- 2 days ago
In this session you will learn
1. What is two phase in Pressure relief valve
2. Why it critical
3. how to size the orifice for two phase flow
4. Omega Method
5. Homogeneous Equilibrium Method
1. What is two phase in Pressure relief valve
2. Why it critical
3. how to size the orifice for two phase flow
4. Omega Method
5. Homogeneous Equilibrium Method
Category
📚
LearningTranscript
00:00hi friends welcome to the channel this is the last session and the part two of
00:05orifice sizing for two-phase i hope you have already watched the part one for the
00:11orifice sizing for the two-phase for the psv relief psv or pressure relief wall so let's start
00:21disclaimer for our channel and the content you shown in this videos
00:28in the first session of sizing for two-phase flow we learned what is two-phase flow in psv
00:36and the models then homogeneous equilibrium model omega model homogeneous frozen flow model how to
00:42select the correct model also we learned different methods for two-phase flow calculation which is what
00:49the introduction of that that is method one direct integration of a centropic nozzle flow method two
00:55sizing for two-phase flashing or non-flashing flow through psv and method third is sizing for
01:01sub cooling liquid at parv inlet using the omega method so in this session we will go one by one
01:08so let's start with method one
01:14the method one direct integration is entropic nozzle flow the inlet nozzle of a relief device is assumed
01:21as a limiting the inlet device always considered as a limiting flow element in the full open relief wall
01:28and to determine the maximum flux through the this nozzle the nozzle is assumed to be adiabatic reversible
01:37this is required for to consider the assumptions of a centropic flash so adiabatic means it is does not
01:46changing any heat and reversible means it does not have any pressure drop when it passing through that
01:52converging nozzles the two-phase flow through the prv is complex because the rapid pressure drop
01:58causes the liquid to flash into vapor and this changes the fluid density and since the
02:05the flow is directly depending on density a normal simple equation will not be accurate for two-phase
02:14the flow is assumed assumed to follow the asymptropic that is a constant entropy path
02:20and the idle perfectly efficient path which guarantees the maximum flux and maximum theoretical flow
02:27capacity through the nozzle so because from the two-phase of relief load we have to calculate the
02:34maximum flux going through that nozzles possible through that nozzle
02:42So, start with the known condition of pressure P0 or temperature T0 at the PSV inlet
02:48and use the property data to find the initial specific entropy which remains constant for all the change
02:54in pressure assume the flow through the assume the flow through the asymptropic nozzle
02:59which is the constant entropy and then generate the property data's or generate the data points
03:05how to generate the data point decrease the pressure by small successive increment generally
03:11with the one psi from inlet pressure of P0 to the till we reach the back pressure
03:18what is whatever our back pressure from inlet pressure inlet pressure to the PSV to the
03:23back pressure at the outlet for each new lower pressure use the constant entropy
03:29to perform the isentropic flash and or a thermodynamic calculation and determine the new state of
03:35fluid specific specifically we have to calculate the density at that pressure so successive pressure
03:43has to decrease from inlet pressure of P0 to the eventual back pressure with a drop of one psi each
03:49time and entropy remains constant. So, based on the pressure variation generate the series of pressure
03:58density data from P1 to rho 1 and so on on the at the constant or isentropic path means constant
04:07entropy path
04:08and then perform the integration to find the maximum flow or a maximum flux calculate G which is the maximum
04:15flux
04:16for each new pressure drop the maximum flux will increase and then start decrease
04:22and the point where G reaches to the maximum value or G max is the choke flow condition from the
04:28TRV.
04:29The pressure at which the G max occurs is a throat pressure which is which is PT. The direct integration
04:36method is a rigorous integration
04:38produced that use the thermodynamics principles and properties
04:43via successive isentropic flash to find one pressure point that is PT within the nozzle where the flow rate
04:51G max is or you can say G is maximized ensuring the PSV size for the true choke flow condition.
04:58So, we have to calculate based on the from the inlet pressure to the back pressure all at all instant
05:06of
05:08pressure parameters we have to calculate density as well and then we have to integrate the density
05:13with the isentropic path and then you have to find out the maximum G which is which will come at
05:19the choke flow
05:20and when the maximum G occurs that is called the throat pressure PT.
