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Lec 19: Transportation of Natural Gas – I

Lec 19: Transportation of Natural Gas – I


Hello everyone and welcome to the class of
transportation of natural gas 1 this class is going to be two parts transportation of
natural gas 1 and 2. So far we had understood how natural gas is being produced from reservoir
to surface and at this surface how it is purified to meet the requirement of customer. To send
this natural gas which is purified at the surface to customer we have to adopt certain
type of transportation mechanism. There could be several ways of transporting purified natural
gas meeting the customer specification which is required record in terms of water removal
in terms of contamination removal. In case of takeout valuable hydro carbon and selling
them separately as well as same time of the customer needs the natural gas that is having
certain amount of energy more than the pure gas even the traces amount of significant
amount of higher hydro carbon where also supplied to customer. So it depends on the regulation
specification of the transportation as well as what could be separated out and at what
extent that could be done in the separation facilities. The transportation can be accomplished
by several means this chart shows on the X axis distance the natural gas is being supplied
from its source to consumer or from its processing plant to consumer and the Y axis is having
gas means how much amount of the gas is being transported. The unit is BCM per year billion
cubic meter per year and the X axis is having distance in globe meter. So this relationship
shows when we are choosing an option to transport the natural gas it depends on several factor
one of the factor is how much quantity is being transported and how long it is going
to travel. If it is of very high amount that needs to travel not very far distance, not
very far in the sense somewhere in this region we can choose either the small pipeline design
system or can compress this natural gas and send it in CNG mode or it could be converting
into some other liquid form all the option can be chosen. And when the distance is going
high we can see depend on the quantity if the quantity somewhere in this region we can
still choose pipeline or CNG or the GTL process. But when the amount is too high for short
distance, short distance means around 1000 kilometer it is not like 1 meter or 1 kilo
meter or the 10 kilo meter it is a 1000 kilo meter distance significant high compared to
one continent to other continent or somewhere one country to other country where it needs
to be transported to a sea line then the mode will be different. So if the distance can
be covered by the land and the pipeline can be lay out even on the onshore offshore and
the quantity is significant high we should choose the pipeline system. And pipeline system
is something that mostly adopted so far for the transportation of natural gas compared
to other means it accounts around 75% natural gas being transported from it is from one
place to other place by the pipeline transportation mode. These are the crude data but approximately
pipeline is dominating the transportation mode when the quantity is high as well as
distance is also too high like more than 1000 we cannot just lay out the pipeline at certain
certain reason because of the geographical or political reason or by some other possibilities
of facing the problem in terms of bay of fry or other things in the pipeline design. Another
mode that is mostly used is LNG liquefied natural gas and if we see on the crude data
those are available in the literature and summarizes the liquefied natural gas accounts
the remaining balance of the transportation around 30% it does not mean other modes are
not being practiced. So LNG mostly account 30% of the gas that is being transported this
is a proven technology at safe mode but very energy intensive required the terminal where
it can be deep freeze or the temperature can go down up to – 160 where this natural gas
that is being transported and the gas which is being transported mostly methane and methane
needs much lower temperature to go the liquid phase. And when we going to – 160 degree
Celsius temperature and liquefying this natural gas terminal are required for the purpose
and when it is in a special type of the tanks transported from one place to other place
in a special type of the tank system again at the other side terminals are required where
it again be converted into gas phase. CNG also a mode of transportation and this is
stand for compressed natural gas it is economical compared to LNG because we do not need to
go to that much low temperature. However the compressor is required to compress that thing
but the handling equipment shipping from one place to other place the type of the tanker
or the shell of vessels are required allow us to send gas in compressed manner in much
economical manner than the LNG. Sea transport can also be accomplished while we are compressing
the natural gas and sending it in the CNG mode the small volume and short distance when
the volume is not too high and when the distance is also not very high that mode should be
adopted and that is here in this region where the CNG is occupying significant part of this
graph. CNG is used in the vehicles now so there are significant number of vehicles on
the road those are running on compressed natural gas if further modification can be some in
the mechanisms of using the CNG this miss here a larger part it is having a better future
prospective. Other technique could also be possible when can convert this natural gas
or methane to liquid that can be done by GTL process we can do it with Fisher Tropsch process
using a specialize catalyst and temperature pressure condition this lighter hydro carbon
compound can be converted into heavier compound or other petro chemical compound those can
be used for other purposes. Like DME Di-methyl ether methanol those can be generated at the
