3ebb005c-b6b2-4896-b1d6-9c7ebfefc60a 34 Javier Ochoa 4 5 false false 0 0 decimal

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Estimate the vapor pressure of ethylbenzene at 460 K, using the Harlacher and Brown constants solved with different nonlinear solvers and SMath Studio installed on an Arch Linux ditstribution Source: Chemical Engineering, July 23, 1984, Nonlinear Models. Example 4: Vapor pressure calculation with the Frost and Kallwarf equation: ln pv = A + B / T + C * ln ( T ) + D pv / T** 2. For vapor pressure between 1.33 kPa and the critical pressure of the component. This trascendental equation requires an iterative solution. A reliable first estimate of pv may be obtained by using the equation neglecting the last term on its right side.

Estimate the vapor pressure of ethylbenzen at 460 K, using the Harlacher and Brown constants:

a 58.1 :

b 6792.54 - :

c 5.802 - :

d 5.75 :

tt 460 :

epsilon 106 -^:

iterations 400 :

pmax 8000 :

Initial guess, according to the authors of the article.

y f y ln a - b tt / - c tt ln * - d y tt 2^/ * - :

p0 a b tt / + c tt ln * + exp :

p0 2345.4501

res y f p0 epsilon epsilon FindRoot :

res f 1.0077 107 -^* -

res 2511.0804

res1 y f y p0 pmax solve :

res1 f 5.6532 1012 -^*

res1 2511.0807

res3 y f y p0 roots :

res3 2511.0807

res3 f 1.1497 1015 -^*

res4 y f p0 epsilon epsilon iterations 110 NewtonRaphson :

res4 2511.0807 311 mat i x J(x) f(x) 0 2345.4501 0.0004 0.0637 - 1 2505.1137 0.0004 0.0022 - 2 2511.0731 0.0004 2.8251 106 -^* - 3 2511.0807 0.0004 4.5964 1012 -^* - 54 mat 31 mat

res5 y f p0 epsilon epsilon iterations 110 Broyden :

res5 2511.0804 411 mat i x B(x) f(x) 0 2345.4501 111 mat 0.0637 - 1 2345.5138 2505.15 11 mat 0.0637 - 2 2505.116 2595.4303 11 mat 0.0022 - 3 2510.8677 2691.4159 11 mat 7.9034 105 -^* - 4 2511.0804 2694.8519 11 mat 1.0077 107 -^* - 64 mat 31 mat

res6 y f p0 pmax epsilon epsilon iterations 110 Secant :

res6 2511.0804 411 mat i x1 x2 X3 f(x1) f(x2) f(X3) 0 2345.4501 8000 2681.228 0.0637 - 1.0096 0.0609 18000 2681.228 2339.5624 1.0096 0.0609 0.0661 - 2 2681.228 2339.5624 2517.3217 0.0609 0.0661 - 0.0023 3 2339.5624 2517.3217 2511.3115 0.0661 - 0.0023 8.5634 105 -^* 4 2517.3217 2511.3115 2511.0804 0.0023 8.5634 105 -^* 1.1418 107 -^* - 67 mat 31 mat