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/* ASCEND modelling environment |
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Copyright (C) 2008-2009 Carnegie Mellon University |
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|
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This program is free software; you can redistribute it and/or modify |
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it under the terms of the GNU General Public License as published by |
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the Free Software Foundation; either version 2, or (at your option) |
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any later version. |
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|
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This program is distributed in the hope that it will be useful, |
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but WITHOUT ANY WARRANTY; without even the implied warranty of |
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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GNU General Public License for more details. |
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|
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You should have received a copy of the GNU General Public License |
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along with this program. If not, see <http://www.gnu.org/licenses/>. |
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*//** @file |
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Routines to calculate saturation properties using Helmholtz correlation |
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data. We first include some 'generic' saturation equations that make use |
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of the acentric factor and critical point properties to predict saturation |
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properties (pressure, vapour density, liquid density). These correlations |
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seem to be only very rough in some cases, but it is hoped that they will |
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be suitable as first-guess values that can then be fed into an iterative |
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solver to converge to an accurate result. |
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*/ |
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|
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#include "rundata.h" |
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#include "sat.h" |
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#include "fprops.h" |
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#include "zeroin.h" |
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|
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// report lots of stuff |
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//#define SAT_DEBUG |
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#define SAT_ERRORS |
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|
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// assertions for NANs etc |
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//#define SAT_ASSERT |
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|
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#ifdef SAT_ASSERT |
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# include <assert.h> |
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#else |
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# define assert(ARGS...) |
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#endif |
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|
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#include <math.h> |
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#include <stdio.h> |
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|
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#define SQ(X) ((X)*(X)) |
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|
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#define TCRIT(DATA) (DATA->data->T_c) |
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#define PCRIT(DATA) (DATA->data->p_c) |
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#define RHOCRIT(DATA) (DATA->data->rho_c) |
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#define OMEGA(DATA) (DATA->data->omega) |
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#define RGAS(DATA) (DATA->data->R) |
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#define TTRIP(DATA) (DATA->data->T_t) |
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|
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#define THROW_FPE |
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|
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#ifdef THROW_FPE |
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#define _GNU_SOURCE |
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#include <fenv.h> |
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int feenableexcept (int excepts); |
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int fedisableexcept (int excepts); |
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int fegetexcept (void); |
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#endif |
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|
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# include "color.h" |
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|
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#ifdef SAT_DEBUG |
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# define MSG(FMT, ...) \ |
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color_on(stderr,ASC_FG_BRIGHTRED);\ |
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fprintf(stderr,"%s:%d: ",__FILE__,__LINE__);\ |
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color_on(stderr,ASC_FG_BRIGHTBLUE);\ |
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fprintf(stderr,"%s: ",__func__);\ |
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color_off(stderr);\ |
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fprintf(stderr,FMT "\n",##__VA_ARGS__) |
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#else |
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# define MSG(ARGS...) ((void)0) |
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#endif |
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|
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#ifdef SAT_ERRORS |
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# define ERRMSG(STR,...) \ |
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color_on(stderr,ASC_FG_BRIGHTRED);\ |
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fprintf(stderr,"ERROR:");\ |
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color_off(stderr);\ |
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fprintf(stderr," %s:%d:" STR "\n", __func__, __LINE__ ,##__VA_ARGS__) |
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#else |
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# define ERRMSG(ARGS...) ((void)0) |
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#endif |
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|
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/** |
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Estimate of saturation pressure using H W Xiang ''The new simple extended |
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corresponding-states principle: vapor pressure and second virial |
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coefficient'', Chemical Engineering Science, |
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57 (2002) pp 1439-1449. |
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|
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This seems to be hopeless, or buggy. Tried with water at 373 K, gives |
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525 kPa... |
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*/ |
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double fprops_psat_T_xiang(double T, const FluidData *data){ |
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double Zc = data->p_c / (8314. * data->rho_c * data->T_c); |
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|
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#ifdef TEST |
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fprintf(stderr,"Zc = %f\n",Zc); |
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#endif |
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|
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double theta = SQ(Zc - 0.29); |
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|
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#ifdef TEST |
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fprintf(stderr,"theta = %f\n",theta); |
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#endif |
