A New Correlation for Calculating Wellhead Production Considering Influences of Temperature, GOR, and Water-Cut for Artificially Lifted Wells

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1 Available from: Shedid A. Shedid Retrieved on: 04 May 2016 IPTC A New Correlation for Calculating Wellhead Production Considering Influences of Temperature, GOR, and Water-Cut for Artificially Lifted Wells Mohamed Ghareeb, Lufkin-Industries, Maadi, Cairo, Egypt. Shedid A. Shedid, Teaxs A & M University, Doha P. O. Box 23874, Qatar. Copyright 2007, International Petroleum Technology Conference This paper was prepared for presentation at the International Petroleum Technology Conference held in Dubai, U.A.E., 4 6 December This paper was selected for presentation by an IPTC Programme Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the International Petroleum Technology Conference and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the International Petroleum Technology Conference, its officers, or members. Papers presented at IPTC are subject to publication review by Sponsor Society Committees of IPTC. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the International Petroleum Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, IPTC, P.O. Box , Richardson, TX , U.S.A., fax Abstract Several classical wellhead production correlations have been developed and widely used all over the world for naturally flowing wells. For artificially flowing wells, many important well and fluid parameters are ignored in these correlations. This results in erroneous results and inaccurate predictions when these correlations are applied. These current correlations are mainly function of tubing head pressure, bean size (which has almost no effect for artificially flowing wells), and gasliquid ratio only. The man objective of this study is to ovecome the limitations of these correlations for artificially flowing wells by development a new correlation capable to predict accurately the wellhead flow production. The new correlation was developed using a set of 1,750 data points from 352 producing wells in Egypt. The newly-developed correlation includes several parameters of tubing size, wellhead and bottom-hole temperatures, producing gas-oil ratio, pay zone depth, and water cut. A sensitivity analysis using the newly-developed correlation about the influences of involved well and reservoir parameters, is carried out. The results indicated that the newly-developed correlation is capable to predict the wellhead production rate accurately. Noteworthy, the variation of producing depth, tubing size and wellhead temperature has real impact on production rate while variation in bottom-hole temperature, water-cut and gas-oil ratio has relatively smaller effect on well production rate. The enhanced prediction of production rate using the new correlation is attributed to its consideration to many other parameters, which were ignored before in Gilbert and other s correlations; such as tubing size, wellhead temperatures, and pay zone depth. 1. Introduction and Literature Review The separator and multiphase meters have been considered and used to determine the oil well production. This has been considered as the most accurate method for calculating the oil and gas flow rates. However, these current methods are rather expensive and time consuming to be achieved. Therefore, it is usually desired to have quick and accurate evaluation of well performance considering wellhead parameters, especially pressure and temperature. Good utilization of pressure and temperatures parameters of producing wells reveals excellent and reliable information about well behavior and can help to make required remedial action(s) in required suitable time. For naturally flowing wells, bean performance correlation is the most widely used to monitor well performance. Most current correlations (Gilbert, 1954; Ros, 1960; Ashong, 1961; Asford, 1973; Secen, 1976; Abdul-Majeed, 1986) for twophase flow across chocks are valid only for critical flow across the choke. The literature presented good correlations for single phase flow of either liquid or gas. However, reliable correlations for twophase are limited and for multiphase are rare and scarce. This is especially true for flow in the subsonic flow region (i.e., flow velocities smaller than that of sound.

