Dynamics of Formation and Dissociation of Gas Hydrates in Pipelines at the Various Modes of Gas Transportation 2012 Heat and Mass Transfer Waerme Und Stoffuebertragung

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O R I G I N A L

Dynamics of formation and dissociation of gas hydratesin pipelines at the various modes of gas transportation

V. Sh. Shagapov R. R. Urazov N. G. Musakaev

Received: 10 November 2010 / Accepted: 26 March 2012 / Published online: 13 April 2012

Springer-Verlag 2012

Abstract In the work a system of ordinary differential

equations has been received on the basis of the methods and

equations of multiphase medium mechanics, this system

describes hydrodynamic processes and processes of heat-

mass exchange in a pipeline in the presence of formation and

dissociation of gas hydrates on walls of the channel. The

various modes of gas transportation have been examined.

1 Introduction

Production of natural gas on the biggest gas fields located

in Western Siberia in Russia is often complicated by the

formation of gas hydrates [10]. Gas hydrates are solid

crystalline compounds formed by the physical combination

of gas and water under pressure and temperatures consid-

erably above the freezing point of water [1,5, 10, 13,20,

22]. In the presence of free water, hydrate will form when

the temperature is below a certain degree: this temperature

is called hydrate temperature Ts. Gas hydrate crystals

resemble ice or wet snow in appearance but do not have the

solid structure of ice. The main framework of the hydrate

crystal is formed with water molecules. The gas molecules

occupy void spaces (cages) in the water crystal lattice:

however, enough cages must be filled with hydrocarbon

molecules to stabilize the crystal lattice. At present a lot of

scientific papers are devoted to research of gas hydrates.

Some references are presented in the articles [2, 17].

Presence of moisture in the gas and reduction of the

temperature when the gas moves in wells, gathering sys-

tems, and gas treatment systems creates the conditions for

gas-hydrates deposition on the walls of the pipes and

equipment. Gas hydrates generate considerable operational

and safety concerns in pipelines [1, 21]. The current

practice in the petroleum industry for avoiding gas hydrate

is to operate outside the hydrate stability zone. During the

flow of natural gas, it becomes necessary to define, and

thereby avoid, conditions that promote the formation of

hydrates. This is essential since hydrates can cause

numerous problems such as completely blocking pipelines

and surface equipment.

Sloan (2000) listed several conditions that tend to pro-

mote the formation of gas hydrates [21]. These are:

the presence of free water and gas molecules that range

in size from methane to butane:

temperatures below the hydrate formation tempera-

ture for the pressure and gas composition considered; high operating pressures that increase the hydrate

formation temperature;

high velocity or agitation through piping or equipment;

the presence of small seed crystal of hydrate;

natural gas at or below its water dewpoint with liquid

water present.

The above conditions necessary for hydrate formation

lead to the following four classic, thermodynamic pre-

vention methods [1,10, 20].

V. Sh. Shagapov

Institute of Mechanics of Ufa Branch RAS, Ufa, Russiae-mail: [email protected]

R. R. Urazov

Ufa State Aviation Technical University,

Branch in the City of Ishimbay,

Ishimbay, Russia

e-mail: [email protected]

N. G. Musakaev (&)

Tyumen Branch of Khristianovich Institute of Theoretical

and Applied Mechanics SB RAS, Tyumen, Russia

e-mail: [email protected]

1 3

Heat Mass Transfer (2012) 48:15891600

DOI 10.1007/s00231-012-1000-3



1. Water removal provides the best protection.

2. Maintaining a high temperature throughout the flow

system, i.e. insulation, pipe bundling, or electrical

heating.

3. Hydrate prevention is achieved most frequently by

injecting an inhibitor, such as methanol or monoeth-

ylene glycol, which acts as antifreezes.

4. Kinetic inhibitors are low-molecular-weight polymersdissolved in a carrier solvent and injected into the

water phase in the pipeline. These inhibitors bond to

the hydrate surface and prevent significant crystal

growth for a period longer than the free water

residence time in a pipeline [11].

Major tasks of gas hydrates formation in pipelines are

traditionally the following: determining of the channel

section subject to sclerosis and its length; the calculation of

speed and time of full overlapping of the channel cross

section. It is also important to know how various methods

of struggle against hydrates formation and the modes of gastransportation influence on the dynamics of formation and

dissociation of gas hydrates. The present work is devoted to

the abovementioned issues in particular.

The proposed theoretical study differs from the works of

other authors in that here an attempt has been made to gen-

eralize the hydraulic quasi-stationary model of the gas flow

in pipes with allowance for the hydration to the case where

this process is limited by the condensation rate of moisture

from the moving gas. The model has been complemented so

that it is possible to study the influence of the introduction of

liquid inhibitors into the gas flow on the hydrate dissociation

dynamics. Besides, warming up of the surrounding rock as aresult of the pipeline maintenance is taken into account.