05:28So, in direct integration isentropic nozzle flow method we have to calculate G max and the formula for the G
05:36max is G
05:38square is equal to minus 2 integration of V into DP by V square which is comes is equal to
05:45density
05:46at the throat to the square into minus 2 integration of DP by P where the max is max is
05:56for the maximum
05:56maximizing the condition which accounts the potential choking of the fluid G is the mass flux
06:04V is your specific volume of the fluid Rho is mass density of the fluid P is the stagnation pressure
06:11of the fluid O is the fluid condition at inlet of the nozzle and T is the fluid condition when
06:17the
06:17throat or nozzle where the cross sectional across area is minimized so which is the your throat point
06:24which is the PT point so in this way we can calculate G
06:31so to calculate the G we need to solve the integration of PT to P0 so to solve the integration
06:39we have to calculate the overall mass density of a fluid at stagnation pressure
06:45overall mass density that is PI at the stagnation pressure PI
06:49so to get the the overall mass density for a mixture in thermal or mechanical equilibrium as we said
06:56no change in heat and no pressure drop can be calculated based on the density of each phase
07:02and the volume fraction of vapor in that mixture so formalize rho is equal to alpha into rho by V
07:12plus
07:121 into 1 minus alpha into rho I so in the the rho is the density of the two phase
07:19mixture
07:20rho V is the density of vapor rho L is the density of the liquid and and alpha is the
07:25volume fraction of vapor phase mixture
07:28which can also determined by alpha by 1 by alpha like this and the volume fraction of a vapor phase
07:34is the mixture is related to the mask or mass quantity of the mixture and mass fraction of the vapor
07:40phase
07:40by the following so in this way we can calculate this
07:49so so in method one when for the sizing direct integration and centropic nozzle flow
07:55once we calculate the maximum flux
07:58G value then orifices can be calculated by using this equation the equation is a which is the area of
08:05surface 277.8 into W divided by KD KB KC KV and G KV we already seen our earlier lecture
08:14so we have to take it from there so A is the area required effective discharge area required in inch
08:20or mm square W is the mass flow KD is the discharge coefficient KV is the back pressure correction factor
08:27KC is a combination correction factor and KV is the viscosity correction factor so based on this and GU
08:33we have already calculated if based on the earlier formula so based on this you can calculate
08:39area required or effective area for the orifice for the method one sizing direct integration is
08:45entropic nozzle flow
08:50so method two sizing for the two-phase flashing and non-flashing flow through the PRV
08:56this method appropriate for the fluids both above or below the thermodynamic critical points
09:02condensing two-phase flow also in condensing two-phase flow the method presents presented can be used in for
09:09the liquids that are saturated and enters the relief device the omega parameter is determined using the
09:15specific volume data obtained using the fluid properties data flash calculation and mixture of
09:20stagnation condition and one additional pressure at the or two points or second pressure will be
09:26calculated 90 percent generally one is at the inlet condition and one as the 90 percent of the inlet
09:32condition so so in this method method two sizing two-phase flashing and non-flashing flow we can
09:39calculate the orifice size with a simple four steps the first step we have to calculate the omega
09:45second step you have to find out the whether the flow is critical or non-critical and then third
09:49stage you have to calculate the maximum flux and four stage you can calculate the
09:54orifice area so first step is calculating the omega parameter
09:59calculating omega parameter using the two-phase pressure specific volume data
10:03so omega is equal to 9 into v9 by v0 minus 1 so v9 is the specific volume evaluated at
10:1090 percent of
10:10prv inlet pressure pressure and po is the when po is determined and the flash calibration should be
10:19carried out is and tropically but the adiabatic flash is sufficiently low called low quality mixture
10:27for thermodynamic critical point and v0 is the specific volume of two-phase system at the prv inlet
10:37so second step is to determine the flow is critical or sub critical so when pc
10:45is greater than or equal to pa then flow is critical when pc is less than or equal to less
10:51than pa then
10:52subcritical flow so pc is a critical pressure and pc can be calculated by eta into po po is your
10:59inlet pressure
11:02so eta is the critical pressure ratio it can be calculated by this method or by following the
11:09approximation by this method so where po is the pressure of the prv inlet and the prv set pressure
11:18plus allowable overpressure and pa is the downstream back pressure so when your critical pressure is less
11:26than your back pressure more than or equal to your back pressure then critical flow happens when
11:33the critical pressure is less than your back pressure then subcritical flow happen
11:41so this graph tells you the correlation between the nozzle critical flow and the flashing and non-flushing
