[Music] welcome after learning all about the processing of the natural gas it is but an important issue to see to it that whenever we are talking of the various types of connections in the various systems in the natural gas plant we have been using many of the correlations to find out the pressure drop inside the pipeline in the various processing systems now you will find that there are some special type of equations which are used in the natural gas systems to estimate the pipeline inside the freeway pressure drop insert the various types of pipelines so in this particular lecture we shall be looking into the pressure drop calculations in the pipelines in the natural gas systems so in this thing we shall study the piping in natural gas systems and we shall be looking into the various piping systems and the pressure drop in the pipeline now this will be including the we know that the piping's are included for transportation of natural gas and other hydrocarbon gases like LPG so and examples are like natural gas gathering systems gas distribution piping and the gas transmission piping so at various places we are using these piping's so we find that the in the piping whenever there is some fluid is flowing there will be some frictional losses and also some losses will happen whenever there is any kind of change in the direction of the flow so this frictional losses is generally called a skin friction and the loss of the pressure due to the change in the flow direction is called the form drag so these kind of drags results in the loss of energy of the flowing fluid and which necessitates to use a compressor or some kind of pump during the flow of the fluid over a long distance so in case of natural gas we also need to have some kind of compressor from what we call the computations we need distance to distance to again reenergize again give the external energy so that the gas can keep flowing so there are various types of losses we have some major loss which are generally in the straight pipe sense and there are minor losses and these are something through the fittings and valves now major minor does not mean that one is greater than the other it is just that we are neither mnemonic which has been made in such a manner that major loss when we say major loss we mean the straight line pipe losses and the minor loss we talk in terms of the fittings and valves etc or there could be something like entrance affect exit losses whenever something is or there is some diverging section the converging sections in all these changes in the area of cross section of the flow also causes some losses so all these things are coming under the minor losses and the total heat loss is the summation of the major loss and the minor loss now here to understand these calculation of losses first you go back to the Bernoulli's equation and we know that in the Bernoulli's equation we have the potential energy the kinetic energy and the pressure energies and other than that we also have some modifications in the made in the Bernoulli equation to account for the frictional losses in the pipeline so this is basically an energy balance equation that is the first law of thermodynamics and in this we know that we suppose we take this kind of a pipeline and here we see that the pipeline in a general case it may have some elevation so this is the elevation of the pipeline za and ZB and this elevation is generally measured by considering the centerline or the central axis of the pipeline so this is this particular curve is giving the central axis of the pipeline so we are measuring the elevation with respect to the some datum some datum and the this centerline and then at the inlet it might be having some velocity and some pressure and at the outset again it might be having some other velocity and pressure now you understand this we have shown that this particular cross section of the pipeline may not remain constant during the flow of the fluid so here we see that on this side it is smaller and on this side it is bigger so what happens that whenever the cross-section is changing it would mean that even if the mass flow rate is constant but depending on the pressure temperature and the cross sectional area the velocity of the fluid may undergo a change and as we know that for in comfortable fluid if the cross sectional area is constant if the mass flow rate is constant then in that case velocity would remain same in the two sections so here we are writing the Bernoulli's equation so this first term is signifying the potential head and this is showing the pressure head this is the kinetic head and this HP is the equivalent head added to the fluid by the compressor that means if you are using some compressor so this compressor itself is adding some energy to the fluid so that is accounted for on this side inlet side and the outlet side we again have the potential head the pressure head the connecticut and now we are adding the frictional losses which are taking place during the flow of the fluid in through this particular section now this is the energy balance which we shall be using time and again to find out the pressure loss in the pipeline now in this pressure loss there are various formulas are developed based on the Bernoulli's equation to find out the performance in terms of the pressure drop and these all these formula which were formula we are we may be encountering we will be using some kind of gas properties like a comfortability factor the gas gravity and with the flow rate the pipeline length the diameter and the pressure along the pipeline so these are the parameters based on which various types of formula have been derived like these are the various types of formulae which have been given in the literature but other than these also there are plenty many so we here we have just come here just considering a few of few of the commonly used formulae which are used in for the piping calculation in the natural gas systems and we shall looking into these equations one by one so first let us go to the general flow equation and this is also called the fundamental equation because because fundamental because this is the one which is based on the theory theory that is the energy balance and from that we derive various other types of equations and this relates the gas flow rate the gas properties pipe size flow temperature with the pressure drop so