CONDENSATE AT "T'S"-1 CALCULATIONS PREDICT CONDENSATE MOVEMENT AT 'T' JUNCTIONS

Jan. 21, 1991
Jan M. H. Fortuin, Peter J. Hamersma, Jaap Hart University of Amsterdam Amsterdam Harry J. Smit, W. P. Baan NV Nederlandse Gasunie Groningen, The Netherlands A model for the prediction of the route preference of condensate at "T" junctions in gas-transportation pipelines has been developed. The double-stream model can be applied to sharp-edged and radiused, regular, and reduced T and Y junctions.
Jan M. H. Fortuin, Peter J. Hamersma, Jaap Hart
University of Amsterdam
Amsterdam
Harry J. Smit, W. P. Baan
NV Nederlandse Gasunie
Groningen, The Netherlands

A model for the prediction of the route preference of condensate at "T" junctions in gas-transportation pipelines has been developed.

The double-stream model can be applied to sharp-edged and radiused, regular, and reduced T and Y junctions.

The model permits an understanding of condensate behavior at a junction. From this knowledge, precautions can be taken to install gas-liquid separators at those pipeline sections where condensate accumulates.

Such accumulations may cause problems in gas-fired appliances or may damage delicate instruments in gas control and compressor stations.

This first part of a two-part series on the model describes its development.

Verification of the model, subject of the concluding article, was derived from experimental results from literature and from experiments carried out at the University of Amsterdam with air-water flow in a horizontal tube with a horizontal regular T (ID: 0.051/0.051 m; 2/2 in.).

Moreover, a comparison has been made between results obtained with the double-stream model and those from high-pressure experiments carried out at the research department of NV Nederlandse Gasunie with natural-gas condensate in a horizontal reduced T (ID: 0.075/0.050 m; 3/2 in.).

The agreement between measured and calculated results was good.

PRACTICAL SIGNIFICANCE

As natural gas is transported through pipelines, small amounts of condensate may be formed as a result of, for example, retrograde condensation of the heavier hydrocarbons present in the gas phase, especially during pressure reduction without preheating.

If the occurring two-phase gas-condensate flow arrives at a T junction in the pipeline, an interesting phenomenon is observed: If a certain fraction of the gas phase is being extracted into the side-arm of the junction, it is uncommon for the liquid condensate to be carried along into the side-arm by the same fraction as the gas.

This so-called unequal phase splitting phenomenon at junctions was reported at first by Oranje 1 and is especially pronounced for gas-condensate flow in which small amounts of liquid occur, that is, liquid holdup values of 5% and lower.

In that case, the liquid stream approaching the junction may not necessarily be split up into two different streams but may flow completely either straight on into the run or into the side-arm ("flip-flop" effect).

Unequal phase splitting brings about a number of difficulties for operating a gas-distribution network. For example, if such a network contains a few successive T junctions, it is possible that the liquid follows a very specific route through the pipeline system.

It may be that a minor change of the pipeline operating conditions (gas flow rate, for example) can result in a totally different route of the condensate in the gas-movement network. This observation is sometimes referred to as "liquid route preference."

A need exists, therefore, for an easy-to-handle theoretical model capable of accurately predicting liquid route preference at junctions of general shape (Fig. 1).

Such a model has been developed at the University of Amsterdam by commission of NV Nederlandse Gasunie, the main gas-transportation company in The Netherlands. Before an elucidation of the new double-stream model, a short review will be given on existing literature models.

LITERATURE MODELS

On the basis of his observations on the flow split at junctions, Oranje 1 stated a rule of thumb:

  • If less than 20% of the gas stream enters a branch line, the liquid condensate will follow the straight line and not enter the branch line.

  • If more than 35% of the gas stream enters a branch line, all of the liquid condensate will enter the branch.

This rule is purely empirical and applicable only at very limited flow conditions.

The pioneering work in modeling the two-phase flow split at junctions has been provided by Saba and Lahey . 2 Their macroscopic model, which has been extended by Seeger,3 is restricted to homogeneous flow without slip between the two phases and is not applicable to low liquid-holdup, gas condensate flow (eL < 0.06; see accompanying "Notations" box).

Azzopardi and coworkers 4 developed phenomenological models for predicting the flow split at junctions, both for vertical and horizontal inlet tubes. Although their work clarified some of the physical phenomena during gas-liquid flow at junctions, it is not always accurate in predicting the flow split during gas-condensate flow.

Models for the two-phase flow split which recently have been published are the so called "geometrical models." Such a model, based on geometrical considerations and flow dynamics nearby the T, has been proposed by Shoham. 5 Geometrical models are not easily applicable to junctions of different shape (Fig. 1).

Generally, it may be stated that for low-liquid holdup (eL < 0.06) gas-condensate flow, occurring in gas-transmission pipelines, the flow split at T junctions is described with inadequate accuracy by existing literature models.

The model developed at the University of Amsterdam describes the liquid route preference during gas-condensate flow (eL < 0.06) under stratified, wavy, and annular flow conditions in junctions.

