1 Petroleum & Coal ISSN Available olie at Petroleum & Coal 57(4) , 05 EFFICIENT ESTIMATION OF GAS LIQUID RATIOS FOR PLUNGER LIFT SYSTEMS IN PETROLEUM PRODUCTION OPERATIONS Arash Kamari, Amir H. Mohammadi,,3, Alireza Bahadori 4 Thermodyamics Research Uit, School of Egieerig, Uiversity of KwaZulu- Natal, Howard College Campus, Kig George V Aveue, Durba 404, South Africa Istitut de Recherche e Géie Chimique et Pétrolier (IRGCP), Paris Cedex, Frace 3 Départemet de Géie des Mies, de la Métallurgie et des Matériaux, Faculté des Scieces et de Géie, Uiversité Laval, Québec (QC), GV 0A6, Caada; 4 School of Eviromet, Sciece & Egieerig, Souther Cross Uiversity, Lismore, NSW, Australia Received May 9, 05; Corrected July 6, 05; Accepted July 7, 05 Abstract Pluger lift systems have the beefits of icreasig productio, as well as sigificatly decreasig methae emissios associated with blowdow operatios. I other words, pluger lift is accouted oe of the most widely accepted ad ecoomical artificial lift techiques, particularly i gas/oil wells with high gas liquid-ratio (GLR). Hece, it is ecessary to preset a reliable ad efficiet method for predictig the applicability performace of pluger lift system. I this commuicatio, a simple method is itroduced for the calculatio of the miimum required gas liquid ratios as a fuctio of the et operatig pressure ad well depth. Usig this dedicated method, satisfactory results are obtaied ad are quatified by the followig statistical error factors: average absolute relative deviatios of the predicted gas-liquid ratio from existig literature-reported values: 6.33 %, ad R-squared: Fially, the method proposed i this study is compared with a itelliget method. Our results show that the method proposed i this study is more accurate ad applicable tha the comparative itelliget techique. Keywords: Gas-liquid ratio; Pluger lift; Method; Net operatig pressure.. Itroductio I petroleum productio, artificial lift refers to the employ of mechaical techiques such as the cotiuous gas-lift (CGL), itermittet gas-lift (IGL) ad pluger lift systems i order to improve the flow of liquids through a producig well. To provide the adequate eergy to the liquid (oil or water) flow, the gas-lift methods are widely utilized as artificial lift techiques where gas is ijected i the productio well . The gas-lift mechaism is that high pressure gas is ijected ito the productio well to lighte the colum of fluid ad allow the reservoir pressure to force the fluid to the surface, the the gas that is ijected, is produced with the reservoir fluid ito the surface . As a result, IGL with pluger is oe of the differet desig optios available to apply for icreasig the liquid flow from a producig well. Pluger lift system is accouted as oe of the most widely accepted ad ecoomical artificial lift techiques, particularly i gas/oil wells with high gas liquid-ratio (GLR). The pluger lift tool is a freetravellig pisto that fits withi the productio tubig ad depeds o well pressure to rise ad solely o gravity to retur to the bottom of the productio well . A pluger lift tool operates i a cyclic process with the well alterately flowig ad shut-i . However, the istallatio of a pluger lift system has led to some ecoomic ad evirometal beefits icludig lower well fewer remedial treatmets, lower capital cost versus istallig beam lift equipmet, cotiuous productio which improves gas productio rates ad icreases efficiecy, decreased paraffi ad scale buildup, lower methae emissios, etc.
