MOST ACCURATE TWO-PHASE PRESSURE-DROP CORRELATION IDENTIFIED

Masud Behnia
University of New South Wales
Sydney

Comparisons between measured oil pipeline pressure-drop values for two-phase flow and predictions by several commonly used correlations indicate that the Beggs and Brill correlation 1 has the lowest average error and therefore best represents the measured values.

The present study compared pressure-drop predictions of several correlations commonly used in the oil industry with large oil pipelines' measured values stored in a data bank.

CORRELATIONS, CALCULATIONS

The need to reduce expensive facilities has often dictated that a single oil pipeline be used simultaneously to transport gas and liquid. In fact, most of the natural gas gathered from wells flows in two-phase pipelines.

Further, the pipe may be carrying a two-phase multi-component mixture (e.g., gas-oil-water). Therefore, designing oil pipelines requires that a two-phase pressure drop be determined as accurately as possible.

Several correlations and calculation procedures for determining two-phase flow parameters have been developed. Some of the correlations go back as far as the 1930s. 2

In most instances, pressure drop and hold-up correlations are developed with experimental data obtained in the laboratory because such experiments generally yield more accurate results than field measurements. Furthermore, such data are more amenable to systematic generation and modeling.

In general, however, these experiments are performed with smaller diameter pipelines (50 mm), and flowrates are naturally much lower than found in oil pipelines in service. In order to check the validity and accuracy of the correlations, many studies have been performed in which the correlation predictions have been compared with experimental data. Most of these studies have used laboratory data for comparison; some have utilized limited field data for analysis.

The important general conclusions of these studies can be summarized as follows:

Most correlations are in best agreement with the data on which they were developed. 3
The errors in prediction of pressure-drop increase as the pipeline diameter increases. 4
The results of different studies are contradictory in determining the most accurate correlations.3 5-8
In some cases, pressure-drop field data have reasonably matched the predicted values from some correlations, 8 9 but in many predictions very large errors have been encountered. 5 8

PRESSURE-DROP CALCULATIONS

In multiphase flow pressure-drop calculations, it is customary to divide the total pressure gradient into three components: friction, elevation, and acceleration. Each is calculated separately and then summed.

For accurate calculation of the pressure gradient, particularly in long pipes, the length is divided into many small increments.

An iterative calculation for each pipe segment is performed starting from the end of the pipe with the known pressure and progressing downstream.

The total pressure gradient of each segment is multiplied by its length to yield the segment's pressure drop. The sum of the total segment pressure drops yields the pipeline's pressure drop.

Because of complexities of two-phase flow for performance of such calculations, it is necessary to use semiempirical or empirical correlations.

These correlations fall into three classes:

omogeneous models, assuming that the gas and liquid phases travel at the same velocity (i.e., no slippage). No consideration is given to the flow regime.
Separated models, assuming that the gas and liquid phases have different velocities (i.e., slip is taken into account).
No attention is paid to the flow regime.
Flow regime models, applying the same principles as separated models. However, the flow pattern is taken into account (i.e., a different separated model for each flow regime).

In general, the correlations from the first two classes are less cumbersome for calculation purposes, but the third class of correlations is more accurate and has become more widely used.

Clearly, classifying flow configurations into different patterns or regimes is subjective and depends largely on the researcher's taste.

Nonetheless, a number of flow-pattern maps have been developed which are widely used in the oil industry. 3 10-12

More recently a general flow-pattern map for all pipe inclination angles has been proposed by Taitel. 13

CORRELATIONS TESTED

An excellent source for the calculation procedures of a number of multiphase pressure-drop correlations is Brill and Beggs. 14

The authors have presented the relevant equations as well as individual computer subroutines for computations of thermophysical and transport properties, pressure drop, liquid hold-up, and flow regime.

For comparison, the present study selected seven popular correlations, one from each of the first two classes previously listed and five from the third class. 14 Each correlation and its designated identifier and classification are as follows:

FB--Fancher and Brown 15 (1)
HB--Hagedorn and Brown 16 (2)
MB--Mukherjee and Brill 17 (3)
DR--Duns and Ros 18 (3)
DU--Dukler, et al. 19 (3)
AZ--Aziz, et al. 20 (3)
BB--Beggs and Brill 1 (3)

For the sake of brevity, the details of correlations are not given here, and the reader is referred to the original references or Brill and Beggs. 14

DATA BANK

The need for a systematic collection of multiphase flow data in large-diameter pipes has been recognized for some time.