source itself and the liquid it is being transported through the tanker or by other media. We will
be discussing the processes like LNG, CNG, GTL in little bit more detail at the later
part of this transportation natural gas lectures. Let us focus on pipeline that account 70%
and mostly used mode of transportation for natural gas to transport from one place to
a very long distance. When we focus on the transportation on the pipeline we can see
a symmetric diagram that shows now natural gas can be transported from one pace to other
place. This figure shows on the left hand side the places from where the natural gas
is getting accumulated or gathering station we can call it and the pipeline are called
gathering pipeline. Here I had mentioned gathering system and when the gathering system is collecting
the gases from various sources like the supply from other source from gas processing plant
where gas was being treated or processed and importing part also. There may be having a
different part in the pipeline system where they can be included through this trunk line
system the long distance trunk line system and put it in the main truck line. So if we
classify this in a broad way we are having three type o pipeline in the system the gathering
system where we are collecting the gases from various sources import gas processing plant
supply sources then it is going through the main trunk line and travelling a very long
distance. And at the other side before it goes to consumer we are having another place
local distribution service load where these gases are further transported in a small diameter
pipeline to consumer ad these lines all the distribution line . Between the gather system
and distribution line there is a main trunk line where the natural gas is transporting
from one place to other place. As already discussed in compressor class the flow is
happening because of the pressure difference and pressure decline because of the friction
losses in the pipeline system that is a several compression stations are required to compress
the gas. Two important aspects here LNG plant liken when natural gas is transported from
one place to other place in the system from gathering system to distribution line may
be the demand and supply is not matching because during the summer time and winter time the
demand is different. In the winter time more natural gas is required to heat the building
the heat the residential areas and for other purposes the natural gas that is being produced
should be stored that could be stored either in the form of LNG plant or it can be stored
underground underground in the depleted oil gas reservoir. Where we know the geological
formation detail sorted this natural gas and whenever the demand is high compared to supply
when use this underground storage or LNG plant processing facilities to match the demand.
Altogether pipeline that is having different diameter different specification and similar
here and the trunk line that is spread over a long distance pass through several like
several path it is going to travel. So when it comes to transportation through pipeline,
pipeline design is very much important because that says depend on the quantity and the distance
how to design the specific diameter pipeline we are going to discuss mechanical aspect
we are just on the flow rate pressure and diameter relationship so the pipeline design
means appropriate size of the pipeline to meet the through port. So we want to send
specified quantity of natural gas from point 1 to point 2 through pipe line that is having
certain diameter and certain length that we need to travel in point 1 and point 2 how
much gas we are going to send through this pipeline depend on pressure difference also.
When there was not demand of natural gas the calculation involved in pipeline design where
good enough to understand the process now the demand is high the pipeline system should
be used very efficiently even at higher pressure or the maximum level pressure to meet the
through port or the requirement of the natural gas at the other end. That is why appropriate
size of pipeline to meet the throw port should be considered in the design appropriate distance
between compression station as already mentioned between this long distance between one and
two there might be N number of compression station are required that is compressing the
natural gas to meet the demand again. So appropriate location of compressor should also be identified
it should be part of the pipeline designs system where the compressor should be installed
and at what horse power working power should be provided to a compressor. So the specified
amount of the natural gas can be transported with the already led out pipeline system.
Pipeline is an equation when we talk we should do the pipeline design the design equation
depends on the diameter and gas quantity to be transported operating pressure and temperature
most of the time it is considered the temperature is not changing and the flow is happening
under isothermal condition and the length and the terrain. How long it is going to travel
and what type of the path it is going to face like it is having just a horizontal flow it
is having some inclination or it should be just a single pipeline should be a combination
of single pipeline or just a bigger diameter single pipeline or may be the looping of the
pipeline with that we will be discussing the transportation of natural gas to. So the complex
equation that have been developed for sizing natural gas pipeline in barriers flow conditions
as already mentioned depend on how much quantity we are supplying what type of terrain it is
going to face the equation we take little bit different form. The typical equations
those are used in the natural gas industry to design the pipeline or to establish the
relationship between the flow rate pressure draw down specification of the pipe line like
the diameter and the length as well as fluid properties that equation can be in a different