2 Basic equations

Natural gas with a given composition is piped through a

horizontal channel, with gas-hydrates being deposited onto

the inner wall. The main linear characteristics of the

channel are:Lis the length of the channel; a0anda1are the

inner and outer radii of the channel.

For the most comprehensive accounting of interphase

mass transfer processes and thermophysical phenomenarelated to them, we assume that the flow of natural gas in a

pipeline consists of two components, namely, the moisture

which is formed by water and methanol and of the

remaining partbasically hydrocarbon mixture. The first

component in the flow can be in gaseous state and in the

form of liquid droplets.

Hereinafter the parameters with the first subscript m in

brackets are related to methanol, which can be in the liquid

and gas phases, with mass concentrationskmland kmv. The

water contained in the flow with the mass concentration kw,

too, can be in two aggregative states: in the form of liquid

droplets with the concentration 1 - kmland as vapor in the

gas phase with the concentration 1 - kmv. Then for the

valueskmandkwin the gas flow the following formulae can

be written:

km

klk

ml 1

k

lk

vk

mv;kw kl1 kml 1 klkv1 kmv:

1

In the present study, several simplifying assumptions are

adopted: the gas-flow velocity is much lower than the

speed of sound; the velocities of the gas and liquid phases

are equal; the flow is quasi-steady; the pressure in the gas

flow and the gas-flow temperature are taken as quantities

averaged over pipe cross sections; for any cross section of

the pipe, the temperatures of both phases (the gas and

liquid temperatures) are assumed identical; phase transition

gas-hydrate is considered within the Stefan problem

statement; the pipeline is oriented horizontally, gravity is

neglected; the radius of curvature of the solid hydrate layer

along the axis of the pipe is considerably large, therefore

the thermal conductivity in the solid layer in the axial

direction can be neglected; the thermal resistance of the

pipe wall is small; conductive heat transfer in gas

compared with the convective can be neglected; the

pressure and the temperature at the inlet of the pipe are

constant; the physical properties of gas and hydrate are

constant; the heat exchange with the surrounding rock

occurs according to the Newton law.

The losses of natural gas on the formation of solid gas

hydrates are usually a small fraction of the gas flow rate mg.Therefore, this value along the length of the pipeline will

be assumed constant and equal to:

mg qgwgS; S pa2; 2

where qg and wg are density and velocity of the gas in a

pipeline;Sand a are area and radius of the live pipeline

section.

Since the gas flow in the tube can be accompanied by

the deposition of gas hydrates then a is a function of the

coordinate z and time t. Coordinate z will be measured

from the input section of the pipeline. For further analysis,

we will introduce the parameter d = d(z, t), which deter-mines the thickness of the gas hydrates layer near the pipe

wall. Then a = a0 - d.

After the initial preparation of gas the moisture content

is usually less than one percent, i.e. the mass content of

moisture in the flow is little. Formation of gas hydrate on a

certain section of the pipeline leads to the impoverishment

of the flow of moisture, and thus helps reduce the rate of

deposits in more remote areas. Therefore, the equation of

mass conservation for water can be written as follows:

1590 Heat Mass Transfer (2012) 48:15891600

1 3



mgdkw

dz Jw; Jw 2pajw: 3

Here jw is the intensity of consumption of moisture on

the formation of gas hydrate, take to the unit area of the

channel inner wall.

Let the mass intensity of formation of gas hydrate per

unit area be equal to jh. For the rate of growth of thethickness of gas hydrate on the inner wall of the pipe the

following equation can be written:

od

ot

jh

qh; 4

where qh is the density of the gas hydrate.

We assume that the gas hydrate is a clathrate compound

with a fixed component composition of the hydrate for-

mation mixture and water. Therefore, the intensity of gas

hydrate formation and consumption of water for hydrating

should be linked to stoichiometric condition:

jw 1 kghjh; 5kgh is the mass concentration of the hydrate formation gas

in the gas hydrate.

Lets make the following equation of the gas state:

p = ZgqgRgTg. Compressibility factorZgwill be defined on

the basis of the LatonovGurevich equation [8]:

Zg 0:17376lnT 0:73p 0:1p T

Tg

Tc; p

p

pc

: 6

whereTgis the gas temperature,p is the pressure,Tcandpcare the critical parameters.

Let us write momentum equation in the following form:

mgdwg

dz S

dp

dzf; f

1

4pasqgw

2g; 7

where fis friction force, assigned to the unit length of the

pipeline.

