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reac92pc.for
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*** reac92 - Calculates the standard molal Gibbs free energy, enthalpy,
*** entropy, heat capacity, and volume of the i[th] reaction
*** (specified in common blocks /icon/ and /reac/) among
*** <= MAXMIN minerals, <= MAXAQS aqueous species, <= MAXGAS
*** gases, and H2O using equations and data given by Helgeson
*** et al. (1978), Tanger and Helgeson (1988), Shock and
*** Helgeson (1988, 1990), Shock et al. (1989, 1991), Johnson
*** and Norton (1991), Johnson et al. (1991), and Sverjensky
*** et al. (1991).
***
*** Computed reaction properties are stored in COMMON blocks
*** /minsp/, /gassp/, /aqsp/, /solvn/, and /fmeq/.
***
*******************************************************************
***
*** Author: James W. Johnson
*** Earth Sciences Department, L-219
*** Lawrence Livermore National Laboratory
*** Livermore, CA 94550
***
*** Abandoned: 8 November 1991
***
*******************************************************************
SUBROUTINE reac92(i,P,TC,Dw,Vw,betaw,alphaw,daldTw,
1 Sw,Cpw,Hw,Gw,Zw,Qw,Yw,Xw,geqn)
*******************************************************************
*** argument units: (w suffixes denote H2O properties)
***
*** P ............ bars
*** TC ........... degC
*** Dw ........... g/cm**3
*** Vw ........... cm**3/mol
*** betaw, Qw .... bars**(-1)
*** alphaw, Yw ... K**(-1)
*** daldTw, Xw ... K**(-2)
*** Sw, Cpw ...... cal/(mol*K)
*** Hw, Gw ....... cal/mol
*** Zw ........... dimensionless
*********************************************
IMPLICIT DOUBLE PRECISION (a-h,o-z)
PARAMETER (MAXMIN = 10, MAXGAS = 10, MAXAQS = 10, MAXRXN = 10)
INTEGER geqn
LOGICAL m2reac(MAXRXN)
CHARACTER*80 rtitle(MAXRXN)
INTEGER nm(MAXRXN), na(MAXRXN), ng(MAXRXN), nw(MAXRXN),
1 rec1m(MAXRXN,MAXMIN), rec1a(MAXRXN,MAXAQS),
2 rec1g(MAXRXN,MAXGAS)
DOUBLE PRECISION coefm(MAXRXN,MAXMIN), coefa(MAXRXN,MAXAQS),
1 coefg(MAXRXN,MAXGAS), coefw(MAXRXN)
COMMON /reac1/ rtitle
COMMON /reac2/ coefm, coefa, coefg, coefw, nm, na, ng, nw,
1 rec1m, rec1a, rec1g, m2reac
SAVE
TK = TC + 273.15d0
CALL solids(nm(i),P,TK)
CALL gases(ng(i),TK)
CALL aqsps(na(i),P,TK,Dw,betaw,alphaw,daldTw,Zw,Qw,Yw,Xw,geqn)
CALL reactn(i,TK,Vw,Sw,Cpw,Hw,Gw)
END
********************************************************************
*** Solids - Computes the standard molal thermodynamic properties of
* nmin minerals at P,T using equations given by
* Helgeson et al. (1978).
SUBROUTINE solids(nmin,P,T)
IMPLICIT DOUBLE PRECISION (a-h,o-z)
PARAMETER (MAXMIN = 10, MXTRAN = 3, IABC = 3)
CHARACTER*20 mname(MAXMIN)
CHARACTER*30 mform(MAXMIN)
INTEGER ntran(MAXMIN), phaser(MAXMIN), getphr, getCpr, Cpreg
DOUBLE PRECISION mwH2O, TtranP(MXTRAN,MAXMIN),
1 PtranT(MXTRAN,MAXMIN)
DOUBLE PRECISION Vmin(MAXMIN), Smin(MAXMIN), Cpmin(MAXMIN),
2 Hmin(MAXMIN), Gmin(MAXMIN)
DOUBLE PRECISION Gfmin(MAXMIN), Hfmin(MAXMIN), SPrTrm(MAXMIN),
2 VPrTrm(MAXMIN),
3 MK1(IABC,MAXMIN), MK2(IABC,MAXMIN),
4 MK3(IABC,MAXMIN), MK4(IABC,MAXMIN),
5 Ttran(MXTRAN,MAXMIN), Htran(MXTRAN,MAXMIN),
6 Vtran(MXTRAN,MAXMIN), dPdTtr(MXTRAN,MAXMIN),
7 Tmaxm(MAXMIN)
COMMON /refval/ mwH2O, R, Pref, Tref, ZPrTr, YPrTr
COMMON /mnames/ mname, mform
COMMON /minref/ Gfmin, Hfmin, SPrTrm, VPrTrm, MK1, MK2, MK3, MK4,
1 Ttran, Htran, Vtran, dPdTtr, Tmaxm, ntran
COMMON /minsp/ Vmin, Smin, Cpmin, Hmin, Gmin, phaser
COMMON /PTtran/ TtranP, PtranT
SAVE
DO 10 i = 1,nmin
phaser(i) = getphr(i,P,T,TtranP)
Cpreg = getCpr(i,T)
CALL Vterms(i,P,T,phaser(i),Vmin(i),VdP,PtranT)
CALL Cptrms('min',i,Cpreg,T,Cpmin(i),CprdT,CprdlT)
CALL pttrms(i,phaser(i),T,Spttrm,Hpttrm,Gpttrm)
Smin(i) = SPrTrm(i) + CprdlT + Spttrm
Hmin(i) = Hfmin(i) + CprdT + VdP + Hpttrm
Gmin(i) = Gfmin(i) - SPrTrm(i)*(T-Tref) +
1 CprdT - T*CprdlT + VdP + Gpttrm
IF ((mname(i) .EQ. 'QUARTZ') .OR.