form the mostly used forms are Weymouth equation, Panhandle equation and modified Panhandle
equation we will discuss this one by one. And optimal balance is sought between pipe
tonnage and pumping horse power record how much quantity is being transported pipeline
and how much energy is required to transport that natural gas that function or that relationship
must be optimized. For economic operation it is important to preserve full pipeline
utilization whatever the mode the pipelines are designed serial parallel or loop pipeline
the entire diameter of the pipeline all this things must be effectively utilized for transporting
natural gas economically. If we go further and see how to set up the mathematical equations
for this pipeline transportation mechanism. The theoretical equation can be set up by
considering the first law of thermodynamics several assumption need to made we will make
the assumption as we go further and solve the problem or solve the equation that is
in the desired form is how my flow rate is related to pressure draw down with other important
parameter like the fluid properties and diameter and length of the pipeline as well as the
inclination if it is travelling through different terrene. So under steady state condition one
dimensional flow we are just assuming the flow is assuming only in one direction that
is Z where we are having the pressure difference P1 – P2 the length of this pipeline is L
if it is having certain inclination like this we can account that with the help of angle
theta that this pipeline is making if the pipeline is inclined at a particular angle
we can adjust the gravity forces accordingly. So for steady state condition one dimensional
flow considering only gas phase is flowing we can modify that terminology saying dry
means only the methane gas mostly the methane gas sweet means most of the impurities already
taken out and compressible that is our natural gas in compressible gas is flowing through
this pipeline of diameter D and length L for this constant diameter D we can set up the
equation considering it is under the horizontal condition or it is at being certain inclination
or the non-horizontal condition the pipeline is layed out. We can see the balance of the
forces of the flow driving force that is allowing the flow happening from P1 to P2 will be balanced
by 3 type of the forces the elevation or potential energy changes that is happening so the pressure
energy will be equal to the potential emery changes happening in the system because of
the friction the pipeline roughness depend on the roughness of the pipeline the friction
forces can be applied and there will be rest in the flow. So the friction losses should
also be accounted in the balance equation as well as kinetic energy change we are ignoring
any shaft work done on the system we are just considering a section of a pipe where we are
saying the pressure is changing from P to P2 flow is happening at that is applying the
first law of thermodynamics we can set up the conservation equation that says dP / dL
=kinetic energy change frictional losses + potential energy change in the system. This
is one type of differential equation if we can interrogate this equation we can get how
the pressure drop is a function of flow rate pipe diameter and fluid properties. If we
look more closely on this equation we can say this equation can be applicable or can
be apply for our system where rho, f and u. Rho is the density of the fluid the gas which
is flowing through the system through this pipeline F is the friction factor that is
offered by the tubing and u is the velocity with means this gas is flowing through this
tube if they can be defined we can solve this equation easily considering any analytic solution
and we can get the desired relationship depends on the system we are having we can simplified
this equation also. So for example when we are having the horizontal flow this angle
should be 0 and we are getting so this angle should be 0 and we are getting sin theta 0
that is equal to 0 means gravity is not contributing into this system and we can ignore it. other
cases could be there when we are saying the cross sectional area of tube is not changing
the flow is not happening at that high rate where the kinetic energy change is also contributing
for this pressure drop we can ignore this kinetic term also. If it cannot be ignored
either one either the gravity or the kinetic we have to include in the equation and more
complex equation need to be solved. Let us go step by step in the first case we area
assuming the gravity is not playing any role as well as kinetic is also not playing role
the pressure drop is happening because of the friction losses only. And when we do so
we get very simplified equation that says the pressure drop because of the friction
can be related with the viscous shear or the frictional losses and that is dP / dL=Rho
some mechanical energy losses of work that is getting converted to heat when the fluid
is flowing through this tube because of the resistance offered by the two line heat will
be releases to the environment and that will be equivalent to the pressure drop happening
because of this friction losses. We can convert this into some flow variable we know how to
do it we did two three time we passed also especially when we are dealing with the WPR
well bore performance relationship where we can establish this is equal to fu square by
2gcD and this is responsible for accounting the fluid properties in terms of f. So thus
if we put all of this here what we are going to get the relationship that says if the flow
through pipeline is having is happening in the horizontal tube and no kinetic energy
is changing we got this form of the equation just substituting this here we will get it.
And that also be related by the definition of friction factor that says friction factor
f=tau / rho u square by 2 if we put that thing we are going to get the similar thing.