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|
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double aa[] = {5.790206, 4.888195, 33.91196 |
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, 6.251894, 15.08591, -315.0248 |
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, 11.65859, 46.78273, -1672.179 |
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}; |
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|
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double a0 = aa[0] + aa[1]*data->omega + aa[2]*theta; |
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double a1 = aa[3] + aa[4]*data->omega + aa[5]*theta; |
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double a2 = aa[6] + aa[7]*data->omega + aa[8]*theta; |
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|
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double Tr = T / data->T_c; |
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double tau = 1 - Tr; |
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|
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double taupow = pow(tau, 1.89); |
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double temp = a0 + a1 * taupow + a2 * taupow * taupow * taupow; |
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|
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double logpr = temp * log(Tr); |
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double p_r = exp(logpr); |
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|
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#ifdef TEST |
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fprintf(stderr,"a0 = %f\n", a0); |
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fprintf(stderr,"a1 = %f\n", a1); |
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fprintf(stderr,"a2 = %f\n", a2); |
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fprintf(stderr,"temp = %f\n", temp); |
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fprintf(stderr,"T_r = %f\n", Tr); |
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fprintf(stderr,"p_r = %f\n", p_r); |
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#endif |
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|
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return p_r * data->p_c; |
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} |
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|
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/** |
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Estimate saturation pressure using acentric factor. This algorithm |
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is used for first estimates for later refinement in the program REFPROP. |
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|
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This is derived from the definition of the acentric factor, |
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omega = -log10(psat(T1) - 1 where T1/Tc = Tr = 0.7 |
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|
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together with the saturation curve obtained if h_fg(T) is assumed constant: |
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ln(psat(T)) = A - B/(T + C) |
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|
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See Sandler 5e, p 320. |
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|
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s Such a curve will pass through (pc,Tc) and (psat(Tr),Tr) where Tr = 0.7, |
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but will probably be inaccurate at Tt. Given additional data, such as the |
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normal boiling point, a better equation like the Antoine equation can be |
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fitted. But we don't use that here. |
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|
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*/ |
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double fprops_psat_T_acentric(double T, const FluidData *data){ |
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/* first guess using acentric factor */ |
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double p = data->p_c * pow(10, -7./3 * (1.+data->omega) * (data->T_c / T - 1.)); |
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return p; |
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} |
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|
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|
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/** |
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Saturated liquid density correlation of Rackett, Spencer & Danner (1972) |
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see http://dx.doi.org/10.1002/aic.690250412 |
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*/ |
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double fprops_rhof_T_rackett(double T, const FluidData *data){ |
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//MSG("RHOCRIT=%f, RGAS=%f, TCRIT=%f, PCRIT=%f",data->rho_c,data->R,data->T_c,data->p_c); |
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double Zc = data->rho_c * data->R * data->T_c / data->p_c; |
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double Tau = 1. - T/data->T_c; |
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//MSG("Zc = %f, Tau = %f",Zc,Tau); |
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double vf = (data->R * data->T_c / data->p_c) * pow(Zc, -1 - pow(Tau, 2./7)); |
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//MSG("got vf(T=%f) = %f",T,vf); |
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return 1./vf; |
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} |
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|
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/* |
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TODO add Yamada & Gunn sat rhof equation eg from RPP5 eq 4-11.4a, should |
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be more accurate? |
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|
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^Sean? I think you are referring to http://dx.doi.org/10.1002/aic.690170613, |
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is that correct? That equation requires extra data for V_SC according to |
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the paper. I don't have RPP5, only RPP4 unfortunately -- JP. |
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*/ |
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|
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/** |
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Inverse of fprops_rhof_T_rackett. TODO: this need checking. |
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*/ |
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double fprops_T_rhof_rackett(double rhof, const FluidData *data){ |
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double Zc = data->rho_c * data->R * data->T_c / data->p_c; |
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double f1 = data->p_c / data->R / data->T_c / rhof; |
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double f2 = -log(f1)/log(Zc); |
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return pow(f2 -1, 3./2); |
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} |
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|
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|
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/** |
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Saturated vapour density correlation of Chouaieb, Ghazouani, Bellagi |
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see http://dx.doi.org/10.1016/j.tca.2004.05.017 |
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*/ |
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double fprops_rhog_T_chouaieb(double T, const FluidData *data){ |
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double Tau = 1. - T/data->T_c; |
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#if 0 |
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double Zc = RHOCRIT(d) * RGAS(d) * TCRIT(d) / PCRIT(d); |
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# define N1 -0.1497547 |
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# define N2 0.6006565 |
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# define P1 -19.348354 |
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# define P2 -41.060325 |
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# define P3 1.1878726 |
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double MMM = 2.6; /* guess, reading from Chouaieb, Fig 8 */ |
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//MMM = 2.4686277; |