2 A. Kamari, A. H. Mohammadi, A. Bahadori/Petroleum & Coal 57(4) , There are differet attempts made to predict the productivity performace of oil/gas well i presece of artificial lift techiques. Brow ad Jesse , Brill et al. , ad Neely et al.  coducted some laboratory experimets o special field istallatios of covetioal IGL, establishig empirical rules for the settig of the operatioal parameters. They preseted useful rules, but those guidelies lack i geerality. Mower et al.  studied impact of pluger geometry o the fallback usig differet plugers. Machado  proposed a mechaistic method couplig empirical correlatios ad physical priciples to determie some variables of the IGL process. The acquired theoretical results by Liao  idicated good agreemet with Brow ad Jesse , Brill et al. , ad Neely et al. . Chaci  itroduced a simple-to-use approach for the determiatio of the productio rate, ad preseted a procedure to choose the appropriate IGL techique. White  proposed the first simple mathematical relatioships for the covetioal IGL ad did experimetal works o laboratory istallatios. To idicate the decreasig liquid fallback i the pluger case, White  performed tests with ad without a pluger. Geerally, measurig flow rate is ot a mior task i the pluger-lift, sice a aperture meter is applied to measure the flow rate, ad the measuremets ca have major limitatios of the rageability, i.e., the rage i which the measuremet is reliable ca be excelled i a pheomeo called overrage of the meter, leadig to big errors i measuremets . Moreover, there are o geeral models/methods or thorough researches of the dyamics of all the IGL process cycles that are coheret for all desigs . The productio egieers require a efficiet method to idetify the performace of the various desigs uder certai field coditios, ad to tue the operatioal parameters to their optimum values. The purpose of the preset study is to develop such a method to predict gas-liquid ratio ad also ratioalize those tasks. Hece, a reliable method is itroduced to estimate the miimum required gasliquid ratios.. Gas Liquid Ratio Data I this study, about 60 samples were gathered from literature  ad applied to develop a efficiet model for predictig the miimum gas-oil ratio. The required data  to develop this model icludes the miimum gas liquid ratio (GLR, SCF/BBL) as a fuctio of et operatig pressure (P, psi) ad the depth of well (d, ft) i -i ad.5-i expadig cycle cotrolled plugers. Regardig the databak collected i this study, gas liquid ratio rages from 900 to SCF/BBL, the well depth rages 4000 to 000 ft, ad et operatig pressure is psi. Here, it should be metioed that the fudametal step i developig reliable predictive models is the selectio of a efficiet ad represetative dataset [6-9]. The rages ad averages of parameters applied for developig the method as well as the reported values of gas liquid ratio are summarized i Table. Table Rages of data used for developig the model; data from  Parameter Mi. Avg. Max. Type Well Depth, ft Iput Net Operatig Pressure, psi Iput Gas Liquid Ratio, Scf/bbl 0 ⁴ Output 3. Developmet of the ew method As metioed earlier, the mai objective of the preset study is to itroduce a accurate, reliable ad applicable method for estimatig the gas liquid ratio durig petroleum productio implemetig pluger lift. To this ed, well depth ad et operatig pressure are cosidered as predictor variables for the calculatio of gas liquid ratio. Furthermore, average absolute relative deviatio (AARD) as a reliable statistical error parameter is cosidered to estimate the accuracy, ad to fid the best model with lowest deviatio from actual data of gas liquid ratio. For miimizig the deviatio i field coditio, the form of method preseted i this study is as follows:
3 A. Kamari, A. H. Mohammadi, A. Bahadori/Petroleum & Coal 57(4) , GLR = ( 8.54 (.396 P d) P d P w (P ) 3 (8.958 P w) ) 0 4 () d= Well depth, ft ;P = Net operatig pressure, psi; GLR= Gas liquid ratio, SCF/BBL. Havig developed the method for the estimatio of gas liquid ratio i pluger lift system, some importat statistical error factors icludig average percet relative error (APRE), stadard deviatio of error (SD), root mea square error (RMSE) ad R-squared (R ) have bee employed to evaluate the performace of the ewly developed method i terms of accuracy. Relevat formulas of the abovemetioed error factors are defied as follows:. APRE E r % E i % () i where E i % stads for the relative deviatio of calculated GLR data by the method preseted i this study from its actual value, as follows: GLRexp GLR E i % 00 i,,3,..., (3) GLRexp. AARD: AARD% E % (4) 3. RMSE: RMSE 4. SD: i i GLR i GLR i exp i SD GLR i exp GLRi i GLRi exp (6) 5. R : R GLR i GLR i GLRi exp GLRi i (7) where GLR is the mea of the actual GLR data values preseted i the above formula. 