Tapered-Bean Steam Chokes Revisited

Transcription

1 Tapered-Bean Steam Chokes Revisited Suzanne Castrup, Integrated Sciences Group; Faisal Latif, Vintage Production California LLC; and Ali Al Kalbani, Occidental Petroleum Corporation Summary Controlling and monitoring flow rates at continuous- and cyclicsteam-injection wells are important elements of reservoir-heat management. For nearly 30 years, critical flow chokes have proven to be the most reliable and cost-effective means of controlling steam injection into heavy-oil reservoirs. Flow-control efficiency has been further improved with tapered-bore bean inserts to achieve critical flow, with only 10 to 15% pressure loss across the choke. For the past 10 years, the standard steam-choke assembly has consisted of a 1-in.-outer-diameter (OD) and 6-in.-long bean with a 6 tapered bore inserted inside a 2-in.-OD cage nipple or housing. Larger-diameter cage nipples and bean inserts have been required for steam-injection rates exceeding 500 B/D. More recently, a costcutting practice has been employed using shorter tapered beans inserted in standard choke assemblies. This paper presents the results of field tests conducted to evaluate the effectiveness of shorter tapered-bean length for controlling steam-injection rates. Transition from subcritical to critical flow and overall pressure loss for different tapered-bean lengths are presented. A modified Thornhill-Craver flow-rate equation is provided for critical- and subcritical-flow regions. and measured rates are compared, and their relative uncertainties are assessed. Introduction A Thornhill-Craver-style choke with removable tapered-bore bean insert, as shown in Fig. 1, is the most commonly used device for controlling flow rate to steamflood injectors and cyclic-steam wells. Under critical-flow conditions, steam-flow rate depends only on upstream pressure, steam quality, and the diameter of the bean throat, expressed in 64ths of an inch. While tapered-bore chokes follow the same critical-flow principles as straight-bore chokes, steam pressure exiting a tapered-bore bean can be as high as 80 to 85% of the upstream pressure. The pressure-recovery process that occurs in the tapered-bore bean is based on the flow of compressible fluids through converging/diverging nozzles. The diverging or tapered portion of the bean acts as a diffuser that decelerates the fluid and increases the pressure. The diffuser recovers some of the kinetic energy of the fluid as it decelerates and uses it to recompress the expanded fluid to a higher pressure. As discussed by Shapiro (1953), a 6 tapered-bore angle has been shown to provide maximum pressure recovery and, thus, the highest possible exit pressure. This angle also acts to minimize flow separation from the tapered wall, further reducing pressure loss. Pressure curves for subsonic, sonic, and supersonic flow through a tapered-bore bean are shown in Fig. 2. For dry steam (i.e., 100% quality), the critical pressure P c is equal to 55% of the inlet or upstream pressure P 1. Griston (1995) has shown that P c = 0.55P 1 also applies to wet steam. Under subsonic-flow conditions, the exit or downstream pressure P 2 is greater than P c, and the tapered-bore bean acts like a conventional Venturi tube. As P 2 is reduced, the pressure in the bean throat reaches P c, the flow velocity reaches the speed of sound, and a shock wave forms. of the shock wave, pressure recovery occurs as the velocity decreases along the tapered portion of the bean. Until recently, it has been assumed that a 6-in. tapered-bean length is required to achieve maximum pressure recovery. However, Copyright 2012 Society of Petroleum Engineers This paper (SPE ) was accepted for presentation at the SPE Western North American Regional Meeting, Anchorage, 7 11 May 2011, and revised for publication. Original manuscript received for review 5 July Paper peer approved 31 August bean-throat diameters greater than 28 / 64 in. exceed the design limits for this bean length. In such instances, more-expensive choke assemblies must be used to accommodate larger-diameter bean inserts. It would be beneficial to use a shorter tapered-bean length that could accommodate larger throat diameters, while maintaining critical flow at