AMSTERDAM MODEL

The present model has been based on observations of the static pressure distribution in the vicinity of a T junction during single-phase gas flow.

A representative example has been given in Fig. 2 which reveals that the straight-tube pressure drop in the inlet, run, and branch can be predicted properly with the standard methods (Fanning pressure drop; Blasius friction factor).

The presence of the T, however, causes a disturbance of the static pressure distribution in such a manner that for the inlet-to-run gas flow, a static pressure recovery arises; whereas for the inlet-to-branch gas flow, a static pressure decrease occurs.

As a result a pressure difference (DELTA P2 3 = P2 - P3) exists between the run and the branch just after the T.

The static pressure recovery and the static pressure decrease for single-phase gas follow in a straightforward manner from the steady-state macroscopic mechanical energy balance or Bernoulli equation.

The Bernoulli equation states that along a streamline, the sum of the reductions of pressure, kinetic energy, and potential energy is equal to the frictional energy loss.

Considering a steady-state single-phase gas flow through a dividing T junction, the Bernoulli equation can be applied to (Fig. 3a) inlet-torun gas flow G1 2 (Equation 1, equations box) and inlet-to-branch gas flow G1 3 (Equation 2).

In Equations 1 and 2, WGi (where: i = 1, 2, 3 for inlet, run, and branch, respectively) represents the root mean square of the axial velocity of gas in the gas phase. By definition, Equation 3 follows in which v represents the time-averaged local axial velocity of a fluid and < v > the cross-sectional average of v.

The value of the constant depends on the shape of the velocity profile of the fluid; a subsequent section here gives more details about .

The quantities k1 2 and k1 3 in Equations 1 and 2 represent the friction-loss coefficients for dividing single-phase gas flow in a pipe T. The values of k1 2 and k1 3 depend on the fraction of the gas extracted into the branch and on the geometry of the junction (SEE FORMULA Fig. 1).

Values of k1 2 and k1 3 for single-phase fluid flow in a pipe T can be calculated with correlations published by Gardel.6

If gas-condensate flow in the inlet occurs, the behavior of small quantities of liquid nearby the T junction can be elucidated on the basis of Fig. 2.

For the situation as sketched in this figure, the liquid approaching the junction will undergo a static pressure increase in the run due to a velocity drop after the junction and a static pressure decrease in the branch due to friction and a velocity build-up in the branch.

The resulting pressure difference between run and branch (DELTA P2 3) is caused by the flow split of the gas and can be interpreted as a driving force for the liquid route preference.

It is a matter of balance between this driving force and the axial momentum of the liquid in the inlet whether the liquid will be extracted into the junction, flow straight on into the run, or subdivide into two different streams.

For example, if the liquid in the inlet carries small momentum in the axial direction, which is not unusual during gas-condensate flow, only a small pressure difference (DELTA P2 3) is sufficient to force the liquid completely into the branch.

If, however, the liquid flow in the inlet has a large momentum 1/2 rhoLW2 L1, even a large pressure difference DELTA P2 3 between run and branch may be insufficient to extract all the liquid into the side-arm, and the liquid stream will be split or flow straight on into the run.

BERNOULLI APPLICATIONS

For gas-condensate flow in a junction, therefore, the extended Bernoulli equation can be applied to each of the four occurring streams (Fig. 3b):

  • Inlet-to-run gas stream G1 2 (Equation 1)

  • Inlet-to-branch gas stream G1 3 (Equation 2)

  • Inlet-to-run liquid stream L1 2 (analogous to Equation 1, but with subscript L)

  • Inlet-to-branch liquid stream L1 3 (analogous to Equation 2, but with subscript L).

Solving the resulting set of four equations leads to a general macroscopic model, the double-stream model, describing the liquid route preference in junctions.

Values of the liquid mass intake fraction (lambda L) into a horizontal branch during gas-condensate flow through a horizontal main tube can be obtained if the following assumptions are made (see also Fortuin 7):

  • The liquid holdup in the inlet is small (epsilon (Variant) L1 < 0.06).

  • The pressure difference between run and branch is equal for gas and liquid: (DELTA P2 3)L = (DELTA P2 3)G.

  • The velocity profiles of the gas are equal in inlet, run, and branch.

  • The velocity profiles of the liquid are equal in inlet, run, and branch.

  • In the direct vicinity of the junction, the values of the liquid holdup (or void fraction) in each of the three legs are approximately equal.

  • The contribution of the potential energy of the gas phase can be neglected.

  • For a reduced T junction (D3 < D1; Fig. 1), the difference between centers of gravity of the liquid in branch and run approximately equals the difference in the heights of the branch and run.

  • The difference of friction-loss coefficients of the liquid phase (k1 3 - k1 2)L is equal to that of the gas phase (k1 3 - k1 2)G which means that the difference k1 3 - k1 2 Of the friction-loss coefficients can be obtained from correlations developed for single-phase gas flow in junctions (for example, from Gardel 6).

With these assumptions taken into account, the aforementioned set of four Bernoulli equations can be solved to result in Equation 4 (equations box) in which 0 lambda L 1.

