| 1 | c======================================================================= |
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| 2 | subroutine massflowrateCO2(P,T,Sat,Radius,Matm,Ic) |
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| 3 | c |
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| 4 | c Determination of the mass transfer rate for CO2 condensation & |
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| 5 | c sublimation |
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| 6 | c |
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| 7 | c newton-raphson method |
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| 8 | c CLASSICAL (no SF etc.) |
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| 9 | c |
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| 10 | c inputs: Pressure (P), Temperature (T), saturation ratio (Sat), |
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| 11 | c particle radius (Radius), molecular mass of the atm (Matm) |
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| 12 | c output: MASS FLUX Ic |
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| 13 | c |
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| 14 | c Authors: C. Listowski (2014) then J. Audouard (2016-2017) |
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| 15 | c======================================================================= |
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| 16 | USE comcstfi_h |
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| 17 | |
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| 18 | implicit none |
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| 19 | |
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| 20 | include "microphys.h" |
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| 21 | |
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| 22 | |
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| 23 | |
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| 24 | c arguments: INPUT |
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| 25 | c ---------- |
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| 26 | REAL T,Matm |
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| 27 | REAL*8 SAT |
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| 28 | real P |
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| 29 | DOUBLE PRECISION Radius |
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| 30 | c arguments: OUTPUT |
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| 31 | c ---------- |
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| 32 | DOUBLE PRECISION Ic |
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| 33 | c Local Variables |
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| 34 | c ---------- |
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| 35 | DOUBLE PRECISION Tcm |
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| 36 | DOUBLE PRECISION T_inf, T_sup, T_dT |
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| 37 | DOUBLE PRECISION C0,C1,C2 |
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| 38 | DOUBLE PRECISION kmix,Lsub,cond |
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| 39 | DOUBLE PRECISION rtsafe |
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| 40 | DOUBLE PRECISION left, fval, dfval |
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| 41 | c function for newton-raphson iterative method |
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| 42 | c -------------------------- |
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| 43 | EXTERNAL classical |
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| 44 | |
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| 45 | Tcm = 110!dble(T) ! initialize pourquoi 0 et pas t(i) |
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| 46 | T_inf = 0d0 |
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| 47 | T_sup = 800d0 |
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| 48 | T_dT = 0.001 ! precision - mettre petit et limiter nb iteration? |
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| 49 | |
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| 50 | 666 CONTINUE |
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| 51 | |
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| 52 | call coefffunc(P,T,Sat,Radius,Matm,kmix,Lsub,C0,C1,C2) |
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| 53 | |
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| 54 | if (isnan(C0) .eqv. .true.) C0=0d0 |
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| 55 | c FIND SURFACE TEMPERATURE (Tc) : iteration sur t |
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| 56 | cond = 4.*pi*Radius*kmix |
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| 57 | Tcm = rtsafe(classical,T_inf,T_sup,T_dT,Radius,C0,C1,C2) |
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| 58 | if (Tcm.LE.0d0 .or. isnan(Tcm)) then ! unsignificant cases where S<<<Seq and Ncores <<1e-10 |
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| 59 | Tcm = T |
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| 60 | endif |
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| 61 | c THEN COMPUTE MASS FLUX Ic from FINAL Tsurface (Tc) |
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| 62 | Ic = (Tcm-T) |
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| 63 | Ic = cond*Ic/Lsub |
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| 64 | c regarder de combien varie la solution Ic entre Tcm et Tcm+T_dT |
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| 65 | |
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| 66 | RETURN |
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| 67 | |
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| 68 | END |
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| 69 | |
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| 70 | |
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| 71 | c**************************************************************** |
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| 72 | FUNCTION rtsafe(funcd,x1,x2,xacc,Radius,C0,C1,C2) |
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| 73 | * |
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| 74 | * Newton Raphsen routine (Numerical Recipe) |
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| 75 | * |
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| 76 | c**************************************************************** |
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| 77 | |
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| 78 | implicit none |
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| 79 | |
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| 80 | INTEGER MAXIT |
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| 81 | DOUBLE PRECISION x1,x2,xacc |
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| 82 | DOUBLE PRECISION rtsafe |
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| 83 | DOUBLE PRECISION Radius |
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| 84 | DOUBLE PRECISION C0,C1,C2 |
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| 85 | |
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| 86 | |
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| 87 | EXTERNAL funcd |
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| 88 | |
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| 89 | PARAMETER (MAXIT=10000) !Maximum allowed number of iterations. Using a combination of Newton-Raphson and bisection, |
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| 90 | !find the root of a function bracketed between x1 and x2. The root, returned as the function value rtsafe, |
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| 91 | !will be refined until its accuracy is known within !!±xacc. funcd is a user-supplied subroutine which |
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| 92 | !returns both the function value and the first derivative of the function. |
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| 93 | |