2 The majority of current correlations for multiphase flow are valid only for critical flow condition. The most popular correlation was developed by Gilbert (1954) but it is valid for critical flow occurring when the upstream pressure of the choke is at least 70 % higher than the downstream pressure or when the ratio of down stream pressure to upstream pressure is equal to In general, the literature (Abdul-Majeed, 1986; Al- Attar and Abdul-Majeed, 1988) reveals that keeping the ratio of downstream pressure to upstream pressure in the range from 0.50 to 0.60 secures the critical flow condition of the choke. In naturally-flowing wells, the production rate is controlled by means of surface choke (or bean). Economides et al (1993) indicated that the two-phase flow through actual wells has not been described theoretically yet. Therefore, many empirical correlations have been developed for this purpose of the determination of two-phase flow through a choke. These correlations are usually applied for critical flow condition. This is the condition when gas-liquid mixture flows through choke at velocity sufficient enough to reach sonic velocity. When this condition occurs, the flow is called critical flow and changes in pressure downstream of the choke do not affect the flow rate. Accordingly, Gilbert (1954) developed his correlation to calculate the production rate as follows: 10 R Q Pwh = S 1.89 (1) Re-arranging equation (1) yields, Q = 10 P wh RS (2) Where Q is gross liquid rate (bbl/d), P wh is well (or tubing) head pressure (psig), S is bean size (1/64 inch), and R is gasliquid ratio (MSCF/BBL). Following the same approach of Gilbert (1954), Ros (1960) developed a very similar correlation but with different correlating exponents as follows: 17 R Q P wh = S (3) Achong (1961), Ashford (1973), Secen (1976) developed similar correlations with different constant and exponents in the same form of Gilbert correlation. Tantway et al (1995) developed a computer program to calculate these exponents for different local oil fields in Egypt. All of the previouslymentioned studies used Gilbert s form, which can be written in a general form as follows; C R Qa b Pwh = (4) S d A list of most popular correlations used to predict wellhead production rate for naturally-flowing wells is presented in Appendix A. This list includes Gilbert, Achong, Poettmann, Omana, and Ashford correlations. Abdul-Majeed (1986) performed a sensitivity study about correlations predicting two-phase flow through wellhead choke using data from 210 Iraqi well tests. The data included production rate, choke size, upstream pressure, gas-liquid ratio, and API gravity of oil. He concluded that Gilbert s correlation yielded relatively accurate results but Omana s correlation is poor in accurate prediction of production rate. Al-Attar and Abdul-Majeed (1988) compared the correlations of multiphase flow performance through a wellhead choke using a statistical analysis based upon production data from 155 well tests from Iraqi wells. They concluded that Ashford correlation provided overpredicted production rates, and Poettmann correlation produced underpredicted production rates. The study also concluded that Gilbert, Poettmann, and Ashford correlations for oils in the range of 38 to 45 API gravity resulted in underpredicted production rates. 2. Development of a New Correlation Although the tubing-head pressure is a factor considered for calculating production rate in several bean performance equations, it is not a factor at all for predicting the production rate in an artificial lift system. This is mainly attributed to the absence of critical flow conditions in the case of artificial lift system in which the choke is either disconnected or kept fully opened. For the goal of the development the new correlation for artificially flowing wells, the wellhead temperature is considered a function of some producing well and reservoir parameters. The proposed function of these parameters can be presented in the following mathematical form: T th = f T( bh a,q b,wc c, H d, A e,gor f ). (5) Consideration of direct and reverse proportionality of these parameters with wellhead temperature and insertion of a constant of proportion (K), based on actual measured data, results in:

3 2 A New Correlation for Calculating Wellhead Production IPTC Tth = K T Q WCH A GORd bha e b fc (6) Re-arranging equation (6) yields: T H A GORd e f Q b = th K T WC bha C (7) Actual data from 352 producing wells of flow rate (Q), wellhead temperature (T th), tubing cross-sectional area (A), gas-oil ratio (GOR), bottom-hole temperature (T bh) are used as shown in Fig. 1 and Fig 2. Figures 1-a to 1-d present the systematic approach used to develop the direct proportionality of actual production rate and wellhead temperature for different gas-oil ratios and water-cut equals zero. Figures 2.a and 2.b show the variation of actual rate with wellhead temperature for different water-cuts. The same approach is applied for other considered well and reservoir parameters involved in the new correlation. Then, the least square method was applied using all data points together and the resultant equation was solved using Gaussian elimination method. A FORTRAN computer program was developed to calculate the constant K and coefficients a, b, c, d, e, and f. The final form of the developed correlation is given by: 2