Here the terms are having their usual meaning like the pressure the unit may be different
and depend on the unit system chosen and in numerical coefficient any appear there if
all the unit system are matching there wil be any numerical coefficient. We did this
several time in the past so we can ignore this time and rho flow density now a fluid
is not incompressible the density will change and we know from our properties of natural
gas class how to relate rho with the local condition that is P and temperature this is
a compressibility should be small Z. Z compressibility 29 gamma Z is the molecular weight of the
natural gas or the apparent molecular weight of that natural gas. Similarly when we converting
this into the flow properties like the velocity of the fluid we know u it is difficult to
measure the velocity of u. But you can convert that into some quantity those are locally
can be evaluated or can be considered for example we can convert by knowing the flow
rate and cross sectional are u q/A again q is a property of temperature and pressure
we can convert it to q is the standard condition and we will get the expression we did this
few times before also should not be having any problem to understand how we got the expression
for rho and u. When we put in this equation we will see now this function is in terms
of pressure and temperature serious it was in terms of fluid density and velocity and
they are the function of local condition we converted them both density and velocity to
pressure condition. And when we do so we are going to get the expression that is appear
like this after substituting the value we can also get this expression. So this is rho
value we got the equation how the pressure drop is happening when the fluid is flowing
or the gas is flowing through a pipeline of the diameter D at a particular length in this
pipeline we can estimate the pressure at the end or at any location after solving this
differential equation but again the problem is not solved because we see here when we
converted this we are having f and u . This equation which is a balance equation or energy
balance equation under certain condition says how the pressure drop is related to fluid
properties and it shows the basic equation for the development of any pipeline equation
under certain assumption those assumption may create some problem or some deviation
from the result obtained by this equation. For example ahhh gravity, kinetic energy were
not considered steady state condition may not be ahh a case when is happening and shaft
work is not considered there might be some addition work done on the natural gas form
the outside but under certain assumption those we had discussed this mathematical equation
is good enough to represent the flow through horizontal pipeline under steady state condition
through a pipeline of constant diameter. The difference in this equation originated by
the method using handling the compressibility factor and friction factor so in this equation
we will see the compressibility is appearing and F is spearing and both are having dependency
on other parameter. Similarly we will see u also depend because by the definition u
is also function of temperature and pressure now. When we integrate this equation considering
all this terms are constant although those are not constant we will see we will get this
kind of expression where it says inside the integral we are having the pressure, temperature
and compressibility temperature may be assume constant may be taken average similar the
pressure either we are evaluating it locally or we are taking it as a constant or the average
by any mean once we know the temperature and pressure as well as gamma Z of this system
we can calculate the compressibility as we know from our properties of our natural gas
class how to calculate the compressibility. We were discussed one example to understand
the processor of performing the pipeline design integrating this equation may result in a
simple expression but before we go further we see the friction factor eu is function
of Reynolds number and of the relative reference of the pipe we cannot take it out of the derivative
term because it is function of Reynolds number. Reynolds number is a function of flow rate,
flow rate is a function temperature and pressure. Similar for u also so let us see what we can
do or each term when we go further for velocity we can simply this can be converted in terms
of temperature and pressure and we can put it inside the integral side for the F friction
factor it depends on which form we are going to calculate the friction factor value. So
if we look in the literature we see the friction factor versus Reynolds number relationship
that is also called the Moody’s chart relationship that account for the changes happening in
the value of friction factor when a gas or any fluid is passing through a tube of some
roughness and some diameter. So this relationship is log log scale on the Y axis is the friction
factor on the X axis it is Reynolds number and there are several lines those represent
for different relative roughness of the pipe. If we classify this chart we can see there
are four reason when is laminar flow where the flow is not dependent of the roughness
of the pipe it just a Viscos flow or not very high flow rate is present in the system. In
most of the cases in pipe line design we are in the turbulent region before we hit the
turbulent region there is transient region where the distribution in the value of friction
factor is not that high with respect to f salient divided by d then the third reason
is complete turbulent region and forth one is smooth pipe region where it is not depending
much on the Reynolds number jus tit deepens on the roughness of the pipe. It is important
to understand the chart is in terms of Moody’s chart not in the finding friction factor for
so value of F we are getting from where is a Moody’s friction factor fm that is I mention
here fm is a function of Reynolds number and roughness depend on which reason we are it
is depending on Reynolds number or not it is depending on the relative roughness of
the pipe or not and what value should be chosen depends on under what condition the flow is
happening through the pipeline. For example in the laminar region we can see here form
this chart this is the region where the friction factor is just function of Reynolds number
and it is having the reciprocal relationship. So the Moody’s friction factor is just can
be calculated by 64 divided by the Reynolds number you do not need to worry about roughness
of the pipe and if it is finding friction factor chart we will see the relationship
between fm=4 times finding friction factor accordingly the adjustment need to be done.
I case of finding friction factor we will get ff=16 / Nre so we are seeing here the
16 by Nre this point we will see this chart is respect the finding friction factor otherwise
it is Moody friction factor. The relationship in laminar region can be established by well-known
phenomena of Hagen-Poiseulle flow in the pipeline. Due to the characteristic of the complex nature
of the curve several equations have been designed for this region all three region transient
region, turbulent region and smooth pipe region. And accordingly we can choose which region
the flow is happening in the pipeline not only the region where the flow is happening
in the pipe line but we can see how it is changing with respect to Reynolds number and
F salient D several expressions have been reported in the literature in the form of
correlation we can choose based on the limit range or condition is specified for each expression
and that we can see in the next slide. We already discussed similar kind of the things
when we were developing the relationship before wpr. In wpr we were having the vertical flow
of the gas from pwf to phf we discuss the phenomena with some inclination later on we
solve the problem for vertical flow system. Let us come back to our problem where we said
the friction factor f is a function of Reynolds number and of relative roughness of pipe.
