Twu-Sim-Tassone equation of state - Revision history

Proxima Centari: Added the exact values for Z_c and the parameters a & b

2024-04-09T03:06:37Z

Added the exact values for Z_c and the parameters a & b

← Older revision		Revision as of 05:06, 9 April 2024
Line 1:		Line 1:
	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]].
Line 11:		Line 11:
	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):		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==

Carl McBride: Defined symbols used.

2011-11-07T15:33:10Z

Defined symbols used.

← Older revision		Revision as of 17:33, 7 November 2011
Line 9:		Line 9:
	:<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=0.470507 \frac{ R^2T_c^2}{p_c}</math>

Carl McBride: Replaced P_c with p_c to be consistent

2011-11-07T15:27:05Z

Replaced P_c with p_c to be consistent

← Older revision		Revision as of 17:27, 7 November 2011
Line 9:		Line 9:
	:<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, 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=0.470507 \frac{ R^2T_c^2}{p_c}</math>
	:<math>b_c=0.0740740 \frac{ RT_c}{~~P_c~~}</math>
			:<math>b_c=0.0740740 \frac{ RT_c}{p_c}</math>

	==References==		==References==

Carl McBride: Added an internal link

2011-11-07T11:20:12Z

Added an internal link

← Older revision		Revision as of 13:20, 7 November 2011
Line 3:		Line 3:
	:<math>Z_c = \frac{p_cv_c}{RT_c} = 0.296296 </math>		:<math>Z_c = \frac{p_cv_c}{RT_c} = 0.296296 </math>

	it better represents the compressibility than many of than the [[Redlich-Kwong equation of state]]s, including the 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]].

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

Carl McBride: Slight tidy + internal and external links

2011-11-07T11:17:49Z

Slight tidy + internal and external links

← Older revision		Revision as of 13:17, 7 November 2011
Line 1:		Line 1:
	Twu, Sim and Tassone presented a cubic equation of state for accurate representation of ~~hydrocarbon~~ that has become known as the '''Twu-Sim-Tassone''' or '''TST equation of state'''<ref>~~Twu, C~~.H., ~~et al,~~ "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 ~~<math>Z_c</math> of 0.2962, it better represents many the compressibility of than the [[Redlich-Kwong equation of state~~]]~~, including the Soave modified version, and the [[Peng and Robinson equation~~ of ~~state]]. This allows it to better represent long chain hydrocarbons<ref>Twu, C.H., Sim, W.D., Tassone, V. "Getting a Handle on Advanced Cubic Equation of State." ''Measurement & Control'', pp~~. ~~58-65, (2002~~)~~.</ref>.~~		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)

	The equation follows the general cubic form resulting in the equation:		:<math>Z_c = \frac{p_cv_c}{RT_c} = 0.296296 </math>

			it better represents the compressibility than many of than the [[Redlich-Kwong equation of state]]s, 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):

	:<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:		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):

	:<math>a=\frac{~~0.427481R~~^2T_c^2}{P_c}</math>		:<math>a_c=0.470507 \frac{ R^2T_c^2}{P_c}</math>
	:<math>b=\frac{~~0.086641RT_c~~}{P_c}</math>		:<math>b_c=0.0740740 \frac{ RT_c}{P_c}</math>

	==References==		==References==
	<references/>		<references/>
			;Related reading
			*[http://www.aiche.org/uploadedFiles/CEP/Issues/110258.pdf Chorng H. Twu, Wayne D. Sim and Vince Tassone "Getting a Handle on Advanced Cubic Equation of State", Chemical Engineering Progress '''November''' pp. 58-65 (2002)]
	[[category: equations of state]]		[[category: equations of state]]

Josephrpeterson at 03:03, 7 November 2011

2011-11-07T03:03:23Z

← Older revision		Revision as of 05:03, 7 November 2011
Line 5:		Line 5:
	:<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]].		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:

			:<math>a=\frac{0.427481R^2T_c^2}{P_c}</math>
			:<math>b=\frac{0.086641RT_c}{P_c}</math>