4 IPTC M. GHAREEB and S. A. SHEDID 3 Q= x 4 TthT WC3.27bh1.2H A0.81 GOR (8) Where, T th is wellhead temperature ( o F), T bh is bottom hole temperature ( o F), A is tubing cross-sectional area (in 2 ), GOR is producing gas/oil ratio (scf/stb), and WC is producing watercut (%). In order to test the accuracy of developed correlation versus actual measured production rates, Figure 3 is developed and shows very good accuracy of predicted production rates with correlation factor (R 2 ) of The newly-developed correlation of equation (8) considered many well and reservoir parameters which were not included in the previous correlations, such as; water-cut, wellhead and bottom-hole temperatures, and producing depth. This is in addition to other parameters appeared in Gilbert and other correlations, such as; GOR and wellhead pressure. 3. Results and Discussion All measured actual wellhead production rates from 352 producing well are plotted versus predicted ones using the newly-developed correlation, equation 8, and graphically depicted in Figure 3. This Figure reveals accurate prediction results with an excellent correlating coefficient of The accurate prediction of wellhead production rate is mainly attributed to the consideration of more well and reservoir parameters; such as water-cut, wellhead and bottom-hole temperatures, producing depth, and tubing size. The importance of each single parameters involved in this new correlation is also investigated by performing a sensitivity analysis. The results of this analysis are presented in Figures 4 to 8. Figure 4 presents the predicted wellhead production versus wellhead temperature for different pay zone depths. It provides a general conclusion that the increase of wellhead temperature increases wellhead production. This can be attributed to the reduction of oil viscosity because of the increase of wellhead temperature. This means for oil fields in hot areas, the wellhead production will be higher than that ones in cold areas. This Figure, Figure 4, also reveals that pay zone of higher producing depth is expected to have higher wellhead production rate for the same wellhead surface temperature. Figure 5 shows the predicted wellhead production rate versus wellhead temperature for different gas-oil ratios (GORs). It confirms the same conclusion, drawn-above for the effect of pay zone depth, that the increase of surface temperature increases the wellhead production rate but for different GORs. This may be attributed to that the increase in GOR will cause lighter mixture of liquid and gas resulting in higher liquid production. It also indicates that the increase of GOR by 40 times (from 25 to 1,000 scf/stb) has a minor effect on the increase of wellhead production rate. Figure 6 depicts graphically the predicted wellhead production versus wellhead temperature for different tubing areas (or sizes). It reveals that the increase of tubing size increases the production rate. This is because of the increase of area open to flow, as proven by continuity equation (Q = velocity x area). It also proves that the increase of tubing area has a major effect of increment of wellhead production. This also confirms the conclusions attained before by Abdel-Majjed (1986). Figure 7 indicates the calculated wellhead production versus wellhead temperature for different bottom-hole temperatures. This is based actual field data used to develop the newlydeveloped correlation, equation 8. It may be explained that the increase of wellhead temperature decreases the oil viscosity and then increases the production rate. This is confirmed using field data from different oil wells and at different bottom-hole temperatures. Figure 8 presents the calculated wellhead production versus wellhead temperature for different water-cuts. It shows that the increase in water-cut decreases the oil wellhead production. It also proves that the influence of water-cut on oil production increment is minor for water-cuts below 50 %. In general, some conclusions can be drawn based upon the results using the newly-developed correlation sensitivity of the importance and deep impact of producing depth, tubing size and wellhead temperature on oil production and also minor influence of GOR, bottom temperature and water-cut. 4. Conclusions This study was undertaken to review current correlations for wellhead performance and to develop a new correlation considering new important parameters affecting wellhead production rate. The following conclusions are drawn: 1. Current bean performance correlations for naturally and artificially flowing wells are limited in application to the fields they were developed for and new correlating coefficients should be developed for other wells/fields. 2. Current correlations predicting wellhead production rate are very sensitive to choke size change and limited I application to naturally-flowing wells. 3

5 4 A New Correlation for Calculating Wellhead Production IPTC A new correlation was developed for quick and accurate prediction of wellhead production considering several well and formation parameters, ignored before in classical correlations. 4. Sensitivity analysis of factors affecting wellhead production rate indicated that producing depth, tubing size, and bottomhole temperatures have a real impact while gas-oil ratio, wellhead temperature, and water-cut have a minor effect on predicted values of wellhead production rate. Nomencltaure A Tubing cross-sectional area, in 2. C Proportionality constant (C = 10 for Gilbert, C =17 for Ros, and C = 1.03 for Poettmann-Beck) D Bean size, 1/64 inch F water-oil ratio G Gas-liquid ratio, scf/bbl GOR Gas-oil ratio, scf/bbl K Correlating constant H Well producing depth, 1000 ft Q Gross liquid rate, bb/d P Tubing head pressure, psig R Gas-liquid ratio, MSCF/bbl N Dimensionless Number P Pressure, psia S Bean size, 1/64 inch T Temperature, o F WC Water-cut, ratio to flow metering Applied Sci Res., 9, Sec. A, p. 374, Achong, I. B. Revised bean and performance formula for Lake Maracaibo wells published by the University of Zulia, Maracaibo, Venezula, Secen, J. A., Surface choke measurement equation improved by field testing analysis Oil and Gas Journal, pp , August Tantawy, M., Elayouty, E. D., and Elgibaly, A. Comparative investigation of bean performance correlation for flowing oil wells, Journal of Engineering and Applied Science, vol. 42, No. 4, pp , Poettmann, F. H., and Beck, R. L. New charts developed to predict gas-liquid flow through chokes World Oil, March 1963). 8. Omana, R., Houssiere, C. Jr., Brown, K. E., Brill, J. B., Thompson, R. E., Multiphase flow through chokes paper SPE 2682, Ashford, F. E. An evaluation of critical multiphase performance through wellhead chokes Journal of Petroleum Technology (JPT), August Abdul-Majeed, G. H. Correlations developed to predict two-phase flow through wellhead chokes paper SPE 15839, Al-Attar, H. H., and Abdul-Majeed, G. H. Revised bean performance formula for East Baghdad oil wells Journal of SPE Production Engineering, February 1988, pp Sub/Superscripts b bottom PB Poettmann-Beck h head g gas L Liquid viscosity Q flow rate o oil th tubinghead w well w water References 1. Economides, M. J., Hill, A. D., Ehlig-Economides., Petroleum Production Systems, Prentice Hall PTR, New Jersey, p. 229, Gilbert, W. E, Flowing and gas-lift well performance API Drilling and Production Practice, p. 143, Ros, N. C. J. An analysis of critical simultaneous gas/liquid flow through a restriction and its application 4

