Problem 44897. Calculate value of Ra for three runs. Flow rates

Created by A C

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<div style = "text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; "><div style="block-size: 81px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 40.5px; transform-origin: 407px 40.5px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Problem 5.31, page 220, from Felder and Rousseau Elementary Principles of Chemical Processes book</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">The problem is posted here:</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style=""> </span></span><a target='_blank' href = "https://ibb.co/2MYDKQT"><span style=""><span style="">&lt;https://ibb.co/2MYDKQT</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">&gt;</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">I worked the problem out. It was fun and challenging for me. I wanted to share. Work it out any way you want and learn.</span></span></div></div></div>

Problem 5.31, page 220, from Felder and Rousseau Elementary Principles of Chemical Processes book

The problem is posted here:
<https://ibb.co/2MYDKQT>

I worked the problem out. It was fun and challenging for me. I wanted to share. Work it out any way you want and learn. My answers for Ra are [5.6267 7.4260 5.5061]. Yours answer might be different. They might be right or wrong.

Here my code.
 
% Read in the values of Rf, Rt, Rp, the fuel gas component mole fraction xa, xb, xc, 
% xd, and xe, and the percent excess air PX, and to find the  required value of Ra.
% Methane = a , ethane = b, propane = c, n-butane = d, isobutane = e

% The linear proportionalities between the in and out signals and the
% corresponding process variables may be determined by:

% Fuel Temperature (K)

Tf1 = 25+273; Tf2 = 35+273; Rt1 = 14; Rt2 = 27;

% Fuel Pressure (atm) assume Patm = 1 atm

Pf1 = 1; Pf2 = 1 + 20000/101325; Rp1 = 0; Rp2 = 6;

% Fuel Flow rate (L/h)

Vf1 = 0; Vf2 = 2000*1000; Rf1 = 0; Rf2 = 10;

% Air Flow Rate (L(STP/h)

Va1 = 0; Va2 = 100000*1000; Ra1 = 0; Ra2 = 25;

% data readings

Rf = [7.25,5.8,2.45];
Rt = [23.1, 7.5 46.5];
Rp = [7.5, 19.3, 15.8];

% data mole%

xa = [.81,.58,0];
xb = [.08, .31, 0];
xc = [.05, .06, .65];
xd = [.04, .05, .25];
xe = [.02, 0, .10];

% data percent excess air

PX = [.15,.23,.33];

% Linear equations R => x T(K)

slopeT = 1/((Rt2 - Rt1)/(Tf2 - Tf1));
Tb =  Tf1 - slopeT*Rt1;
%Rt = linspace(Rt1,Rt2,11);

T = Rt*slopeT + Tb;

% Linear equations R => x Pa(atm)

slopeP = 1/((Rp2 - Rp1)/(Pf2 - Pf1));
Pb =  Pf2 - slopeP*Rp2;
%Rp = linspace(Rp1,Rp2,11);

P = Rp*slopeP + Pb;

% Linear equations R => x V(L/h)

slopeRf = 1/((Rf2 - Rf1)/(Vf2 - Vf1));
Vb =  Vf1 - slopeRf*Rf1;
%Rf = linspace(Rf1,Rf2,11);

Vf = Rf*slopeRf + Vb;

% assume ideal gas behavior PV = nRT, R = constant find n(Kmol/h)

R = 0.08206; %(atm *L)/(gmol*k)
nf = ((P.*Vf)./(R*T))/1000; % Kmol/h

% species' mole in the fuel mixer Kmol/h

nfa = nf.*xa;
nfb = nf.*xb;
nfc = nf.*xc;
nfd = nf.*xd;
nfe = nf.*xe;

% Theoretical O2
% combustion chemical equations:

% 1. CH4 + 2O2 > CO2 + 2H2O methane

% 2. C2H6 + 3.5O2 > 2CO2 + 3H2O ethane

% 3. C3H8 + 5O2 > 3CO2 + 4H2O propane

% 4. C4H10 + 6.502 > 4CO2 + 5H2O BUTANE

% 5. C4H10 + 6.502 > 4CO2 + 5H2O ISOBUTANE

% no2s, s = stoichiometric when its assumes the species are completely consumed.

nO2s = nfa*2 + nfb*3.5 + nfc*5 + nfd*6.5 + nfe*6.5; %(kmol O2/h)

% excess of O2

nO2_feed = PX.*nO2s + nO2s; %kmol O2/h

% assume 21 mole%O2 and 79 mole%N2

nair_feed = nO2_feed/.21; %Kmol air/h

% assume air behavior is ideally PV = nRT find V() using T(stp) =273K,P(stp) = 1atm
% 1000gmol = 1 kmol

Vair = (nair_feed.*273*.08206)*(1000); %(L/h)

% Linear equations R => x V(L(STP)/h)

slopeVa = (Ra2 - Ra1)/(Va2 - Va1);
Vab =  Ra1 - slopeVa*Va1;
Ra = Vair.*slopeVa + Vab

Solve

Solution Stats

14 Solutions
9 Solvers

Last Solution submitted on Dec 30, 2020

Last 200 Solutions

Problem Comments

2 Comments

2 Comments

Gergely Patay on 17 Jul 2019

Please reformulate the statement to a real Cody problem. This is not a blogging site.

A C on 31 Jul 2020

I think I did.

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