Yes we know by the definition of f or from the Moody’s chart it depends on how to estimate
the relative roughness ed. It is defined as relative roughness of the pipe to the pipe
internal diameter f salient by d it is the value should be provided by the vendor who
design the pipe or who is supplying the pipeline. Incase it is not available we can calculate
by performing certain experiment and see comparing the pressure drop is happening in a particular
pipeline compared the very smooth pipeline. We can estimate this value or in other case
when we do not have the value we are dependent on somebody we can choose very acceptable
value of F salient that is 0.0006 inches and divided by the diameter we can calculate the
relative roughness where we know the relative roughness of we need to know the Reynolds
number to read the Moody’s chart. We know by the definition of Reynolds number rho Reynolds
number=rho eD / mu by adjusting the parameter as we did in previous classes we can establish
the relationship Reynolds number=20 q gamma g mu D. So it depends on q and q depends on
temperature and pressure that is why when we are going to read the Moody’s chart we
should know the flow rate. And if we are going to calculate the flow rate we have to perform
the iteration. So depend on the flow regime we are in the laminar region, turbulent region,
transient region or later turbulent region we can establish the either we can read the
chart and get the value of f for the single phase and multi-phase the system will be different
we have to be little bit careful when we are taking about the multiphase system. For the
laminar flow now we know Moody friction factor is 64/ NRe in case of turbulent single phase
flow system for f value there are several expression only few of them are included in
this several we discussed already in the class of wpr. So for smooth wall pipe Drew Koo and
McAdams in 1930 they had designed or establish the correlation that says when you are in
the Reynolds number where 10 to the power 3 to 10 to the power 6 you can use this expression
and that says it does not depend on F salient D you can just establish the value of F knowing
the Reynolds number value. And this is for smooth pipe when it is a rough pipe Nikuradse
say had developed ahh relationship and that relationship is widely used for the pipe line
design because it do not depend on the Reynolds number and you see here this is just eD that
is F salient D. So calculate the value of F we need to know only the roughness of the
pipe and if roughness of the pipe is known we can get the value of F. This is valid for
large value of Reynolds number where the effect of relative roughness is dominant it is not
the value of Reynolds number but the effective roughness that is more contributing towards
ahh deviation in the F value depend on the condition. So for F salient D value we can
use this expression Guo and Gallambor showed that this expression given by the Nikuradse
for friction factor is valid not only for the gas flow but gas flow with some solid
and liquid mist this same expression can be used. Further the expression accounting the
range of the flow where both F salient by D as well as Reynolds number are going to
dominate the phenomena is developed by Colebrook in 1938 and the relationship says we can also
include Reynolds number in Nikuradse expression which accounts for the Reynolds number effect
on the calculation of f. This expression can be put back to Nikuresade if we assume the
Reynolds number effect is not significant this equation will be similar to what Nikuresade
has proposed. Now in this equation the problem is on the left hand side we are having the
friction factor and the right hand side we are having the friction actor also solve this
kind of the equation we need to perform the iteration processor either by the or Newton-
Raphson method or other optimization method we can perform trial and error processor the
iteration processor to establish the relationship. And to avoid this difficulty Jain in 1976
modify this equation and proposed equation that says you can use this equation which
is having eD and Reynolds number both but does not need iteration and this equation
proposed by Jain is recommended for all calculation requiring friction factor determination to
a system where the turbulent flow is happening. So let us comeback to our theoretical equation
where we say this equation which was accounting for change in potential energy change in frictional
losses and ahh kinetic energy change for those are continuity to pressure drop with the help
of non-parameter like how to convert rho and velocity into temperature and pressure condition
we could establish this relationship. And that relationship says now if we know f how
to count it can we take it constant or not similarly for u2 you can solve this expression
we know u2 cannot be taken out it has to go inside of the integral sign using this relationship
when we integrate this we are going to get this expression. To integrate this equation
we have to make certain assumption for the temperature we can assume the isothermal process
is happening there is not temperature changes happening or temperature changes happening
is represented by the average temperature T bar. Similarly the compressibility factor
Z is measured as average temperature and average pressure condition. So average temperature
can be calculated like this compressibility factor z is measured at average temperature
an average pressure condition. So average temperature can be calculated d like this
like the if any temperature changes happening we can average out and for pressure also we
can go by the arithmetic average p1 + p2 / 2 at this temperature and at this pressure we
can calculate the compressibility factor and that can be taken out of the internal sign
assuming it is constant in the process. And when we integrate this we will see after during
the separation of pressure term on the left hand side and others on the right hand side
we got this expression if we can re arrange the things we are going to get in terms of
q where inside the root we are having p1 square – p square D to the power 5 then D to the
power 5 came because u square we are having this q / A. So when we square it q / A square
and from it become D to the power 4 1D was already there we could get D to the power
5 here. After adjustment seeing this is Tb Pb at a particular tape temperature and pressure
we can relate Q with pressure draw down or pressure difference in the square form D to
the power 5 means the diameter of the pipeline gamma g specific gravity or property of the
natural gas average temperature average compressibility f is still there the F value will be put up
there and the L the length of the tubing. S all are having the usual meaning here depend
on the unit system specified for each we will get this C the numerical coefficient here