a high downstream pressure. The results of field tests to evaluate the effect of the taperedbean length on pressure recovery are presented. The ratio of downstream to upstream pressure at which transition from critical to subcritical flow occurs is shown for the different tapered-bean lengths. Steam rates calculated using a Thornhill-Craver criticalflow equation are compared with measured rates. Uncertainty analysis results are presented to show the relative error contributions of bean-throat diameter, pressure, quality, and other steam properties to the overall accuracy of the calculated rates. Field Tests Field tests were conducted to evaluate the performance of 3-in.- and 4-in.-long tapered beans inserted inside conventional and tapered-cage nipples. The tapered-cage nipple is machined to extend the 6 taper downstream of the shortened bean, as shown in Fig. 3. The two main objectives of the tests were to 1. Determine the maximum pressure ratio, P 2 /P 1, at which transition from critical to subcritical flow occurs for each choke configuration. 2. Evaluate the applicability of the Thornhill-Craver equation for computing steam rates. Test Setup and Procedure. Flow-rate tests using a tapered bean and standard-cage nipple were conducted at a cyclic-steam well completed with slotted liner. Flow-rate tests using tapered choke bodies and tapered beans were conducted at a steamflood injector completed with limited-entry perforations. Steam qualities and rates exiting each choke were measured with a separator vessel, and upstream and downstream pressures were measured with pressure transmitters. A gate valve downstream of each choke was used to control the downstream pressure. After each choke configuration was installed, the steam rate, quality, and pressures were allowed to stabilize, and data were collected for 20 to 30 minutes. Several downstream pressure adjustments were then made, first increasing in value and then decreasing in value. The steam conditions were allowed to stabilize after each adjustment, and data were collected for 20 to 30 minutes. Transition From Critical to Subcritical Flow. By definition, critical flow occurs when flow rate remains constant despite changes in downstream pressure. The test data summarized in Tables 1 through 3 can be used to determine when critical flow is achieved through each tapered-bore bean. Thornhill-Craver * is the most commonly used equation for calculating steam rate through a static choke at critical-flow conditions. Steam-flow rate, in B/D cold-water equivalent (cwe), is calculated from Eq. 1, proposed by Griston (1995): 2 W = d ( L / d ) P (1) c t t t The empirical coefficient 57.3 incorporates the unit conversion constant and the flow coefficient. The geometry factor ( L/d) *The basic gas-flow-rate equation for Thornhill-Craver chokes was first published by Cook and Dotterweich (1946). 1 1 May 2012 SPE Production & Operations 205

2 Cage Nipple P 1 P t P 2 Bull Plug Tapered Bean Tee Junction Hammer Union Flow Out P P Throat Subsonic Flow P c Sonic Flow P 1 Supersonic Flow P t > P c & P 2 > P t P t = P c & P 2 > P t Shock P t < P c & P 2 < P t Flow In Fig. 1 Tapered bean inserted inside a standard Thornhill- Craver-style choke assembly L Distance From Bean Inlet Fig. 2 Pressure curves for subsonic, sonic, and supersonic steam flow through a tapered-bore bean, reproduced courtesy of Integrated Sciences Group (Castrup 2011). When the pressure in the bean throat reaches P t = P c = 0.55P 1, the fluid reaches sonic velocity and the flow is choked, and a shock wave forms within the throat. of the shock wave, the velocity is subsonic, and diffusion or pressure rise occurs along the tapered portion of the bean. Tapered Bean incorporates the bean throat length L t and diameter d t. The density for two-phase steam is calculated with the vapor-phase and liquid-phase specific volumes ν v1 and ν l1, and the vapor mass fraction x 1 at upstream pressure P 1 : ( ) 1 Tapered Section of Cage Nipple Fig. 3 Tapered bean inserted inside a cage nipple that has been machined to extend the 6 taper downstream of the bean. 1 = x1 v1+ 1 x1 l (2) The steam quality upstream of the choke x 1 is estimated from the measured downstream quality x 2, assuming adiabatic expansion as