Slug-flow frictional

The frictional pressure gradient is obtained by different correlations described in following sections. In a horizontal flow, (dp/dz)elev = 0, it is an ideal case to perform experiments excluding the term of elevation pressure drop. Because of nonhomogeneity of the slug flow, the acceleration pressure gradient term is different from that shown above it is given in Section 3.5.2.2. 

The Bernoulli equation can now be written for the liquid in channel flow in the bottom part of the tube, and for the liquid in slug flow in the upper part. The acceleration terms are then neglected, and the friction factors for each type of liquid flow found from the Blasius equation and from true Reynolds numbers. The resulting equations cannot be readily evaluated because of the two hydraulic-radius terms involved in the two types of flow, and an unknown fraction defining the relative mass of liquid in each part of the tube. 

It has been observed clearly in experiments [1-6] that when a slug moves horizontally, there is a relative motion between the slug and the pipeline wall, but there is no relative motion between the particles within the slug. In general, granular materials are cohesionless but frictional. Therefore, k is determined by using Mohr s circle as shown in Fig. 6 [4]. In Fig. 6, Line II represents slug-flow conditions and lies between Lines I and III (i.e. (j)w < < )s <... 

Bubble and slug flow. The frictional pressure drop is calculated as follows ... 

Equations 8.57 and 8.58 are satisfactory except at low liquid rates when the frictional pressure drop is a very small proportion of the total pressure drop. Frictional effects can then even be negative, because the liquid may then flow downwards at the walls, with the gas passing upwards in slugs. 

The liquid in the film alongside the Taylor bubble flows in the opposite direction, with negligible interfacial shear from the gas on the bubble. The average gradient due to friction and acceleration across a slug unit is... 

The frictional pressure gradient in the liquid slug can be calculated using Eqs. (3-103) and (3-104), when the flow rates of liquid and gas are written in terms of the flow rate on the slug. Thus,... 

Figure 16 Relative increase of friction and mass transfer due to gas-liquid Taylor flow, compared to developed laminar flow in small tubes. represents the dimensionless length of a liquid slug. Re the Reynolds number based on the liquid.

In this equation, it is assumed that both the gas and the liquid move in slugs at the same velocity through the orifice. The contribution of the orifice effects to the total pressure drop is small and is of significance only in monolith blocks with high cell density and at high liquid flow rates. The frictional and static pressure drops prevail. The orifice effects may arise if blocks of monoliths stacked on top of each other are used. The contribution of these effects will depend on the extent of obstruction and the length of individual blocks. 

Two-phase flow often presents design and operational problems not associated with liquid or gas flow. For example, several different flow patterns may exist along the pipeline. Frictional pressure losses are more difficult to estimate, and in the case of a cross-country pipeline, a terrain profile is necessary to predict pressure drops due to elevation changes. The downstream end of a pipeline often requires a separator to separate the liquid and vapor phases, and a slug catcher may be required to remove liquid slugs. 

The pressure drop over a unit cell is then given by the sum of the frictional pressure drop of the Uquid flowing in the slug Api) and the pressure drop over the Taylor gas bubble (Ape). The length of a unit cell is + is and thus the number of unit cells per unit length of channel is 1/(Lb + Ls). The pressure drop over a tmit length of channel is therefore given by... 

Equation 2-6 clearly indicates that the friction factor is dependent on the flow. It will be demonstrated that there is a relationship between the friction factor and the Reynolds number of the flow. In USCS units, density is expressed in slugs/ft. ... 

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