Explicit Method Predicts Temperature and Pressure Profiles of Gas-Condensate Transmission Pipelines

PSIG 03B2 Explicit Method Predicts Temperature and Pressure Profiles of Gas-Condensate Transmission Pipelines Saeid Mokhatab, Chemical Engineering Department, Faculty of Engineering, The University of Tehran, Tehran, Iran

Copyright 2003, Pipeline Simulation Interest Group This paper was prepared for presentation at the PSIG Annual Meeting held in Bern, Switzerland, 15 October – 17 October 2003. This paper was selected for presentation by the PSIG Board of Directors following review of information contained in an abstract submitted by the author(s). The material, as presented, does not necessarily reflect any position of the Pipeline Simulation Interest Group, its officers, or members. Papers presented at PSIG meetings are subject to publication review by Editorial Committees of the Pipeline Simulation Interest Group. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of PSIG 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, Pipeline Simulation Interest Group, P.O. Box 22625, Houston, TX 77227, U.S.A., fax 01-713-586-5955.

ABSTRACT Predicting flow temperature and pressure changes has become increasingly important for use in both the design and operation stages of multiphase pipelines. This study has presented simple analytical equations for predicting these parameters at any point along the two-phase, gas/gas-condensate transmission lines, considering basic laws of momentum and energy conservation. The Masjed Soleiman to Mahshahr gas/condensate pipeline, located in the south west of Iran, used as an example to show the impact of the present explicit method on proper prediction of flow temperature and pressure profiles in the pipelines carrying gas and condensate.

been reported for the use of explicit methods for this purpose2. The focus of this paper is on gas/condensate systems and consequently describing a simple, easy-to-use analytical method to predict flow parameters of gas/condensate transmission lines.

Analysis The application of the energy balance for steady state and onedimensional flow in two-phase pipelines obeys the first law of thermodynamics for a compressible fluid as follows3:

dh m dq  dV   dz  − + Vm  m  + g  = 0 dx dx  dx   dx 

1

The enthalpy term includes the change in temperature resulting from the expansion of the gas as it experiences a pressure drop along the pipeline. This effect is known as the Joule-Thomson effect4. In other word, the two-phase flow enthalpy change can be determined as follows:  dT  dh m  dP   = Cp m   − η   dx  dx  m   dx  m

2

Where:

Introduction To transport natural gas, pipelines must often span great distances across undulating terrain in varying ambient temperature. Liquid condensation in pipelines, however, commonly occurs because of the multicomponent nature of the transmitted natural gas and its associated phase behavior, as well as the inevitable temperature and pressure variations that occur along the pipeline. The presence of condensates creates several operational problems such as hydrate, wax deposition, corrosion, etc. Such problems can be avoided if the flow pressure and temperature profiles are determined. In fact, in order to better size of the pipelines and downstream processing facilities, these parameters must be predicted along the pipeline1. Many attempts have been made to predict flow conditions in two-phase pipelines. However, few efforts have

C p m = C p L H L + C p G (1 − H L )

3

The values of Cp and η are determined from the modified Peng and Robinson5 equation of state. However, some correlations for calculating fluid properties are adopted. The heat flow due to conduction from the surrounding to the pipeline per unit mass of two-phase flow is: dq/dx = [2πUR ( Ts – Ta) ] / mm

4

Where Ta is an adjusted mixture temperature and can be determined as follows6:

2

SAEID MOKHATAB

;α ≤ 0.95 Tm  Ta =  µ  2 Tm + 0.5 G VG ;α > 0.95   KG 

5

and: α=

Km ρmC p m

6

The U-Value is the combined value of the heat transfer coefficients from the fluid of the individual pipe to its wall, through the wall, and from the wall to the carrier fluid. A minimum heat transfer coefficient for fluid-wall heat transfer is given by Brill and Beggs3. The final required relationship which relates the velocity to the pressure, is the momentum equation as follows7:  dV   Vm Vsg Vm  m  =   dx   p

 dP     dx  m 

7

Therefore, flowing gas-condensate temperature can be determined by substitution of Equations 2 to 7 in Equation 1 as follows:  dT   dP    + A 0 (Ta − Ts ) = − A1  − A 2  dx  m  dx  m

8

Where: A0 = (2πUR) / (Cpm × mm)

 Vm Vsg  − η A1 =   p × cp  m   A2 =

g  dz    c p m  dx 

that they are limited by the range of data on which they were based and, generally, could not be used for all two-phase flow systems. This restriction on their application has recently led researchers to develop mechanistic models that are based more on physical principles than on experimental data. Therefore, in this study after consideration different types of flow regimes in two-phase, gas/condensate transmission pipelines10,11, a fundamental analytical model, developed from the basic laws of momentum conservation is used for determination of pressure gradient in such pipelines. Notice that the amount of liquid in the system is assumed to be small, and the gas flow rate gives a sufficiently high Reynolds number that the fluid flow regime can be assumed to be annular-mist flow or stratified flow regime12,13.