4. Results ad Discussio To compare the results obtaied by the ewly proposed method (Eq. ()), a itelliget techique called least square support vector machie (LSSVM) algorithm [0-] was applied i this study. As a result, the LSSVM approach has oly two adjustable parameters (γ ad σ ) which should be tued by usig a optimizatio approach. To this ed, the coupled simulated aealig approach (CSA) was used with the LSSVM algorithm. Cosequetly, the LSSVM tuig parameters have bee optimized usig CSA tuig method. As a cosequece, the optimized values of the LSSVM model proposed i this study for the estimatio of miimum required gas liquid ratios are ad for σ ad γ, respectively. Table lists the results obtaied by both Eq. () ad LSSVM model for the estimatio of gas liquid ratios i pluger lift system. As it is clear i the table, the results obtaied from Eq. () are i better agreemet with the actual data of gas liquid ratio tha the results of LSSVM model. The AARD for Eq. () ad LSSVM model are reported 6.3 ad 7.3, respectively. (5)
4 A. Kamari, A. H. Mohammadi, A. Bahadori/Petroleum & Coal 57(4) , Table Accuracy results of the developed models for predictio of miimum gas-liquid ratio Performace AARD, % APRE, % SD RMSE R² Eq. () LSSVM approach This idicates that Eq. () is more appropriate for the estimatio of gas liquid ratios i pluger lift system. Figs. ad illustrate the scatter diagram (left view) ad relative error distributio diagram (right view) for the ewly developed equatio ad the LSSVM model, respectively. As clear from the figures, the predicted data by Eq. () are more matched with the actual gas liquid ratio data. Moreover, the distributio of relative error aroud zero lie for Eq. () is less tha the LSSVM model. Additioally, the error aalysis coducted i this study clearly idicates that the LSSVM model uderestimates the actual gas liquid ratio data with respect to the APRE= 3.3%. Furthermore, the method developed i this study is more applicable tha the LSSVM model, because the LSSVM approach is a complex mathe-matical algorithm while the proposed method is a simple equatio. Therefore, it ca be cocluded that Eq. () is a promisig choice for applicatio i petroleum egieerig calculatios related to productio optimizatio, ad artificial lift systems. Figure The results obtaied by Eq. (); left view: scatter diagram; right view: relative error distributio plot Figure The results obtaied by the LSSVM model; left view: scatter diagram; right view: relative error distributio plot To idicate smooth performace of the developed equatio ad also a further compariso betwee literature-reported gas liquid ratio data  ad the obtaied values by the ewly proposed method, the tred plot of the miimum gas-oil ratio versus et operatig pressure is sketched. Figs. 3 ad 4 illustrate the tred plot of the miimum gas-oil ratio values versus et operatig pressure for ad.5 iches pluger lift, respectively. These figures show
5 A. Kamari, A. H. Mohammadi, A. Bahadori/Petroleum & Coal 57(4) , satisfactory agreemet for the ewly developed method i compariso with the literaturereported gas liquid ratio data. Figure 3 The performace of proposed equatio (Eq. ()) for the determiatio of gas-liquid ratio i compariso with the data for ich pluger lift. Fig. The performace of the proposed equatio (Eq. ()) for the determiatio of gasliquid ratio i compariso with the data for.5 ich pluger lift 5. Coclusio I this study, a reliable method was itroduced for the estimatio of gas liquid ratio i pluger lift as a fuctio of et operatig pressure ad well depth. Furthermore, least square support vector machie techique (LSSVM) as a well-kow itelliget techique has bee applied i order to compare the performace predictio of equatio preseted i this study. The results illustrate that the equatio proposed i this ivestigatio is more accurate tha the itelliget techique, ad gives better results ad ca be advatageously used for predictio of the miimum gas-liquid. Furthermore, the method itroduced ca easily be utilized i ay productio simulatio software ad ca provide good accuracy ad performace for the miimum gas-liquid estimatio.
