Yiing-Mei WuMobil Research & Development Corp.

Paulsboro, N.J.

A method for estimating minimum oil-flow velocity in an oil-water multiphase stream sufficient to entrain all free water has been improved to account for water volume in the flowing oil.

Removing all free water in a flowing oil-water stream eliminates a separated settled-water phase which could cause corrosion damage to the transfer lines.

Such harmful oil field impurities as hydrogen sulfide and carbon dioxide dissolved in the free-water phase can contribute to the problem.

The method described here improves on one developed by M. Wicks and J.P. Fraser.1

The method is reviewed here as a basis for presenting the improved approach for calculating the minimum flow velocity that takes into consideration water content already in the oil.

### Analogous flows?

Flow characteristics of the liquid-liquid system (oil and water) are needed for a definition of stream velocity required to entrain all the free water. Three flow patterns are relevant for this system (Fig. 1) (45516 bytes).

Water will be entrained in stratified-dispersed flows and fully dispersed (mist) flows but not in stratified flows. Transitional criteria will be discussed and compared with experimental data from the literature.

The analogy between liquid-solid flow and liquid-liquid flow is often used as a convenient way to describe the far more complicated interaction involved in the latter system by the simpler behavior of the former.

Following that approach, two premises were used by Wicks and Fraser to develop the minimum stream velocity:

1.Once entrained in the flowing oil, the water droplets behave as solid particles.

2.The lower limit of the velocity for net axial transport of solid particles (or water) equals the upper limit of the velocity required for a stationary layer of solid particles.

When the water volume ratio is small and the interaction between water droplets is negligible, the first premise reasonably describes the nature of water entrained flows.

The second premise, however, introduces a degree of concern in the analysis. The flow patterns of the two systems differ so much from each other that correlation is difficult, especially correlation in the transition stages.

The new approach offered here uses characteristic flow patterns and relevant physical properties such as drop size and phase height to deduce the transition criteria. Examples are discussed.

### Maximum drop size

Since water is entrained in flowing oil in the form of droplets, it is essential to know the maximum drop size that can be sustained in the flow.

J.O. Hinze employed a dimensional analysis to examine the forces controlling the breakup of a liquid drop in the continuum of another liquid.2 Assuming the effect of the viscosity of the fluid inside the drop is negligible, Hinze concluded that the dynamic pressure force of the turbulent motions is the factor determining the size of the largest drops.

Deformation or breakup occurs if the dynamic pressure force, caused by changes in velocity over a distance approximating the diameter of the drop, is greater than the counteracting interfacial tension force. The two forces can be incorporated into a dimensionless Weber number.

In the case of liquid drops dispersed in a gas phase, the critical value of Weber number for breakup is shown in Equation 1 in the accompanying box.

For liquid-liquid dispersion, Equation 2 applies.

In Equation 1, Ug is the maximum value of the gas velocity relative to that of the drop. In Equation 2, vw2w is the average value of the squares of velocity differences over a distance equal to dmax.

For oil-water flows, Equation 2 should be used to calculate the maximum drop size. Brauner and Maron3 modified Equation 2 to yield Equation 3a where C1 is to be determined experimentally and is about 0.725 for liquid-liquid systems (as opposed to gas-liquid systems).

Brauner and Maron applied turbulence theory (for flow in a pipe) to determine the average square velocity, or the kinetic energy term in Equation 2 and derived Equations 3a-d.

In his derivation, however, Hinze assumed the simplest case of isotropic, homogeneous turbulence to relate the kinetic energy to the drop diameter. Equations 2 and 3a-d are therefore applicable only if local isotropy applies.

If that is the case, the maximum drop size of entrained droplets can be calculated by using Equations 3a-d.

### Stratified flow

Provided they are small enough, the droplets in a liquid continuum may maintain their shape in such a way that the surface-tension forces overcome those due to buoyancy. Under these conditions, Equation 4a applies.

Dispersed water drops of a size larger than dcr (Equation 4b) will agglomerate and eventually settle at the conduit bottom. There they will form a continuous phase or slugs, depending on the amount of the dispersed phase and the interaction with the pipe walls.

As shown in Fig. 2 (38925 bytes), for a lower phase height Hw dcr (corresponding to a greater lower phase flow rate), the available lower phase space allows the agglomeration and stratification.

On the other hand, for Hw

A simple transition criterion from two continuous stratified layers to a stratified-dispersed upper layer was proposed3 and is shown in Equation 5a.

### Mist flow

If the flow velocity is sufficient, fully developed mist flow will become possible. Once the concept of the maximum drop size has been established, one can easily arrive at the condition necessary for sustaining a fully developed mist flow.

If the maximum drop size (dmax) is smaller than the critical size (dcr), the small drops are stable and a fully dispersed pattern may prevail. Thus, a fully dispersed pattern is expected only when dmax/dcr

From Equations 3a-d, the maximum drop size decreases with increasing oil velocity; note that U in Equation 3d can be substituted by Uos because Uws is usually very small.

Therefore, a minimum oil velocity (and the required pump speed) can be calculated to bring the flow into the fully developed mist regime.

Based on the present discussion on flow transition, however, the relative amount of water in the pipe is also important and must be considered.