Modeling Stratified Flow Calculation of pressure gradient in this flow regime is performed by writing a momentum balance for each phase as follows10,11:  dP  − τLSL + τiSi − ρLgA L sin θ − A L   = 0  dx  m

12

 dP  − τGSG − τiSi − ρG gA G sin θ − A G   = 0  dx  m

13

Where the required parameters in the above equations, can be determined by Taitel and Dukler10,11 method. The amount of liquid holdup in this flow regime is also calculated as follows:

HL = 1 −

9 10

11

The Equation 8 may be solved numerically if values for U, c p and η are available and if a relationship between m

pressure gradient and distance is known. In other word, a key element of the temperature profile determination is the correct prediction of the two-phase flow pressure gradient. Since most of gas-condensate transmission pipelines in field applications have large diameter and operate in high pressure conditions, they could not be modeled with the present two-phase flow correlations8,9. These correlations often prove inadequate in

PSIG 03B2

2  1  −1 h L   h   h  cos  2 − 1 −  2 L − 1 1 −  2 L − 1  π   D    D   D  

14

In the above equation, the amount of liquid level, hL , can be determined by simultaneous solving of Equations 12 and 13.14

Modeling Annular Flow In this flow regime, calculation of pressure gradient is performed similar to stratified flow. In other word, Equations 12 and 13 are equally valid for annular flow regime with the exception that the gas does not wet the pipewall (τG = 0) and the film thickness is used instead of liquid level15,16 .

Discussion of Results The present method was tested to perform a prediction on the Masjed Soliman to Mahshahr gas/condensate transmission pipeline (168 km long and 48.26cm in diameter) that traverses a hilly terrain with 14 elevation changes. The gas-condensate composition is given in Table 1. Also Table 2 reports the

PSIG 03B2

Explicit Method Predicts Temperature and Pressure Profiles of Gas-Condensate Transmission Pipelines

pipeline data needed for all the runs17 . Figures 1 and 2 show respectively the results of the temperature and pressure profiles of Masjed Soleiman to Mahshahr two-phase pipeline calculated by two different methods. As shown in these figures, results of the present explicit method show good agreement with the obtained results of Shariati et al.17 implicit method. Also, Figure 1 shows that the flow temperature drops significantly, as much as 25°C, below the temperature of the surroundings, due to Joule-Thomson cooling.

m:gas-liquid mixture p: constant pressure s: surrounding sg: superficial gas

References 1. Cawkwell,

Conclusions The main objective of the present study has been the development of a relatively simple explicit method for predicting flow temperature and pressure profiles in twophase, gas/gas-condensate transmission pipelines. Results demonstrate the ability of the method to predict reasonably accurate pressure gradient and temperature gradient profiles under operating conditions, where the author feels that his method can serve as a simple predictive tool for use in both the design and operation stages in two-phase pipelines.

2.

Nomenclature

5.

µ : viscosity α : thermal diffusion coefficient ρ: density θ: inclination angle η : Joule-Thomson coefficient τ: shear stress m: mass flow rate A: area of cross-section occupied by each phase C: specific heat g: gravitational constant h: enthalpy, liquid level in pipe H: holdup K: thermal conductivity coefficient P: pressure q: heat flow per unit mass flow R: pipe radius s: occupied perimeter by each phase T: temperature U: overall heat transfer coefficient V: velocity x: distance z: height above datum

Subscripts a: adjusted G: gas h: constant enthalpy i: interface L: liquid

3

3. 4.

6. 7.

8. 9. 10.

11. 12. 13.