1 (mname(i) .EQ. 'COESITE')) THEN
Hmin(i) = Hmin(i) - VdP
Gmin(i) = Gmin(i) - VdP
CALL quartz(mname(i),P,T,Ttran(1,i),
1 Vmin(i),Smin(i),Hmin(i),Gmin(i))
END IF
10 CONTINUE
RETURN
END
************************************************************************
*** getCpr - Returns the effective phase region for temperature
*** integration of Cpr(T) for mineral imin (i.e., the
*** phase region specified by T at 1 bar).
INTEGER FUNCTION getCpr(imin,T)
IMPLICIT DOUBLE PRECISION (a-h,o-z)
PARAMETER (MAXMIN = 10, MXTRAN = 3, IABC = 3)
INTEGER ntran(MAXMIN)
DOUBLE PRECISION Gfmin(MAXMIN), Hfmin(MAXMIN), SPrTrm(MAXMIN),
2 VPrTrm(MAXMIN),
3 MK1(IABC,MAXMIN), MK2(IABC,MAXMIN),
4 MK3(IABC,MAXMIN), MK4(IABC,MAXMIN),
5 Ttran(MXTRAN,MAXMIN), Htran(MXTRAN,MAXMIN),
6 Vtran(MXTRAN,MAXMIN), dPdTtr(MXTRAN,MAXMIN),
7 Tmaxm(MAXMIN)
COMMON /minref/ Gfmin, Hfmin, SPrTrm, VPrTrm, MK1, MK2, MK3, MK4,
1 Ttran, Htran, Vtran, dPdTtr, Tmaxm, ntran
SAVE
getCpr = 1
DO 10 i = 1,ntran(imin)
IF (T .GT. Ttran(i,imin)) getCpr = getCpr + 1
10 CONTINUE
RETURN
END
***********************************************************************
*** quartz - Revises the standard molal Gibbs free energy (G), enthalpy
*** (H), entropy (S), and volume (V) of quartz or coesite to
*** account for V(T) > 0 using equations (109) through (115),
*** Helgeson et al. (1978).
SUBROUTINE quartz(mname,P,T,TtPr,V,S,H,G)
IMPLICIT DOUBLE PRECISION (a-h,o-z)
CHARACTER*20 mname
INTEGER qphase
DOUBLE PRECISION k, mwH2O
COMMON /refval/ mwH2O, R, Pr, Tr, ZPrTr, YPrTr
COMMON /qtzcon/ aa, ba, ca, VPtTta, VPrTtb, Stran
SAVE
*** VPrTra = VPrTr(a-quartz)
*** Vdiff = VPrTr(a-quartz) - VPrTr(coesite)
*** k = dPdTtr(a/b-quartz)
DATA VPrTra, Vdiff, k / 22.688d0, 2.047d0, 38.5d0 /
***** set qphase = phase region of quartz
IF ((T .LE. TtPr) .OR. (P .GE. (Pr + k*(T-TtPr)))) THEN
qphase = 1
ELSE
qphase = 2
END IF
***** set Pstar and Sstar *****
IF (T .LE. TtPr) THEN
Pstar = Pr
Sstar = 0.0d0
ELSE
IF (qphase .EQ. 2) THEN
Pstar = P
Sstar = 0.0d0
ELSE
Pstar = Pr + k*(T-TtPr)
Sstar = Stran
END IF
END IF
IF (qphase .EQ. 2) THEN
***** set volume to beta-quartz *****
V = VPrTtb
ELSE
***** calculate volume of alpha-quartz per eqn (109) *****
V = VPrTra + ca*(P-Pr) + (VPtTta - VPrTra - ca*(P-Pr))*(T-Tr) /
1 (TtPr + (P-Pr)/k - Tr)
END IF
IF (mname .EQ. 'COESITE') V = V - Vdiff
***** leading constant for [G,S]Vterm below
***** is a coversion factor (cal/cm**3/bar)
IF (mname .EQ. 'QUARTZ') THEN
GVterm = 0.23901488d-1 * (VPrTra*(P-Pstar) + VPrTtb*(Pstar-Pr) -
1 0.5d0*ca*(2.0d0*Pr*(P-Pstar) - (P**2-Pstar**2)) -
2 ca*k*(T-Tr)*(P-Pstar) +
3 k*(ba + aa*ca*k)*(T-Tr)*DLOG((aa + P/k)/(aa + Pstar/k)))
ELSE
GVterm = 0.23901488d-1 * ((VPrTra-Vdiff)*(P-Pstar) +
1 (VPrTtb-Vdiff)*(Pstar-Pr) - 0.5d0*ca*(2.0d0*Pr*(P-Pstar) -
2 (P**2-Pstar**2)) - ca*k*(T-Tr)*(P-Pstar) +
3 k*(ba + aa*ca*k)*(T-Tr)*DLOG((aa + P/k)/(aa + Pstar/k)))
