Solids Transport

8/4/2019 Solids Transport

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INTEC ENGINEERING, INC. DEEPSTARMULTIPHASE DESIGN GUIDELINE

16.0 SOLIDS TRANSPORT

16.1 Introduction

The hydrocarbons produced from a reservoir are sometimes accompanied by small

quantities of solids such as sand or fracturing materials (proppants). Fo r example, the

Forties field produces i n the region of 5 to 40 pounds of sand for every thousand barrels

of oi l produced. This sand norma lly collects in the separators and is either removed by

manual intervention during maintenance periods or flushed out using a jetting system.

When the South East Forties development was considering using seabed templates

connected to the existing Forties Alpha platform by two 5 km pipelines, there was

concern that the sand produced might settle out in the pipeline causing pigs to become

stuck. The removal of sand may be relati vely simple using pigging, prov ided that only

small amounts are deposited. The removal of larger quantities may be difficult and time

consuming. To design such systems required knowledge on how the sand is transported

and when it will accumulate. Thi s prompted experimental work to be undertaken

(Reference 1). Again in 1990 the Forties Foxtrot development highlighted the need for a

better understanding of solids transport in multiphase pipe line systems.

The results of experimental work are presented here as a guide to predicting the critical

conditions required to prevent solids accumulating in multiphase oil and gas pipelines.

This is necessary to prevent pigs from becoming stuck and to prevent possible corrosion

under solid deposits in pipelines. Because of the possible stabilization of solid deposits

by heavy hydrocarbons, inhibitors, and the potential for accelerated corrosion under

deposits, it is recommended to operate multiphase flowlines above the settling velocity to

avoid solid deposition and below critical erosion velocit ies to limit material loss.

This work is limited to solids that are heavier than the carrying fluids (i.e., sand and

proppants) and may not be applicable to other solid substances formed by chemical

reaction such as hydrates, asphaltenes and waxes.

16.2 Solid Particulate Settling Characteristics and Flow Regimes

Flow regimes for solids transport in liquid/solid and liquid/gas/ solid systems are

illustrated in Figure 16.2-1.

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INTEC ENGINEE RING, INC. DEEPST AR

MUL TIPH ASE DESIGN GUIDELINE

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16.2.1 Liquid/Solid Systems:

Stationary bed

At very low liquid flowing velocities a stable solid bed is formed with particles at the

bottom and no grains move at all. With an increase in the velocity a stable bed height is

reached where the particles at the top are transported further downstream to increase the

length of the bed. The upper surface of the bed is flat at very lo w flowrates but becomes

wavy as the flowrate increases. A t higher liquid flowrates the height of the stationary bed

decreases. A n equilibrium bed is reached when the shear at the upper surface of the bed

transports solids downstream at a rate equal to the solid inflow rate.

Moving dunes

If the liquid flowrate is increased further the bed breaks up and the particles arrange

themselves into moving dunes in which the grains on the upper surface o f the dune are

rolled along from back to front (downstream). The grains then fall into the sheltered

region at the front of the dune. The dune passes over these particles until they are once

again on the top surface. The motion of dunes is similar to sand dunes in the desert and

to snow drifts. Smaller dunes move faster than larger ones and a given length of

stationary deposit wil l break up into a number of dunes, each with a characteristic length

and velocity.

Scouring

As the flowrate is increased further the grains roll along the top of the dunes with

sufficient momentum that they escape from the sheltered downstream region and are

swept away as individual scouring grains. Dunes can still survive in this erosional

environment by replenishment from upstream particles.

Dispersed

At high liquid flowrates the dunes are dispersed. The solids particles now move in the

produced fluid in an erratic pattern. However, a strong concentration gradient is usually

observed.

16.2.2 Liquid/Gas/Solid Systems

Since the solids are heavier than the carrying fluids they are usually transported along the

bottom of the pipe when the concentration is low. For this reason the flow patterns

observed in single phase solid/liquid flow are similar to those seen in stratified

liquid/gas/solid flow since the liquid occupies the lower part of the pipe and the flowing

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velocity is steady. However this is not the case when the gas/liquid flow regime is plug

or slug flow, as the depth of the film and the velocities vary.

