Slug Length Prediction

We need to estimate the slug lengths for the various cases. As mentioned in the text, the use of correlations for slug length prediction is not very accurate. Unless a transient model is available, however, these predictions are the best available method.

The output for the Pipephase "SLUG" option prints tables summarizing the predictions of the Brill, et al. correlation. It also indicates an approximate slug length for severe slugging. The Brill, et al. predictions will be used as the basis for predicting slug length in

hydrodynamic slug flow, and the Pots πss method will be used as the basis for predicting

slug length in severe slugging. These estimates will be checked against the predictions of the Hill & Wood model for hydrodynamic slugging and the predictions of the OLGA transient model.

In severe slugging, the operation is cyclic:

• The low spot fills with liquid, blocking the flow;

• Liquid builds in the pipeline and riser until the pressure behind the liquid slug builds to

a high enough level to push the slug out;

• The liquid exits the system as a slug, increasing in velocity as the gas behind the slug

expands;

• When the gas has exited the riser, liquid will fall back down the riser, and drain in from

the pipeline, starting the cycle again.

The slug length is estimated by:

Ls = Lr / πss

where Lr is the riser height in feet.

The slug length should not vary much for a constant rate, since the operation in cyclic. The maximum slug length therefore is approximately equal to the average slug length.

The values for the slug length reported in Pipephase for the 3 severe slugging conditions

a) For the 10" Line, Year 12 - Ls = 2392 ft.

b) For the 12" Line, Year 8 - Ls = 3140 ft

c) For the 12" Line, Year 12 - Ls = 829 ft

The large decrease in the slug length for the 12" line, year 12 is due to the large increase in holdup in the line predicted by Beggs and Brill. The accuracy of this value is doubtful.

For the hydrodynamic slugging cases, the "SLUG" report in Pipephase contains predictions of the average slug length and the slug length distribution using the Brill, et al. model. As detailed in the text, the Brill method is based on a very small amount of data, and it doesn’t account for most of the variables, which play a part in slug flow.

To use the Brill slug length model to estimate the maximum size of a slug for equipment selection, the designer needs to estimate the slug length corresponding to a design occurrence frequency. A reasonable philosophy would be to design the separator/slug catcher for the once per year slug. Estimating the average slug frequency from the Pipephase "SLUG" report, the number of slugs per year can be calculated. The slug distribution table above can be used to estimate the slug length corresponding to one occurrence in this number of slugs per year.

For example, the year 1 rate through the 10" line gives a slug frequency of 98.4 seconds by the Brill model. This frequency corresponds to

(365 D/yr * 86,400 sec/D) / 98.4 sec = 320,500 slugs/yr

If one slug per year can be greater than the design slug, the design slug must be at the

(1 - 1/320500) * 100 = 99.9997 percentile

The average slug, according to Brill, is 293 ft long. The maximum allowable slug would then be about 10.5 times as long as the average or 3080 ft long.

The design percent slug was calculated for all the other hydrodynamic slug cases. The design slug was close to the 99.9999% slug length for all cases, using the one slug per

year criteria. Tabulating the 99.9999% data for the hydrodynamic slug cases gives design slug lengths (in feet) for the various cases of:

Year No. 8 inch 10 inch 12 inch

1 2152 3153 4250

4 2079 3050 4113

8 1943 2847 3140*

12 1848 2392* 829*

* Terrain slugs

To calculate the liquid surge requirements for the separator based on these slug lengths, additional information is needed. Since the slugs consist of aerated liquid, the liquid holdup in the slug must be known in order to determine the volumetric rate entering the separator. The surge volume required also depends in large measure on the capacity of the liquid dump valves on the separator.

The Pipephase "SLUG" table includes a calculation of the liquid holdup in the slug, based on the Brill, et al. method. The tabulated value for the "liquid from the slug" is equal to:

Volslug = Vm Hls Ap ts

where Hls is the liquid holdup in the slug, Ap is the pipe cross-sectional area, and ts

is the time that the liquid slug exits the pipeline.

The required surge volume for the separator is:

Volsurge = Volslug - ts Qdump

where Qdump is the volumetric capacity of the dump valve.

For this example, we will assume that the volumetric capacity of the dump valve is 1.33

times the design oil rate. This assumption gives a Qdump of 1.35 ft

3

/sec. The separator is also assumed to be a 2-phase separator.

With these assumptions, the design surge volumes (ft3) for the hydrodynamic slugging cases are:

Year No. 8 inch 10 inch 12 inch

1 145 561 1398

4 195 654 1506

8 101 294 —

12 0 — —

It is more difficult to estimate the slug volumes for the severe slugging cases using only steady state analysis. For a crude approximation of the behavior, use the following:

a) Slug buildup phase

When the slug is building up, there is essentially no flow out of the pipeline. The time required to build the slug is approximately:

tbu = Ls/vsl

The liquid rate out of the line is ~0 during this time.

b) Slow gas expansion phase

After the gas pressure has built to a high enough level to push the slug, the liquid rate

out of the line is approximately equal to the mixture velocity, Vm. The time required

for this phase is tsg.

c) Fast gas expansion

When the liquid slug is shorter than the riser pipe, the gas behind the slug expands rapidly. The velocities in the riser may reach 60-80 ft/sec. This time period is so much smaller than the others that it can be assumed to be virtually instantaneous. The liquid rate is so high that essentially all the liquid produced during this time goes into the separator surge.

With this simplified model, the flowrates out of the pipe can be estimated. The slug cycle time (tc) is equal to tbu + tsg. The liquid produced during one cycle is equal to tc * Vsl * Ap.

volume of liquid exiting during the fast gas expansion is equal to the riser volume. The remainder of the liquid must exit during the slow gas expansion phase. Therefore,

(tbu + tsg) Vsl Ap = (tsg Vm Ap) + (Lr Ap)

tsg = [(tbu Vsl) - Lr] / Vsg

tsg = (Ls - Lr) / Vsg

To illustrate the use of these equations, we will check the outlet rates for the 10" line at

year 12. The values for the key parameters are Ls = 2392 ft. Vsg = 0.90 ft/sec, Vsl = 0.69

ft/sec, Ap=0.492 ft

2

, and Lr = 100 ft. The value for tbu = 2392/0.69=3467 sec. The value

for tsg = (2392-100)/0.90 = 2547 sec.

The model indicates that the liquid flowrate out of the line is: 0 ft3/sec for 0<t<3467

(0.90+0.69) * 0.492 = 0.782 ft3/sec for 3467<t<6014

Infinity for t=6014, Volume=0.492 x 100-49.2 ft3

Since the 0.782 ft3/sec is less than the Qdump of 1.35 ft3/sec, the liquid will not accumulate

in the separator during the slow gas expansion phase. The required surge volume therefore is 49.2 ft3.

Completing these calculations for the other severe slugging cases gives the following

tabulation for the required surge volumes (ft3) for all the cases:

Year No. 8 inch 10 inch 12 inch

1 145 561 1398

4 195 654 1506

8 101 294 935

12 0 49 71

Using the Brill analysis, the required surge volume for the downstream separator would be 654 ft3 for the 10" line.