Evaluation of Reid and True Vapor Pressures 
Author's Data: Housam BINOUS and Mahmoud Kammoun
Department of Chemical Engineering
National Institute of Applied Sciences and Technology
Tunis, TUNISIA
Email: binoushousam@yahoo.com

Tunisian Gas produces gasoline that is stabilized for safe storage and transport. The Reid Vapor Pressure (RVP) is a measure of the vapor-locking potential of the material. RVP is the vapor pressure of the material at 100°F or 37.8°C.
A stabilized gasoline must have an RVP between 10 and 12 psia. The stabilization column separates the LPG from the stabilized gasoline. In the present notebook, we show how we can compute the True Vapor Pressure (TVP) from the measures of P and T of the condensate. Values of P and T were obtained from a HYSYS simulation. We use both the Antoine equation and the modified Antoine equation. Both equations give accurate results.  The calculated TVP and the TVP given by HYSYS are in agreement. 
In addition, the RVP is very close to the TVP. Usually, these two properties differ by a factor of 1.05 to 1.1.

Off[General::spell]

Off[Solve::ifun]

Using 3 data points  (T1,P1), (T2,P2) et (T3,P3) obtained from HYSYS simulation. Antoine's equation is used with P in psia and T in °F

P1=120.57;

T1=266.95;

P2=101.53;

T2=251.11;

T3=222.27;

P3=72.519;

sol=Solve[{P1==10^(A1-B1/(C1+T1)),P2==10^(A1-B1/(C1+T2)),P3==10^(A1-B1/(C1+T3))},{A1,B1,C1}]

TVP==10^(A1-B1/(C1+100.04))/.sol

TVP=11.0256 psia is similar to the average value of TVP given by HYSYS = 11.17 psia

Method based on data interpolation of HYSYS P-T data. P in mmHg and T in °F

Transpose[{{258.574667138268,1008.63616713827,1758.69766713827, 2508.75916713827,3258.82066713827,4008.88216713827,	4758.94366713827,5509.00516713827,6259.06666713827},
{60.3001482527406,130.640978147698,	165.935451775639,191.037184914289,210.989910558537	227.777900548473,242.404960885871,255.451175727443	267.298315430660,7009.12816713827,278.196040592059}}]

Interpolation[%]

FindRoot[%[x]==100.04,{x,500}]

x 14.696/760/.%

Interpolation gives a poor result with a TVP value equal to 11.96 .

Using FindMinimum with 10 data points. Antoine equation is used and P and T are expressed in mmHg and °F, respectively. We find the following values for the Antoine coefficients: A2=5.14258,B2=2031.53 and C2=396.689 .

Psatcal={258.574667138268,1008.63616713827,1758.69766713827, 2508.75916713827,3258.82066713827,4008.88216713827,	4758.94366713827,5509.00516713827,6259.06666713827,7009.12816713827} 14.696/760

T={60.3001482527406,130.640978147698,	165.935451775639,191.037184914289,210.989910558537,	227.777900548473,242.404960885871,255.451175727443,	267.298315430660,278.196040592059}

PsatTheo=Map[10^(A2-B2/(C2+#))&,T]

sol=FindMinimum[Sum[(Psatcal[[i]]-PsatTheo[[i]])^2,{i,1,9}],{A2,7},{B2,1200},{C2,240}]

TVP==10^(A2-B2/(C2+100.04))/.sol[[2]]

Plt1=ListPlot[Transpose[{Psatcal,T}],PlotStyle->{RGBColor[1,0,0],PointSize[0.015]}]

Plt2=Plot[10^(((A2-B2/(C2+To))/.sol[[2]])),{To,40,300},PlotStyle->RGBColor[0,0,1]]

Show[Plt1,Plt2/.x_Line:>Map[Reverse,x,{2}]]

Model fits very well the data obtained using HYSYS and the TVP calculated using Antoine's equation is 11.2916 psia which is close to the average value given by HYSYS=11.17 psi

FindMinimum with 29 data points chosen close to TVP. Antoine equation is used and P and T are expressed in mmHg and °F, respectively.

Transpose[{{103.429866855307,22.5426833624779},{155.144800282961,38.4646086223261},{206.859733710615,50.5006865232840},{258.574667138268,60.2984122721283},{310.289600565922,68.6237249121891},{362.004533993575,75.8999428644320},{413.719467421229,82.3871788290326},{465.434400848883,88.2572933132446},{517.149334276536,93.6302270576644},{568.864267704190,98.5931116956126},{620.579201131843,103.211480838245},{672.294134559497,107.535920209467},{724.009067987151,111.606283705064},{775.724001414804,115.454538900049},{827.438934842458,119.106931521887},{879.153868270112,122.585082556521},{930.868801697765,125.907177259240},{982.583735125419,129.088539255778},
{1034.29866855307,132.142304096201},{1086.01360198073,135.079761639310},{1137.72853540838,137.910772884623},
{1189.44346883603,140.643904028841},{1241.15840226369,143.286680176930},{1292.87333569134,145.845843784505},
{1344.58826911899,148.327268530764},{1396.30320254665,150.736392489830},{1448.01813597430,153.077857433041},
{1499.73306940195,155.355961134161},{1551.44800282961,157.574665899286}}]