6 A. Kamari, A. H. Mohammadi, A. Bahadori/Petroleum & Coal 57(4) , Refereces  Satos OG, Bordalo SN, Alhaati FJ. Study of the dyamics, optimizatio ad selectio of itermittet gas-lift methods a comprehesive model. Joural of Petroleum Sciece ad Egieerig 00; 3:  Ayatollahi S, Narimai M, Moshfeghia M. Itermittet gas lift i Aghajari oil field, a mathematical study. Joural of Petroleum Sciece ad Egieerig 004; 4:  Bahadori A, Zahedi G, Zedehboudi S, Jamili A. Estimatio of Miimum Required Gas Liquid Ratio (GLR) to Support Pluger Lift Istallatio i Wells Usig a Simple Method. Petroleum ad Coal 0.; 54:  Sadro G, Wiggis M. A dyamic pluger lift model for gas wells. Old Productio & Facilities 00.; 6:  Brow K, Jesse F. Evaluatio of Valve Port Size, Surface Chokes ad Fluid Fall-Back i Itermittet Gas-Lift Istallatios. Joural of Petroleum Techology 96; 4:  Brill J. A Aalytical Descriptio of Liquid Slug Flow I Small-Diameter Vertical Coduits. Joural of Petroleum Techology 967;  Neely A, Motgomery J, Vogel J. A field test ad aalytical study of itermittet gas lift. Old SPE Joural 974; 4:  Mower L, Lea J, Beauregard E, Ferguso P. Defiig the characteristics ad performace of gas-lift plugers. SPE Aual Techical Coferece ad Exhibitio, -6 September, Las Vegas, Nevada; 985.  Machado R. Modelagem e simulação umérica do mecaismo de gas lift itermitete. Uiversity of São Paulo, Ouro Preto: SN.; 988.  Liao T. Mechaistic Modelig of Itermittet Gas Lift. PhD Thesis, Uiversity of Tulsa; 99.  Chaci J. Selectio of Optimum Itermittet Lift Scheme for Gas Lift Wells, Uiversity of Tulsa Ceteial Petroleum Egieerig Symposium, 9-3 August, Tulsa, Oklahoma; 994.  White G. Combie gas lift, plugers to icrease productio rate. World Oil;(Uited States) 98; 95:  Mota F, Mirada FC, Ramos IC. Icreasig the measurability rage of a gas flow rate sesor by time series measuremets. Joural of Petroleum Sciece ad Egieerig 03; :  White G, O'Coell B, Davis R, Berry R, Stachal L. A Aalytical Cocept of the Static ad Dyamic Parameters of Itermittet Gas Lift. Joural of Petroleum Techology 963; 5:  Beeso C, Kox D, Stoddard J. Pluger Lift Correlatio Equatios ad Nomographs, Fall Meetig of the Petroleum Brach of AIME, -5 October, New Orleas, Louisiaa; 995.  Eriksso L, Johasso E, Müller M, Wold S. O the selectio of the traiig set i evirometal QSAR aalysis whe compouds are clustered. Joural of Chemometrics 000; 4:  Kamari A, Gharagheizi F, Bahadori A, Mohammadi AH. Rigorous Modelig for Predictio of Barium Sulfate (Barite) Depositio i Oilfield Bries. Fluid Phase Equilibria 04; 366: 7 6.  Kamari A, Hemmati-Sarapardeh A, Mirabbasi, SM, Nikookar M, Mohammadi AH. Predictio of sour gas compressibility factor usig a itelliget approach. Fuel Processig Techology 03; 6:  Kamari A, Khaksar-Mashad A, Gharagheizi F, Mohammadi AH, Ashoori S. Robust Model for the Determiatio of Wax Depositio i Oil Systems. Idustrial & Egieerig Chemistry Research 03; 5:  Suykes JA, Vadewalle J. Least squares support vector machie classifiers. Neural processig letters 999; 9:
7 A. Kamari, A. H. Mohammadi, A. Bahadori/Petroleum & Coal 57(4) ,  Suykes JAK, Va Gestel T, De Brabater J, De Moor B, Vadewalle J. Least Squares Support Vector Machies. st ed. Sigapore: World Scietific Publishig Compay; 00.  Istallig Pluger Lift Systems I Gas Wells. USA: Techical reported by Natural Gas STAR Parters 006; 4. Correspodig authors ;