Las primeras Ordenanzas de ingenieros: la Ordenanza de 1.71846

(a) Stratified and Flow Regimes

The approach used for calculating the pressure drop and liquid hold-up in the stratified-smooth, stratified-wavy and annular-mist flow regimes is identical. In each case a segregated flow is assumed and the liquid hold-up and pressure drop are determined using a similar calculation procedure to that employed when determining the equilibrium liquid level for flow regime identi-fication (Section 4.3.1).

However, for stratified-wavy or annular flows the assumptions of a smooth interface and no liquid entrainment in the gas phase are not correct. To take account of the effects of inter-facial waves and droplet entrainment the pressure drop equations in the gas and liquid layers have been modified.

Inter-facial waves are accounted for by using the inter-facial friction factor equation of Andreussi and Hanratty (6). This leads to the prediction of greater losses through an increased inter-facial stress term. The overall effect of using the Andreussi-Hanratty equation is to increase the predicted pressure drop and decrease the predicted liquid hold-up at high flowrates.

The entrainment of liquid droplets in the gas phase can be accounted for by treating the gas/droplet mixture as a single modified gas phase. The density and viscosity of this

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BP Design Manual Section 4. Gas/Condensates

gas/droplet phase are calculated assuming that the mixture is homogeneous:

= +

= density of gas/droplet mixture = gas viscosity (kg/m/s)

= liquid viscosity (kg/m/s)

= viscosity of gas/droplet mixture (kg/m/s)

In these equations the droplet concentration is the ratio of the cross-sectional area occupied by the liquid droplets to that occupied by the gas/droplet mixture. It is related to the entrainment fraction (the ratio of the liquid mass flux transported as droplets to the total liquid mass flux) as follows:

where:

= entrainment fraction

= liquid superficial velocity (m/s)

= gas superficial velocity (m/s)

The treatment of the gas and droplets as a single phase is based on the following assumptions:

l The droplets are transported at the velocity of the gas. Thus drag between the gas and the droplets can be ignored.

l There is no momentum transfer between the gas/droplet phase and the liquid layer due to the droplet entrainment and deposition processes.

l The droplet entrainment and deposition processes do not need to be separately but can be accounted for within the calculation of the entrainment fraction.

Unfortunately there is little entrainment fraction data available for horizontal stratified and annular flow. The method used within the mechanistic model is based on data obtained by Shell on their high pressure (7). There is evidence that this method may under-predict the entrainment fraction at high gas flowrates.

The inclusion of entrainment fraction also leads to an increase in pressure drop and a decrease in the liquid hold-up predictions.

Section 4. Gas/Condensate BP Multiphase Design Manual

Gas, Liquid and Bubble Flows

The calculation of the liquid hold-up and pressure drop in the liquid, gas and dispered bubble flow regimes is conducted by assuming the flow is a homogeneous mixture. The flow is treated as a single-phase with the mixture density and viscosity:

+ +

V liquid superficial velocity (m/s)

V gas superficial velocity (m/s)

(c) Normal Slug Flow

At present no mechanistic model is available for accurately calculating the pressure drop and hold-up in normal slug flow. Thus, the empirical method of Beggs and is used when normal slug flow is predicted (see Section 3.1.3).

(d) Terrain-Induced Slug Flow

If terrain-induced slug flow is predicted the hold-up and pressure drop are calculated from the maximum stable liquid accumulation determined in Appendix 3B.

This maximum stable liquid accumulation is the maximum volume of liquid that can be retained in an uphill section of at a given gas velocity. It is calculated by assuming that slugs form at the start of the uphill section of flowline, pass through the line shedding liquid from their rear and then collapse just before they reach the end. The shed film forms a counter-current liquid film which flows back to the start of the uphill section of where it builds up to form the next slug.

Liquid flowing into the uphill section of leads to the continuation of short slugs into the next section. However, the liquid retained in the uphill section remains equal to the maximum stable. liquid accumulation.

For terrain-induced slugging the liquid hold-up in an uphill section of is simply equal to the ratio of the maximum stable liquid accumulation to the total volume of the pipeline section.

From Appendix 3B this is:

BP Multiphase Design Manual Section 4. 4. Gas/Condensates

+ 0.59 + 0.59 H,

H,

+ 0.59 + 0.59

where:

H, = liquid hold-up = slug hold-up

mixture velocity (m/s)

The slug hold-up is calculated using a steady state correlation at present the method of Gregory is employed (Appendix 3A).

The calculation of pressure drop for terrain-induced slugs assumes that the flow is homoge-neous with the mixture density and viscosity based on the calculated hold-up:

= +

= H,

= H, + +

This approach ensures that a good approximation to the hydrostatic component of the sure gradient is obtained. This component is normally much greater than the frictional compo-nent when terrain-induced slugging is encountered.

Section 4. Gas/Condensate BP Multiphase Design Manual

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BP Multiphase Design Manual

Section 4. Gas/Condensates I

4.4 Sphered Liquid Volume

As discussed in Section 4.2.4 the sphered liquid volume, for a that has not yet achieved equilibrium, can be estimated as the total volume of liquid that has entered the following the launch of the previous sphere.

For the equilibrium case the sphered liquid volume is equal to the total liquid volume in the line, calculated using the Mechanistic Model, less that swept out of the pipeline as a liquid film during the sphere transit time. To determine the sphered liquid volume the growth of the slug in front of the sphere must be calculated, using the mass balance equation, throughout the sphere’s passage through the line.

The process involved with the passage of a sphere through the is shown below:

Figure 2. Growth of liquid slug during sphering growth where:

H, = liquid film hold-up = sphered slug hold-up

L, sphere to pipe cross-sectional area ratio = velocity of liquid at sphere (m/s)

liquid velocity (m/s)

V mixture velocity (m/s)

= sphered slug fluid velocity (m/s)

V sphere velocity (m/s)

v, = sphered slug front velocity (m/s)

The mathematical details of the approach required to calculate the sphered slug volume will not be discussed in this design method. However, the general approach is to determine the rate of growth of the sphered slug as it passes through the collecting liquid from the preceding film. Liquid leakage passed a sphere that does not fully block the pipe can also be included.

Thus, a combination of three equations for:

(a) The mass balance at the front of the growing slug

(b) The mass balance at the sphere (if liquid leakage passed the slug is modelled)

(c) The growth of the slug due to the differential velocity between the slug front and sphere

Section 4. Gas/Condensate BP Multiphase Design Manual

lead to the required method for integrating the slug length as the sphere passes through the flowline.

For the special case of a horizontal flowline, zero pressure drop, no liquid leakage passed the slug and a sphered slug hold-up equal to unity, this equation reduces to:

where:

= total liquid holp-up in the line prior to sphering

Vout = liquid volume leaving the line during passage of sphere

This approximate form for calculating the sphered slug volume has been employed in the BPX program.

BP Multiphase Design Manual Section 4. Gas/Condensates