we want to calculate pressure drop and this pressure drop is related to all these operating parameters of the fluid and it involves some friction factor and whenever we talk affection factor we need against some other formula to find out the friction factor and again there are some formula which are again we shall look into like Colebrook right formulas and modified Colebrook right equation and the AG equation so these kind of formula are used to find out the friction factor so to develop this a particular flow equation we will not go into detail of this because these details have been given in in standard fluid mechanics books and the difference I have also given some standard fluid mechanics books so you can look into those books to find out how one derives these equations here I shall just mention you that the basis of the derivation that here we find that we take some kind of pipe line with a diameter D and this is the inside diameter of the pipe line and then some pressure at the inlet and some pressure p2 at the outlet and the length of this particular section is taken to be ill the fluid is at a temperature of TF and the flow rate is Q and in this case we are assuming that the temperature is remaining constant but the pressure is varying from the inlet to outlet and please understand that if the pressure is remaining constant or pressure is not varying then there cannot be any flow so in that way the p1 has to be more than p2 that Inlet pressure has to be more than the outlet pressure now here we have the as thermal equation that is if you consider the TF to remain constant then this is the equation we shall be able to derive so this is the equation by which we can find that what is flow rate and here we take some standard temperature sometimes we need to take some base temperature pressure because the gas is generally compressible so it's density changes with both temperature and pressure so that is why we need to define the or we need to mention the flow rate with respect to some standard or base temperature pressure so here in this case this TS and PS are the some standard temperature pressure and these are the actual pressures in the pipeline this gamma G is the compressibility factor TF is a fluid temperature le is the length of the section of the pipe and Z is the consummatory factor D is the inside diameter of the pipeline now in this case you will find that there is some kind of this constant now this constant value may change depending on the units we are using somebody may use the SI unit system and sometimes we may use the FPS that is the food pounds second so british-owned is what we call so depending on the kind of Units unit system we are using to derive these equations this the magnitude of this particular constant will remain same and in this case you see that this has been defined in terms of the FPS system that is the flow rate is in the standard cubic feet per day thus pressure is in PSI that is the pounds per square inch absolute the temperature is in ranking and the pie the length of the pipe lands in miles and diameter is in inches so whenever you are using this particular equation you have to be careful that you are sticking to this particular units where to find the flow rate so if you are making any kind of mistake in unit then you will get wrong result now here in similar the same equation has been put in terms of the SI unit now you can see here that other remains the same except that this particular thing is changing the constants changing and of course there is something called the transmission factor and we shall look into transfer factor later on now as we said that the pressure is varying while we are constant constant now because the pressure pad is so does the complicity of the gas so to find out the conservatory of the gas earlier we learned mainly methods in our earlier lectures so in these lectures we found that this ability is determined maybe from some equation or using some some kind of figures and in these sometimes we need the reduced pressure so whenever we are talking about this reduced pressure reduce temperatures so we need to fix the temperature we need to fix the pressure so in this case because the pressure is varying so what is done for a quick estimation the pressure is taken to some average and somebody can use the arithmetic average but better than the arithmetic average we can use this particular expression which has been given here so this has been found to be better representation of the average pressure inside the pipeline so that is why this particular in this you see that it is P 1 plus P 2 minus P 1 P 2 divided by P 1 plus P 2 if you look at this expression if you find that this is some kind of an harmonic average and this is particular thing if you divide by 2 and multiply by 2 this is some kind of an away arithmetic average so it is that means this expression is considering both the arithmetic average and the harmonic average of the pressure and then this transmission factor if this is related to this Darcy's friction factor and this we will find that there are different types of friction factor later on now in that equation order equation the elevation effect was not taken into account that is the difference between za and ZB now in this case if you take the aleutian effect in the account then what will find we land up in such an equation and you see that this length this equivalent length is taken to be J into L and this J is given by this particular expression e to the power X that is exponential to the power s minus 1 divided by s and this L is the actual length of the pipeline between stream upstream and downstream ends and this equivalent that means because of elevation this is the equivalent length even though this is actual length now this elevation correction factor will be defined later on and this is this starting this is the elevation correction factor and we shall see that if there are many segments with the pipeline the whole pipeline consists of many segments and each segment has different elevations so what we need to do to find out the equivalent length over the whole system what we do we use this particular equation and in this equation we find that this L I represents the various sections and for each is I we have some particular J I and one particular si value so this way we are able to account for the elevation and this