pressure drops from P 1 to P 2 across the choke. The vapor and liquid enthalpies h v and h l (at upstream and downstream pressures, respectively) are obtained from published steam tables or from empirical equations. * x2( hv2 hl2)+ hl2 hl1 x1 = (3) h h v1 l1 and computed values for each choke configuration are listed in Tables 1 through 3. Plots of flow-rate ratio vs. pressure ratio for the different choke configurations are shown in Fig. 4. The transition from critical to subcritical flow for the 3-in. tapered bean occurs at a pressure ratio of 0.80, while the transition occurs at a pressure ratio of 0.85 for the 4-in. tapered bean. The results for the 4-in. tapered bean are very similar to the results reported by Griston and Abate (1996) *See, for example, steam-property equations reported by Al-Najjar and Abdul-Ahad (1989). TABLE 1 TEST DATA FOR 3-IN. TAPERED BEAN AND TAPERED-CAGE NIPPLE, BEAN-THROAT DIAMETER = 34 / 64 IN. Test P 1 (psia) P 2 (psia) Pressure P 2 / P 1 Quality, x 2 (%) Quality, x 1 (%) W m Critical Flow W c Flow Rate W m/w c May 2012 SPE Production & Operations

3 TABLE 2 TEST DATA FOR 4-IN. TAPERED BEAN AND TAPERED-CAGE NIPPLE, BEAN-THROAT DIAMETER = 34 / 64 IN. Test P 1 (psia) P 2 (psia) Pressure P 2 / P 1 Quality, x 2 (%) Quality, x 1 (%) W m Critical Flow W c Flow Rate W m/w c for a 6-in. tapered bean. The tapered-cage nipple does not appear to enhance the pressure-recovery process. However, adding the tapered section may prevent flow impingement and erosion of the cage nipple as steam exits the shortened bean. The 3- and 4-in.-long tapered beans can accomodate throat diameters up to 48 / 64 and 44 / 64 in., respectively. The tapered-cage nipple and 3-in. tapered-bean insert were stock items purchased from a local manufacturer. The tapered-cage nipple and 4-in. taperedbean insert were special-ordered items purchased from the same local manufacturer. The incremental price for the special-order choke and bean was negligible. The incremental price between the standard and tapered choke bodies was also negligible. vs. Rates. Eq. 1 can be generalized to calculate steam-flow rate under critical- or subcritical-flow conditions. This generalized form is given in Eq. 4. For critical flow, Z =1, and for subcritical flow, Z is computed from a polynomial equation that best fits the flow-rate-ratio vs. pressure-ratio curves shown in Fig W = d Z ( L / d ) P (4) t t t 1 1 Comparison of calculated and measured steam rates under critical- and subcritical-flow conditions is shown in Figs. 5 and 6, respectively. The solid diagonal line denotes an equivalency of the calculated and measured rates. The dashed lines denote ±10% bounding limits for the equivalency line. Data for a 6-in. tapered bean published by Griston and Abate (1996) and for a 6-in. straight bean published by Griston (1995) are included to illustrate the validity of Eq. 4 for fixed steam chokes with a variety of bean inserts. Uncertainty Analysis Uncertainty is inherent in any measurement or calculation process. For example, errors in steam-pressure and quality measurements will directly affect the accuracy of calculated flow rates. In addition, reliable rate calculations depend upon the accuracy of other steam properties, such as density and enthalpy. Therefore, it is important to quantify how each flow parameter affects the overall uncertainty of the calculated rates. An uncertainty analysis was conducted to estimate the relative error contributions of steam pressure, steam quality, bean-throat diameter, bean-throat length, flow coefficient, and calculated steam properties. A first-order Taylor-series expansion of Eq. 4 was used TABLE 3 TEST DATA FOR 4-IN. TAPERED BEAN AND STANDARD-CAGE NIPPLE, BEAN-THROAT DIAMETER = 34 / 64 IN. Test P 1 (psia) P 2 (psia) Pressure P 2 / P 1 Quality, x 2 (%) Quality, x 1 (%) W m Critical Flow W c Flow Rate W m/w c May 2012 SPE Production & Operations 207