For the dependence of the friction coefficient s upon

Reynolds numberRe the following expression can be used[9]:

s 1:8 lgRe 1:50:5; Re 2aqgwg

lg: 8

The equation for the temperature alteration along the

pipeline taking into account calorific effects of water and

methanol vapor condensation can be put down thefollowing way:

mgcgdTg

dz

mg

qg

dp

dz mglw

dkl1 kml

dz mglm

dklkml

dz

Qgr;Qgr 2paqgr:

9

Here cg is specific heat capacity of gas at constant

pressure; lw and lm are heat of vaporization of water and

methanol;qgris intensity of the heat transfer from the gas

flow to the wall of the pipe per unit area of the pipe wall.

During operation of pipelines their thermal interaction

with the surrounding rock occurs, which is accompanied by

heating of the nearby ground layer. To describe the

external heat exchange of the pipeline in general it is

necessary to solve the following problem:

oTG

ot v

o2

TG

or2

1

r

oTG

or

t[ 0; r a2;

kGoTG

or arGTr TG t[ 0; r a2:

oTG

ot 0; t[ 0; r! 1:

v kG=qGcG;

10

whereTG,kG,qGand cGare respectively temperature, heat

conductivity, density and specific heat capacity of the

ground; a2 is an external radius of the pipeline.

The described problem of external heat for the examinedprocesses can be accurately and efficiently solved on the

basis of the integral method [3, 6, 7].

The system of Eqs. (1)(10) describes the flow of a wet

natural gas in a pipeline in the presence of methanol in the

flow. When methanol is absent, the gas motion is described

by the same system, provided that in the Eqs. (1), (9)

kml = 0 and kmt = 0.

The formation of gas hydrates on the walls of a channel

can occur in two ways. The first method is called the mode

of thermal balance. It is implemented with sufficient

income of substances that form hydrates (gas and water) to

the gas hydrate surface. In this case, the intensity of gashydrate formation is limited by the intensity of heat

abstraction from the surface of phase transitions (the sur-

face of the gas hydrate). The temperature of the inside wall

of a pipe at the site where the solid phase is formed is also

the temperature of the phase transitions surface Tr

. It is

believed that the temperatureTr

is equal to the equilibrium

hydrate formation temperature Ts, corresponding to the

value of gas pressure p in the flow (Tr= Ts(p)) [3]. Con-

sequently, the intensity of gas hydrate depositing in this

mode will be determined from the condition of the thermal

balance on the surface of the gas hydrate layer:

lsjh qrG qgr; 11

where ls is specific heat of phase transition at hydrate

formation; qrG is heat transfer rate from the inner surface

of the gas hydrate layer into the ground surrounding the

pipeline.

In case of insufficient flow of water to the surface of the

gas hydrate the second mode is realized, which will be

called the mode of moisture deficit. We assume that the

intensity of gas hydrate depositing is completely limited by

Heat Mass Transfer (2012) 48:15891600 1591

1 3



the process of the entry of moisture to the surface of the

gas hydrate layer. At that the temperature of the surface

Tr

must satisfy the condition of existence of gas hydrate

TrB Ts(p), corresponding to the pressure p in the flow.

To set the intensity of the moisture saturation of the gas

hydrate surface we assume in addition that the moisture

concentration in the gas phase near the surface of the

solid phase is equal to zero (kwr = 0). In accordance withthat, the internal surface of the gas hydrate will be the

adsorbent surface, on which the received moisture

instantly becomes a part of the gas hydrate. Then, using

the known equations [9, 19] for heat transfer and the

analogy of the processes of heat transfer and diffusion in

a turbulent flow we will receive the following equation

for the intensity of moisture entry to the surface of the

gas hydrate:

jw DqgkwSh;

Sh 0:021Re0:8Pr0:43D; PrD m=D; m ggqg: 12Here D and m are coefficients of diffusion and kinematic

viscosity;Pr(D)is diffusion Prandtl number;Shis Sherwood

number.

For the intensity of heat transfer from flow to the inner

surface of the pipe wall or to the gas hydrate surface the

following correlation is true:

qgr 1

2akgNuTg Tr;

Nu 0:021Re0:8Pr0:43; Pr mvg; vg kg

qgcg; 13

where Nu is Nusselt number; kgis heat conductivity of the

gas.The intensity of heat transfer q

rGtaking into account the

thermal resistance of the layer of gas hydrate deposits and

the thermal insulation layer on the outer surface of the

pipeline can be written down as follows:

qrG arGTr TG;

1

2aarG

1

2khln

a0

a

1

2k1ln

a1

a0

1

2k2ln

a2

a1

1

2a2aG;

1

2a2aG

1

kgln

h

a2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih

a2

21

s0

@

1

A: 14

Here kh, k1, k2 and kG are heat conductivity of a gas

hydrate, tube walls, insulation material and the ground;TGis the temperature of the surrounding rock at the boundary

of the pipeline r= a2. For the heat transfer coefficient of

the groundaGthe equation of Forchheimer is used [9,19],

in which h is the depth of the pipeline.

