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# -*- coding: utf-8 -*- Copyright (C) 2016, Caleb Bell <Caleb.Andrew.Bell@gmail.com>
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.'''
'EQ114', 'EQ115', 'EQ116', 'EQ127']
r'''DIPPR Equation # 100. Used in calculating the molar heat capacities of liquids and solids, liquid thermal conductivity, and solid density. All parameters default to zero. As this is a straightforward polynomial, no restrictions on parameters apply. Note that high-order polynomials like this may need large numbers of decimal places to avoid unnecessary error.
.. math:: Y = A + BT + CT^2 + DT^3 + ET^4 + FT^5 + GT^6
Parameters ---------- T : float Temperature, [K] A-G : float Parameter for the equation; chemical and property specific [-]
Returns ------- Y : float Property [constant-specific]
Examples -------- Water liquid heat capacity; DIPPR coefficients normally listed in J/kmol/K.
>>> EQ100(300, 276370., -2090.1, 8.125, -0.014116, 0.0000093701) 75355.81
References ---------- .. [1] Design Institute for Physical Properties, 1996. DIPPR Project 801 DIPPR/AIChE ''' return A + B*T + C*T**2 + D*T**3 + E*T**4 + F*T**5 + G*T**6
r'''DIPPR Equation # 101. Used in calculating vapor pressure, sublimation pressure, and liquid viscosity. All 5 parameters are required. E is often an integer. As the model is exponential, a sufficiently high temperature will cause an OverflowError. A negative temperature (or just low, if fit poorly) may cause a math domain error.
.. math:: Y = \exp\left(A + \frac{B}{T} + C\cdot \ln T + D \cdot T^E\right)
Parameters ---------- T : float Temperature, [K] A-E : float Parameter for the equation; chemical and property specific [-]
Returns ------- Y : float Property [constant-specific]
Examples -------- Water vapor pressure; DIPPR coefficients normally listed in Pa.
>>> EQ101(300, 73.649, -7258.2, -7.3037, 4.1653E-6, 2) 3537.44834545549
References ---------- .. [1] Design Institute for Physical Properties, 1996. DIPPR Project 801 DIPPR/AIChE ''' return exp(A+B/T+C*log(T)+D*T**E)
r'''DIPPR Equation # 102. Used in calculating vapor viscosity, vapor thermal conductivity, and sometimes solid heat capacity. High values of B raise an OverflowError. All 4 parameters are required. C and D are often 0.
.. math:: Y = \frac{A\cdot T^B}{1 + \frac{C}{T} + \frac{D}{T^2}}
Parameters ---------- T : float Temperature, [K] A-D : float Parameter for the equation; chemical and property specific [-]
Returns ------- Y : float Property [constant-specific]
Examples -------- Water vapor viscosity; DIPPR coefficients normally listed in Pa*S.
>>> EQ102(300, 1.7096E-8, 1.1146, 0, 0) 9.860384711890639e-06
References ---------- .. [1] Design Institute for Physical Properties, 1996. DIPPR Project 801 DIPPR/AIChE ''' return A*T**B/(1 + C/T + D/T**2)
r'''DIPPR Equation #104. Often used in calculating second virial coefficients of gases. All 5 parameters are required. C, D, and E are normally large values.
.. math:: Y = A + \frac{B}{T} + \frac{C}{T^3} + \frac{D}{T^8} + \frac{E}{T^9}
Parameters ---------- T : float Temperature, [K] A-E : float Parameter for the equation; chemical and property specific [-]
Returns ------- Y : float Property [constant-specific]
Examples -------- Water second virial coefficient; DIPPR coefficients normally dimensionless.
>>> EQ104(300, 0.02222, -26.38, -16750000, -3.894E19, 3.133E21) -1.1204179007265151
References ---------- .. [1] Design Institute for Physical Properties, 1996. DIPPR Project 801 DIPPR/AIChE ''' return A + B/T + C/T**3. + D/T**8. + E/T**9.
r'''DIPPR Equation #105. Often used in calculating liquid molar density. All 4 parameters are required. C is sometimes the fluid's critical temperature.
.. math:: Y = \frac{A}{B^{1 + (1-\frac{T}{C})^D}}
Parameters ---------- T : float Temperature, [K] A-D : float Parameter for the equation; chemical and property specific [-]
Returns ------- Y : float Property [constant-specific]
Examples -------- Hexane molar density; DIPPR coefficients normally in kmol/m^3.
>>> EQ105(300., 0.70824, 0.26411, 507.6, 0.27537) 7.593170096339236
References ---------- .. [1] Design Institute for Physical Properties, 1996. DIPPR Project 801 DIPPR/AIChE ''' return A/B**(1 + (1-T/C)**D)
r'''DIPPR Equation #106. Often used in calculating liquid surface tension, and heat of vaporization. Only parameters A and B parameters are required; many fits include no further parameters. Critical temperature is also required.
.. math:: Y = A(1-T_r)^{B + C T_r + D T_r^2 + E T_r^3}
Tr = \frac{T}{Tc}
Parameters ---------- T : float Temperature, [K] Tc : float Critical temperature, [K] A-D : float Parameter for the equation; chemical and property specific [-]
Returns ------- Y : float Property [constant-specific]
Examples -------- Water surface tension; DIPPR coefficients normally in Pa*S.
>>> EQ106(300, 647.096, 0.17766, 2.567, -3.3377, 1.9699) 0.07231499373541
References ---------- .. [1] Design Institute for Physical Properties, 1996. DIPPR Project 801 DIPPR/AIChE ''' Tr = T/Tc return A*(1.-Tr)**(B + C*Tr + D*Tr**2. + E*Tr**3.)
r'''DIPPR Equation #107. Often used in calculating ideal-gas heat capacity. All 5 parameters are required. Also called the Aly-Lee equation.