6 R ρ m =350.4γ o γ g G V R= sg = T Z G( R s ) (A-3) (A-3-a) (A-3-b) Vsl P Bo M 1 L V, and M (A-3-c) L = L = ρ L ρ g 1 R IPTC M. GHAREEB and S. A. SHEDID 5 Appendix A: List of correlations for wellhead performance Gilbert (1954) Omana (1969) + ρ L Pwh =10 GLRD Ql (A-1) N ql =0.263N Nρ 3.49 Pl3.19 λ0.657l N D1.8 (A-4) Achong (1961) 17 GLR 0.65 Q Nρ= g ρ ρ L (A-4-a) Pwh = D1.88 (A-2) Poettmann and Beck (1963) N Pl = x 2 P l λ l = 1 (A-4-c) 1 ρσ L L V R = V sg,where (A-4-b) 86,400 A Co PB x P Q = ρ m V L ( M L ) R x N D 1+ R sl ρ σ 1.25 ρ L L L =0.1574D 64 (A-4-d) N ql =1.84q l (A-4-e) σl 5

7 6 A New Correlation for Calculating Wellhead Production IPTC Omana correlation is restricted to critical flow, requiring that q 1/q 2 > 1.0 and P 1/P 2 < It is best suited for to low viscosity liquids and bean sizes of 14/64 or less. Ashford (1973) 1.53CD P 2 (Mm +151 )( Pγg sr W+ w) Q= x w) B Fo + wo (Mm +111 )( PγgG W+ M m = T Z G R( S ) (A-5) (A-5-a) W W =γ O +F WO γ W F WO =water oil ratio/ (A-5-b) (A-5-c) (a) Q vs T th for WC = zero, GOR = zero up to 100 scf/stb. Q = T R2 = up to 200 scf/stb. temperature, of Well-head (b) Q vs T th for WC = zero, GOR = 6

8 (C) Q vs T th for WC = zero, GOR = 200 up to 300 scf/stb. (d) Q vs T th for WC = zero, GOR = zero up to 400 scf/stb. GOR. Fig. 1. Variation of actual Q with T th for different 7

9 (a) Q vs T th for WC = 20 to 50 % and Well- head temperature, of GOR = 0 to 100 scf/stb. (b) Q vs T th for WC = 50 to 90 % and GOR = 0 to 100 scf/stb. Fig. 2. Variation of actual Q with T th for different values of WC and GOR.

10 Q actual, BFPD Fig. 3. Calculated Q versus actual measured Q GOR = 100 scf/bbl A = sq in WC = 1 % Tbh = 190 F depth =4000 ft depth =6000 ft depth =8000 ft Wellhead temperature. o F Fig. 4. Effect of producing depth on flow rate using new correlation.

11 10 A New Correlation for Calculating Wellhead Production IPTC Wellhead temperature, o F Fig. 5. Effect of GOR on production using new correlation. 8 IPTC M. GHAREEB and S. A. SHEDID Depth = 5 (1000) ft GOR = 100 scf/bbl Tbh = 190 F WC = 1 % tubing, 3 1/2" tubing, 2 7/8" tubing, 2 3/8" Wellhead Temperature, o F 180

12 Fig. 6. Effect of tubing size on production using new correlation Depth = 5 (1000) ft GOR = 100 scf/bbl WC = 1 % Tb=170 of Tb=185 of Tb=200 of Wellhead temperature, o F Fig. 7. Effect of wellhead temperature on production using new correlation. 9

13 12 A New Correlation for Calculating Wellhead Production IPTC Wellhead Temperature, o F Fig. 8. Effect of water-cut on production using new correlation. 10