A basis for developing a simple-to-use multiphase-pressure-drop correlationthat could be applied to the design or assessment of pipelines with flows ofoil and gas mixtures was established. Simple correlations for predicting thepressure drop are proposed and tested with a data bank from the oilindustry.
Numerous correlations are available for the prediction of multiphasepressure drop in pipes currently used in the industry. Most are pressure dropin pipes currently used in the industry. Most are difficult to use andgenerally require sophisticated computer pro- grams for the calculation ofpressure drop. Brill and Beggs re- viewed several of these correlations, whichare not repeated here. Baker and Gravestock's recent evaluation ofpressure-drop and holdup predictions for gas-condensate pipelines showed thatwhile the accuracy of the pressure-drop predictions is better, most of thecorrelations produce significantly large errors. In another study concernedmainly with air/water mixtures, holdup and pressure-drop correlations indicatedincreasing error with increasing pipe diameter. In most instances, correlationsare based on experimental data obtained in the laboratory because carefullycontrolled experiments generally yield more accurate results than fieldmeasurements. Furthermore, such data are more amenable to systematic generationand modeling. Because pipeline sizes and flow rates are considerably smallerunder such conditions, however, data correlations based on laboratoryexperiments generally produce large errors compared with correlations fromfield data. To reduce produce large errors compared with correlations fromfield data. To reduce these errors in applications of such predictions to fieldconditions, accurate scale-up techniques need to be developed.
The need for systematic collection of multiphase-flow data in large-diameterpipes (i.e., greater than 100 mm) has been recognized for some time. To thisend, the American Gas Assn. (AGA) sponsored a project for the development of adata bank. The data contained in the bank came from a wide variety of sources;some were taken from oil company records representing either normal productionor special test conditions. In preliminary design calculations of pipelines, anaccurate preliminary design calculations of pipelines, an accurate estimate ofpressure drop from simple-to-use correlations is desirable. Furthermore, inexisting pipelines, the change in flow parameters and conditions results in achange in the pressure drop parameters and conditions results in a change inthe pressure drop in the pipe. The aim of this study was to develop asimple-to-use correlation based on the existing data of the AGA bank for thepressure-drop estimation. pressure-drop estimation.
An earlier experimental pilot study with air/water mixtures indi- cated asignificant ordering of data with a combination of mixture Reynolds and Froudenumbers. We used this ordering as the basis for developing the pressure-dropcorrelation based on the data bank. Table 1 lists the parameter ranges coveredby the AGA data bank.
From the data-parameter range, it is apparent that the volumetric flow rateis predominantly gas; therefore, detailed consideration of the pipelineelevation profile was not deemed important for a steady-state flow. On thebasis of an earlier approach, the data were plotted in terms of the averagenondimensional pressure gradient, vs. the mixture Froude number, NFr, definedby
(1) and (2)
where = total pressure drop, g = gravitational acceleration, L = pipelength, and pm and vm = mixture density and velocity, re- spectively. Unfortunately, not all the measurements in the bank could be used to plot thedata in these coordinates because of a lack of information on mixture densityin some instances. Only some 200 points could be plotted in the chosencoordinates. Fig. 1 shows the distribution of the number of data points fordifferent pipe diameters. pipe diameters. The data initially were mapped on theMandhane et al. flow-pattern map (Fig. 2). The data used here fall in theannular/annularmist flow regime. Furthermore, the data were plotted in terms ofdimensionless pressure drop vs. Reynolds number (Fig. 3). Two groupings of datapoints are obvious: one set indicates a pressure drop varying from about 0.01to about 1; the other indicates an essentially constant pressure drop forReynolds numbers up to 4 × 10 . This difference is believed to be the result ofdifferent pipe geometries and heat-transfer effects. Because of this particulargrouping of the data into two sets, the classic Reynolds-number/ particulargrouping of the data into two sets, the classic Reynolds-number/friction-factor-type pressure-drop correlation does not prove satis-factory.
Fig. 4 shows the data from the bank plotted as . There is a significantordering, which seems surprising consider- ing that in data selection nodetailed account was taken of the flow structure, holdup, elevation, andheat-transfer effects.
Using a single-phase approach, one can arrive at a simple relationshipbetween pressure drop and Froude number. A typical orifice equation has theform
where q=volumetric flow rate, Kd=discharge coefficient, d=diameter, and Fa=approach factor. Eq. 3 can be expressed in nondimensional form as
Therefore, the dimensionless pressure gradient is proportional to the Froudenumber squared. Note that Eqs. 4 apply to singlephase flow; however, someelements of such behavior would be expected in certain types of multiphaseflow. A second-order regres- sion fit to data gave the following value of theconstant in Eq. 4b.
This correlation is also plotted in Fig. 4. The deviations of individualdata points from the estimated value given by Eq. 5 were calculated as (6)where and, =measured and estimated pressure drops, respectively. Fig. 5 showsthis deviation for each data point. The correlation indicates a maximum of 50%overprediction; however, over most of the Froude number range, the error isless than 35 %. The relatively significant error at Proude numbers less than0.3 is presumably caused by heat-transfer effects associated with longpipelines.