Error to find the Molor Volume using Lee/Kesler Data Table

clear,clc,close all
filename = 'Data.xlsx'

filename = 'Data.xlsx'

DataStruct = importdata(filename);
Coefficients = DataStruct.data.DataGeneral

Coefficients = 8×15

1.0e+03 * 0.0399 0 0.1509 0.0490 0.0746 0.2980 6.0000 0.0208 0.0000 -0.0000 0.0000 -0.0000 -0.0062 0.1800 0 0.0709 0.0001 0.4172 0.0771 0.1240 0.2980 1.0000 0.0331 0.0122 -0.0121 0.0044 -0.0002 -0.0108 0.2590 0 0.0440 0.0002 0.3042 0.0738 0.0940 0.2980 1.2000 0.0250 0.0552 -0.0337 0.0079 -0.0001 -0.4036 0.2282 -0.3935 0.0280 0.0000 0.1262 0.0340 0.0892 0.2980 6.0000 0.0261 0.0082 -0.0020 0.0002 0.0000 -0.0080 0.2210 0 0.0320 0.0000 0.1546 0.0504 0.0734 0.2980 6.0000 0.0297 0.0061 -0.0012 0.0001 -0.0002 -0.0099 0.2379 0 0.0365 0.0001 0.3247 0.0831 0.0810 0.2980 1.2000 0.0321 -0.0135 0.0199 -0.0068 -0.0000 -0.1016 0.2287 -0.0923 0.1538 0.0002 0.5564 0.0456 0.2760 0.2980 6.0000 0.1031 0.0042 -0.0011 0.0001 -0.0019 -0.1333 0.4224 -0.0960 0.0180 0.0003 0.6471 0.2206 0.0559 0.5000 1.7000 0.0301 0.0068 0.0068 -0.0025 0.0001 -0.2509 0.2234 -0.2418

Z0_table = DataStruct.data.DataZ0

Z0_table = 41×16

0 0.0100 0.0500 0.1000 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.5000 2.0000 3.0000 5.0000 7.0000 10.0000 0.3000 0.0029 0.0145 0.0290 0.0579 0.1158 0.1737 0.2315 0.2892 0.3479 0.4335 0.5775 0.8648 1.4366 2.0048 2.8507 0.3500 0.0026 0.0130 0.0261 0.0522 0.1043 0.1564 0.2084 0.2604 0.3123 0.3901 0.5195 0.7775 1.2902 1.7987 2.5539 0.4000 0.0024 0.0119 0.0239 0.0477 0.0953 0.1429 0.1904 0.2379 0.2853 0.3563 0.4744 0.7095 1.1758 1.6373 2.3211 0.4500 0.0022 0.0110 0.0221 0.0442 0.0882 0.1322 0.1762 0.2200 0.2638 0.3294 0.4384 0.6551 1.0841 1.5077 2.1338 0.5000 0.0021 0.0103 0.0207 0.0413 0.0825 0.1236 0.1647 0.2056 0.2465 0.3077 0.4092 0.6110 1.0094 1.4017 1.9801 0.5500 0.9804 0.0098 0.0195 0.0390 0.0778 0.1166 0.1553 0.1939 0.2323 0.2899 0.3853 0.5747 0.9475 1.3137 1.8520 0.6000 0.9849 0.0093 0.0186 0.0371 0.0741 0.1109 0.1476 0.1842 0.2207 0.2753 0.3657 0.5446 0.8959 1.2398 1.7440 0.6500 0.9881 0.9377 0.0178 0.0356 0.0710 0.1063 0.1415 0.1765 0.2113 0.2634 0.3495 0.5197 0.8526 1.1773 1.6519 0.7000 0.9904 0.9504 0.8958 0.0344 0.0687 0.1027 0.1366 0.1703 0.2038 0.2538 0.3364 0.4991 0.8161 1.1341 1.5729

