F. Ferrini, P. FoschiTechfem

Fano, Italy

G. GiacchettaUniversity of Ancona

Ancona, Italy

A. Pareschi B. RiminiUniversity of Bologna

Bologna, Italy

The efficiency of currently available correlations for two-phase gas-condensate flows is undermined by the presence of water in these flow systems. Water radically modifies the pressure-loss mechanism.

Five models have been developed for estimating the global pressure loss of such pipelines in actual operation.

The results of these calculations are compared with field data contained in the American Gas Association's Multiphase Pipeline Data Bank which concerns different measurements relative to three lines of two-phase gas-condensate mixtures in the presence of water.

The available correlations greatly underestimate pressure losses even if the water concentration is low compared to the entire liquid phase. In fact, the two-phase condensate-gas system becomes a three-phase water-condensate-gas flow in which the physical properties of liquid phases are quite different from each other.

The purpose of the work reported on here was to define some physical schemes of the fluid system and translate them into mathematical models able to take into consideration the interactions between the liquid phases.

### MODELS

A three-phase water-condensate-gas mixture is assumed.

Only one liquid, named "equivalent liquid," is used in place of the two liquid water-condensate phases. The physical properties of this equivalent liquid, density, and viscosity are allotted on the basis of the different models described later.

Superficial tension is considered fixed in each model at that of oil. The volumetric flow rate is calculated as the sum of the volumetric flow rates of the two liquid phases in the pipe.

The physical properties of the gas phase are the same in every model.

- The equivalent-oil model presents the most simplified hypothesis.
The two-phase water-condensate system is replaced with a single-phase equivalent-liquid flow, the properties of which, density and viscosity, are the same as that of oil. In this way the presence of water is neglected.

- For the liquid-mixture model, an equivalent liquid replaces the two liquid systems. Its density and viscosity are assumed as linear combinations having the same physical properties as water and oil, as a function of the liquid phase's transport concentrations.
- For the liquid-emulsion model, a water-in-oil emulsion is assumed as the equivalent liquid.
Its density is calculated as the average density of water and oil, according to their respective transport concentration rates. The emulsion viscosity is greatly influenced by the concentrations of the two phases.

If water is 70%, the emulsion viscosity could be even 20 times the oil viscosity.1

In the cases under consideration here, the water-concentration rates are quite low and, in these conditions, the emulsion is not always formed. In any case, the viscosity of any emulsion would not be very different from the oil viscosity.

The developed model assumes that the liquid phases always form an emulsion and fixes its viscosity as 20 times that of the oil.

It then calculates the pressure losses suffered by the emulsion-gas system.

- Other models are the two-phase equivalent liquid-gas flow model and three-phase water-oil and oil-gas flow model.

The different physical properties of water and oil suggest that the holdup phenomenon might occur between the two liquid phases. These phases are replaced by an equivalent liquid.

Its density is the average density of oil and water, as a function of their in situ concentrations, Its viscosity is that considered necessary to give the same frictional pressure loss as the two-phase water-condensate system, flowing in the fraction of section assigned them by the global holdup.

This section is characterized by its hydraulic diameter, calculated by considering as wet profile only that part of the pipe in touch with the liquids, thus neglecting the liquid-gas interface.

### HOLDUP CALCULATIONS

Two different iterative procedures are developed to calculate the equilibrium holdup values.

- For the two-phase equivalent liquid-gas flow model, the starting value of the global liquid holdup is calculated by application of the equivalent-oil model. Then the water-in-oil holdup is calculated considering the two liquid phases flowing in the part of the section attributed to each by the global holdup.
In this way it becomes possible to calculate a hypothetical average liquid density considering the in situ concentrations of the two liquid phases.

A hypothetical viscosity could also be defined by imposition of the balance of the pressure losses between the two-phase water-oil flow and the hypothetical liquid flow with the density calculated previously.

Then we revalue the holdup this liquid would have if flowed with the gas at the actual physical conditions of the system. This holdup is assumed as the new starting value for another iteration, until the equilibrium holdup is found.

In these conditions the physical properties of the equivalent liquid are known, and it is then possible to replace the two-phase water-condensate with it. The increase of the global holdup, caused by the presence of water, is valued by the equations and correlations used to estimate the frictional pressure loss.