The transition from the first mode of gas hydrate

depositing in the calculations to the second is as follows.

The process of gas hydrate depositing begins at the section

z = zs, where the condition Tr = Ts(p). Below this section

(z C zs) the intensity of depositing is determined by for-

mula (11) taking into account Eqs. (13), (14) and the

temperature dependence of the wall Tr= Ts(p). In

accordance with Eq. (3) for the pipeline section z C zsthere will be lowering of the concentration of moisture kw,

i.e. decrease of moisture in the flow. Therefore, in a cer-

tain section z = z* the intensity of moisture transfer, cal-

culated by formula (12), will be equal to the value ofwater consumption, determined by formulas (5) and (11).

This means that in this section the second mode of gas

hydrate depositing of occurs. After this section (z[z*) the

intensity jh is determined on the basis of (12) [thus it is

necessary to take into account the stoichiometric con-

dition (5)]. The current temperature of the inside surface

of the gas hydrate deposit Tr

in the area of the pipeline

z[z* is determined from the condition of thermal balance

(11).

3 Conditions of gas hydrate formation in a pipeline

For the formation of gas hydrate two conditions [9,12] are

to be fulfilled. The first is the availability of natural gas

containing water in liquid form. The second is the rela-

tively low temperature and relatively high pressure of gas.

Therefore, for the formation of solid deposits on the inner

wall of the pipeline it is necessary that its temperature Tr

should be below the dew point for moisture contained in

the gas. For a given gas composition the equilibrium

temperatureTsof joint coexistence of solid gas hydrate, gas

and water is a function of pressure p. If the condition

TrB Ts(p), is fulfilled then on the inner surface of the

pipeline will be the depositing of the gas hydrate will

occur.

In accord to the first condition the gas hydrates forma-

tion can occur in those areas where the gas temperature

near the pipe wall is below the dew for moisture contained

in the gas. The dew point near the wall comes in the section

where the following condition is satisfied:

pwexp Tw

Tr

kvpZvRv

ZgRg: 15

where kv = qv/qg; pw* and Tw* are approximation param-

eters; Rv is a reduced gas constant for water steam.

After the dew point occurrence it is necessary to observe

the change of temperature of the pipe wall Tr

. For the

dependence of the equilibrium temperature of hydrate

formation Ts on the pressure p approximation [3] is com-

monly used:

Tsp Thln p=ps0 Ts0; 16

where Th* is an empirical parameter, with the same

dimension as a temperature and dependent on the natural


1 3



gas composition. Thus, upon the occurrence of the dew

point near the pipe wall for the formation of gas hydrate it

is necessary to satisfy the conditions:

Tr Tsp: 17

The temperature of gas hydrate formation depends on

the concentration of the inhibitor kmlin water: Ts = Ts(kml)

[9, 12]. Therefore, consumption of methanol in its supplyin the pipeline should be such that the temperature of

hydrate formation was not higher than the minimum

temperature of the inner wall. This temperature is in most

cases equal to the temperature of the surrounding ground,

i.e. Ts B TG.

In the presence of methanol in the droplets of water,

irrigating the pipe wall, the surface temperature of gas

hydrate will decrease. Moreover, the magnitude of this

temperature is determined by the current concentration of

methanol in the irrigating liquid drops. By selecting the

consumption of methanol and, consequently, its concen-

tration one can achieve such mode of operation of thepipeline, in which the temperature of its inner surfaceT

ris

lower than the corresponding temperature TGand Tg. Then

the heat needed for dissociation of a gas hydrate can come

from the gas flow, as well as from the ground. With this

method of removal of gas hydrate plaques the water educed

as result of the gas hydrate dissociation will additionally

get into the flow. Therefore, the concentration of methanol

in the droplets of water will decrease and will lead to

increase of temperature Tr

on the lower sections of the

pipeline. The calculation must take into account this

circumstance.

Suppose that at a certain section of the pipeline the

methanol is introduced with mass flowmm0. Mingling with

the moisture in the flow methanol will form a binary vapor-

droplet mixture. Basing on the data of [12] lets assume

that the magnitude of temperature reduction depends lin-

early on the concentration of methanol in drops. Then, for

the temperature of gas hydrate dissociation the following

expression is valid:

Tms Ts Tmkml; 18

Ts is the temperature of dissociation in the absence of

methanol.Suppose that the temperature Tr

on irrigated surface

layer is equal to the value determined by the expression

(18), and the intensity of the decomposition layer of the gas

hydrate will be determined from the condition of thermal

balance (11). At that for the intensity of heat transfer from

the flow to the inner surface of the pipe wall or to the

surface of gas hydrate, when it is present on the surface of

the pipe wall, the Eq. (13) can be used. For the intensity of

heat qrG between the inner wall of the pipe and the sur-

rounding rock we will use Eq. (14). The rate of change of

thickness of the hydrate layer on the walls of the pipeline

and the mass intensity of decomposition of this layer jh are

related by Eq. (4).