s is also given in various manners in before the type of unit system we are using so if we are using FPS unit then this is the particular expression we are using to find out the flow rate and here you see that the only thing we find that the outlet pressure has got some kind of modification due to the elevation this particular thing is taken to be 1 when we do not have any elevation effect so and this s is given by this particular expression and this h2 h1 are the elevations that means at the inlet and outlet the difference between the inlet and outlet elevation is given by this h2 and h1 and we see that again this for calculating de is again we have to use the particular system of units and in this case the we are using the FPS unit a similar expression can also be given for the SI unit so this is the expression of the s and again you find that the constant value has changed for both the Q and the s for the SI unit now for the complicity factor we have many equations we will not be going through all the equations these cards method we already studied in our earlier lectures so here we shall be looking into only a few of those which are very common that is the whole whole Yarber equation and cnj equation so this is the Yarbrough equation now in this case you find this is the particular expression given for the whole Yarber equation in this case we find the constant factor which is given in terms of the reduced density and the pseudo reduced temperature about which we learned earlier and this pseudo reduced temperature is obtained by dividing the actual temperature by the pseudo critical temperature and then we have the pseudo reduced pressure so using the pseudo determine reduced temperature to reduce pressure and the reduced density we find the expression for the Z and in this case this pseudo reduced density is unknown and which is obtained from again solving this particular expression so here you see that this is a highly nonlinear equation equation and to solve this particular equation for this pseudo reduced density what you need to do is that you have to use some suitable numerical technique to find out the root of the equation for example you may use the newton-raphson method to find out this value of the fuel reduced sorry reduced density now in this equation you have these two parameters a and B over so this a and B parameters can be found out from this a and B here so these two parameters again can be given in terms of the pseudo reduced temperature so using these particular values you can use the all Yarbrough method and they're very common method is the CNG method and this method is generally used for a pressure of more than 100 psi a so for this the Z is given by this particular expression and you see this expression is much simpler than the whole Yarbrough and in fact it is much simpler than the other expressions I have just shown so this is a very popular expression in the natural gas systems and so we find that this this the CNG stands for the California natural gas association okay so this is the here using the temperature of the fluid directly and here we have the average pressure and here is the gas gravity and for pressure less than 100 psi a the Z is taken to be almost equal to 1 that is we are being may take it to be an ideal gas long we find that the flow rate increases with the decrease in the gas gravity or the gas density and decrease in the ecology factor a decrease in the gas temperature increase in the pipeline pipe length for a given pressure drop between the inlet and the outlet and increase in the inside diameter so these deductions we have made from the earlier equations I have shown you so you can easily see from the equations how the flow rate would vary with the pressure temperature and the pipeline dimension and here we also find that the if the temperature of the gas is higher we find out flow rate will decrease so for higher flow rate we need to see to that the gas remains at a lower temperature now the frictional pressure drop we had which we have found in the expression in the expressions of the flow rate coming now this depends on the fluid flow rate the specific gravity of the fluid the fluid viscosity the inside diameter of the pipe the pipe length and the pipe right proof Ness so these are the common factors which determine the pressure drop through a pipe line for that first we need to know the gas velocity why because this gas velocity is related to the flow rate and also the kind of fluid regime flow regime we are having whether it's a laminar flow or turbulent flow or transition flow that will also be determined by this gas velocity through the reynolds number so we need to know that how to find out this gas velocity now this gas velocity is generally should be the receptive velocity between the pipe line and the fluid now in this case the pipe line is generally wave a static it is not moving though because the pipeline is not moving so the relative velocity between the fluid and the pipeline is the absolute velocity of the gas Rosetta velocity means we subtract one from the other so five levels it is zero and the gas velocity is its own value three if I subtract some value from 0 it remains the same so the absolute velocity of the fluid itself is the visitor velocity of the fluid and the velocity is generally given by this particular expression in terms of the volumetric flow rate and the cross sectional area now generally the gas is compressible so the volumetric area varies with both temperature pressure so what we do we relate this total this mass flow rate for the standard condition and the given condition because mass flow rate will remain the same no matter what the temperature and pressure are so we said that is Q dot Rho is the mass flow rate at the given condition and Q s dot and mu Rho is our the mass is now this product is the mass flow rate and some standard condition so we will equate this and after putting this it's this equation of state in terms of the Z value that is to consider it to be a non-ideal gas we find that this is the if you do some kind of mathematical manipulations we find ultimately we arrive at this expression which gives us the velocity in terms of the standard volumetric flow rate the pressure and the temperature and the competitive factor and generally for the standard temperature pressure this Z is this constant factor is taken