- For the three-phase water-oil and oil-gas flow model, unlike the similar model previously discussed, the equilibrium holdups are estimated based only on physical and geometrical instead of energy considerations.

The three-phase system flowing in the pipe is analyzed as the sum of two different but connected two-phase flows: water-oil and oil-gas.

The holdups that will be estimated are those that satisfy the simultaneous balances of the two different but interdependent systems. These two flows are substituted by an equivalent liquid-gas two-phase system so that the part of the section attributed to the equivalent liquid is the same as that in which the two-phase water-condensate flows.

The starting holdup is obtained by application of the equivalent-liquid-oil model.

First of all we examine the system of the liquid phases flowing in that part of the section attributed to them by the global holdup value. In this way we estimate the water holdup in the oil.

Thus it is possible to pass to the oil-gas system, removing the water and the part of the section occupied by it.

With the available correlations, the oil-in-gas holdup value is calculated. From this value, it is possible to deduce the fraction of section occupied by the liquid phases simultaneously flowing and then the global holdup.

Comparing this holdup with the starting one enables the iterations to proceed until the convergence is found.

### CALCULATION HYPOTHESIS

Detailed information about the line and fluid characteristics is necessary analytically to estimate the pressure losses of systems flowing in pipes. These data are drawn from the AGA Multiphase Pipeline Data Bank and refer to two-phase gas-condensate flows in the presence of water.

Three different lines are examined. For each we have the following information: length (900-1,200 m; 2,953-3,936 ft), detailed altimetric profile, internal diameter (6-10 in.), fluid composition, gaseous hydrocarbon, condensate hydrocarbon, and water flow rates (liquid-phase transport concentration is about 1-10%; water concentration, referred to the liquid phases, is about 1-6%).

For every line, however, pressure and temperature values are assigned, both in entrance and in exit from the pipe. The correlations available in literature were used to carry out the different calculation processes.

The fluid-dynamics part of the problem consists of the equations for the evaluation of pressure losses (frictional term and hydrostatic term) and holdup.

The frictional head-loss term is valued by the Dukler correlation2 with the Colebrook-White expression.3 The hydrostatic term is valued differently as a function of the inclination of the calculation steps.

In uphill tracts of line, the contribution of each phase is considered, but in downhill tracts hydrostatic recovery is attributed to the gas-phase only.4 The holdup value is calculated by the Eaton correlation.5

For the physical property evaluations of each phase (compositional part), different methods are used.

For the liquid phases, values from literature were adopted: water and oil density, respectively, 1,000 and 720 kg/cu m; viscosity, 0.001 and 0.00035 Pascal sec; superficial tension, 0.065 and 0.0093 Newtons/m.

These properties are assumed constant along the direction of flow, assuming their variations as a function of thermodynamic quantities of the examined systems to be negligible.

The viscosity and density of the gas phase have been derived from suitable calculation processes from the AGA data-bank value at standard conditions. These values are then related to the pipeline thermodynamic conditions.

The viscosity is assumed constant and equal to the average between the input and the output viscosity values. Variations are quite small and their influence on the calculations is negligible.

The stepwise calculation is used to value the density with a fixed temperature profile. The profile chosen is linear between the input and output temperature values for each pipe, no information about heat-transfer conditions being available.

In each calculation step, the input density has been estimated at the fixed temperature and at a pressure agreeing with the pressure losses valued in the preceding steps (hydrostatic and frictional), the density being assumed constant for each step.

### HEAD-LOSS ESTIMATES

The head losses of three pipelines in actual operation are estimated with physical schematizations and analytical models, and the results compared with available measured values.

The results obtained by application of each model are represented in Figs. 1-5, respectively.

For every model the results of more measurements for each pipe are reported. In the following graphics the measured head-loss values appear in the abscissa, whereas in the ordinate the calculated head-loss values are reported.

Fig. 1 relates to the equivalent-oil model. Here, the difference between the physical properties of the liquid phases are neglected, and this figure shows that this model produces results far from the true measured values.

Fig. 2 shows the liquid-mixture model results. Because of the low water percentage, the physical properties of the mixture that this model supposes possible are not far from the oil properties.

These results do not present appreciable differences compared to the equivalent-oil model results.

The hypothesis to assume for the physical properties of the mixture, the linear combinations of the characteristics of each liquid phase, has merely the purpose of a sensitivity analysis. This leaves, however, some perplexities as to the physical meaning of average viscosity.