Moisture, formed during the dissociation of gas hydrate,

enters the flow and leads to decrease of the methanolconcentration in vapour-droplet mixture. The intensity of

the water isolation jw in that case is connected with the

intensity of dissociation of gas hydrates by (5).

It is known that methanol does not enter into chemical

reactions. Therefore, its mass flow downstream from the

site of injection is constant, and the mass flow of water will

increase due to additional income as the result of dissoci-

ation of gas hydrates. For a quantitative description of this

process we write the equation of mass conservation for

methanol and water:

mgklkml 1 klkvkmv mm0;

mgd

dz kl1 kml 1 klkv1 kmv 2pajw: 19

Furthermore, we assume that the mass concentrations

kmland kmvare related by equations, which can be obtained

on the basis of Raoults and Daltons Laws.

Rmkvkmvp RgpmsTNml; 20

Rwkv1 kmvp RgpwsT1 Nml;

Nmlkml

lm

kml

lm

1 kmll

w

1

; 21

where Nml is molar concentration of methanol in droplets

of liquid;lmandlware molar mass of methanol and water;

pms(T) and pws(T) are equilibrium saturation pressures for

the methanol and water, corresponding to the temperature

Tand approximated by the following expressions:

pms pmexp Tm

T

; pws pwexp

Tw

T

: 22

In calculating the dissociation of gas hydrates on the

inner walls of the pipeline it is necessary to know the value

of the mass contents of methanol in drops kml in eachsection. According to expression (18), this value

determines the change of equilibrium temperature of

hydrate formation. Eqs. (19)(21) represent the system

consisting of four equations with four unknowns.

Therefore, this system can be uniquely solved relative to

kml. Omitting the cumbersome transformations, we will

write down the resulting expression for finding kml:


1 3



A1k3ml B1k

2ml C1kml E1 0; 23

where

A1 BC2D BCD BCB kwC 1

2;

B1 A 2ACAC2 B 2BC 2BC2D BCD

AB ABCD

C1 2AC 2AC2 BCBC2D AB ABC2D

kwC2 kwBC; ABCABC

2D 2kwC2

kwB 2 BkwC;

E1 AC2 ABCD;

A mm0

mg; B

Rgpms

Rmp ; C

lmlw

; D Rmpws

Rwpms:

Expression (23) is a cubic equation with real coefficients,

which can have multiple roots (including complex). We

are interested in those roots which are presented in the

interval (0, 1). Other values of kml have no physical

meaning.Using the Eqs. (19)(21) we can also obtain the value

of the required consumption of methanol to prevent

hydrate deposits. In the absence of hydrate formation

mass flow of moisture mw will be maintained along the

whole length of the pipeline. Then, in accordance with

Eq. (19) for jw = 0 the following expression can be

written down:

mgkl1 kml 1 klkv1 kmv mw0: 24

Suppose that for reducing of the temperature of hydrate

formation to the necessary value T

ms

TG is required

concentration of methanol kml is required. Then, on the

basis of Eqs. (20), (21) we can write the expression for the

mass concentration of vapor in the gas flow and the mass

concentration of methanol in the mixture of water vapour

and methanol:

kv pmsTGN

mlRg

pkmvRm;

kmv 1 pwsTG1 N

mlRm

pmsTGNmlRw

1: 25

On the other hand on the basis of (24) it is possible to

receive

kl mw0=m k

v 1 k

mv

1 kml kv 1 kmv

: 26

Substituting (25) and (26) in (19), we will obtain the

formula for calculating the minimum consumption of

methanol, in which there is no formation of gas hydrate

deposits on the inner wall of the pipe:

mm0 mklk

ml 1 k

l k

v k

mv: 27

4 Calculations results

Let us determine the change of the parameters of gas flow

in an underground pipeline, taking into account the evo-

lution of gas hydrate deposits on the inner walls of the

channel.

Lets consider the calculations for the gas flow in a

pipeline with constant pressure at the inlet. The following

parameters are used in the calculations: pipe length

L= 10 km, inner radius a0 = 0.11 m, initial temperature

of the ground TG0 = 6 C, inlet pressure p0 = 3.2 MPa,

mass flow mg = 0.7 kg/s, gas temperature Tg0 = 50 C,

moisture content kw0 = 3 9 10-

3. On the figures thex-axis unless indicated additionally corresponds to coor-

dinate z counted from the input section of the pipeline.