Psatcal={103.43,155.145,206.86,258.575,310.29,362.005,413.719,465.434,517.149,568.864,\
620.579,672.294,724.009,775.724,827.439,879.154,930.869,982.584,1034.3,1086.\
01,1137.73,1189.44,1241.16,1292.87,1344.59,1396.3,1448.02,1499.73,1551.45} 14.696/760

T={22.5427,38.4646,50.5007,60.2984,68.6237,75.8999,82.3872,88.2573,93.6302,98.\
5931,103.211,107.536,111.606,115.455,119.107,122.585,125.907,129.089,132.142,\
135.08,137.911,140.644,143.287,145.846,148.327,150.736,153.078,155.356,157.575}

PsatTheo=Map[10^(A2-B2/(C2+#))&,T]

Length[PsatTheo]

sol=FindMinimum[Sum[(Psatcal[[i]]-PsatTheo[[i]])^2,{i,1,29}],{A2,7},{B2,1200},{C2,240}]

TVP==10^(A2-B2/(C2+100.04))/.sol[[2]]

The TVP calculated using Antoine's equation is 11.3059 psia which is close to the average value given by HYSYS=11.17 psia

Computing TVP with the modified Antoine equation.

Psatcal=Map[Log,{103.43,155.145,206.86,258.575,310.29,362.005,413.719,465.434,517.149,568.864,\
620.579,672.294,724.009,775.724,827.439,879.154,930.869,982.584,1034.3,1086.\
01,1137.73,1189.44,1241.16,1292.87,1344.59,1396.3,1448.02,1499.73,1551.45} 101.325/760]

T=({22.5427,38.4646,50.5007,60.2984,68.6237,75.8999,82.3872,88.2573,93.6302,98.\
5931,103.211,107.536,111.606,115.455,119.107,122.585,125.907,129.089,132.142,\
135.08,137.911,140.644,143.287,145.846,148.327,150.736,153.078,155.356,157.575}-32)/1.8+273.15

PsatTheo=Map[(A2+B2/(C2+#)+D2 Log[#]+E2 #^F2)&,T]

We purposely set C2=0.

C2=0;

Off[FindMinimum::cvmit]

sol=FindMinimum[Sum[(Psatcal[[i]]-PsatTheo[[i]])^2,{i,1,29}],{A2,45},{B2,-4800},{D2,-7},{E2,0.000000005},{F2,5},MaxIterations->10^4]

(A2+B2/(C2+To)+D2 Log[To]+E2 To^F2)/.sol[[2]]/.To->37.8+273.15

Exp[%]

N[% 14.696/101.325,10]

We obtain an TVP=11.306 psia when we use FindMinimum built-in function.

sol=NMinimize[{Sum[(Psatcal[[i]]-PsatTheo[[i]])^2,{i,1,29}],10^-7<E2<10^-6},{A2,B2,D2,E2,F2},MaxIterations->10^3]

(A2+B2/(C2+To)+D2 Log[To]+E2 To^F2)/.sol[[2]]/.To->37.8+273.15

Exp[%]

N[% 14.696/101.325,10]

F2/.sol[[2]]

T

(E2 T^F2)/.sol[[2]]

(A2+B2/(C2+T)+D2 Log[T])/.sol[[2]]

We obtain a value of the TVP equal to 11.306 psia when we use NMinimize built-in function.

Solution using GAMS. The GAMS file is available upon request from the author.

We purposely set C2=0 and obtain the following model parametres: 
A2L= 41.741;  B2L= -4499.610;  D2L= -4;  E2L= 1 E-7 and  F2L= 2.276.

A2L=41.741;  
B2L=-4499.610;  
D2L=-4.000;  
E2L=10^-7;  
F2L=2.276;

(A2L+B2L/(C2L+To)+D2L Log[To]+E2L To^F2L)/.C2L->0/.To->37.8+273.15

Exp[%]

% 14.696/101.325

plt1=ListPlot[Transpose[{E^Psatcal,T}],PlotStyle->{RGBColor[1,0,0],PointSize[0.015]}]

plt2=Plot[E^((A2L+B2L/(C2L+To)+D2L Log[To]+E2L To^F2L))/.C2L->0,{To,240,360},PlotStyle->RGBColor[0,0,1]]

Show[plt1,plt2/.x_Line:>Map[Reverse,x,{2}]]

Solution With GAMS gives TVP=11.339 psia.

Conclusion: The calculated TVP and the TVP given by HYSYS are in agreement. 
The Reid Vapor Pressure given by HYSYS is equal to 11.13 psia, which is close to the TVP predicted by HYSYS and calculated using our approach.