that may get different numerical number. But here again this equation we go after doing
the integral after making certain assumption we see the Q on the lift hand side is again
depend on f that is friction factor and if f is calculated by Reynolds number iteration
are required to come out the accurate solution of this equation. The specified substitution
used may be diameter depended then we already know if we are f that is just depending on
diameter of the tube either it is small di or capital Di or it is depends on the Reynolds
number only Panhandle equation derived based on certain assumption. So in the Weymouth
equation is just a function of the diameter and in Panhandle equation it is a function
of just Reynolds number we will see this in the coming slide. So now the equation that
has been developed here is only for horizontal we had considered theta=0 and we had neglected
this term as well as the kinetic term assuming constant diameter tube. Now we can derive
the same equation considering the theta is not 0 it is having particular inclination
the pipeline is having inclination from the surface we can establish the relationship
for non-horizontal flow condition also we will do this later on. So let us go for the
horizontal flow what we got when we convert the unit as mentioned in the last slide the
numerical coefficient c that is appearing in the last will get change now the q will
also get change here it become qh it means the flow rate is measured per hour standard
cubic feet per hour and the numerical coefficient appear here remaining things are same it has
been taken out outside and this term is called transmission factor So when by f and its root
is called transmission factor the Moody’s friction factor may be a function of flow
rate and pipe roughness that we discussed depends on the functionality of f this may
take different form for fully turbulent reason for f may be defined like this where it’s
not a function of Reynolds number just the relative roughness eD or in other term F salient
/ D we can say using this it is not depending on the Reynolds number if not complete turbulent
reason is there F depends on the Reynolds number and we have to calculate the Reynolds
number put it in the equation of f which uses the Reynolds and iteration need to be performed
to calculate the qh value. So not depend on the f functionality chosen mathematical equation
that is the solution of simple balance equation may take different form. So for example Weymouth
equation it is widely used for the horizontal low eliminate the trial and error processor
just assuming f is the function of diameter only and if we express f in this form 0.032
divided by D to the power 1 / 3 we will get qh again qh means standard cubic feet per
hour the flow rate with respect to some base temperature and pressure will take this form.
Here because of D the D to the power 5 got converted D to the power 16/3 other things
are almost same. The Weymouth equation commonly used in the natural gas industries to establish
the relationship between q, pressure, temperature diameter of the pipe and other properties
But this equation is under certain assumption what we assume no mechanical work is done
steady flow is happening isothermal condition is assume so T either it is isothermal constant
temperature or T bar is chosen to represent the flow constant compressibility factor Z
bar it is constant. So it is calculated either at a average pressure that average pressure
could be just athematic average P1 / P1 + P2 / P2 or may be the athematic average of
compressibility itself. So compressibility is calculated at pressure P1 and then P2 we
got Z1 and Z2 take the arithmetic average of both we are going to get the average value
of compressibility or it might be defined in other form where how the compressibility
is changing with respect to in pressure in this pressure range p1 to p2 integrating the
area where that curve in the form of p1 to p2 zDp where integrating from p1 to p2 divided
by this range p1 to p2 we can get the average value of the compressibility. The pressure
may be chosen either athematic average or may be other more complex form which provide
the accurate value of the average representation of the pressure that depends on the how pressure
is changing with respect to p1 and p2 can it be taken as average. Similarly the compressibility
factor z how it is changing linearly with respect to pressure may be just average is
good enough or if it is not changing linearly with respect to pressure we may use this area
under the curve to calculate compressibility value that average condition or it is the
average value of the compressibility factor. We also assume the flow is horizontal theta
is 0 and no kinetic energy changes happening in the system. If any of the assumption mentioned
here is not applicable we have to modify the equation because the results obtained by setting
the mathematical equation by under this assumption will deviate from the real results and that
is can be done by including term into the equation like we did in wpr where the flow
was happening at a inclination will angle and we assume gravity plus important role
in fact in a vertical pipeline system gravity place major role to place the pressure draw
down around 75% and that is where we can we could establish the relationship. Similar
we can do for a transportation of natural gas pipeline also(refer time:49:37) another
method that is panhandle A equation panhandle had given two equation pan handle and modify
panhandle equation we can say pan handle equation and pan handle equation. In pan handle equation
for the horizontal flow it is proposed the f is not just a function of diameter it is
a function of Reynolds number only. In another terms Reynolds number include the diameter
so it is including the diameter but including the roughness of the pipe and if it assume
in this manner putting the equation that we had we are going to get the resultant pipeline
flow equation in this form this is little bit complex because Reynolds number will impose
all these parameter this system to be included. And we will get this expression where all
the terms are like P1 P2 are there average temperature average compressibility factor
l are there gamma g power got change and d to the power also got change here the numerical
coefficient again depend on the unit system and here it is consider as q is the gas flow
rate in cfd cubic feet per day measured at based temperature and based pressure other
terms are same as we already considered for the Weymouth equation. In Panhandle as we
already consider for the Weymouth equation in Panhandle B equation this is modified form
of Panhandle A equation where it is assumed the modification has been done in terms of
so the power of the Reynolds number and the numerator coefficient both are little bit