END IF
SVterm = 0.23901488d-1 * (-k*(ba + aa*ca*k)*
1 DLOG((aa + P/k)/(aa + Pstar/k)) + ca*k*(P-Pstar)) -
2 Sstar
G = G + GVterm
S = S + SVterm
H = H + GVterm + T*SVterm
END
************************************************************************
*** getphr - Returns phase region for mineral imin at P, T; and, as a
*** side effect, TtranP(1..MXTRAN,imin) as f(P).
***
*** getphr = 1 ... TtranP(1,imin) > T [or imin lacks transn]
*** getphr = 2 ... TtranP(1,imin) < T [< TtranP(2,imin)]
*** getphr = 3 ... TtranP(2,imin) < T [< TtranP(3,imin)]
*** getphr = 4 ... TtranP(3,imin) < T
INTEGER FUNCTION getphr(imin,P,T,TtranP)
IMPLICIT DOUBLE PRECISION (a-h,o-z)
PARAMETER (MAXMIN = 10, MXTRAN = 3, IABC = 3)
CHARACTER*20 mname(MAXMIN)
CHARACTER*30 mform(MAXMIN)
INTEGER ntran(MAXMIN)
DOUBLE PRECISION TtranP(MXTRAN,MAXMIN), mwH2O
DOUBLE PRECISION Gfmin(MAXMIN), Hfmin(MAXMIN), VPrTrm(MAXMIN),
2 SPrTrm(MAXMIN),
3 MK1(IABC,MAXMIN), MK2(IABC,MAXMIN),
4 MK3(IABC,MAXMIN), MK4(IABC,MAXMIN),
5 Ttran(MXTRAN,MAXMIN), Htran(MXTRAN,MAXMIN),
6 Vtran(MXTRAN,MAXMIN), dPdTtr(MXTRAN,MAXMIN),
7 Tmaxm(MAXMIN)
COMMON /mnames/ mname, mform
COMMON /minref/ Gfmin, Hfmin, SPrTrm, VPrTrm, MK1, MK2, MK3, MK4,
1 Ttran, Htran, Vtran, dPdTtr, Tmaxm, ntran
COMMON /refval/ mwH2O, R, Pref, Tref, ZPrTr, YPrTr
SAVE
****** phase region 1 ******
getphr = 1
IF (ntran(imin) .EQ. 0) RETURN
IF (dPdTtr(1,imin) .EQ. 0.0d0) THEN
TtranP(1,imin) = Ttran(1,imin)
ELSE
TtranP(1,imin) = Ttran(1,imin) + (P-Pref)/dPdTtr(1,imin)
END IF
IF (T .LE. TtranP(1,imin)) RETURN
****** phase region 2 ******
getphr = 2
IF (ntran(imin) .EQ. 1) RETURN
IF (dPdTtr(2,imin) .EQ. 0.0d0) THEN
TtranP(2,imin) = Ttran(2,imin)
ELSE
TtranP(2,imin) = Ttran(2,imin) + (P-Pref)/dPdTtr(2,imin)
END IF
IF (T .LE. TtranP(2,imin)) RETURN
****** phase region 3 ******
getphr = 3
IF (ntran(imin) .EQ. 2) RETURN
IF (dPdTtr(3,imin) .EQ. 0.0d0) THEN
TtranP(3,imin) = Ttran(3,imin)
ELSE
TtranP(3,imin) = Ttran(3,imin) + (P-Pref)/dPdTtr(3,imin)
END IF
IF (T .LE. TtranP(3,imin)) RETURN
****** phase region 4 ******
getphr = 4
RETURN
END
************************************************************************
*** Vterms - Computes Vmin(P,T), Vmin*dP, and (if necesary) PtranT.
SUBROUTINE Vterms(imin,P,T,phaser,Vmin,VdP,PtranT)
IMPLICIT DOUBLE PRECISION (a-h,o-z)
PARAMETER (MAXMIN = 10, MXTRAN = 3, IABC = 3)
CHARACTER*20 mname(MAXMIN)
CHARACTER*30 mform(MAXMIN)
INTEGER phaser, ntran(MAXMIN)
DOUBLE PRECISION mwH2O, PtranT(MXTRAN,MAXMIN)
DOUBLE PRECISION Gfmin(MAXMIN), Hfmin(MAXMIN), VPrTrm(MAXMIN),
2 SPrTrm(MAXMIN),
3 MK1(IABC,MAXMIN), MK2(IABC,MAXMIN),
4 MK3(IABC,MAXMIN), MK4(IABC,MAXMIN),
5 Ttran(MXTRAN,MAXMIN), Htran(MXTRAN,MAXMIN),
6 Vtran(MXTRAN,MAXMIN), dPdTtr(MXTRAN,MAXMIN),
7 Tmaxm(MAXMIN)
COMMON /refval/ mwH2O, R, Pref, Tref, ZPrTr, YPrTr
COMMON /mnames/ mname, mform
COMMON /minref/ Gfmin, Hfmin, SPrTrm, VPrTrm, MK1, MK2, MK3, MK4,
1 Ttran, Htran, Vtran, dPdTtr, Tmaxm, ntran
SAVE
Vmin = VPrTrm(imin)
DO 10 i = 1,phaser-1
10 Vmin = Vmin + Vtran(i,imin)
VdP = Vmin*(P - Pref)*0.23901488d-1
****** return if Pressure integration does not cross
****** phase transition boundaries
IF (ntran(imin) .EQ. 0) RETURN
IF (dPdTtr(1,imin) .EQ. 0.0d0) RETURN
IF (T .LE. Ttran(1,imin)) RETURN
IF ((ntran(imin) .EQ. 1) .AND. (phaser .EQ. 2)) RETURN
IF ((ntran(imin) .EQ. 2) .AND. (phaser .EQ. 3)) RETURN
IF ((ntran(imin) .EQ. 2) .AND. (phaser .EQ. 2) .AND.