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double PPP = Zc / (P1 + P2*Zc*log(Zc) + P3/Zc); |
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fprintf(stderr,"PPP = %f\n",PPP); |
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//PPP = -0.6240188; |
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double NNN = PPP + 1./(N1*D->omega + N2); |
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#else |
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/* exact values from Chouaieb for CO2 */ |
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# define MMM 2.4686277 |
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# define NNN 1.1345838 |
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# define PPP -0.6240188 |
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#endif |
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|
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double alpha = exp(pow(Tau,1./3) + sqrt(Tau) + Tau + pow(Tau, MMM)); |
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return data->rho_c * exp(PPP * (pow(alpha,NNN) - exp(1-alpha))); |
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} |
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|
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void fprops_sat_T(double T, double *psat, double *rhof, double *rhog, const PureFluid *d, FpropsError *err){ |
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*psat = d->sat_fn(T,rhof,rhog,d->data,err); |
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} |
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|
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/** |
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Calculate the triple point pressure and densities using T_t from the FluidData. |
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*/ |
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void fprops_triple_point(double *p_t_out, double *rhof_t_out, double *rhog_t_out, const PureFluid *d, FpropsError *err){ |
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static const PureFluid *d_last = NULL; |
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static double p_t, rhof_t, rhog_t; |
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if(d == d_last){ |
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*p_t_out = p_t; |
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*rhof_t_out = rhof_t; |
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*rhog_t_out = rhog_t; |
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return; |
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} |
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|
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if(d->data->T_t == 0){ |
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ERRMSG("Note: data for '%s' does not include a valid triple point temperature.",d->name); |
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} |
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|
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MSG("Calculating for '%s' (type %d, T_t = %f, T_c = %f, p_c = %f)",d->name, d->type, d->data->T_t, d->data->T_c, d->data->p_c); |
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fprops_sat_T(d->data->T_t, &p_t, &rhof_t, &rhog_t,d,err); |
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if(*err)return; |
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d_last = d; |
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*p_t_out = p_t; |
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*rhof_t_out = rhof_t; |
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*rhog_t_out = rhog_t; |
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MSG("p_t = %f, rhof_t = %f, rhog_t = %f", p_t, rhof_t, rhog_t); |
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} |
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|
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|
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typedef struct{ |
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const PureFluid *P; |
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double logp; |
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FpropsError *err; |
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double Terr; |
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#ifdef SAT_DEBUG |
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int neval; |
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#endif |
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} SatPResidData; |
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|
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static ZeroInSubjectFunction sat_p_resid; |
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static double sat_p_resid(double rT, void *user_data){ |
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#define D ((SatPResidData *)user_data) |
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double p, rhof, rhog, resid; |
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fprops_sat_T(1/rT, &p, &rhof, &rhog, D->P, D->err); |
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if(*(D->err))D->Terr = 1/rT; |
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resid = log(p) - D->logp; |
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MSG("T = %f --> p = %f, rhof = %f, rhog = %f, RESID %f", 1/rT, p, rhof, rhog, resid); |
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//if(*(D->err))MSG("Error: %s",fprops_error(*(D->err))); |
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//if(*(D->err))return -1; |
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#ifdef SAT_DEBUG |
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D->neval++; |
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#endif |
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return resid; |
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#undef D |
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} |
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|
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|
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/** |
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Solve saturation conditions as a function of pressure. |
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|
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Currently this is just a Brent solver. We've tried to improve it slightly |
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by solving for the residual of log(p)-log(p1) as a function of 1/T, which |
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should make the function a bit more linear. |
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|
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TODO Shouldn't(?) be hard at all to improve this to use a Newton solver via |
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the Clapeyron equation? |
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|
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dp/dT = h_fg/(T*v_fg) |
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|
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where |
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|
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h_fg = h(T, rhog) - h(T, rhof) |
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v_fg = 1/rhog - 1/rhof |
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rhof, rhog are evaluated at T. |
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|
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We guess T, calculate saturation conditions at T, then evaluate dp/dT, |
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use Newton solver to converge, while checking that we remain within |
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Tt < T < Tc. It may be faster to iterate using 1/T as the free variable, |
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and log(p) as the residual variable. |
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|
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TODO Better still would be to reexamine the EOS and find a strategy similar to |
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the Akasaka algorithm that works with with rhof, rhog as the free variables, |
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see helmholtz.c...? Method above uses nested iteration on T inside p, so is |
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going to be slooooooow, even if it's fairly reliable. |
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*/ |
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void fprops_sat_p(double p, double *T_sat, double *rho_f, double *rho_g, const PureFluid *P, FpropsError *err){ |
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if(*err){ |
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MSG("ERROR FLAG ALREADY SET"); |