Z1_table = DataStruct.data.DataZ1

Z1_table = 41×16

0 0.0100 0.0500 0.1000 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.5000 2.0000 3.0000 5.0000 7.0000 10.0000 0.3000 -0.0008 -0.0040 -0.0081 -0.0161 -0.0323 -0.0484 -0.0645 -0.0806 -0.0966 -0.1207 -0.1608 -0.2407 -0.3996 -0.5572 -0.7915 0.3500 -0.0009 -0.0046 -0.0093 -0.0185 -0.0370 -0.0554 -0.0738 -0.0921 -0.1105 -0.1379 -0.1834 -0.2738 -0.4523 -0.6279 -0.8863 0.4000 -0.0010 -0.0048 -0.0095 -0.0190 -0.0380 -0.0570 -0.0758 -0.0946 -0.1134 -0.1414 -0.1879 -0.2799 -0.4603 -0.6365 -0.8936 0.4500 -0.0009 -0.0047 -0.0094 -0.0187 -0.0374 -0.0560 -0.0745 -0.0929 -0.1113 -0.1387 -0.1840 -0.2734 -0.4475 -0.6162 -0.8608 0.5000 -0.0009 -0.0045 -0.0090 -0.0181 -0.0360 -0.0539 -0.0716 -0.0893 -0.1069 -0.1330 -0.1762 -0.2611 -0.4253 -0.5831 -0.8099 0.5500 -0.0314 -0.0043 -0.0086 -0.0172 -0.0343 -0.0513 -0.0682 -0.0849 -0.1015 -0.1263 -0.1669 -0.2465 -0.3991 -0.5446 -0.7521 0.6000 -0.0205 -0.0041 -0.0082 -0.0164 -0.0326 -0.0487 -0.0646 -0.0803 -0.0960 -0.1192 -0.1572 -0.2312 -0.3718 -0.5047 -0.6928 0.6500 -0.0137 -0.0772 -0.0078 -0.0156 -0.0309 -0.0461 -0.0611 -0.0759 -0.0906 -0.1122 -0.1476 -0.2160 -0.3447 -0.4653 -0.6346 0.7000 -0.0093 -0.0507 -0.1161 -0.0148 -0.0294 -0.0438 -0.0579 -0.0718 -0.0855 -0.1057 -0.1385 -0.2013 -0.3184 -0.4270 -0.5785

Chem_list = DataStruct.textdata.DataGeneral(2:9,1)

Chem_list = 8×1 cell array
    {'Ar'  }
    {'Cl2' }
    {'CO2' }
    {'N2'  }
    {'O2'  }
    {'HCl' }
    {'CCl4'}
    {'H2O' }

Chem_indx = listdlg('PromptString','Please choose the chemical under invesigation.',...
    'SelectionMode','single','ListString',Chem_list)

Error using matlab.internal.lang.capability.Capability.require
Support for Java user interfaces is required, which is not available on this platform.

Error in listdlg (line 58)
Capability.require(Capability.Swing);

Chem =Chem_list{Chem_indx}
promt ={'Enter Temperature (C):','Enter pressure(bar):'}
dlgtitle = 'Input'
dims = [1 35]
answer = inputdlg(promt,dlgtitle,dims)
T = str2num(answer{1}) + 273.15;
P = str2num(answer{2});
Tc = Coefficients(Chem_indx,3);
Pc = Coefficients(Chem_indx,4);
Tr = T/Tc;
Pr = P/Pc;
Pr_ind = find(Z0_table(1,:)>Pr,1)-1;
Tr_ind = find(Z0_table(:,1)>Tr,1)-1;
Pr_match = (Z0_table(1,Pr_ind) == Pr);
Tr_match = (Z0_table(Tr_ind,1) == Tr);
if(Pr_match && Tr_match)
    disp('Perfect match, no interpolation needed!')
    Z0 = Z0_table(Tr_ind,Pr_ind);
elseif (Pr_match && ~ Tr_match)
    disp('Need to interpolate temperature')
    Tr_1 = Z0_table(Tr_ind,1)
    Tr_2 = Z0_table(Tr_ind+1,1)
    Z0_1 = Z0_table(Tr_ind,Pr_ind) 
    Z0_2 = Z0_table(Tr_ind+1,Pr_ind)
    Z0 = interpolate(Z0_1,Z0_2,Tr_1,Tr_2,Tr)
elseif (~Pr_match && Tr_match)
    disp('Need to interpolate pressure')
    Pr_1 = Z0_table(1,Pr_ind)
    Pr_2 = Z0_table(1,Pr_ind+1)
    Z0_1 = Z0_table(Tr_ind,Pr_ind) 
    Z0_2 = Z0_table(Tr_ind+1,Pr_ind)
    Z0 = interpolate(Z0_1,Z0_2,Pr_1,Pr_2,Pr)
    