In Equation 4, the following dimensionless parameters have been defined:

  • lambda L and lambda G, the mass fraction of liquid and gas, respectively, taken off into the branch.

  • lambda 0, a parameter which is a function of the difference k1 2 - k1 3 of the friction-loss coefficients k1 2 and k1 3 for dividing single-phase flow in a junction (Equation 5).

  • a, the ratio of diameters of main tube and branch (a = D1/D3).

  • FrL1 3, a dimensionless modified Froude number defined by Equation 6.

  • K, the ratio of average kinetic energies per unit volume of gas in the gas phase and of liquid in the liquid phase in the inlet of the junction (Equation 7).

According to Equation 7, the value Of K depends not only on the densities and superficial velocities in the inlet of both phases, but also on the liquid holdup (eL1) in the inlet and on the constants G and L. These constants depend on the shape of the velocity profiles of gas and liquid in the inlet of the junction.

The effect of velocity profiles of gas and liquid in the inlet on G and L will be discussed presently.

According to Equation 4, the branch liquid mass intake fraction (lambda L) is a quadratic function of the branch gas mass intake fraction (lambda G), the geometry of the junction (affecting a, FrL1 3, the difference k1 2 - k1 3 of friction loss coefficients, and lambda 0), the ratio of kinetic energies of gas and liquid in the inlet (K), and the velocity profiles of gas and liquid in the inlet (affecting the values of G and L).

For gas-liquid flow through a horizontal dividing regular T junction (D1 = D 2 = D3), Equation 4 reduces to Equation 8.

For horizontal dividing regular sharp-edged T junctions (R/D1 = 0), a constant average value of lambda 0 = 0.07 can be assumed for simplicity.

INLET HOLDUP, VELOCITY PROFILE

It is clear that a thorough knowledge of the liquid holdUp (eL1) in the inlet of the junction is crucial for a determination of the liquid route selectivity.

For small liquid holdup values (eL1 < 0.06) during gas-liquid flow in the inlet of a horizontal T junction, the relation shown in Equation 9 holds true (Hart 8).

In this equation, ReLs1 represents the superficial liquid Reynolds number in the inlet [SEE FORMULA].

The mean square velocity (W2 ; Equation 3) depends on the shape of the velocity profile of a flowing fluid.

Under industrial low liquid-holdup conditions (eL < 0.06), the gas flow is turbulent, but the liquid flow can be either laminar or turbulent. If in the inlet both the gas flow and the liquid flow are turbulent, approximately flat velocity profiles for both phases can be assumed, resulting in c, L =1

If in the inlet the gas flow is turbulent (G =), however, and the liquid film is laminar, [SEE FORMULA].

If in this case the laminar liquid film has a parabolic velocity profile, it can be derived that L =154 and a = 0.65.

Laminar liquid-film flow in the inlet occurs under conditions described by Equation 10.9

In Equation 10, I1 is the mass flow rate of the liquid film in the inlet per unit width of wetted wall, and Q1 is the fraction of the cross-sectional area of the inlet tube wall wetted by the liquid film during stratified-wavy and annular flow. Correlations for obtaining Q1 values have been published elsewhere.8

REFERENCES

  1. Oranje, L., "Condensate behavior in gas pipelines is predictable," OGJ, July 2, 1973, pp. 39-44.

  2. Saba, N., and Lahey, R.T., "The analysis of phase separation phenomena in branching conduits," Int. J. Multiphase Flow, Vol. 10, pp. 1-20.

  3. Seeger, W., Reimann, J. and Mueller, U., "Two-phase flow in a T junction with a horizontal inlet, Part 1: phase separation," Int. J. Multiphase Flow, Vol. 12, pp. 575-585.

  4. Azzopardi, B.J., and Memory, S.B., "The split of two-phase flow at a horizontal T-annular and stratified flow," 4th Int. Conf. Multiphase Flow, Nice, France, June 1989, pp. 19-21.

  5. Shoham, O., Brill, J.P., and Taitel, Y., "Two-phase flow splitting in a tee junction-experiment and modelling," Chem. Eng. Sci., 1987, Vol. 42, pp. 2667-2676.

  6. Gardel, A., "Les pertes de charge dans les a coulements au travers de branchements en te," Bulletin Technique de la Suisse Romande, 1957, Vol. 9, pp. 122-130, and Vol. 10, pp. 143-148.

  7. Fortuin, J.M.H., Hart, J., and Hemersma, P.J., "Route selectivity for gas-liquid flow in horizontal T junctions," AIChE J., 1990, Vol. 36, pp. 805-808.

  8. Hart, J., Hamersma, P.J., and Fortuin, J.M.H., "Correlations predicting frictional pressure drop and liquid holdup during horizontal gas-liquid pipe flow with a small liquid holdup," Int. J. Multiphase Flow, 1989, Vol. 15, pp. 947-964.

  9. Bird, R.B., Stewart, W.E., and Lightfoot, E.L., Transport Phenomena, John Wiley & Sons, New York, 1960, p. 212.

    Copyright 1991 Oil & Gas Journal. All Rights Reserved.