1 (T .LT. Ttran(2,imin))) RETURN
****** take account of cross-boundary pressure integration
IF ((ntran(imin) .EQ. 1) .OR.
1 ((phaser .EQ. 1) .AND.(T .LT. Ttran(2,imin)))) THEN
PtranT(1,imin) = Pref + (T - Ttran(1,imin))*dPdTtr(1,imin)
VdP = 0.23901488d-1 * (
1 VPrTrm(imin)*(P - Pref) +
2 Vtran(1,imin)*(PtranT(1,imin) - Pref))
RETURN
END IF
****** ntran(imin) = 2 and T .GE. Ttran(2,imin) ******
PtranT(2,imin) = Pref + (T - Ttran(2,imin))*dPdTtr(2,imin)
IF (phaser .EQ. 2) THEN
VdP = 0.23901488d-1 * (
1 (VPrTrm(imin) + Vtran(1,imin))*(P - Pref) +
2 Vtran(2,imin)*(PtranT(2,imin) - Pref))
ELSE
PtranT(1,imin) = Pref + (T - Ttran(1,imin))*dPdTtr(1,imin)
VdP = 0.23901488d-1 * (
1 VPrTrm(imin)*(P - Pref) +
1 Vtran(1,imin)*(PtranT(1,imin) - Pref) +
2 Vtran(2,imin)*(PtranT(2,imin) - Pref))
END IF
RETURN
END
************************************************************************
*** Cptrms - Computes the standard molal heat capacity and heat capacity
*** temperature integrals, evaluated from Tref to T at 1 bar.
SUBROUTINE Cptrms(phase,i,Cpreg,T,Cpr,CprdT,CprdlT)
IMPLICIT DOUBLE PRECISION (a-h,o-z)
PARAMETER (MAXGAS = 10, MAXMIN = 10, MXTRAN = 3, IABC = 3)
CHARACTER*3 phase
CHARACTER*20 mname(MAXMIN), gname(MAXGAS)
CHARACTER*30 mform(MAXMIN), gform(MAXGAS)
INTEGER ntran(MAXMIN), Cpreg
DOUBLE PRECISION mwH2O
DOUBLE PRECISION Gfmin(MAXMIN), Hfmin(MAXMIN), VPrTrm(MAXMIN),
2 SPrTrm(MAXMIN),
3 MK1(IABC,MAXMIN), MK2(IABC,MAXMIN),
4 MK3(IABC,MAXMIN), MK4(IABC,MAXMIN),
5 Ttran(MXTRAN,MAXMIN), Htran(MXTRAN,MAXMIN),
6 Vtran(MXTRAN,MAXMIN), dPdTtr(MXTRAN,MAXMIN),
7 Tmaxm(MAXMIN)
DOUBLE PRECISION Gfgas(MAXGAS), Hfgas(MAXGAS), VPrTrg(MAXGAS),
2 SPrTrg(MAXGAS), MKg(IABC,MAXGAS), Tmaxg(MAXGAS)
COMMON /refval/ mwH2O, R, Pref, Tref, ZPrTr, YPrTr
COMMON /mnames/ mname, mform
COMMON /minref/ Gfmin, Hfmin, SPrTrm, VPrTrm, MK1, MK2, MK3, MK4,
1 Ttran, Htran, Vtran, dPdTtr, Tmaxm, ntran
COMMON /gnames/ gname, gform
COMMON /gasref/ Gfgas, Hfgas, SPrTrg, VPrTrg, MKg, Tmaxg
SAVE
IF (phase .EQ. 'gas') THEN
Cpr = Cp(T,MKg(1,i),MKg(2,i),MKg(3,i))
CprdT = CpdT(Tref,T,MKg(1,i),MKg(2,i),MKg(3,i))
CprdlT = CpdlnT(Tref,T,MKg(1,i),MKg(2,i),MKg(3,i))
RETURN
END IF
***** phase = "min" *****
IF (Cpreg .EQ. 1) THEN
Cpr = Cp(T,MK1(1,i),MK1(2,i),MK1(3,i))
CprdT = CpdT(Tref,T,MK1(1,i),MK1(2,i),MK1(3,i))
CprdlT = CpdlnT(Tref,T,MK1(1,i),MK1(2,i),MK1(3,i))
RETURN
END IF
IF (Cpreg .EQ. 2) THEN
Cpr = Cp(T,MK2(1,i),MK2(2,i),MK2(3,i))
CprdT = CpdT(Tref,Ttran(1,i),MK1(1,i),MK1(2,i),MK1(3,i)) +
2 CpdT(Ttran(1,i),T,MK2(1,i),MK2(2,i),MK2(3,i))
CprdlT = CpdlnT(Tref,Ttran(1,i),MK1(1,i),MK1(2,i),MK1(3,i)) +
2 CpdlnT(Ttran(1,i),T,MK2(1,i),MK2(2,i),MK2(3,i))
RETURN
END IF
IF (Cpreg .EQ. 3) THEN
Cpr = Cp(T,MK3(1,i),MK3(2,i),MK3(3,i))
CprdT = CpdT(Tref,Ttran(1,i),MK1(1,i),MK1(2,i),MK1(3,i)) +
2 CpdT(Ttran(1,i),Ttran(2,i),MK2(1,i),MK2(2,i),MK2(3,i)) +
