R/Kspc.R

In seacarb: Calculates parameters of the seawater carbonate system

# Copyright (C) 2003 Jean-Pierre Gattuso and Aurelien Proye
#
# This file is part of seacarb.
#
# Seacarb is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or any later version.
#
# Seacarb is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License along with seacarb; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
#
#
"Kspc" <-
function(S=35,T=25,P=0){

nK <- max(length(S), length(T), length(P))

##-------- Creation de vecteur pour toutes les entrees (si vectorielles)

if(length(S)!=nK){S <- rep(S[1], nK)}
if(length(T)!=nK){T <- rep(T[1], nK)}
if(length(P)!=nK){P <- rep(P[1], nK)}


#---- issues de equic----
tk = 273.15;           # [K] (for conversion [deg C] <-> [K])
TC = T + tk;           # TC [C]; T[K]
Cl = S / 1.80655;      # Cl = chlorinity; S = salinity (per mille)
cl3 = Cl^(1/3);   
ION = 0.00147 + 0.03592 * Cl + 0.000068 * Cl * Cl;   # ionic strength
iom0 = 19.924*S/(1000-1.005*S);
ST = 0.14/96.062/1.80655*S;   # (mol/kg soln) total sulfate


bor = (416.*(S/35.))* 1e-6;   # (mol/kg), DOE94   
	# --------------------- Kspc (calcite) ----------------------------
	#
	# apparent solubility product of calcite
	#
	#  Kspc = [Ca2+]T [CO32-]T
	#
	#  where $[]_T$ refers to the equilibrium total 
	# (free + complexed) ion concentration.
	#
	#  Mucci 1983 mol/kg-soln
	
	tmp1 = -171.9065-0.077993*TC+2839.319/TC+71.595*log10(TC);
	tmp2 = +(-0.77712+0.0028426*TC+178.34/TC)*sqrt(S);
	tmp3 = -0.07711*S+0.0041249*S^1.5;
	log10Kspc = tmp1 + tmp2 + tmp3;
	
	Kspc = 10^(log10Kspc);
	
	for(i in (1:nK)){	
		if (P[i] > 0.0)
		{
		
		RGAS = 8.314510;        # J mol-1 deg-1 (perfect Gas)  
		R = 83.14472;             # mol bar deg-1 
		                        # conversion cm3 -> m3          *1.e-6
	                        #            bar -> Pa = N m-2  *1.e+5
		                        #                => *1.e-1 or *1/10
		
		
		# index: K1 1, K2 2, Kb 3, Kw 4, Ks 5, Kf 6, Kspc 7, Kspa 8,
		#        K1P 9, K2P 10, K3P 11
		
		#----- note: there is an error in Table 9 of Millero, 1995.
		#----- The coefficients -b0 and b1
		#----- have to be multiplied by 1.e-3!
	
		#----- there are some more errors! 
		#----- the signs (+,-) of coefficients in Millero 95 do not
		#----- agree with Millero 79
		
		
		
		a0 = c(-25.5, -15.82, -29.48, -25.60, -18.03, -9.78, -48.76, -46, -14.51, -23.12, -26.57);
		a1 = c(0.1271, -0.0219, 0.1622, 0.2324, 0.0466, -0.0090, 0.5304, 0.5304, 0.1211, 0.1758, 0.2020);
		a2 = c(0.0, 0.0, 2.608*1e-3, -3.6246*1e-3, 0.316*1e-3, -0.942*1e-3, 0.0, 0.0, -0.321*1e-3, -2.647*1e-3, -3.042*1e-3);
		b0 = c(-3.08*1e-3, 1.13*1e-3, -2.84*1e-3, -5.13*1e-3, -4.53*1e-3, -3.91*1e-3, -11.76*1e-3, -11.76*1e-3, -2.67*1e-3, -5.15*1e-3, -4.08*1e-3);
		b1 = c(0.0877*1e-3, -0.1475*1e-3, 0.0, 0.0794*1e-3, 0.09*1e-3, 0.054*1e-3, 0.3692*1e-3, 0.3692*1e-3, 0.0427*1e-3, 0.09*1e-3, 0.0714*1e-3);
		b2 = c(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0);
		
		deltav = c(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0);
		deltak = c(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0);
		lnkpok0 = c(0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0);
		
		for (ipc in 1:length(a0))
		{
		  deltav[ipc]  =  a0[ipc] + a1[ipc] *T[i] + a2[ipc] *T[i]*T[i];
		  deltak[ipc]   = (b0[ipc]  + b1[ipc] *T[i] + b2[ipc] *T[i]*T[i]);  
		  lnkpok0[ipc]  = -(deltav[ipc] /(R*TC[i]))*P[i] + (0.5*deltak[ipc] /(R*TC[i]))*P[i]*P[i];
		}
		
		Kspc[i] = Kspc[i]*exp(lnkpok0[7]);
	}	
	}
	attr(Kspc,"unit") = "mol/kg"
	return(Kspc)
	}