In the liquid-emulsion model, the results of which are reported in Fig. 3, the emulsion forming is assumed. Its viscosity, amplified, is fixed as 20 times the oil viscosity, thus attributing to the frictional term the responsibility of the head-loss increase because of the presence of water.

Comparing these results with the measured values, however, one can see that the frictional term has little influence on the phenomenon.

The two-phase equivalent liquid-gas flow model adopts a different approach to the problem, assuming that the two liquid phases are not mixable and that a slippage between them, with the relative increase of one phase with respect to the other, could happen given their different physical properties.

In Fig. 4, results obtained by the two-phase equivalent liquid-gas flow model are reported. This graphic shows an appreciable approach of the calculated pressure-loss values to the experimental data.

Unlike the liquid-emulsion model, this one attributes the largest amount of responsibility in the pressure-loss phenomenon to the hydrostatic term.

In fact, the two-phase equivalent liquid-gas flow model values the pressure variation as a result of the gravitational term by considering the in situ liquid-phase density, estimating the holdup of one liquid phase against the other. Also the frictional term is modified by the presence of water.

### ENERGY CONSIDERATIONS

But as already shown by the previous model, the frictional term is unable to justify the difference between calculated and measured head-loss values. This scheme supposes the existence of an equilibrium between the global holdup of the liquid phases and the pressure variation occurring as they flow in the part of section they occupy.

This fact means that the holdup evaluation is obtained by application of the energy considerations, or rather by correlations used to value the pressure losses which start from energy considerations. This reason probably reduces the sensitivity of this model to the slippage between the liquid phases.

The three-phase water-oil and oil-gas flow model defines the equilibrium situation by supposing the coexistence of the two-phase flows, water-condensate and condensate-gas, differentiated in the global system, and by imposing the congruence of their holdup. The results obtained are reported in Fig. 5.

In this case the closeness, or even the coincidence, of the calculated and measured values appears more evident. Also, this model attributes to the hydrostatic term the widest responsibility of the increase in pressure losses as a result of the presence of water.

Moreover, as regards the two-phase equivalent liquid-gas flow model, this trend is larger because the global holdup value is higher than these schemes assume as the indicator of the phenomenon.

The results obtained by application of the equivalent-oil model show that it is unacceptable to neglect the presence of water, even if its percentage seems numerically negligible.

To assume the perfect miscibility of two liquids brings no appreciable improvements to the calculated pressure-loss values. Again, the liquid emulsion model appears inadequate, considering moreover that the effect of the emulsion on the pressure losses has been amplified by an overestimation of its viscosity.

The results demonstrate that the frictional term cannot be considered the only one able to justify the higher pressure losses.

It is then necessary to analyze this fluid system as a three-phase system considering the slippage and the relative mechanical energy exchanges between phases.

The two-phase equivalent liquid-gas flow model and the three-phase water-oil and oil-gas flow model have been stressed to show there exists a holdup between the liquid phases and that the holdup must be assumed as the indicator entity to estimate the real head loss.

Moreover they showed the large influence of the hydrostatic head-loss term.

These models attribute the responsibility of the loss increase especially to this term. The results seem to indicate this approach as the most adequate and they individualize the three-phase water-oil and oil-gas flow model as the most efficient to tackle this problem.

### REFERENCES

- Woelfin, W., "The viscosity of the crude-oil emulsion," API Drilling & Production Practice, 1942, p. 148.
- Dukler, A. E., Wicks, M., and Cleveland, R. G., "Frictional pressure drop in two phase flow: a comparison of existing correlations for pressure loss and holdup," AlChE Journal, Vol. 10 (1964), p. 38ff.
- Colebrook, C. F., "Turbulent flow in pipes with particular reference to the transition region between the smooth and rough pipes," Journal Institute of Civil Engineering, 1949, p. 39ff.
- Gregory, G. A., Fogaresi, M., and Aziz, K., "Multiphase flow in pipes and its applications to the production and transportation of oil and gas," course notes, Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, 1982.
- Eaton, B. A., et al., "The prediction of flow pattern, liquid holdup and pressure losses occurring during continuous two phase flow in horizontal pipelines," Journal of Petroleum Technology, Vol. 19 (1967), p. 815ff.

*Copyright 1990 Oil & Gas Journal. All Rights Reserved.*