else
    disp('Bilinear interpolation needed')
    Pr_1 = Z0_table(1,Pr_ind)
    Pr_2 = Z0_table(1,Pr_ind+1)
    Tr_1 = Z0_table(Tr_ind,1)
    Tr_2 = Z0_table(Tr_ind+1,1)
    Z01_1_1 = Z0_table(Tr_ind,Pr_ind)
    Z01_1_2 = Z0_table(Tr_ind,Pr_ind+1)
    Z01_2_1 = Z0_table(Tr_ind+1,Pr_ind)
    Z01_2_2 = Z0_table(Tr_ind+1,Pr_ind+1)
    Z0_1 = interpolate(Z0_1_1,Z0_2_1,Tr_1,Tr_2,Tr)
    Z0_2 = interpolate(Z0_1_2,Z0_2_2,Tr_1,Tr_2,Tr)
    Z0 = interpolate(Z0_1,Z0_2,Pr_1,Pr_2,Pr)
end

Z = Z0;
R = 8.3144;
P = P*100000
Molar_Volume = (R*T*Z)/P

Answer 1

[Walter Roberson]

Pr = P/Pc;

That value is being calculated -- and it is not an integer.

Pr_match = (Z0_table(1,Pr_ind) == Pr);

Z0_table is an array of floating point numbers that are not integers, and you are doing == comparisons against a calculated value. == between numeric values has the following rules:

• false if either or both of the values are any of the forms of NaN
• true if both of the values represent or both of the values represent
• true if the numeric difference between the items is zero
• false otherwise

In the case where both of the values are class single or class double the conditions can be rephrased as:

• false if either or both of the values are any of the forms of NaN
• true if both of the values are exactly 0, including if one is negative zero and the other is non-negative zero
• true if the two values are bitwise exactly the same (excluding NaNs)
• false otherwise

There is no approximation involved. If one of the values is equivalent to 0.333333333333333 and the other is equivalent to 0.333333333333334 then == will say they are not equal.

T = 1/3;
1-2*T == T        %--> will be false!

Next:

Pr_ind = find(Z0_table(1,:)>Pr,1)-1;

What happens if there are no such entries and Pr_ind ends up empty?

[Walter Roberson]

Perhaps you should be extracting the first row as marginal values for one coordinates, and the first column as marginal values for the other coordinate, and then use interp2()

[NANDEESWARAN]

Thanks you so much sir. Still I cannot able to figure out got error. I go through step by step again. Thanks for your time and valuabe information. I really appreciate your help.

[Walter Roberson]

As a general rule:

• never use == to compare floating point values that have been calculated two different ways, except possibly if they are definitely integers
• consider using ismembertol() instead, or abs(a-b)<=tolerance instead of a==b
• linspace() and the : operator probably do not work the way you expect them to, so if you use them with floating point values, the results might not be exactly what you expect
• MATLAB does not use decimal computations, it uses binary. 1/10 cannot be exactly represented in any finite-length binary fixed-point or floating-point number representation. This is not a MATLAB bug, and it is not a "bug" that Mathworks chose binary instead of decimal. If you choose any finite-length "base" numeric representation, there will always be ratios that cannot be exactly represented. For example in decimal, if 1/3 = 0.333333333333333 then twice that is 0.666666666666666 and three times it is 0.999999999999999 -- so 3 * (1/3) is not exactly 1 and that would hold true even if you used 50000 decimal places. If you use "base N" arithmetic for any integer base N > 1, then the ratio 1/(N+1) cannot be exactly represented in a finite length. The problem is in mathematics, not in MATLAB.

[NANDEESWARAN]

Thank you so much sir. I appreciate your help and tips.