M.G., and Charles, M.E., “Pressure, Temperature Predicted for Two-Phase Pipelines,” Oil & Gas J., 101- 107 (May 27, 1985). Mokhatab, S., and Vatani, A., “A New Algorithm Predicts Pressure and Temperature Profiles of Gas/GasCondensate Transmission Pipelines", paper accepted for presentation at Rio Pipeline Conference & Exhibition, Rio de Janeiro, Brazil (22-24 Oct., 2003). Brill, J.P., and Beggs, H.D., “Two-Phase Flow in Pipes,” 6th Edition, Tulsa University Press, Tulsa, OK (1991). Coulter, D.M., and Bardon, M.F., “Revised Equation Improves Flowing Gas Temperature Prediction,” Oil & Gas Journal, 107-108 (Feb. 1979). Peng, D.Y., and Robinson, D.B., “A New Two-Constant Equation of State,” Ind & Eng. Chem., 15, 1, 59-64 (1976). OLGA2000 User’s Manual, “Transient Multiphase Simulator”, SCANDPOWER Company, Norway (1997). Vatani, A., and Mokhatab, S., “Hydraulic Design Principles of Two-Phase Flow Pipelines”, Jahad Daneshgahi Institute Press, Faculty of Engineering, The University of Tehran, Tehran, Iran (2002). Mokhatab, S., “Correlation Predicts Pressure Drop in Gas-Condensate Pipelines,” Oil & Gas J., 100, 4, 66-68 (Jan.28, 2002). Mokhatab, S., “New Correlation Predicts Liquid Holdup in Gas-Condensate Pipelines”, Oil & Gas J., 100, 27, 6869 (July 8, 2002). Taitel, Y., and Dukler, A.E., “A Model for Prediction of Flow Regime Transition in Horizontal and Near Horizontal Gas-Liquid Flow”, AICHE. J, 22, 47-55, (1976). Taitel, Y., and Dukler, A.E., “A Theoretical Approach to the Lockhart & Martinelli Correlation For Stratified Flow”, Int. J. Multiphase Flow, 2, 591-595, (1976). Mokhatab, S., “Model Aids Design of Three-Phase, GasCondensate Transmission Lines”, Oil & Gas J., 100,10, 64-68 (Mar. 11, 2002). Mokhatab, S., “Transient Three-Phase Flow Under Hydrodynamic Pigging Operation in Gas-Condensate Transmission Pipelines”, paper accepted for presentation at Cairo International Gas Technology Conference, Cairo, Egypt (March 3-5, 2003).

4

SAEID MOKHATAB

14. Landman, M.J., “Non-Unique Holdup and Pressure Drop in Two-Phase Stratified Inclined Pipe Flow”, Int. J. Multiphase Flow, 17, 377-394 (1991). 15. Taitel, Y., Shoham, O., and Brill, J.P., “Simplified Transient Solutions and Simulation of Two-Phase Flow in Pipelines,” Chem. Eng. Science J., 44, 6, 1353-1359, (1989). 16. Taitel, Y., and Barnea, D., “Simplified Transient Simulation of Two-Phase Flow Using Quasi-Equilibrium Momentum Balances”, Int. J. Multiphase Flow, 23, 3,

PSIG 03B2

493-501 (1997).

17. Shariati, A., Moshfeghain, M., and Maddox, R.N., “Effect of C6+ Characterization on Two-Phase Flow Pipelines,” Int. Journal of Modeling & Simulation, 19, 4, 352-356 (1999).

Table 1 Composition of the transported gas-condensate Component H2S N2 CO2 C1 C2 C3 iC4 nC4 iC5 nC5 C6+

Mole percent 25.60 0.20 9.90 62.90 0.70 0.20 0.06 0.09 0.04 0.05 0.26

Table 2 Other pipeline data Inlet pressure, Bar Inlet temperature, °C Surrounding temperature,°C Flow rate, MMSCM/D Overall heat-transfer coefficient, W/m2.°C

80.29 35 25 5.1 1.41

PSIG 03B2

Explicit Method Predicts Temperature and Pressure Profiles of Gas-Condensate Transmission Pipelines

5

Figure 1 Temperature profiles for Masjed Soleiman to Mahshahr two-phase pipeline Pipeline Temperature profile 40 35

Temperature,C

30 25

Present Method

20

Shariati et al.Method

15 10 5 0 0

20

40

60

80

100

120

140

160

180

Distance,Km

Figure 2 Pressure profiles for Masjed Soleiman to Mahshahr two-phase Pipeline Pipeline pressure Profile

90 80

Shariati et al.Method

Pressure,bar

70 60

Present Method

50 40 30 20 10 0 0

20

40

60

80

100

120

140

160

180

Distance,Km

____________________________________________________________________________________________________________

Author Biography Saeid Mokhatab, MSc., is a senior consultant and researcher in the gas industry with special expertise in the design and engineering of

multiphase flow transportation pipelines. He has participated in charge of various international gas-engineering projects and has also published 20 academic and industrial oriented papers/books. He is currently a Technical Editor of SPE Production & Facilities Journal, an Editorial Consultant to PetroMin & Hydrocarbon Asia Magazines, Referee in several scientific committees, and an active member in a number of professional organizations.