Twu-Sim-Tassone equation of state: Difference between revisions

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m (Replaced P_c with p_c to be consistent)
(Added the exact values for Z_c and the parameters a & b)
 
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Twu, Sim and Tassone presented a cubic [[Equations of state|equation of state]] for accurate representation of hydrocarbons that has become known as the '''Twu-Sim-Tassone''' or '''TST equation of state'''<ref>[http://dx.doi.org/10.1016/S0378-3812(01)00663-X Chorng H. Twu, Wayne D. Sim and Vince Tassone "A versatile liquid activity model for SRK, PR and a new cubic equation-of-state TST", Fluid Phase Equilibria '''194-197''' pp. 385-399 (2002)]</ref>.  With a critical [[compressibility factor]] of (Eq. 5)
Twu, Sim and Tassone presented a cubic [[Equations of state|equation of state]] for accurate representation of hydrocarbons that has become known as the '''Twu-Sim-Tassone''' or '''TST equation of state'''<ref>[http://dx.doi.org/10.1016/S0378-3812(01)00663-X Chorng H. Twu, Wayne D. Sim and Vince Tassone "A versatile liquid activity model for SRK, PR and a new cubic equation-of-state TST", Fluid Phase Equilibria '''194-197''' pp. 385-399 (2002)]</ref>.  With a critical [[compressibility factor]] of (Eq. 5)


:<math>Z_c = \frac{p_cv_c}{RT_c} =   0.296296  </math>
:<math>Z_c = \frac{p_cv_c}{RT_c} = \frac{8}{27} </math>


it better represents  the compressibility than many of than the [[Redlich-Kwong equation of state]]s, including the [[Redlich-Kwong equation of state#Soave modification | Soave modified version]], and the [[Peng and Robinson equation of state]].
it better represents  the compressibility than many of than the [[Redlich-Kwong equation of state]]s, including the [[Redlich-Kwong equation of state#Soave modification | Soave modified version]], and the [[Peng and Robinson equation of state]].
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:<math>p=\frac{RT}{V_m-b}-\frac{a}{(V_m-0.5b)(V_m+3b)}</math>
:<math>p=\frac{RT}{V_m-b}-\frac{a}{(V_m-0.5b)(V_m+3b)}</math>


Where <math>V_m</math> is the molar volume, and <math>a</math> and <math>b</math> are the attractive and repulsive parameters akin to those of the [[Van der Waals equation of state]].  Relations exists between <math>a</math> and <math>b</math> and the critical parameters <math>T_c</math> and <math>p_c</math> in the forms (Eqs. 3 and 4):
where <math>V_m</math> is the molar volume, <math>R</math> is the [[molar gas constant]], <math>T</math> is the [[temperature]], <math>p</math> is the [[pressure]], and <math>a</math> and <math>b</math> are the attractive and repulsive parameters akin to those of the [[Van der Waals equation of state]].  Relations exists between <math>a</math> and <math>b</math> and the critical parameters <math>T_c</math> and <math>p_c</math> in the forms (Eqs. 3 and 4):


:<math>a_c=0.470507  \frac{ R^2T_c^2}{p_c}</math>
:<math>a_c= Z_c \frac{343}{216}\frac{R^2T_c^2}{p_c}</math>


:<math>b_c=0.0740740  \frac{ RT_c}{p_c}</math>
:<math>b_c= Z_c \frac{RT_c}{4p_c}</math>


==References==
==References==

Latest revision as of 04:06, 9 April 2024

Twu, Sim and Tassone presented a cubic equation of state for accurate representation of hydrocarbons that has become known as the Twu-Sim-Tassone or TST equation of state[1]. With a critical compressibility factor of (Eq. 5)

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z_c = \frac{p_cv_c}{RT_c} = \frac{8}{27} }

it better represents the compressibility than many of than the Redlich-Kwong equation of states, including the Soave modified version, and the Peng and Robinson equation of state.

The equation follows the general cubic form resulting in the equation (Eq. 2):

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p=\frac{RT}{V_m-b}-\frac{a}{(V_m-0.5b)(V_m+3b)}}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V_m} is the molar volume, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle R} is the molar gas constant, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T} is the temperature, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p} is the pressure, and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} are the attractive and repulsive parameters akin to those of the Van der Waals equation of state. Relations exists between Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} and the critical parameters Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_c} and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p_c} in the forms (Eqs. 3 and 4):

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_c= Z_c \frac{343}{216}\frac{R^2T_c^2}{p_c}}
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b_c= Z_c \frac{RT_c}{4p_c}}

References[edit]

  1. ↑ Chorng H. Twu, Wayne D. Sim and Vince Tassone "A versatile liquid activity model for SRK, PR and a new cubic equation-of-state TST", Fluid Phase Equilibria 194-197 pp. 385-399 (2002)
Related reading
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