To this end, the American Gas Association sponsored a project for the development of a data bank. 21 Data contained in the bank came from a wide variety of sources, some from company records representing either normal production or special test conditions.

In some cases, tests were conducted by different companies to produce data for the bank. Initially, some 10 different companies and groups provided data for the bank.

The original data were grouped into 107 different lines.

For some lines, several data points were available.

The lines were classified according to the flowing fluid system, gas-condensate and gas-oil. These were referred to as system types: compositional and black-oil, respectively.

In the version of the bank used for this study were 241 data points for black-oil and 243 data points for compositional.

The gas-condensate data have been compared previously with the predictions from a few correlations 6 and will not be discussed here. The ranges of the black-oil data parameters utilized by the present study are given in Table 1.

The distribution of the number of data points with respect to the size of the pipe is given in Fig. 1. It is evident that the majority of the data points are from the larger diameter pipes of the order of 0.5 M.

In order to determine the type of flow pattern pertinent to each measurement, the data were mapped on the Mandhane flow regime map 3 (Fig. 2).

As shown there, the data used in the present study fall in the annular/annular-mist flow regimes.

COMPUTATIONS

To perform the pressure-drop calculations with the correlations just noted, all the required input data for the relevant subroutines 14 were initially identified. This information was extracted from the bank and entered into a data file.

Unfortunately, not all the data points contained all the required information and only 197 data points were entered into the data file. The seven subroutines were modified so that they all had a similar call statement.

A Fortran 77 computer program was written for the calculation of the pressure drops as follows:

Read an input data point from the data file. It should be noted that this data information was in SI units.
Convert the SI units to U.S. units because the pressure-drop subroutines required such units.
Divide the pipe length into 100 segments and call each of the seven subroutines to determine the pressure drop in each segment.
Sum the respective segment pressure drops for each of the correlations to determine the total pressure drop.
Convert all of the calculated pressure drops to SI units.
Write the measured and the seven calculated pressure-drop values in the output data file.
Repeat Steps 1-6 for all data points.

It should be pointed out that dividing the pipe length into 100 segments was found to be more than adequate for a consistently accurate calculation.

Once the output data file was generated, it was used as the input to an error-analysis program.

ERROR ANALYSIS

In order to quantify the degree of success of a correlation in predicting the measured pressure drop, a percentage deviation term was defined for each calculation as shown in Equation 1.

When this value is positive, the correlation is overpredicting the measured pressure drop.

An average deviation (error) for each correlation is based on the total number of data points (N) and is defined by Equation 2.

Although it is customary to regard the average deviation as the degree of overall success in predicting the measured data, this can be misleading unless the spread of error is considered. The scattering of predictions with respect to the data can be determined from standard deviation (S) and root mean square (RMS) error (Equations 3 and 4).

A computer program was written for performing the error analysis and calculating the above values.

The program used the data file containing all the values of the measured and previously calculated pressure drops.

Once the deviation values were computed, the program plotted the calculated pressure drops and the percentage deviations vs. the measured pressure drops.

CALCULATIONS VS. DATA

The data from the bank were utilized to calculate the pressure drop in the pipeline with the seven correlations. Once again, it should be noted that the majority of data is from large oil pipelines of about 0.5 m in diameter.

The results are presented in the form of calculated pressure drop and percentage deviation vs. measured pressure drop in Fig. 3.

These figures suggest the following conclusions:

FB and HB correlations generally underpredict the pressure drop with most of the deviation in a 20-80% underprediction band.
MB correlation mostly overpredicts with the bulk of the deviation in the 0-100% overprediction range.
DR correlation mainly underpredicts with the majority of calculations in the 080% band.
DU correlation has a deviation of 0-120% for most of the data.
AZ correlation predictions are mostly in the -100 to +100% range.
BB correlation has a deviation mostly in the -50 to +50% range.

A composite plot of the average error, standard deviation, and RMS error for all tested correlations is given in Fig. 4.

It is evident that for the data tested, the Beggs and Brill correlation has the lowest average error (14%) followed by Aziz (20%).

Dukler correlation has the highest positive (overprediction) value of average error (51%). Fancher and Brown correlation has the largest negative value (underprediction) of average error (-64%).

Although Aziz has a low average error, it exhibits a standard deviation and RMS error of 78 and 80, respectively. Hagedorn and Brown and Fancher and Brown correlations showed the lowest standard deviations (22) followed by Beggs and Brill (29).

Overall, it appears that the set of actual, measured pressure-drop data is best represented by the Beggs and Brill correlation. 1

REFERENCES

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