.. math:: Y = A + B\left[\frac{C/T}{\sinh(C/T)}\right]^2 + D\left[\frac{E/T}{ \cosh(E/T)}\right]^2
Parameters ---------- T : float Temperature, [K] A-E : float Parameter for the equation; chemical and property specific [-]
Returns ------- Y : float Property [constant-specific]
Examples -------- Water ideal gas molar heat capacity; DIPPR coefficients normally in J/kmol/K
>>> EQ107(300., 33363., 26790., 2610.5, 8896., 1169.) 33585.90452768923
References ---------- .. [1] Design Institute for Physical Properties, 1996. DIPPR Project 801 DIPPR/AIChE .. [2] Aly, Fouad A., and Lloyd L. Lee. "Self-Consistent Equations for Calculating the Ideal Gas Heat Capacity, Enthalpy, and Entropy." Fluid Phase Equilibria 6, no. 3 (January 1, 1981): 169-79. doi:10.1016/0378-3812(81)85002-9. ''' return A + B*((C/T)/sinh(C/T))**2 + D*((E/T)/cosh(E/T))**2
r'''DIPPR Equation #114. Rarely used, normally as an alternate liquid heat capacity expression. All 4 parameters are required, as well as critical temperature.
.. math:: Y = \frac{A^2}{\tau} + B - 2AC\tau - AD\tau^2 - \frac{1}{3}C^2\tau^3 - \frac{1}{2}CD\tau^4 - \frac{1}{5}D^2\tau^5
\tau = 1 - \frac{T}{Tc}
Parameters ---------- T : float Temperature, [K] Tc : float Critical temperature, [K] A-D : float Parameter for the equation; chemical and property specific [-]
Returns ------- Y : float Property [constant-specific]
Examples -------- Hydrogen liquid heat capacity; DIPPR coefficients normally in J/kmol/K.
>>> EQ114(20, 33.19, 66.653, 6765.9, -123.63, 478.27) 19423.948911676463
References ---------- .. [1] Design Institute for Physical Properties, 1996. DIPPR Project 801 DIPPR/AIChE ''' t = 1.-T/Tc return A**2./t + B - 2.*A*C*t - A*D*t**2. - C**2.*t**3./3. - C*D*t**4./2. - D**2*t**5./5.
r'''DIPPR Equation #115. No major uses; has been used as an alternate liquid viscosity expression, and as a model for vapor pressure. Only parameters A and B are required.
.. math:: Y = \exp\left(A + \frac{B}{T} + C\log T + D T^2 + \frac{E}{T^2}\right)
Parameters ---------- T : float Temperature, [K] A-E : float Parameter for the equation; chemical and property specific [-]
Returns ------- Y : float Property [constant-specific]
Examples -------- No coefficients found for this expression.
References ---------- .. [1] Design Institute for Physical Properties, 1996. DIPPR Project 801 DIPPR/AIChE ''' return exp(A+B/T+C*log(T)+D*T**2 + E/T**2)
r'''DIPPR Equation #116. Used to describe the molar density of water fairly precisely; no other uses listed. All 5 parameters are needed, as well as the critical temperature.
.. math:: Y = A + B\tau^{0.35} + C\tau^{2/3} + D\tau + E\tau^{4/3}
\tau = 1 - \frac{T}{Tc}
Parameters ---------- T : float Temperature, [K] Tc : float Critical temperature, [K] A-E : float Parameter for the equation; chemical and property specific [-]
Returns ------- Y : float Property [constant-specific]
Examples -------- Water liquid molar density; DIPPR coefficients normally in kmol/m^3.
>>> EQ116(300., 647.096, 17.863, 58.606, -95.396, 213.89, -141.26) 55.17615446406527
References ---------- .. [1] Design Institute for Physical Properties, 1996. DIPPR Project 801 DIPPR/AIChE ''' tau = 1-T/Tc return A + B*tau**0.35 + C*tau**(2/3.) + D*tau + E*tau**(4/3.)
r'''DIPPR Equation #127. Rarely used, and then only in calculating ideal-gas heat capacity. All 7 parameters are required.
.. math:: Y = A+B\left[\frac{\left(\frac{C}{T}\right)^2\exp\left(\frac{C}{T} \right)}{\left(\exp\frac{C}{T}-1 \right)^2}\right] +D\left[\frac{\left(\frac{E}{T}\right)^2\exp\left(\frac{E}{T}\right)} {\left(\exp\frac{E}{T}-1 \right)^2}\right] +F\left[\frac{\left(\frac{G}{T}\right)^2\exp\left(\frac{G}{T}\right)} {\left(\exp\frac{G}{T}-1 \right)^2}\right]
Parameters ---------- T : float Temperature, [K] A-G : float Parameter for the equation; chemical and property specific [-]
Returns ------- Y : float Property [constant-specific]
Examples -------- Ideal gas heat capacity of methanol; DIPPR coefficients normally in J/kmol/K
>>> EQ127(20., 3.3258E4, 3.6199E4, 1.2057E3, 1.5373E7, 3.2122E3, -1.5318E7, 3.2122E3) 33258.0
References ---------- .. [1] Design Institute for Physical Properties, 1996. DIPPR Project 801 DIPPR/AIChE ''' return A+B*((C/T)**2*exp(C/T)/(exp(C/T) - 1)**2) + \ D*((E/T)**2*exp(E/T)/(exp(E/T)-1)**2) + \ F*((G/T)**2*exp(G/T)/(exp(G/T)-1)**2) |