Figure1 shows the temperature distribution of the gas,

ground and hydrate formation at the initial time moment. In

the section z = 2 km, the gas temperature is equal to the

temperature of hydrate formation, i.e. starting from this

section and below, there is a zone of hydrate formation, and

on the inner walls of the pipeline gas hydrates can be

formed.

Lets consider how the process works. Figures 2 and3

shows the distribution along the pipelines length of

the pressure and moisture content along the length of thepipeline at different time moments, Fig.4 shows the

change of the profile of deposits change in time. Time of

the pipeline operation is 30 days. During this period, the

cross section area at the narrowest point reduced to 35 %

from the original (Fig.4).

Because of the narrowing of the pipelines cross sec-

tion in some time the pressure decreases after the plug

(Fig.2), which results, because of gas adiabatic expan-

sion, in temperature reduction after the minimum cross

Fig. 1 Temperature versus coordinate z at the initial time moment.

1the gas temperature, 2the hydrate formation temperature,

3the ground temperature


1 3



section. This, in turn, according to the results of previous

works [14, 18] intensifies the process of gas hydrate

formation. The area in which gas hydrates are formed is

not stationary and shifted to the right (Fig. 3). Increasing

of the maximum of water content curve can be indicative

of the intensification of sclerotic and dissociation pro-

cesses. Figure4 shows that the evolution of the profile of

gas hydrate deposits is characterized by two features:

hydrates decompose on the left edge of the layer of solid

deposits and the thickness of the deposits increases

downstream.

Lets explain the causes of these features, taking into

account Fig. 5. With time due to heating of the surroundinglayers of ground the temperature in the pipeline before the

layer of solid deposits increases. It leads to the shift of the

left border of the zone of hydrate formation (corresponding

to the cross section z = zs, marked by the dashed line) to

the mouth of the pipe. For the hydrates, which remained to

the left of this area (to the left of the shaded area), the

condition of it existence TrB Ts(p) is violated. These

hydrates dissociate, saturating the gas slow with additional

moisture. Water content is increasing from 3 9 10-3 to

4.3 9 10-3, Fig.5b. To the right of section z = zs, which

corresponds to the maximum thickness of deposits, the

conditions of gas hydrates existence are performed and at

the downstream sections hydrates are formed. At that, the

water contained in the flow is spent for formation of

hydrates, which is observed on Fig.5a (shaded area).

Figure6 shows the change of thickness of gas hydrate

deposits on the channel inner wall at feeding the inhibitor

(methanol) with the mass flow rate of 250 kg/day into the

flow. Calculations show that at the left edge there is

intensive destruction of the hydrate block. The volume of

gas hydrate deposits decreased by more than in 1.5 times

with in 2 days. It is possible to conclude that at low

thickness of gas hydrate deposits, the supply of inhibitors

to the flow is an effective tool to struggle against already

formed layer of solid deposits.

The opposite effect from the use of inhibitors is

observed when the solid deposits are of considerable

thickness (Fig.7). The cross section area after 36 days is

about one tenth of the original area. With such significant

restriction of cross section area, supply of methanol with

the mass flow rate of 250 kg/day or more does not prevent

Fig. 2 Pressure versus coordinate z at various moments of time.

Curves 1, 2, 3 and 4 correspond to t= 0, 10, 20 and 30 days,

respectively

Fig. 3 Moisture content versus coordinate z at various moments of

time. Curves 1, 2 and 3 correspond to t= 10, 20 and 30 days,respectively

Fig. 4 The profile diagram of

the gas hydrates deposits on the

internal walls of the pipeline.Curves 1, 2 and 3 correspond to

t= 10, 20 and 30 days,

respectively


1 3



from the full overlapping of the pipes cross section

(Fig.8). The situation does not change either when the

expenditure of methanol increases.

Lets define the reasons of such effect. Lets analyze the

water-temperature conditions in the pipeline, which were

formed in the area prone to sclerotic process in 3.5 h after

the start of methanol supply (Fig.9). Inhibitors con-

sumption of 250 kg/day reduces the temperature of hydrate

formation to -12 C and at the current temperature of the

gas in the region I it contributes to intensive dissociation of

the layer of hydrate deposits. Water released in large

quantities at the hydrates dissociation (Fig. 9b, region I),

reduces the concentration of methanol that, according to

Eq. (18), raises the temperature of hydrate formation. As a

result, in the cross section z = zs (corresponds to the

minimum cross section area of the pipe) the temperatures

of the gas and hydrate formation become equal.

Next to the right boundary of region I there is the adi-abatic expansion of gas. Therefore, the gas temperature

decreases and becomes less than the temperature of hydrate

formation at the current pressure and concentration of

methanol. Then the region II corresponds to the zone of

hydrate formation and there the hydrates will be formed.

