Hence, considering oil productionvolume and also the quantity of injected gas are critical variables during designing of the IGLmethod, whereas a lower value of injected gas can decrease significantly the oil production and ahigher value can increase the operational costs (De Souza et al., 2010).
To investigate the applicability of artificial gas-lift several attempts have been reported in theliterature. Camponogara et al. (2010) proposed an automation system for integrated operation ofgas-lift platforms, thereby bridging the gap between surface facilities and downhole devices. Wanget al. (2002) converted the mixed-integer nonlinear program into a mixed-integer linear programmingproblem by piecewise-linearizing the nonlinear constraints and then applying meta-heuristics tosolve gas-lift optimization problem. De Souza et al. (2010) developed a model for the analysisof CGL systems using an optimization algorithm coupled to a stationary two-phase flow networkmodel. Salahshoor et al. (2013) implemented adaptive growing and pruning radial basis functionartificial neural networks to recursively capture the essential dynamics of casing–heading instabilityin a nonlinear model structure. Their results indicated the superior performance of the developedmodel under different scenarios. Despite recent technological advances, the operating processes andfield experiments, artificial intelligence techniques can be further enhanced in a number of ways,particularly in the development of more accurate models and the design of mathematical algorithmicsolutions to the problems thus, all with the aim of increasing performance and prediction approaches.Therefore, an alternative mathematical algorithm, namely least squares supported vector machine(LSSVM) is applied to predict the unloading gradient pressure using gas-lift.
2. DATABANK
To achieve a reliable predictive model, the applicability and accuracy is directly associated with thevalidity of the data set used for its development (Eriksson et al., 2000; Kamari et al., 2013a; Kamariet al., 2013b; Kamari et al., 2014). Therefore, 87 samples were collected from literature (Cholet,2000) and applied to develop an efficient model for predicting the unloading gradient pressure.The required data (Cholet, 2000) to develop this predictive model includes the unloading gradientpressure (psi/ft) as a function of the preselected design daily production rate (bbl/day) and tubingsize (inch). Ranges and averages of the aforementioned parameters as well as the literature reportedvalues of the unloading gradient pressure are shown in Table 1.
In order to develop a reliable predictive model for prediction of the unloading gradient pressure twoinput parameters have been considered, including design oil production rate and the tubing size. The
TABLE 1Ranges and Averages of the Data Employed to Construct the Predictive Technique (e.g., LSSVM)
available database is randomly separated into two sub-data sets consisting of the Training/Learningset and the Test set. To propose the newly predictive CSA-LSSVM model, 80% of the main unloadinggradient pressure data points randomly selected for the Training phase and the 20% have beenassigned for testing phase, respectively.
3. DEVELOPMENT OF THE PREDICTIVE MODEL
The support vector machine (SVM) is one of the most powerful algorithms known in solvingregression and classification problems, which have been proposed based on structural risk mini-mization and statistical learning theory (Suykens and Vandewalle, 1999; Vapnik, 2000). Suykensand Vandewalle (1999) presented LSSVM methodology, which is a modified version of classicalSVM algorithm introduced by Cortes and Vapnik (1995). Quadratic programming is applied to solveclassical SVM form, which is often convoyed by large memory requirement and is time consumingwhile LSSVM strategy implements equality constraints to replace the original convex quadraticprogramming problem (Chamkalani et al., in press).
In presence of a dataset {(x1, y1) , . . . , (xm,ym)}n×, where each output yi ∈ and the input xi ∈,LSSVM for regression problem is introduced as minimization of following formula (Suykens et al.,2002; Cawley and Talbot, 2007):
min J (w, ξ ) = 1 − 2w2 + 1
2μ
m∑
i=1
(ξi)2 (1)
s.t. : yi = wT ϕ (xi) + b + ξi, i = 1, 2, . . . , m
where ϕ(xi) is a nonlinear function that maps the input space into a higher dimensional space. Byintroducing Lagrange multipliers and exploiting the optimality constraints, the decision function ofEq. (1) takes the following form:
f (x) =N∑
k=1
αiK(x, xj ) + b (2)
where αi stands for the introduced Lagrange multiplier and K(x,xj) denotes the Kernel function asfollows:
K (x, xk) = � (x)T .� (xk) (3)
As a result, the radial basis function (RBF) kernel has been used in this study as formulated below(Suykens and Vandewalle, 1999; Liu et al., 2005; Eslamimanesh et al., 2012):
K(xi, xj ) = exp(−xi − x2
j /σ2) (4)
where σ is an adjustable parameter called kernel bandwidth.