3 CpdT(Ttran(2,i),T,MK3(1,i),MK3(2,i),MK3(3,i))
CprdlT = CpdlnT(Tref,Ttran(1,i),MK1(1,i),MK1(2,i),MK1(3,i))+
2 CpdlnT(Ttran(1,i),Ttran(2,i),MK2(1,i),MK2(2,i),MK2(3,i))+
3 CpdlnT(Ttran(2,i),T,MK3(1,i),MK3(2,i),MK3(3,i))
RETURN
END IF
***** Cpreg = 4 *****
Cpr = Cp(T,MK4(1,i),MK4(2,i),MK4(3,i))
CprdT = CpdT(Tref,Ttran(1,i),MK1(1,i),MK1(2,i),MK1(3,i)) +
2 CpdT(Ttran(1,i),Ttran(2,i),MK2(1,i),MK2(2,i),MK2(3,i)) +
3 CpdT(Ttran(2,i),Ttran(3,i),MK3(1,i),MK3(2,i),MK3(3,i)) +
4 CpdT(Ttran(3,i),T,MK4(1,i),MK4(2,i),MK4(3,i))
CprdlT = CpdlnT(Tref,Ttran(1,i),MK1(1,i),MK1(2,i),MK1(3,i)) +
2 CpdlnT(Ttran(1,i),Ttran(2,i),MK2(1,i),MK2(2,i),MK2(3,i))+
3 CpdlnT(Ttran(2,i),Ttran(3,i),MK3(1,i),MK3(2,i),MK3(3,i))+
4 CpdlnT(Ttran(3,i),T,MK4(1,i),MK4(2,i),MK4(3,i))
RETURN
END
*********************************************************************
*** Cp - Returns the standard molal heat capacity at T.
DOUBLE PRECISION FUNCTION Cp(T,a,b,c)
IMPLICIT DOUBLE PRECISION (a-h,o-z)
SAVE
Cp = a + b*T + c/T**2
RETURN
END
*********************************************************************
*** CpdT - Returns the integral CpdT evaluated from T1 to T2.
DOUBLE PRECISION FUNCTION CpdT(T1,T2,a,b,c)
IMPLICIT DOUBLE PRECISION (a-h,o-z)
SAVE
CpdT = a*(T2 - T1) + b/2.0d0*(T2**2 - T1**2) -
2 c*(1.0d0/T2 - 1.0d0/T1)
RETURN
END
*********************************************************************
*** CpdlnT - Returns the integral CpdlnT evaluated from T1 to T2.
DOUBLE PRECISION FUNCTION CpdlnT(T1,T2,a,b,c)
IMPLICIT DOUBLE PRECISION (a-h,o-z)
SAVE
CpdlnT = a*DLOG(T2/T1) + b*(T2 - T1) -
2 c/2.0d0*(1.0d0/T2**2 - 1.0d0/T1**2)
RETURN
END
*********************************************************************
*** pttrms - Computes phase transition terms for Smin, Hmin, and Gmin.
SUBROUTINE pttrms(imin,phaser,T,Spttrm,Hpttrm,Gpttrm)
IMPLICIT DOUBLE PRECISION (a-h,o-z)
PARAMETER (MAXMIN = 10, MXTRAN = 3, IABC = 3)
CHARACTER*20 mname(MAXMIN)
CHARACTER*30 mform(MAXMIN)
INTEGER ntran(MAXMIN), phtran, phaser
DOUBLE PRECISION Gfmin(MAXMIN), Hfmin(MAXMIN), VPrTrm(MAXMIN),
2 SPrTrm(MAXMIN),
3 MK1(IABC,MAXMIN), MK2(IABC,MAXMIN),
4 MK3(IABC,MAXMIN), MK4(IABC,MAXMIN),
5 Ttran(MXTRAN,MAXMIN), Htran(MXTRAN,MAXMIN),
6 Vtran(MXTRAN,MAXMIN), dPdTtr(MXTRAN,MAXMIN),
7 Tmaxm(MAXMIN)
COMMON /mnames/ mname, mform
COMMON /minref/ Gfmin, Hfmin, SPrTrm, VPrTrm, MK1, MK2, MK3, MK4,
1 Ttran, Htran, Vtran, dPdTtr, Tmaxm, ntran
SAVE
Spttrm = 0.0d0
Hpttrm = 0.0d0
Gpttrm = 0.0d0
DO 10 phtran = 1,phaser-1
Spttrm = Spttrm + Htran(phtran,imin)/Ttran(phtran,imin)
Hpttrm = Hpttrm + Htran(phtran,imin)
Gpttrm = Gpttrm +
1 Htran(phtran,imin)*(1.0d0 - T/Ttran(phtran,imin))
10 CONTINUE
RETURN
END
**********************************************************************
*** gases - Computes the standard molal thermodynamic properties of
* ngas gases at P,T using equations given by
* Helgeson et al. (1978).