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} |
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if(p == P->data->p_c){ |
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MSG("Requested pressure is critical point pressure, returning CP conditions"); |
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*T_sat = P->data->T_c; |
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*rho_f = P->data->rho_c; |
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*rho_g = P->data->rho_c; |
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return; |
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} |
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/* FIXME what about checking triple point pressure? */ |
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|
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|
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SatPResidData D = { |
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P, log(p), err, 0 |
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#ifdef SAT_DEBUG |
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,0 |
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#endif |
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}; |
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MSG("Solving saturation conditions at p = %f", p); |
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double p1, rT, T, resid; |
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int errn; |
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double Tt = P->data->T_t; |
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if(Tt == 0)Tt = 0.2* P->data->T_c; |
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errn = zeroin_solve(&sat_p_resid, &D, 1./P->data->T_c, 1./Tt, 1e-10, &rT, &resid); |
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if(*err){ |
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MSG("FPROPS error within zeroin_solve iteration ('%s', p = %f, p_c = %f): %s" |
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, P->name, p, P->data->p_c, fprops_error(*err) |
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); |
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} |
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if(errn){ |
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ERRMSG("Failed to solve saturation at p = %f.",p); |
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*err = FPROPS_SAT_CVGC_ERROR; |
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return; |
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}else{ |
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if(*err){ |
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ERRMSG("Ignoring error inside zeroin_solve iteration at T = %f",D.Terr); |
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} |
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*err = FPROPS_NO_ERROR; |
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} |
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T = 1./rT; |
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fprops_sat_T(T, &p1, rho_f, rho_g, P, err); |
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if(!*err)*T_sat = T; |
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MSG("Got p1 = %f, p = %f in %d iterations", p1, p, D.neval); |
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} |
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|
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|
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/** |
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Calculate Tsat based on a value of hf. This value is useful in setting |
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first guess Temperatures when solving for the coordinates (p,h). |
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This function uses the secant method for the iterative solution. |
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*/ |
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void fprops_sat_hf(double hf, double *Tsat_out, double *psat_out, double *rhof_out, double *rhog_out, const PureFluid *P, FpropsError *err){ |
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double T1 = 0.4 * P->data->T_t + 0.6 * P->data->T_c; |
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double T2 = P->data->T_t; |
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double h1, h2, p, rhof, rhog; |
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fprops_sat_T(T2, &p, &rhof, &rhog, P, err); |
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if(*err){ |
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ERRMSG("Failed to solve psat(T_t = %.12e) for %s",T2,P->name); |
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return; |
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} |
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double tol = 1e-6; |
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h2 = P->h_fn(T2,rhof,P->data, err); |
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if(*err){ |
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ERRMSG("Unable to calculate h(T=%f K,rhof=%f kg/m3",T2,rhof); |
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} |
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if(hf < h2){ |
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ERRMSG("Value given for hf = %.12e is below that calculated for triple point liquid hf_t = %.12e",hf,h2); |
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*err = FPROPS_RANGE_ERROR; |
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return; |
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} |
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|
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int i = 0; |
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while(i++ < 60){ |
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assert(T1 >= P->data->T_t - 1e-4); |
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assert(T1 <= P->data->T_c); |
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MSG("T1 = %f\n",T1); |
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fprops_sat_T(T1, &p, &rhof, &rhog, P, err); |
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if(*err){ |
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ERRMSG("Failed to solve psat(T = %.12e) for %s",T1,P->name); |
| 400 |
return; |
| 401 |
} |
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h1 = P->h_fn(T1,rhof, P->data, err); |
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if(*err){ |
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ERRMSG("Unable to calculate h"); |
| 405 |
return; |
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} |
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if(fabs(h1 - hf) < tol){ |
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*Tsat_out = T1; |
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*psat_out = p; |
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*rhof_out = rhof; |
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*rhog_out = rhog; |
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return; /* SUCCESS */ |
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} |
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if(h1 == h2){ |
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MSG("With %s, got h1 = h2 = %.12e, but hf = %.12e!",P->name,h1,hf); |
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*err = FPROPS_SAT_CVGC_ERROR; |
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return; |
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} |
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|
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double delta_T = -(h1 - hf) * (T1 - T2) / (h1 - h2); |
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T2 = T1; |
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h2 = h1; |
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while(T1 + delta_T > P->data->T_c)delta_T *= 0.5; |
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T1 += delta_T; |
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if(T1 < P->data->T_t)T1 = P->data->T_t; |
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if(i==20 || i==30)tol*=100; |
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} |
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fprintf(stderr,"Failed to solve Tsat for hf = %f (got to T = %f)\n",hf,T1); |
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*Tsat_out = T1; |
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*psat_out = p; |
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*rhof_out = rhof; |
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*rhog_out = rhog; |
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*err = FPROPS_SAT_CVGC_ERROR; |
| 434 |
} |
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|
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