modified to propose more accurate equation to account the relationship between the and
the other parameter and the equation will take this form. We are not going to put this
value and reaching this equations it is an exercise you can do and the important is you
will get this expression of Q in different for depend on how f is chosen and how f is
related to one particular parameter like F salient D and Reynolds number or it is just
a diameter or it is just a Reynolds number. And with respective Reynolds number also it
is in ex-form and the biform as it is done in Pan handle A and Pan handle B model. Let
us understand what is this transmission factor under root 1 by f that is appear in the mathematical
equation that we established for the flow through pipeline and that form dependence
on system that we chosen so for the smooth pipeline system we can say jus tit is a function
of Reynolds number when Weymouth equation consider on the diameter and handle consider
Reynolds number with different numerical coefficient then Pan handle equation. For the rough pipe
we can just ignore Reynolds number and can just include the eD relative roughness of
the pipe to have the transmission factor and ultimately that transmission factor we give
us value of f friction factor. Another thing that did not count in establishing the relationship
is pipeline efficiency all pipeline flow equation developed so far are based on the consideration
that only gas is flowing through the pipe this is single phase system. But in actual
practice water condensate and sometime small amount of the oil or also present if the gag
get accumulated in a pipeline and some part of the pipeline miss if they reduce the effective
diameter through which can gas can flow. They create some more problems also we discussed
later on but the presence of these liquid in the pipeline reduce the efficiency of pipeline
to transport the amount of the gas from one place to other place that it important with
respect to the transportation. There are often scale formation or junk left in the line and
to account all these terms there should be terms that is should be multiply with the
expression obtained that says the correction in the flow rate that is actually transported
then the theoretical value. So the equations based on certain assumption considering ideal
gases are giving us the flow rate that theoretical can be transported for calculating the actual
value it can be multiplied by the pipeline efficiency that comes in the range of 0.85
to 0.95 compared to clean line and the table source for a type of line it is a dry gas
you can use 0.9 to if casing head gas where the a gas is having all sort of the impurities
as well as higher carbon number hydrocarbons then the efficiency will reduce 0.77 only
and the gas and condensate are present then the efficiency will further go down 0.6. And
depend on the liquid condense this also says how much liquid is content in the system in
gallon per MMcf the efficiency factor should be multiplied by theoretical equation should
get the actual value of the gas that can be transported through the pipeline which has
been designed to transport the gas. So in summary we can see in a horizontal flow system
we are having the Weymouth equation, panhandle equation, Panhandle B equation and only difference
is how the F is chosen we are going to get the difference things. Here the Q is mentioned
in QH that is why the different numerical coefficient 18.062 is appearing here if it
also transport to per day we will see this same value and we are above the same value
that is summarizes in this table also. So if all these three equation can be represented
in the empirical formula here this is a more general way of expressing the flow through
pipeline or flow through horizontal pipeline we can say the a1, a2, a3, a4, a5 can be written
for each equation Weymouth, Panhandle and Panhandle B equation we can summarize from
this table like for example Weymouth here it is 433.5 as I said this is in hours if
we convert this into days we will get the similar thing 433.5. And others like here
we got 16/3 if we divide this we are going to get this same value with respect to the
diameter q5 2.667. So this represent the general where the coefficient value a1, a2, a3, a4,
a5 depends on which model equation is chosen and what are the unit area associated with
each parameters involved in this expression. These expression are certain under certain
assumption no mechanical work under steady state condition isothermal constant value
compressibility factors only the flow happening in one direction that is also with the horizontal
flow and no kinetic energy change is happening in the system. If kinetic energy changes in
the system we are having this system u du and if this is there we know how to convert
this u similar this u will also get converted and we have to include this in the expression
and addition term we will be getting in our system that will like – 4qzT / p square
Psc Tsc standard temperature conditions so this will also become Qsc to the power 2 dP
/ P to the power and when we are including this term in our ahh energy balance equation
ultimately we will get in the form of P1 square – p2 square addition term we will get because
of the kinetic energy is lnp1/p2 along with that terms here. So for the horizontal flow
there are some other equations also available in the literature like this Clinedinst equation
that is account how the pressure changes happening in the system is going to affect the behavior
of the natural gas is the deviation of natural gas from the ideal gas can be represented
by this equation. So the compressibility factor is inside the integral sign and it is integrated
from 0 to first reduce pressure at condition one and 0 to reduce pressure at condition
two here we can get the expression and this expression may give us more accurate result
in terms of the deviation of natural gas is more compared to ideal gas. So the Zb gas
deviation factor is calculated at Tb Pb normally accepted as 1.0 based on the pseudo critical
pressure the value of integral function have been calculated for various gas in one of
the appendix there are several data have been compiled for this method. The expressions
are usual here q is Mcf per say pressure is in psia D is in inch length and feet P are
pseudo reduce pressure ahh which is having no unit and T bar is in degree ranking and
gamma g is gas gravity. (refer time: 01:00:13) When we talk about Weymouth equation for non-horizontal
flow we see the gas transmission line for the non-horizontal flow are often appears
when we talk about long distance natural gas flow system and at several places the natural
gas is not natural gas pipeline is not horizontal but it is having certain inclination from
the surface and depend on the terrain is going to cross this might be appearing very frequently.