4. PERFORMANCE EVALUATION
To evaluate the performance of the newly developed LSSVM model in predicting the unloadinggradient pressure as a function tubing size and design oil production rate, a number of statisticalparameters have been applied including average percent relative error (APRE), average absolutepercent relative error (AAPRE), standard deviation of error (SD), root mean square error (RMSE),
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and coefficient of determination (R2). Definitions and equations of aforementioned parameters areas follows:
1. AREP.
(5)
in which, Ei% represents the relative deviation of the estimated parameter with respect to theexperimental/actual value. Therefore, the parameter (Ei%) can be expressed as follows:
(6)
2. AAREP.
(7)
3. RMSE.
(8)
4. SD.
(9)
5. R2.
(10)
where X is the mean of the literature-reported the unloading gradient pressure values pre-sented in the previous formula.
5. RESULTS AND DISCUSSION
In this work, an efficient model for predicting the unloading gradient pressure using continuousgas-lift has been developed using LSSVM method coupled with coupled simulated annealing (CSA)optimization approach. As a result, CSA optimization strategy determines most appropriate parame-ters to perform a fine-tuning step. The LSSVM parameters involving γ and σ 2 must be optimized inorder to obtain an accurate, efficient and reliable predictive model. The optimized values of the newlydeveloped CSA-LSSVM model are 2,775615194 and 153244439,8 for σ 2 and γ , respectively. As
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TABLE 2Statistical Analysis to Assess the LSSVM Technique for Determination of the Unloading Gradient
pointed out earlier, to evaluate the accuracy of the newly developed CSA-LSSVM tool in predictingthe unloading gradient pressure, statistical error analysis, in which Er, RMSE, Ea, SD, and R2, andgraphical error analysis, in which crossplot and error distribution is sketched, are employed. Table 2lists the result of statistical error analysis of the newly developed LSSVM model for estimation of theunloading gradient pressure. The R2 and average absolute relative deviation of CSA-LSSVM modelin testing phase are reported 0.998 and 1.9, respectively. Figure 1 illustrates point-point comparisonbetween the estimated and the literature-reported data for the unloading gradient pressure. As canbe seen in this figure, approximately all data pint have been matched. Figure 2 (top plot) displaysthe scatter diagram that compares CSA-LSSVM model outputs versus the literature-reported theunloading gradient pressure. A tight cloud of points about 45a line for training phase and testing datasets demonstrates the robustness of the newly proposed CSA-LSSVM model. Furthermore, Figure 2(bottom plot) represents the error distribution of the proposed CSA-LSSVM tool for predictionof the unloading gradient pressure. This figure confirms that the newly proposed CSA-LSSVMmodel has the low scatter around the zero error and the small error range to estimate the unloadinggradient pressure. The acquired results show that very good agreement exists between the predictionof CSA-LSSVM and the literature-reported data of the unloading gradient pressure.
To demonstrate a further comparison between literature-reported data and the obtained values bythe newly proposed CSA-LSSVM, the trend plot of the unloading gradient pressure versus design oil
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FIGURE 1 Estimated values of unloading gradient pressure versus the real data through the point-to-point scheme.
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FIGURE 2 Crossplot (top plot) and relative deviation curve (bottom plot) for the developed LSSVM model.
production rate considering tubing size is sketched. Figure 3 illustrates the trend plot of the unloadinggradient pressure versus design oil production rate for various tubing sizes. This figure shows verygood agreement for the newly developed in comparison with the literature-reported the unloadinggradient pressure data. Here, it should be noted that the CSA-LSSVM has been developed by usingtwo adjustable parameters while other predictive models require more adjustable parameters, whichmay lead to deviation and normally are not accurate enough out of the ranges that they have beenderived from.
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LSSVM, Tubing Size=1.315 in
LSSVM, Tubing Size=1.9
LSSVM, Tubing Size=2.063
FIGURE 3 The performance of the LSSVM model for the determination of the unloading gradient pressure incomparison with the data for various tubing sizes.
6. CONCLUSIONS
A novel LSSVM predictive system optimized via CSA method was proposed in this research studyto calculate the unloading gradient pressure, considering tubing size and design oil rate are theinput variables. According to the statistical analysis, a high value of R2 (e.g., 0.999) and a lowextent of absolute average relative error percentage (e.g., 1.084) were obtained. Hence, a trustworthytechnique to forecast the unloading gradient pressure was introduced on the basis of the LSSVMmethod which can result in accurate determination of optimum injection and production rates duringgas-lift processes.
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