4 Flow Rate W m /W c in. tapered bean, tapered choke body 4-in. tapered bean, standard choke body 4-in. tapered-bore bean, tapered choke body Pressure P 2 /P 1 Fig. 4 Flow-rate-ratio vs. pressure-ratio curve showing the transition from critical to subcritical flow. to approximate the propagation of the different error sources. * A commercially available software application was used to facilitate the uncertainty-analysis calculations. Heuristic estimates of error-containment limits, containment probabilities, and error distributions used in the analysis are listed in Table 4. Error limits are based on manufacturer-specified instrument accuracy and on standard deviations of repeat measurements. Error limits for computed steam properties, such as enthalpy and specific volume, are based on deviations from tabulated data. The nominal steam rate was computed to be 590 B/D cwe, with an overall uncertainty of 15 B/D cwe. This translates to an overall uncertainty of approximately 2.5% of the calculated rate. *A discussion of first-order Taylor series expansion and error propagation for multivariate measurements can be found in ANSI/NCSL Z , U.S. Guide to the Expression of Uncertainty in Measurement (1997). The corresponding error-containment limits are ±29.6 B/D cwe or ±5% of the calculated rate with containment probability. A Pareto chart of the relative error contributions to overall uncertainty in the calculated rate is shown in Fig. 7. The bean-throatdiameter error contributes nearly 35% of the overall uncertainty. Errors in the subcritical-flow correction factor and flow coefficient contribute 18 and 17%, respectively. pressure error contributes approximately 13% of the overall uncertainty. Conclusions Field-test results show that pressure recovery can be achieved through shorter tapered-bean lengths of 3 to 4 in. Maximum pressure recovery is achieved with a 4-in. long tapered bean, with transition from critical to subcritical flow occurring at a pressure ratio P 2 /P 1 of Pressure recovery for the 3-in. tapered bean is diminished, with transition from critical to subcritical flow occur- Critical Flow B/D cwe in. tapered bean 4-in. tapered bean 6-in. tapered bean (Griston & Abate) 6-in. straight bean (Griston) Critical Flow B/D cwe Fig. 5 vs. measured flow rate for critical-flow conditions. The solid diagonal line denotes an equivalency of the calculated and measured rates, and the dashed lines denote ±10% bounding limits for the equivalency line. 208 May 2012 SPE Production & Operations

5 Subcritical Flow B/D cwe in. tapered bean 4-in. tapered bean 6-in. tapered bean (Griston and Abate) 6-in. straight bean (Griston) Subcritical Flow B/D cwe Fig. 6 vs. measured flow rate for subcritical-flow conditions. The solid diagonal line denotes an equivalency of the calculated and measured rates, and the dashed lines denote ±10% bounding limits for the equivalency line. ring at a pressure ratio of 0.8. There does not appear to be any added pressure-recovery benefit by using a tapered-cage nipple. However, the tapered section may prevent flow impingement and erosion of the cage nipple as steam exits the shorter bean. The 6-in. tapered-bean length can accommodate throat diameters up to 28 / 64 in., whereas the 4- and 3-in. tapered-bean lengths can accomodate throat diameters up to 44 / 64 and 48 / 64 in., respectively. Consequently, the shorter tapered-bean lengths provide a cost-effective and efficient means of controlling the wellhead steam rates and pressures required for a variety of applications, including fracturing of diatomite reservoirs and profile control using limited-entry perforations. The Thornhill-Craver equation can be used to calculate steamflow rate through tapered beans with shorter lengths. In general, the accuracy of the calculated rates depends upon the accuracy of the bean-throat diameter, subcritical-flow correction factor, and upstream steam pressure and quality. Test data show that predicted steam rates are within ±10% of measured rates when accurate pressures and qualities are used. The Thornhill-Craver equation can also be used to compute the bean-throat diameter needed to achieve a desired steam rate for a given upstream steam pressure and quality. Nomenclature d = diameter, in. h = enthalpy, Btu/lbm L = length, in. P = steam pressure, psia v = specific volume, ft 3 /lbm Z = subcritical-flow correction factor = density, lbm/ft 3 Subscripts 1 = upstream of choke 2 = downstream of choke c = critical flow TABLE 4 ERROR SOURCES FOR STEAM-FLOW-RATE CALCULATION Variable Nominal Value ± Error Containment Limits Error Containment Probability (%) Error Distribution Flow coefficient Subcritical flow-correction factor, Z pressure, P psia psia pressure, P psia 18.9 psia quality, x 2 70% 5% 99% Vapor specific volume at P 1, v v ft 3 /lb ft 3 /lb 99% Liquid specific volume at P 1, v l ft 3 /lb ft 3 /lb 99% Vapor enthalpy at P 1, h v Btu/lb 12.0 Btu/lb 99% Liquid enthalpy at P 1, h l Btu/lb 4.9 Btu/lb 99% Vapor enthalpy at P 2, h v Btu/lb 12.0 Btu/lb 99% Liquid enthalpy at P 2, h l Btu/lb 4.8 Btu/lb 99% Bean-throat diameter, d 0.53 in in. Bean-throat length, L 0.25 in in. May 2012 SPE Production & Operations 209