For that case we have to account how the gravity term is going to affect the relationship because
in this kind of the system the gravity will also be important. Considering that thing
we have to establish the relationship again and that says this terms cannot be ignored
however kinetic energy can still be ignored if the constant diameter pipe is used. So
considering gas flow from one point to another point in a non-horizontal pipe the first law
of thermodynamics is for. Here this is pressure so here this is specific volume that is 1
/ rho del Z is just the inclination we can say lz=it is similar to ahh elevation vertical
distance from this to this. This is del z and f is having usual meaning u is having
usual meaning d and del L again this can be described the pressure drop is happening in
this del Z length can be gamma g / 144. 144 is because of the conversion factor like this
gamma is ok we know how to convert this density of the gas and the pressure and temperature
term Again the velocity we already did this (refer time: 01:02:08) in our wpr class in
wpr class when we understand if we are having the gravity term friction term and pressure
term altogether is in the separation of very well after making certain assumption we can
convert this in the form of pdp upon some constant + some p constant and interrogate
this from p1 to p2 for length L and where we had taken this a + bp square=x and we
could integrate this by I have in the very well of separation. And finally we got the
expression in the form of e to the power some value here if we do the same thing we will
get the (refer time: 01:02:58) same expression instead of repeating the expression what I
can show you the Weymouth equation for non-horizontal flow will be distinguish by this term compared
to what we had for the horizontal flow is e to the power s. While s is function of gamma
g this elevation del z average temperature average compressibility the del z is equal
to outlet elevation – the inlet elevation del z is positive when outlet is higher than
inlet. So the sign will depend on the elevation it is upward or it is downward if the flow
is happening at general and rigorous form of Weymouth equation with compensation for
elevation cn be represented like this where the difference from this equation to this
equation is this Lp L is the effective length of the pipeline that means if the effective
length of the pipeline is included here we can get more general and rigorous form of
the flow. So (()) (01:04:04) this expression is return for Weymouth equation similar can
be written for the Pan handle A and Panhandle B. (refer time: 01:04:12) In the effective
length is e to the power s – 1 divided by S multiply by actual length and when there
is a situation when multiple different elevations are appearing in the path way we can adjust
again with the effective length le considering these multiple inclination either upward or
downward considering formula e to the power S1 – 1 / S1 multiply by L1 and then in the
next term it will be e to the power S1 + S2 e to the power S2 – 1 / S2 L2 and if we write
the end term it will be e to the power s1 + s2 + sn e to the power sn – 1 / sn. So
summation of each individual segment or in individual segment we can get the effective
length value here. Here S is having the same value only the thing is del zi for each segment
the del z will be different. So we can establish our relationship for horizontal as well as
for non-horizontal flow condition. Now in the next class we will understand (refer time:
01:05:36) using the Weymouth equation how to establish the relationship between Q and
other parameter we may solve one problem on that and how to layout the pipeline design
considering the concept of series pipeline like here where the pipeline diameter change
it is in the series and when we are establishing the parallels this is parallel this is series
combination and this is looped where some part of the pipeline is series and some part
in the parallel mode. We will consider all this with Weymouth equation the colleague
we can do with other form of the equation because the equation differ in terms of how
friction factor is included in the balance equation. So with this I would like to end
my today’s lecture and tomorrow’s lecture along with the pipeline we will also discuss
about other mode of natural gas transportation thank you thank you very much.

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