Plug flow

In plug flow, the gas bubbles move along the top of the pipe and have little effect on thesolids flow with the full range of regimes already mentioned possible (Section 16.2.1).

As the amount of gas is increased the bubble depth increases and the fluctuating

velocities affect the transport similar to that described in slug flow.

Slug flow

In slug flow the transport of solids is complicated as the solid may settle during the

passage of the film region and may be transported in the slug body . There can be a large

diameter effect as the depth o f the film varies and shields the bottom of the pipe from the

turbulence of the slug. A bed can be formed i f either the slug or film does not transportthe solid. In cases where the solid is transported in the slug, only the mot ion is

intermittent. The frequency between slugs may be a factor i f bed compaction and

stabilization by other products is a possibility.

Fo r slug flow in slightly uphill inclined pipes the solid may be transported backwards due

to the reverse flow in the film region. Therefore, the overal l motion of the sand depends

on the efficiency of the forward transport by the slug and the reverse motion caused by

the film region.

Low holdup wavy flow

In wet gas pipelines the liquid can be transported as a thin film along the bottom of the

pipe, in which case the solid concentration in the film can be high, and in the extreme

may appear as a wet solid bed. In this case little is known about the conditions required to

remove the wet solids.

Annular flow

In annular flow the sol ids may be transported in the liquid film and the gas core. Since

the velocities are high in annular flow the usual concern is whether the erosion rate isexcessive rather than i f the sol ids will be transported or not.

Several factors can significantly complicate the analysis of the conditions required to

prevent the accumulation of solids in multiphase pipelines. These include :

Three phase flow effects (gas, oi l, and water flow)

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Preferential wetting of the solids by another phase (i.e., water wet solids removal by

the oil phase)

Bed stabilization by other products (i.e., wax)

Effect ofinhibitors or other chemicals

16.2.3 Predicting the Limit of a Stationary Deposit

The conditions required to prevent the formation of stationary deposits in multiphase

pipelines can be estimated using a method developed by X F E in 1993 (Reference 2). The

model is based upon a series of equations derived by Thomas (Reference 3) for

calculating the friction velocity at the limit of solid transport in a liquid/solid system.

The friction velocity is related to the pressure gradient and has been extended by X F E to

the case of transporting solids in multiphase systems. This is accomplished by estimating

the flowing conditions that give rise to the same pressure gradient that is required to

transport solids in the liquid/solid system. The model is hence called the minimum solids

transport pressure drop model. The Thomas equations are used to predict the flowing

pressure gradient associated with the minimum transport condition in liquid/solid flow

where enough energy is passed to a solid particle to enable it to remain in the bulk of the

fluid phase and to be transported downstream. Using this pressure gradient, a locus of

points can plotted on a two-phase flow pattern map for a constant pressure gradient equal

to the pressure gradient at the minimum transport condition.

In the X F E model the two phase pressure gradient is predicted using the method of Beggs

and Bri l l by guessing values for the gas superficial velocities for a given liquid superficial

velocity and calculating the two-phase pressure gradient. Iterations are performed until

the velocities produce a pressure gradient equal to that for the minimum transport

condition calculated by the Thomas equations for the same liquid flowing velocity. The

calculation is repeated for a range ofliquid velocities to yield a locus ofvelocities above

which the pressure gradient should be sufficient to transport the solids along the pipeline.

16.2.4 Determinat ion of Pressure Gradient at the Minimum Transport Condition

Thomas derived several equations for the minimum transport condition depending on thesolids concentration and whether the solids particle diameter is smaller or larger than the

laminar sub-layer in the liquid. The first step in the analysis is to determine the solids

particle diameter and the thickness of the laminar sub-layer, however, since the thickness

of the laminar sub-layer depends on the Reynolds number, some iteration is required.

The initial assumption is that the particle diameter is greater than the thickness of the

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laminar sub-layer and check for this condition after the friction velocity has been

calculated.