6 Bean-Throat Diameter, d t Subcritical Flow Correction Factor, Z Flow Coefficient P 1 Vapor Enthalpy at P 1, h v1 Vapor Enthalpy at P 2, h v2 Vapor Specific Volume at P 1, v v1 Quality, x 2 Bean-Throat Length, L t Liquid Specific Volume at P 2, v v1 Liquid Enthalpy at P 1, h l Error Contribution to Overall Uncertainty, % Fig. 7 Pareto chart showing the relative error contributions to overall uncertainty in the calculated flow rate. l = liquid phase t = bean throat v = vapor phase Acknowledgments The authors would like to thank Brad Tuck and Richard Yoch of Vintage Production California LLC and Richard Akery and Dan Hutchinson of Steam Testing Solutions for their assistance with the field tests. We would also like to thank Integrated Sciences Group and Vintage Production California LLC for allowing us to publish this work. References Al-Najjar, H.S.H. and Abdul-Ahad, P.G Equation Calculates Properties of Saturated Steam. Oil Gas J. 87 (September 4, 1989): ANSI-NCSL Z , U.S. Guide to the Expression of Uncertainty in Measurement Charlotte, North Carolina: National Conference of Standards Laboratories. Castrup, S Steam Distribution and Metering, fourth edition (short course book). Bakersfield, California: Integrated Sciences Group. Cook, H.L. and Dotterweich, F.H Report on the Calibration of Positive Flow Beans Manufactured by Thornhill-Craver Company, Inc., Houston, Texas, Aug. 10, Kingsville, Texas: Dept. of Engineering, Texas College of Arts and Industries. Griston, S Evaluation of Steam Flow Rate Equations for Wellhead Chokes. Oral presentation SPE given at the SPE Western Regional Meeting, Bakersfield, California, USA, 8 10 March. Griston, S. and Abate, T Field Test of Tapered-Bore Chokes for Steam Flow Control. Paper SPE presented at the SPE Western Regional Meeting, Anchorage, May. Shapiro, A.H The Dynamics and Thermodynamics of Compressible Fluid Flow, Vol. 1. New York: John Wiley and Sons. Suzanne Castrup is Vice President of Integrated Sciences Group. She has over 30 years of experience in thermally enhanced oil recovery. Prior to joining Integrated Sciences Group, she was Technical Advisor for Thermal EOR in Chevron s Western Basins Group. She was also a Production/Reservoir Engineer, managing both cyclic steam stimulation and steamflood projects in several heavy-oil properties in the Cymric and Midway Sunset fields. She has published numerous technical papers and holds several patents relating to heavy oil recovery. She is a recipient of the 2006 SPE Western Region Award and the 2007 SPE International Facilities and Construction Award for distinguished contributions to petroleum engineering. Faisal Latif is a Production/Operations Engineer with Vintage Production California LLC (VPC), working with the Thermal Reservoir Management Team. Prior to joining VPC in March 2009, he worked as a Staff Operations Engineer with Occidental of Elk Hills. Latif also worked at Schlumberger as a Senior Field Engineer, responsible for real-time geophysical data acquisition for both openhole and cased-hole operations. He holds a BS degree in electrical engineering from the University of Kansas. Ali Al Kalbani is a Production Engineer with Occidental of Oman LLC, working in the Thermal Reservoir Management Team. He previously worked as Production/Operation Engineer with Vintage Production California LLC in the Thermal Reservoir Management Team between August of 2008 and December of 2010 as a cross-posting assignment. Prior to joining VPC, he worked as an Associate Engineer with Occidental of Oman LLC. Al Kalbani holds a BS degree in petroleum engineering from Sultan Qaboos University. 210 May 2012 SPE Production & Operations