11:46system it tells about the critical pressure ratio based on the omega value so based on the omega parameter
11:52you can and you can see the critical pressure ratio whether it is a non-flashing or flashing service
11:59like when it crosses above the one it will start in the flashing zone and before one it is a
12:06non-flashing
12:07zone or less than one it's a non-flashing zone
12:12so step three is the calculating the mass flux which is g g max we have to calculate again so
12:20for critical
12:20flow g can be calculated at eta c square root of po by v into w so eta c is
12:27a critical mass flow
12:31subcritical flow if it is subcritical flow this is the formula to calculate the g so where g is the
12:38mass flux po is the inlet is the pressure at the prv inlet v is the specific volume of the
12:44two-phase
12:45system and eta a is the back pressure ratio which is the back pressure to inlet pressure of the psv
12:55so
12:56in this way we can calculate the g based on the critical flow or no and subcritical flow
13:03then step 4 is calculating the required area for the prv or the orifice size so the formula is
13:10simple again the same formula 277.8 w by kd by kb by kc by kb into g so where
13:19a is the required effect
13:21to discharge our area w is the mass flow rate kd is the discharge coefficient kb is a back pressure
13:26correction factor kc is the combination correction factor and kb is the viscosity correction factor so
13:32viscosity correction factor we have calculated in our earlier lecture so that video can be seen for the
13:37kb calculation so in this way we can calculate the orifice size area for the method 2 which is the
13:44sizing for two-phase flashing and non flashing flow through the prv the third method is method 3 sizing
13:52the subcooled liquid at prv inlet using the omega method so this is for the basically for the subcooled
13:59liquid the method used for the sizing or handling the subcooled in including saturated liquid at the inlet
14:06no condensable vapor or non-condensable gases should be present at the inlet so for this
14:12this method to be when we have to use this method there is no condensable vapor or non-condensable
14:17gases like nitrogen or anything should not be present and the subcooled liquid either flashes upstream
14:22or downstream of the prv throat depending on the which subcooling region it falls
14:28and the equation in this section also apply to all liquid scenarios
14:33so first step to calculate is a omega parameter again so how to calculate omega omega calculated 9
14:39divided by p or 10 p rho 10 by rho 9 minus 1 so rho 10 is the density of
14:47the pr density at the prv inlet
14:49and p 9 is the density at the density evaluated at the 90 percent of the saturation pressure which is
14:58a ps
14:59so in this way you can calculate omega parameter
15:07the step 2 is determine the subcooling region
15:12so ps is greater than or equal to nst by po which then it is a low subcooling region so
15:18ps is your
15:19saturation pressure nst is your transition saturation pressure and po is your inlet pressure
15:26so saturation pressure is less than the nst into po which then it's a high subcooling region
15:31flashing occurs at the throat in this case flashing occurs upstream of the throat so before
15:36at the inlet it is happening and it is you can say on the uh flash occurs in the throat
15:41or at the
15:42outlet you can say so ns uh eta eta st is transition saturation pressure eta st you can calculate based
15:50on the omega omega parameter and where the po is the pressure of the prv at the inlet
16:00so step 3 is to determine the critical subcritical flow and then the subcooling region that is its
16:07subcooling region means it is though it is flashing at the inlet of the psv or in the throat or
16:13at the
16:14outlet of the psv so uh for the low subcooling region pc is greater than equal to pa then the
16:22critical
16:23flow so pc is your uh critical pressure if it is a greater than or equal to your back pressure
16:28then
16:29it's a critical flow and if the critical pressure is less than the back pressure then it's a subcritical
16:35flow so pa is the downstream back pressure of the psv or you can say back pressure of the psv
16:42and then for high subcooling region use the following uh comparison ps is your saturation
16:49pressure when if it is greater than your back pressure then it's a critical flow and if the
16:54ps is less than your back pressure then it's a subcritical flow or all liquid flow so where the
17:00pc is your critical pressure pc can be calculated as pc into uh eta c by po so po is
17:06your inlet pressure
17:07if this is eta eta is a critical pressure ratio based on the c figure this is from the epi
17:14value
17:17so step 3 is to calculate the max flux max flux is the g so to calculate g this is
17:23the formula
17:24and in this formula we have to uh uh change change the eta values this eta value and this pressure
17:33value
17:34based on the subcritical or sub cooling and uh sub high sub cooling low sub cooling region and
17:40flow critical and non-critical so uh to calculate the g max in case of low sub cooling region and
17:48the flow
17:48is critical then eta c eta c is critical pressure for n so in that case when the flow is
17:56critical and
17:57sub low low low sub cooling region then eta c which is the critical pressure ratio to be used instead
18:04of