16.2.5 Partic le Diameter

It is important to use the correct particle size in the analysis as this affects the calculationof the particle settling velocity and also determines which method is used, depending on

whether the particle is smaller or larger than the laminar sub-layer . Fo r single sized

particles this is no problem. However, the solids produced with oil and gas usually

contains a wide range of particle sizes. Figure 16.2-2 shows the particle size distribution

for the Forties field sand and shows that the size varies from 45 microns to over 1 mm.

For most cases it is recommended to use the mean particle diameter or d50 value (in this

case 255 microns) for the determination of the minimum transport criteria. Though it is

also recommended to investigate the sensitivity of the results to the particle diameter

used.

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16.2.6 Thickness of Laminar Sub-layer

The thickness of the laminar sub-layer is related to the pipeline diameter and the

Reynolds number for the case of a smooth pipe with a Reynolds number


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(c) New ton 's law:

For Re > 500

ws = 1.74 [gd ( p s- p l) / p l ] 0 5

Where the particle Reynolds number is given by:

Re = (1488 d ws p I) /m

Since the Reynolds number depends on the particle settling velo city, the correct equation

to use is found by calcula ting the settling velocit y and Reynolds number by each equation

and comparing the Reynolds number with the applicable limits for each method. Fo r

particles o f between 50 and 1000 microns in oi l, the appropriate l aw is likely to be either

Stoke's or the intermediate law.

The particle settling velocity can be used to estimate the flowing conditions required to

transport solids in vertica l pipes. For liquid /gas/solid flow it is required to consider in

which phase the solid particles are transported.

16.2.8 Friction Velocity at Minimum Transport Condition

When the particle diameter is larger than the laminar sub-layer then the friction velocity

at deposition for the limiting condition of infinite dilution is correlated by:

uo* = [0.204 ws (u /d) (u/D) - 0 6 {(p s-p l) /p l} - 0 2 3 ] 0 7 1 4

where:

ws = particle settling velocit y (ft/s)

uo* = friction velocity at minimum transport condition for infinite dilution (ft/s)

d = solids particle diameter (ft)

u = kinematic viscos ity (ft2/s)

When the solids concentration is high the friction velocity is modified by the following

relationship:

(uc*/u,*) = 1 + 2.8 (ws / u o * ) 0 3 3 F 0 . 5

Where uc* is the friction velocity at the minimum transport condition for a given

concentration and F is the solids concentration volume fraction in ft3

/ft3

.

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Fo r most cases of interest in oil and gas pipelines, the solids concentration is low and the

first equation is usually sufficient to determine the friction velocity for minimum

transport. However, i f the liquid holdup is small, the concentration correction may be

required.

When the solids particle diameter is smaller than the laminar sub-layer the expression for

the friction velocity at the min imum transport condition is:

u* = [100ws (u / d )2 7 1 ] 0 2 6 9

Given the friction velocity and the Reynolds number, the thickness of the laminar sub

layer can be calculated and the appropriate friction velocity expression checked.

16.2.9 Pressure Gradient at Minimum Transport Condition

Following the above procedure determines the friction velocity at the minimum transport

condition for the l iquid phase. This is easily used to calculate the associated single phase

pressure gradient at this condi tion using the expression:

A Pmtc = (4 p l m2 ) / [144 gc D]

where:

gc = 32.174

A two-phase flow pressure drop calculation can now be used to determine the l iquid and

gas velocity combinations, which result in the same two-phase flow pressure gradient. It

is useful to plot the locus ofthese points on a flow pattern map to indicate the conditions

under which solids may or may not be transported. Alternatively comparing the two-

phase pressure drop with the minimum transport condition for the condit ions of interest

will indicate whether solids are deposited or not. F igure 16.2-3 shows a compar ison of

the model predictions with some experimental data.

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Figure 16.2-3: Comparisons of the model with BHRA data

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16.3 References

1.Fairhurst, CP, "Sand Transport in the South East Forties Pipe Line" , BHRA,1983.

2. Smith, M " A Model for Predicting Sol ids Transport in Near Hor izon tal Multi-phase Oi l

and Gas Pipe Lines", X F E report 8/2/1993.

3. Wasp, Kenny and Gandhi, "Solid-Liquid Flow Slurry Pipe Line Transportation", Gulf

Publishing Company, Clausthal, Germany, 1979.

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Solids Transport