SUBROUTINE gases(ngas,T)
IMPLICIT DOUBLE PRECISION (a-h,o-z)
PARAMETER (MAXGAS = 10, IABC = 3, TS1BAR = 99.6324d0)
LOGICAL error
CHARACTER*20 gname(MAXGAS)
CHARACTER*30 gform(MAXGAS)
INTEGER specs(10)
DOUBLE PRECISION mwH2O
DOUBLE PRECISION Vgas(MAXGAS), Sgas(MAXGAS), Cpgas(MAXGAS),
2 Hgas(MAXGAS), Ggas(MAXGAS)
DOUBLE PRECISION Gfgas(MAXGAS), Hfgas(MAXGAS), VPrTrg(MAXGAS),
2 SPrTrg(MAXGAS), MKg(IABC,MAXGAS), Tmaxg(MAXGAS)
DOUBLE PRECISION states(4), props(46)
COMMON /refval/ mwH2O, R, Pref, Tref, ZPrTr, YPrTr
COMMON /gnames/ gname, gform
COMMON /gasref/ Gfgas, Hfgas, SPrTrg, VPrTrg, MKg, Tmaxg
COMMON /gassp/ Vgas, Sgas, Cpgas, Hgas, Ggas
SAVE
DATA specs / 2,2,2,5,1,0,2,0,4,0 /
DATA states / 0.0d0, 1.0d0, 0.0d0, 0.0d0 /
TC = T - 273.15d0
DO 10 i = 1,ngas
IF ((gname(i) .EQ. 'H2O,g') .AND. (TC .GE. TS1BAR)) THEN
*** use Haar et al. (1984) equation of state to
*** compute H2O,g properties at 1 bar, T > Tsat(1 bar) =
*** 99.6324 C. Note that for T < Tsat(1 bar),
*** thermodynamic properties of metastable H2O,g are
*** calculated using parameters estimated by J. W. Johnson
*** (3/90) that facilitate smooth transition into the
*** Haar et al. (1984) equation at Tsat.
***
*** Beacuse (1) P = 1 bar, and (2) thermodynamic properties
*** of steam are independent of dielectric properties,
*** specs(8..9) can be safely hardwired, as above.
states(1) = TC
CALL H2O92(specs,states,props,error)
Vgas(i) = VPrTrg(i)
Sgas(i) = props(5)
Hgas(i) = props(9)
Ggas(i) = props(3)
Cpgas(i) = props(13)
ELSE
Vgas(i) = VPrTrg(i)
CALL Cptrms('gas',i,1,T,Cpgas(i),CprdT,CprdlT)
Sgas(i) = SPrTrg(i) + CprdlT
Hgas(i) = Hfgas(i) + CprdT
Ggas(i) = Gfgas(i) - SPrTrg(i)*(T - Tref) +
1 CprdT - T*CprdlT
END IF
10 CONTINUE
RETURN
END
************************************************************************
*** aqsps - Computes the standard partial molal thermodynamic properties
*** of naqs aqueous species at P,T using equations given by
*** Tanger and Helgeson (1988), Shock et al. (1991), and
*** Johnson et al. (1991).
SUBROUTINE aqsps(naqs,P,T,Dw,betaw,alphaw,daldTw,Z,Q,Y,X,geqn)
IMPLICIT DOUBLE PRECISION (a-h,o-z)
PARAMETER (MAXAQS = 10)
CHARACTER*20 aname(MAXAQS)
CHARACTER*30 aform(MAXAQS)
INTEGER geqn
DOUBLE PRECISION mwH2O
DOUBLE PRECISION Vaqs(MAXAQS), Saqs(MAXAQS), Cpaqs(MAXAQS),
2 Haqs(MAXAQS), Gaqs(MAXAQS),
7 VQterm(MAXAQS), SYterm(MAXAQS), CpXtrm(MAXAQS),
8 HYterm(MAXAQS), GZterm(MAXAQS)
DOUBLE PRECISION Gfaqs(MAXAQS), Hfaqs(MAXAQS), SPrTra(MAXAQS),
2 a(4,MAXAQS), c(2,MAXAQS), wref(MAXAQS),
3 chg(MAXAQS)
COMMON /refval/ mwH2O, R, Pref, Tref, ZPrTr, YPrTr
COMMON /aqscon/ eta, theta, psi, anion, cation, gref
COMMON /anames/ aname, aform
COMMON /aqsref/ Gfaqs, Hfaqs, SPrTra, c, a, wref, chg