In the section z & 3 km curve 1 reaches the minimum.

After that the gas temperature rises due to heat exchange

with the ground and the heat flow released during the

formation of hydrates. The transition from region II to the

following region occurs in the section where the curves 1

and 2 are leveled again. The behavior of the curve of

moisture content shows that in region III the dissociation of

hydrates occurs as well.

Thus, the main reason of the negative result of the use of

methanol at a significant narrowing of cross section is an

outstanding noticeable manifestation of the JouleThom-

son effect next to the narrowed part of the pipeline.

We I would like to elaborate on the process of hydrate

formation in the zone II. The values of the temperatures of

gas and the inner surface of the pipeline are in the negative

region. The question arises: in this area will form ice

crystals or gas hydrates?

It is known that during the formation of gas hydrate in

the area of negative temperatures, the following processes

are possible [4, 12]:

1. Water ? ice ? hydrate

2. Water ? hydrate.

The degree of stability of the solid phase being formed

during the second process is higher. Thus, with high

probability it can be claimed that the formation of solid

Fig. 5 The change of the thickness of gas hydrate layer, the

temperatures (a) and moisture content (b) depending on coordinate

z. 1the gas temperature, 2the hydrate formation temperature,

3the thickness of the gas hydrate layer

Fig. 6 The thickness of gas

hydrate layer versus coordinate

z by methanol injection in thegas flow. The shaped line 1

corresponds to the profile of gas

hydrates deposits at the initial

time moment (the layer was

formed within 30 days). Curves

2 and 3 correspond to t= 20

and 30 h, respectively. Mass

flow rate of the inhibitor is

250 kg/day


1 3



phase in the gaswater system at the time of condensation

of water vapour at sub-zero temperatures the process of

hydrate formation will be dominant.

In area III (Fig. 9) a certain interest is represented by the

results received for the process of the gas hydrates disso-

ciation at temperatures less than 0 C. The specified tem-

perature mode satisfies the area of stability of ice-gas

system and gas hydrates should decompose. But, consid-

ering last data [15], it is possible to assume that the self-

preservation effect should appear and possibly the intensity

of hydrate dissociation, received in calculations, is a little

exaggerated.

Lets consider the results of calculations for the gas flow

in a pipeline with the constant pressure pL = 3.1 MPa at

the output. Analysis of Figs. 10 and 11 suggests that till

24 days formation of the deposits profile proceeds at mode

similarly considered above. Later, however, before the first

zone of solid deposits the secondary zone will be formed. It

is caused by the circumstance that increasing pressure upon

an input leads, according to (16), to raise of the temperature

of hydrate formation and hence displacement of the zone of

hydrate formation to the left.

Lets consider the mode of transportation of natural gas in

the pipeline at the given pressure at the input and output

of the pipeline. At calculations the following data was

used: p0 = 3.2 MPa, pL = 3 MPa, the gas temperature

Tg0 = 50 C. The gas flow rate mgunknown function of

time. Change of pressure over the time and the length of the

pipeline and change of the gas mass flow over time are shown

in Fig.12. In process of a thickening of the gas hydrate layer

(Fig.13) the gas flow rate decreases and the pressure, before

the solid deposits layer, increases. The zone of hydrate for-

mation displaces to the output section. This explains the

emergence of a secondary zone of hydrate deposits.

5 Conclusion

A mathematical model describing the flow of natural gas in

a pipeline is developed. This model takes into account

phase transitions, formation or dissociation of gas hydrates

deposits on the inner walls of pipes, heat exchange of the

pipe with the surrounding rock.

It has been found that at various modes of gas trans-

portation the formation of the deposits profile at the initial

stage occurs identically: on the left edge the hydrate block

dissociates, and after the maximum thickness of the layer

the growth of hydrates occurs. Thus the motion of the

hydrate block towards the pipe inlet is observed. At later

stages, under certain conditions the position of the hydrate

block is stabilized at first and then can be shifted in the

opposite direction.



internal walls of the pipeline.

Curves 1, 2, 3 and 4 correspond

to t= 10, 20, 30 and 36 days,

respectively



z by methanol injection in the

gas flow. The shaped line

corresponds to the profile of gas

hydrates deposits in the initial

time moment (the layer was

formed within 36 days). Thesolid line corresponds to time

3.5 h. Mass flow rate of the

inhibitor is 250 kg/day


1 3


http:///reader/full/dynamics-of-formation-and-dissociation-of-gas-hydrates-in-p

Fig. 9 The change of the

thickness of gas hydrate layer,

the temperature (a) and

moisture content (b) depending

on coordinate z . 1the gas

temperature,2the hydrate

formation temperature, 3the

thickness of the gas hydrate

layer



internal walls of the pipeline.