18:05simpler eta and if the flow is subcritical then eta a should be used in place of eta so eta
18:14is a back
18:15pressure ratio which we have seen in earlier slides it is a back pressure ratio and this is your critical
18:23pressure pressure pressure ratio critical pressure pressure ratio similarly if the high sub cooling
18:29region and the flow is critical then ps shall be used instead of p so ps is your saturation pressure
18:41saturation pressure and if the flow is subcritical then you have to use pa instead of p so pa is
18:49your
18:49downstream back pressure back pressure back pressure back pressure it is your back pressure so based on
18:55these uh regions or in critical non-critical flow you can calculate the g value and g is the maximum
19:02flux and eta is a back pressure ratio only so step four is the calculate the required area for the
19:12prv
19:13so in si units to calculate area for the orifice it is 16.67 into q into uh rho kdy
19:23kb kv and g so a is
19:25your required effective area of discharge g is your maximum flux q is your volumetric flow rate kd is your
19:30discharge coefficient kb is your back pressure correction factor kc is combination factor and kv is your viscosity
19:36correction factor so based on this formula you can calculate the orifice size for the subcooled liquid
19:43at prv inlet using the omega method so in this way we are completed the all the three methods
19:49uh for the isentropic calculation then flashing non-flashing and then this third one is the subcooling method
19:58so conclusion for this uh presentation for the sizing of two-phase relief basically we learned the three
20:06methods uh uh the homogeneous equilibrium method then omega method and then uh and also the three uh
20:15different uh methods for the calculation of uh orifice sizes for the orifice size so first was the
20:23uh integration of a centropic nozzle equation then second which is the two-phase flashing non-flashing
20:29and third one is the uh subcooled liquid at the inlet so homogeneous generally the model homogeneous
20:36model is used for the uh integration of a centropic nozzle equation which is more rigorous method and
20:43the other two the flashing and non-flashing flow method where the simplified analysis analytical
20:50equation used based on the omega similarly for the uh subcooling liquid also it is used the omega method
20:59so this uh homogeneous direct integration method is requires the rigorous thermodynamic property package
21:05like the process simulator and the perform the successive isentropic flashes to determine the density at
21:11different uh pressures which we are dropping at the dropping from the inlet of the psv to the up till
21:21the back
21:22pressure by the drop of around 1 1 psi however for flashing non-flashing omega method we are we are
21:30just
21:30calculating the omega parameter based on the specific condition at 90 percent of the inlet pressure
21:37and that's why it's approximating approximate the two-phase effect similarly uh for the subcooling
21:45liquid we use the simplified liquid centric equation and omega parameter to account the partial flashing
21:51again for the uh this method is widely applicable the homogeneous equilibrium model or the
21:58isentropic nozzle flash uh can handle any two-phase mixture flashing non-flashing and subcool and that are
22:05expected to flash uh however for flashing and non-flashing it it also takes the two-phase mixture
22:11liquid and vapor it will be used for support liquid as well it can handle non-condensable gases as well
22:17whether liquid may and it the liquid or saturation condition may be flash or non-flash till that omega
22:25omega method or flashing non-flashing method is applicable for the subcooling liquid liquid at the inlet
22:32that's significantly below the saturation temperature and only partially flashes within the wall for that
22:39only your subcooling method will be used so homogeneous equilibrium model assumes the uh the phases move
22:45at the same velocity like uh both your liquid and vapors will move at the same velocity and are
22:52continuous thermodynamics equilibrium and remains in the thermodynamic equilibrium means no change in
22:57pressure or no change in heat this entropic flashing it will be done however for the flashing non-flashing
23:04or omega method homogeneous model and omega parameter is derived from from the same basics of homogeneous
23:11equilibrium assumption this is the modified liquid model starts with the liquid flow equation and use
23:19the omega to correct the flow restriction caused by the small amount of vapor created
23:24the g max or maximum flux or maximum flux were determined by the finding the peak value
23:31of the integrated desentropic curve so this this method is more rigorous method however in omega method
23:38required a is calculated directly using the omega parameter at the inlet condition and for the subcooling
23:45required q or volumetric flow rate or a area is based on the liquid density and the omega factor
23:50so in this way uh this is the comparison for the all three methods as well as the
23:56the two models which we have learned in this session
24:01so thank you very much write your question and comment i will be happy to answer it
24:08you can reach us on conceptengineering2025 at gmail.com
24:15links and links for the other sessions are given in this description
24:19you
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