COMMON /aqsp/ Vaqs, Saqs, Cpaqs, Haqs, Gaqs
COMMON /solvn/ VQterm, SYterm, CpXtrm, HYterm, GZterm
SAVE
IF (naqs .EQ. 0) THEN
RETURN
ELSE
CALL gfun92(T-273.15d0,P,Dw,betaw,alphaw,daldTw,
1 g,dgdP,dgdT,d2gdT2,geqn)
END IF
DO 10 j = 1,naqs
****** compute w, dwdP, dwdT, d2wdT2 ******
CALL omeg92(g,dgdP,dgdT,d2gdT2,wref(j),chg(j),
1 w,dwdP,dwdT,d2wdT2,aname(j))
VQterm(j) = 0.4184004d2 * (-w*Q + (-Z - 1.0d0)*dwdP)
*** the leading constant converts cal/(mol*bar) -> cm3/mol
Vaqs(j) = 0.4184004d2 * (a(1,j) +
1 a(2,j)/(psi+P) +
2 a(3,j)/(T-theta) +
3 a(4,j)/(psi+P)/(T-theta)) +
4 VQterm(j)
SYterm(j) = w*Y - (-Z - 1.0d0)*dwdT - wref(j)*YPrTr
Saqs(j) = SPrTra(j) + c(1,j)*DLOG(T/Tref) -
2 c(2,j)/theta* (1.0d0/(T-theta) -
3 1.0d0/(Tref-theta) +
4 (1.0d0/theta)*
5 DLOG(Tref*(T-theta)/T/(Tref-theta))) +
6 (a(3,j)*(P-Pref) +
7 a(4,j)*DLOG((psi+P)/(psi+Pref))) *
8 (1.0d0/(T-theta))**2 +
9 SYterm(j)
CpXtrm(j) = w*T*X + 2.0d0*T*Y*dwdT + T*(Z + 1.0d0)*d2wdT2
Cpaqs(j) = c(1,j) + c(2,j)/(T-theta)**2 -
1 (2.0d0*T/(T-theta)**3) * (a(3,j)*(P-Pref) +
2 a(4,j)*DLOG((psi+P)/(psi+Pref))) +
3 CpXtrm(j)
HYterm(j) = w*(-Z - 1.0d0) + w*T*Y - T*(-Z - 1.0d0)*dwdT -
1 wref(j)*(-ZPrTr - 1.0d0) -
2 wref(j)*Tref*YPrTr
Haqs(j) = Hfaqs(j) + c(1,j)*(T-Tref) -
1 c(2,j)*(1.0d0/(T-theta) - 1.0d0/(Tref-theta)) +
2 a(1,j)*(P-Pref) + a(2,j)*DLOG((psi+P)/(psi+Pref)) +
3 (a(3,j)*(P-Pref) + a(4,j)*DLOG((psi+P)/(psi+Pref))) *
4 ((2.0d0*T - theta)/(T - theta)**2) +
5 HYterm(j)
GZterm(j) = w*(-Z - 1.0d0) - wref(j)*(-ZPrTr - 1.0d0) +
1 wref(j)*YPrTr*(T-Tref)
Gaqs(j) = Gfaqs(j) - SPrTra(j)*(T-Tref) -
1 c(1,j)*(T*DLOG(T/Tref)-T+Tref) +
2 a(1,j)*(P-Pref) + a(2,j)*DLOG((psi+P)/(psi+Pref)) -
3 c(2,j)* ( (1.0d0/(T-theta) - 1.0d0/(Tref-theta)) *
4 ((theta-T)/theta) - T/theta**2 *
5 DLOG((Tref*(T-theta))/(T*(Tref-theta))) ) +
6 (1.0d0/(T-theta)) * (a(3,j)*(P-Pref) +
7 a(4,j)*DLOG((psi+P)/(psi+Pref))) +
8 GZterm(j)
GZterm(j) = w*(-Z - 1.0d0)
10 CONTINUE
RETURN
END
************************************************************************
*** omeg92 - Computes the conventinal Born coefficient (w) of the
*** current aqueous species, dwdP, dwdP, and dw2dT2 as a
*** function of g, dgdP, dgdT, d2gdT2, wref, and Z using
*** equations given by Johnson et al. (1991).
SUBROUTINE omeg92(g,dgdP,dgdT,d2gdT2,wref,Z,
1 w,dwdP,dwdT,d2wdT2,aname)
IMPLICIT DOUBLE PRECISION (a-h,o-z)
CHARACTER*20 aname
COMMON /aqscon/ eta, theta, psi, anion, cation, gref
SAVE
IF ((Z .EQ. 0.0d0) .OR. (aname .EQ. 'H+')) THEN
*** neutral aqueous species or H+
w = wref
dwdP = 0.0d0
dwdT = 0.0d0
d2wdT2 = 0.0d0
RETURN
ELSE
*** charged aqueous species other than H+
reref = Z**2 / (wref/eta + Z/(3.082d0 + gref))
re = reref + DABS(Z) * g
w = eta * (Z**2/re - Z/(3.082d0 + g))