Curves 1, 2, 3 and 4 correspondto t= 5, 10, 15 and 20 days,

respectively



z at various moments of time.Curves 1, 2 and 3 correspond to

t= 25, 27 and 30 days,

respectively


1 3



The effectiveness of use of methanol as the means of

struggle against an already formed hydrate block at its

minor thickness is shown. The supply of methanol at a

large thickness of the hydrate block does not prevent the

channel flow section from full overlapping.

Acknowledgments This work was supported by Grant of the

President of the Russian Federation for State Support of Leading

Scientific Schools of the Russian Federation (No. NSh-834.2012.1).

References

1. Ahmed T, McKinney PD (2005) Advanced reservoir engineering.

Gulf Professional Publishing, Oxford

2. Balakin BV (2010) Experimental and theoretical study of the

flow, aggregation and deposition of gas hydrate particles. Doctor

thesis, University of Bergen, Bergen, Norway

3. Bondarev EA, Gabysheva LN, Kanibolotskii MA (1982) Simu-

lation study of the gas-hydrate formation process in piped gas

flow. Translated from Izvestiya Akademii Nauk SSSR, Mek-

hanika Zhidkosti i Gaza 5:105112

4. Bukhgalter EB (1970) Prevention and elimination of gas hydrates

(in Russian). VNIIgazprom, Moscow

5. Caroll J (2003) Natural gas hydrates. A guide for engineers. Gulf

Professional Publishing, Oxford

6. Dubina MM, Krasovitskii BA, Lozovskii AS, Popov FS (1977)

Thermal and mechanical interaction between engineering con-

structions and frozen grounds (in Russian). Nauka, Novosibirsk

7. Goodman J (1958) The heat balance integral and its application to

problem involving change of phase. Trans Soc Mech Eng 80:335

442

8. Gurevich GP, Brusilovskii AI (1984) Reference book on the

calculation of the phase state and properties of gas condensate

mixtures (in Russian). Nedra, Moscow

9. Guzhov AI, TitovVG, MedvedevVF, VasilevVA (1978)Natural-

gas gathering, pipelining and storing (in Russian). Nedra, Moscow

10. Istomin VA, Kvon VG (2004) Gas hydrate prevention and dis-sociation in the systems of gas processing (in Russian), JSC

Gazprom, Moscow

11. Kvamme B, Kuznetsova T, Aasoldsen K (2005) Molecular

dynamics simulations for selection of kinetic hydrate inhibitors.

J Mol Graph Model 23:524536

12. Makogon YF, Sarkisyants GA (1966) Prevention of hydration in

producing and converging gas (in Russian). Nedra, Moscow

13. Makogon YF (1997) Hydrates of hydrocarbons. PennWell Books,

Tulsa

14. Musakaev NG, Urazov RR, Shagapov VSh (2006) Hydrate for-

mation kinetics in piped natural-gas flows. Thermophys Aero-

mech 13(2):295302

Fig. 12 Pressure versus coordinate z at various moments of time (the left figure). The gas flow rate versus time t (theright figure). Curves 1, 2

and3 correspond to t= 0, 30 and 50 days, respectively


the gas hydrates deposits on theinternal walls of the pipeline.

Curves 1, 2 and 3 correspond to

t= 10, 30 and 50 days,

respectively


1 3



15. Nesterov AN, Melnikov VP et al. (2009) Metastable states during

dissociation of gas hydrates. In: Proceedings of the international

conference Gas hydrates resources development, Gubkin

Russian State University of Oil and Gas, Moscow

16. Nigmatulin RI (1991) Dynamics of multiphase media. Hemi-

sphere Publ. Corp, New York

17. Ribeiro CP Jr, Lage PLC (2008) Modelling of hydrate formation

kinetics: state-of-the-art and future directions. Chem Eng Sci

63:20072034

18. Shagapov VSh, Urazov RR (2004) The characteristics of a gas

pipeline in the presence of hydrate deposits. High Temp 42(3):

463470

19. Shagapov VSh, Musakaev NG, Urazov RR (2008) Mathematical

model of natural gas flow in pipelines with allowance for the

dissociation of gas hydrates. J Eng Phys Thermophys 81(2):

287296

20. Sloan ED (1998) Natural gas clathrate hydrates. Marcel Dekker,

New York

21. Sloan ED (2000) Hydrates engineering, monograph 21. Society

of Petroleum Engineers, Richardson, TX

22. Sloan ED (2003) Fundamental principles and applications of

natural gas hydrates. Nature 426:353363


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Dynamics of Formation and Dissociation of Gas Hydrates in Pipelines at the Various Modes of Gas Transportation 2012 Heat and Mass Transfer Waerme Und Stoffuebertragung

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