### Calculation examples

In experiments, Charles, Govier, and Hodgson used an oil mixture with density close to that of water to observe different flow patterns.4

Because there is no density contrast under these conditions, symmetry about the pipe axis exists and the simplest form of horizontal flow results. In two experiments, Charles, Govier, and Hodgson were able to produce mist flow with oil as the continuous phase.

Equations 3a-d were applied to check if dmax can be correctly predicted using the following data: Uos= 41.4528 cm/sec; Uws= 3.048 cm/sec; mo=16.8 cp; ro= 0.998 g/cu cm; D=2.6416 cm; s = 15 dyne/cm.

Note that from Uos and Uws, the volume fraction of oil is about 0.91. Therefore, once formed, the water droplets are sufficiently spaced and the interference effect can be neglected.

From Equations 3a-d, dmax was calculated to be 0.229 cm. This implies that under their experimental condition, no drop with diameter larger than 0.229 cm should be observed.

Since the reported diameters of droplets range from 0.0762 to 0.152 cm, the theoretical value from Equations 3a-d is justified.

Wicks and Fraser reported that a pipeline transporting oil was found to have 26 leaks in a 4-year period.1 They calculated the minimum oil velocity to entrain water to be 60.96 cm/sec.

This implies that if the oil velocity is higher than this value, all the water should be entrained and carried away. But current oil velocity in line, 70.104 cm/sec, is already higher than the minimum.

The line also transports about 22% (vol) of water along with the oil. This corresponds to an oil-to-water ratio of 3.55.

Given D = 15 in. = 38.1 cm, ro= 0.88 g/cu cm, rw = 1 g/cu cm, mo = 20 cp, and s = 20 dyne/cm, dcr is calculated to be 1.01 cm from Equations 4a and b.

With Uos of 70.104 cm/sec, Uws is about 19.81 cm/sec.

If we assume the in situ oil-to-water volume ratio is about the same as the input oil-to-water ratio (hold-up ratio close to 1),5 Hw is estimated to be 13.21 cm.

Compared with dcr and from Equations 5a and b, it is still in the stratified flow regime. This explains why corrosion occurred in this case.

In fact, the oil velocity has to be unreasonably high in this system to reach the stratified-dispersed regime, if the volume of water remains at 22% and any corrosive species remain in the water. Therefore, the only way to eliminate corrosion in this system will be to reduce the water content to less than 1% (vol).

### Effects of water, wetting

The liquid-liquid system is far less studied than the gas-liquid system. Therefore, generalized flow-regime information is less readily available, unlike the case for gas-liquid flows.

The three flow patterns discussed in this article (stratified, stratified-dispersed, and fully dispersed mist) are the most common cases encountered in oil transportation.

Other types of patterns, such as annular and plug, certainly exist and are more complicated. Fortunately, for large oil-to-water ratios when water enters as an impurity, they are seldom observed.

Of concern here has been the effect of water impurity and its removal. Water serves only as a medium for corrosion reactions, however. Other corrosive species are usually responsible for the actual corrosion attack. It should be stressed that effective corrosion control measures should focus on specific cases.

Another important consideration is the wetting of the pipe wall by entrained water droplets. When corrosion damage observed inside a pipe is not restricted to the bottom, general wetting usually is the culprit.

Wetting is caused by the interaction of surface tensions between different phases. Fig. 3 (25027 bytes) illustrates this for a water droplet resting on a solid (metal) surface exposed to an oil phase. The contact angle (q) can be determined by a force balance on the horizontal axis (Equation 6).

If ss-w is much larger than ss-o, q will approach 180 and complete wetting will occur. Even though Equation 6 looks very simple, it is not trivial to measure q experimentally with reproducibility. The roughness of the metal surface complicates the calculation. Therefore, valid experimental data must be obtained before injecting surfactant to manipulate the wetting behavior is considered.

Most corrosion problems suffered in oil transporting pipelines are localized because most of the internal pipe surface is exposed to the noncorrosive species and is passive or has very low corrosion rate. Since the flow velocity is usually low (less than 152 cm/sec), deadleg or local water condensation is detrimental.

In refining operations, however, flow velocities are usually higher, and more corrosive substances are handled. General corrosion or corrosion combined with erosion quite often results from such an environment.

Any consideration of the effect of flow on corrosion should include such environmental factors. Thus, a certain flow pattern is beneficial in one application but not necessarily in another.

References

1.Wicks, M., and Fraser, J. P., Materials Performance, May 1975, pp. 9-12.

2.Hinze, J. O., AIChE, Vol. 1 (1955), No. 3, pp. 289-295.

3.Brauner, N., Maron, D.M., Int. J. Multiphase Flow, Vol. 18, No. 1, pp. 123-140, 1992.

4.Charles, M.E., Govier, G.W., and Hodgson, G.W., Canadian Journal of Chemical Engineering, Vol. 39 (1961), p. 27.

5.Russell, T.W.F., Hodgson, G.W., and Govier, G.W., Canadian Journal of Chemical Engineering, Vol. 37 (1959), p. 9.

### The Author

Wu received a BS in chemical engineering from National Taiwan University, an MS in materials science and engineering from National Sun Yat-sen University, and an MS and PhD in metallurgical engineering from Ohio State University. She is a member of the Electrochemical Society.

*Copyright 1995 Oil & Gas Journal. All Rights Reserved.*