	==References==		==References==

Josephrpeterson at 22:38, 4 November 2011

2011-11-04T22:38:37Z

← Older revision		Revision as of 00:38, 5 November 2011
Line 1:		Line 1:
	Twu, Sim and Tassone presented a cubic equation of state for accurate representation of hydrocarbon that has become known as the '''Twu-Sim-Tassone''' or '''TST equation of state'''<ref>Twu, C.H., et al, "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 <math>Z_c</math> of 0.2962, it better represents many the compressibility of than the [[Redlich-Kwong equation of state]], including the Soave modified version, and the [[Peng and Robinson equation of state]] ~~and has been shown~~ to better represent long chain hydrocarbons<ref>Twu, C.H., Sim, W.D., Tassone, V. "Getting a Handle on Advanced Cubic Equation of State." ''Measurement & Control'', pp. 58-65, (2002).</ref>.		Twu, Sim and Tassone presented a cubic equation of state for accurate representation of hydrocarbon that has become known as the '''Twu-Sim-Tassone''' or '''TST equation of state'''<ref>Twu, C.H., et al, "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 <math>Z_c</math> of 0.2962, it better represents many the compressibility of than the [[Redlich-Kwong equation of state]], including the Soave modified version, and the [[Peng and Robinson equation of state]]. This allows it to better represent long chain hydrocarbons<ref>Twu, C.H., Sim, W.D., Tassone, V. "Getting a Handle on Advanced Cubic Equation of State." ''Measurement & Control'', pp. 58-65, (2002).</ref>.

	The equation follows the general cubic form resulting in the equation:		The equation follows the general cubic form resulting in the equation:

Josephrpeterson at 22:37, 4 November 2011

2011-11-04T22:37:54Z

← Older revision		Revision as of 00:37, 5 November 2011
Line 9:		Line 9:
	==References==		==References==
	<references/>		<references/>

			[[category: equations of state]]

Josephrpeterson at 22:36, 4 November 2011

2011-11-04T22:36:38Z

← Older revision		Revision as of 00:36, 5 November 2011
Line 1:		Line 1:
	Twu, Sim and Tassone presented a cubic equation of state for accurate representation of hydrocarbon that has become known as the '''Twu-Sim-Tassone''' or '''TST equation of state'''<ref>Twu, C.H., et al, "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 <math>Z_c</math> of 0.2962, it better represents many the compressibility of than the Redlich-Kwong, including the Soave modified version, and the Peng-Robinson equation of state and has been shown to better represent long chain hydrocarbons<ref>Twu, C.H., Sim, W.D., Tassone, V. "Getting a Handle on Advanced Cubic Equation of State." ''Measurement & Control'', pp. 58-65, (2002).</ref>.		Twu, Sim and Tassone presented a cubic equation of state for accurate representation of hydrocarbon that has become known as the '''Twu-Sim-Tassone''' or '''TST equation of state'''<ref>Twu, C.H., et al, "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 <math>Z_c</math> of 0.2962, it better represents many the compressibility of than the [[Redlich-Kwong equation of state]], including the Soave modified version, and the [[Peng and Robinson equation of state]] and has been shown to better represent long chain hydrocarbons<ref>Twu, C.H., Sim, W.D., Tassone, V. "Getting a Handle on Advanced Cubic Equation of State." ''Measurement & Control'', pp. 58-65, (2002).</ref>.

	The equation follows the general cubic form resulting in the equation:		The equation follows the general cubic form resulting in the equation:
Line 5:		Line 5:
	:<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 [~~http://www.sklogwiki.org/SklogWiki/index.php/Van_der_Waals_equation_of_state van Der~~ Waals equation of state].		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]].

	==References==		==References==
	<references/>		<references/>

Josephrpeterson: Created page with "Twu, Sim and Tassone presented a cubic equation of state for accurate representation of hydrocarbon that has become known as the '''Twu-Sim-Tassone''' or '''TST equation of state..."

2011-11-04T22:33:55Z

Created page with "Twu, Sim and Tassone presented a cubic equation of state for accurate representation of hydrocarbon that has become known as the '''Twu-Sim-Tassone''' or '''TST equation of state..."

New page

Twu, Sim and Tassone presented a cubic equation of state for accurate representation of hydrocarbon that has become known as the '''Twu-Sim-Tassone''' or '''TST equation of state'''<ref>Twu, C.H., et al, "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 <math>Z_c</math> of 0.2962, it better represents many the compressibility of than the Redlich-Kwong, including the Soave modified version, and the Peng-Robinson equation of state and has been shown to better represent long chain hydrocarbons<ref>Twu, C.H., Sim, W.D., Tassone, V. "Getting a Handle on Advanced Cubic Equation of State." ''Measurement & Control'', pp. 58-65, (2002).</ref>.

The equation follows the general cubic form resulting in the equation:

:<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 [http://www.sklogwiki.org/SklogWiki/index.php/Van_der_Waals_equation_of_state van Der Waals equation of state].

==References==
<references/>