to be unity now depending on the type of unit system we are using again we find we have different expressions for the Q dot and here we have it is for the FPS system and this is for the SI unit okay so depending on that we are finding that we have different types of units so these units have to be taken care of and now we have some something called usual erosional gas velocity and what it means what it means is this this whenever is gases flowing through the pipeline we were suppose we want higher flow rates but but we find that as by as we keep increasing the gas velocity it causes some kind of vibration and noise in the pipeline during the gas flow and the more the velocity of the gas the more the chances of erosion of the from the wall of the pipeline so we need to be careful whenever we are trying to increase the velocity of the gas so this is the expression that has been suggested to find out the maximum allowable gas velocity and this is in the FPS system it is given by 100 divided by root square of the density and after putting the equation of state this is the expression we are getting and in this case the R is taken with the universal gas constant is taken to be this value and this is a density claim a density is in this particular pounds per cubic feet the temperature is an kine and P is in PSIM now generally the operational velocity is taken to be about 50 percent of the maximum allowable velocity that is we are keeping a buffer of 50 percent for the any variation due to some kind of abnormality any variation we are keeping this buffer now the major loss is given in by the Darcy's equation here we have this expression and this v square by 2 G is signifying the connecticut that means this head loss is found out in terms of the loss in the kinetic head of the fluid and here we have is something called the friction factor and this friction factor has been can be found out by using different types of expressions and has been related by different researchers now we have the Reynolds number which determine the type of snow regime and depending on the flow regime we will have different types of friction factor and there are two types of friction factors when the Darcy friction factor and the Fanning friction factor and these two are related by this that the Darcy friction factor is generally four times the Fanning friction factor and in our subsequent lectures we shall be using the Darcy friction factor and we shall not be using FD anymore we shall be using only F and we shall understand that we are talking about the Darcy friction factor now here we have an expression for the laminar flow friction factor and this you can also find out in any standard suit mechanicsburg and this is for the Darcy friction factor it is 64 by re in some books you may find it to be 16 by re and then understand that they are talking about the Fanning friction factor so you may find both type of expressions in the fluid mechanics book so since we are using Darcy friction factor we are using 64 by Reynolds number and Reynolds number as you know it is the DV or the D is a diameter inside diameter of the tube V is the velocity of the fluid Rho is the density and mu is the viscosity or the dynamic viscosity and we have different types of turbulent flow turbulence or maybe in the smooth pipes and in this case the friction factor depends on the Reynolds number alone in case of rough pipe it depends more on the roughness of the pipe than the reynolds number and in between some roughness and smooth pipe the F may depend on both the roughness and the Reynolds number so here we have the Reynolds number expression for different types of units again so here we have the if you are the SI unit then this is the particular expression for the reynolds number and in this case what we have done we have substituted the area of cross section in terms of the pi by 4 d square so that is how we are getting this particular expression for the reynolds number here you find the diameter of the tube is coming in the denominator and it is expressed in terms of the volumetric flow rate of the gas and the temperature pressure and the FPS units we find that rest of the things remains constant only the but this u n-- this value has changed okay so if you take care of these expression units then we have the different types of expressions and here for the turbulent friction factor we have various types of mathematical expressions or we can use the Moody's chart to find out the director leader for affliction factor from this graph so using this graph we can find out the friction factor and the pipe roughness is given like this that the absolute or internal roughness divided by the inner pipe diameter so this is the particular roughness factor we use in this particular expression here you sir find that in this expression we need a by D value and this a by D value has been is defined like this and here in this particular table we find we have the various types of roughness given in terms of the inches or in terms of the millimeter for various types of material like wrought iron galvanized iron cast-iron concrete etc so we are given this and again we have a transmission factor which is given by this particular thing and this is kind of opposite of the friction factor friction factor tells us the kind the resistance and the various transcription factor says that how much gas can get transmitted or transported through the pipeline so the greater the transmission factor the more will the flow rather the less the friction factor more will the flow and this particular expression is given by this F equal to 4 by F square when we are putting in terms of the Darcy friction factor now please understand even if we are using the Fanning friction factor the value of F will change the the value of the transfer factor will remain the constant so we find that if this F is in terms of Fanning friction factor then we know that this 4 into Fanning is the Darcy so this 4 4 will get cancelled so Fanning friction factor will be simply inverse of the square of the transmission factor so before we go there we will see more of these particular expressions in our subsequent lectures and we find that these are the references which you may refer to to find out more detail about this particular friction factor and other rest of the equations for the gas flow rate and the pressure drop thank you