Z3 = DABS(Z**3)/re**2 - Z/(3.082d0 + g)**2
Z4 = DABS(Z**4)/re**3 - Z/(3.082d0 + g)**3
dwdP = -eta * Z3 * dgdP
dwdT = -eta * Z3 * dgdT
d2wdT2 = 2.0d0 * eta * Z4 * dgdT**2 - eta * Z3 * d2gdT2
END IF
END
************************************************************************
*** reactn - Computes the standard molal thermodynamic properties
*** of the i[th] reaction.
SUBROUTINE reactn(i,T,Vw,Sw,Cpw,Hw,Gw)
IMPLICIT DOUBLE PRECISION (a-h,o-z)
PARAMETER (MAXMIN = 10, MAXAQS = 10, MAXGAS = 10, MAXRXN = 10)
CHARACTER*80 rtitle(MAXRXN)
LOGICAL m2reac(MAXRXN)
INTEGER nm(MAXRXN), na(MAXRXN), ng(MAXRXN), nw(MAXRXN),
1 rec1m(MAXRXN,MAXMIN), rec1a(MAXRXN,MAXAQS),
2 rec1g(MAXRXN,MAXGAS), phaser(MAXMIN)
DOUBLE PRECISION mwH2O
DOUBLE PRECISION coefm(MAXRXN,MAXMIN), coefa(MAXRXN,MAXAQS),
1 coefg(MAXRXN,MAXGAS), coefw(MAXRXN)
DOUBLE PRECISION Vmin(MAXMIN), Smin(MAXMIN), Cpmin(MAXMIN),
2 Hmin(MAXMIN), Gmin(MAXMIN),
3 Vgas(MAXGAS), Sgas(MAXGAS), Cpgas(MAXGAS),
4 Hgas(MAXGAS), Ggas(MAXGAS),
5 Vaqs(MAXAQS), Saqs(MAXAQS), Cpaqs(MAXAQS),
6 Haqs(MAXAQS), Gaqs(MAXAQS)
DOUBLE PRECISION VQterm(MAXAQS), SYterm(MAXAQS), CpXtrm(MAXAQS),
1 HYterm(MAXAQS), GZterm(MAXAQS), logKr
COMMON /refval/ mwH2O, R, Pref, Tref, ZPrTr, YPrTr
COMMON /reac1/ rtitle
COMMON /reac2/ coefm, coefa, coefg, coefw, nm, na, ng, nw,
1 rec1m, rec1a, rec1g, m2reac
COMMON /minsp/ Vmin, Smin, Cpmin, Hmin, Gmin, phaser
COMMON /gassp/ Vgas, Sgas, Cpgas, Hgas, Ggas
COMMON /aqsp/ Vaqs, Saqs, Cpaqs, Haqs, Gaqs
COMMON /fmeq/ dVr, dSr, dCpr, dHr, dGr,
2 logKr, dlogKT, dlogKP
COMMON /solvn/ VQterm, SYterm, CpXtrm, HYterm, GZterm
SAVE
***** sum mineral contributions *****
dVrm = 0.0d0
dCprm = 0.0d0
dSrm = 0.0d0
dHrm = 0.0d0
dGrm = 0.0d0
DO 10 j = 1,nm(i)
dVrm = dVrm + coefm(i,j)*Vmin(j)
dCprm = dCprm + coefm(i,j)*Cpmin(j)
dSrm = dSrm + coefm(i,j)*Smin(j)
dHrm = dHrm + coefm(i,j)*Hmin(j)
dGrm = dGrm + coefm(i,j)*Gmin(j)
10 CONTINUE
***** sum gas contributions *****
dVrg = 0.0d0
dCprg = 0.0d0
dSrg = 0.0d0
dHrg = 0.0d0
dGrg = 0.0d0
DO 20 j = 1,ng(i)
dVrg = dVrg + coefg(i,j)*Vgas(j)
dCprg = dCprg + coefg(i,j)*Cpgas(j)
dSrg = dSrg + coefg(i,j)*Sgas(j)
dHrg = dHrg + coefg(i,j)*Hgas(j)
dGrg = dGrg + coefg(i,j)*Ggas(j)
20 CONTINUE
***** sum aqueous species contributions *****
dVra = 0.0d0
dCpra = 0.0d0
dSra = 0.0d0
dHra = 0.0d0
dGra = 0.0d0
DO 30 j = 1,na(i)
dVra = dVra + coefa(i,j)*Vaqs(j)
dCpra = dCpra + coefa(i,j)*Cpaqs(j)
dSra = dSra + coefa(i,j)*Saqs(j)
dHra = dHra + coefa(i,j)*Haqs(j)
dGra = dGra + coefa(i,j)*Gaqs(j)
30 CONTINUE
***** calculate H2O contributions *****
dVrw = coefw(i) * Vw
dSrw = coefw(i) * Sw
dCprw = coefw(i) * Cpw
dHrw = coefw(i) * Hw
dGrw = coefw(i) * Gw
***** calculate reaction properties *****
dVr = dVrm + dVrg + dVra + dVrw
dSr = dSrm + dSrg + dSra + dSrw
dCpr = dCprm + dCprg + dCpra + dCprw
dHr = dHrm + dHrg + dHra + dHrw
dGr = dGrm + dGrg + dGra + dGrw
logKr = -dGr / (2.302585d0 * R * T)
dlogKT = dHr / (2.302585d0 * R * T**2)
dlogKP = -0.23901488d-1 * dVr / (2.302585d0 * R * T)
RETURN
END
******************************************************************
*** gfun92 - Computes the g function (Tanger and Helgeson, 1988;
*** Shock et al., 1991) and its partial derivatives
*** (dgdP, dgdT, d2gdT2) at TdegC, Pbars using the
*** computational algorithm specified by geqn.
***
*** geqn = 1 ...... use Tanger-Helgeson (1988) equations
*** geqn = 2 ...... use Shock et al. (1991) equations
*** without the f(P,T) difference function
*** geqn = 3 ...... use Shock et al. (1991) equations
*** with the f(P,T) difference function
SUBROUTINE gfun92(TdegC,Pbars,Dgcm3,betab,alphaK,daldT,
1 g,dgdP,dgdT,d2gdT2,geqn)
IMPLICIT DOUBLE PRECISION (a-h,o-z)
PARAMETER (TMAX = 1000.0d0, PMAX = 5000.0d0, TOL=1.0d-4)
INTEGER geqn
SAVE
****** initialize g and derivatives to zero
g = 0.0d0
dgdP = 0.0d0
dgdT = 0.0d0
d2gdT2 = 0.0d0