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| 94 | INTEGER j |
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| 95 | DOUBLE PRECISION df,dx,dxold |
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| 96 | DOUBLE PRECISION f,fh,fl,temp,xh,xl |
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| 97 | |
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| 98 | call funcd(x1,fl,df,C0,C1,C2) |
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| 99 | call funcd(x2,fh,df,C0,C1,C2) |
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| 100 | |
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| 101 | |
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| 102 | if ((fl.gt.0..and.fh.gt.0.).or.(fl.lt.0..and.fh.lt.0.) ) then |
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| 103 | x1=0d0 |
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| 104 | x2=1200d0 |
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| 105 | call funcd(x1,fl,df,C0,C1,C2) |
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| 106 | call funcd(x2,fh,df,C0,C1,C2) |
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| 107 | c write(*,*) 'root must be bracketed in rtsafe' |
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| 108 | endif |
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| 109 | |
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| 110 | |
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| 111 | if (fl.eq.0.) then |
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| 112 | rtsafe=x1 |
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| 113 | return |
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| 114 | else if (fh.eq.0.) then |
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| 115 | rtsafe=x2 |
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| 116 | return |
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| 117 | else if (fl.lt.0.) then !Orient the search so that f(xl) < 0. |
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| 118 | xl=x1 |
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| 119 | xh=x2 |
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| 120 | else |
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| 121 | xh=x1 |
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| 122 | xl=x2 |
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| 123 | endif |
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| 124 | rtsafe = .5*(x1+x2) !Initialize the guess for root, |
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| 125 | dxold = abs(x2-x1) !the stepsize before last, |
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| 126 | dx = dxold ! and the last step. |
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| 127 | call funcd(rtsafe,f,df,C0,C1,C2) |
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| 128 | DO 11 j=1,MAXIT !Loop over allowed iterations. |
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| 129 | |
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| 130 | if (((rtsafe-xh)*df-f)*((rtsafe-xl)*df-f).gt.0. ! Bisect if Newton out of range |
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| 131 | * .or. abs(2.*f).gt.abs(dxold*df) ) then ! or not decreasing fst enough |
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| 132 | |
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| 133 | dxold=dx |
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| 134 | dx=0.5*(xh-xl) |
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| 135 | rtsafe=xl+dx |
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| 136 | if (xl.eq.rtsafe) return !Change in root is negligible. Newton step acceptable. Take it. |
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| 137 | else |
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| 138 | dxold=dx |
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| 139 | dx=f/df |
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| 140 | temp=rtsafe |
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| 141 | rtsafe=rtsafe-dx |
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| 142 | if(temp.eq.rtsafe) return |
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| 143 | endif |
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| 144 | |
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| 145 | if(abs(dx).lt.xacc) return !Convergence criterion. The one new function evaluation per iteration. Maintain the bracket on the root. |
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| 146 | call funcd(rtsafe,f,df,C0,C1,C2) |
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| 147 | if(f.lt.0.) then |
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| 148 | xl=rtsafe |
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| 149 | else |
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| 150 | xh=rtsafe |
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| 151 | endif |
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| 152 | 11 ENDDO |
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| 153 | |
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| 154 | rtsafe=0d0 |
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| 155 | write(*,*) 'rtsafe exceeding maximum iterations,Tcm=',rtsafe |
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| 156 | return |
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| 157 | |
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| 158 | END |
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| 159 | |
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| 160 | |
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| 161 | c******************************************************************************** |
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| 162 | subroutine classical(x,f,df,C0,C1,C2) |
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| 163 | c Function to give as input to RTSAFE (NEWTON-RAPHOEN) |
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| 164 | c******************************************************************************** |
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| 165 | |
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| 166 | implicit none |
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| 167 | |
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| 168 | DOUBLE PRECISION x |
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| 169 | DOUBLE PRECISION C0,C1,C2 |
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| 170 | DOUBLE PRECISION f |
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| 171 | DOUBLE PRECISION df |
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| 172 | |
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| 173 | f = x + C0*exp(C1*x) - C2 ! start f |
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| 174 | df = 1. + C0*C1*exp(C1*x) ! start df |
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| 175 | |
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| 176 | return |
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| 177 | END |
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| 178 | |
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| 179 | c******************************************************************************** |
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| 180 | |
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| 181 | subroutine coefffunc(P,T,S,rc,Matm,kmix,Lsub,C0,C1,C2) |
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| 182 | |
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| 183 | c******************************************************************************** |
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| 184 | c defini la fonction eq 6 papier 2014 (Listowski et al., 2014) |
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| 185 | use tracer_mod, only: rho_ice_co2 |
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| 186 | USE comcstfi_h |
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| 187 | |
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| 188 | implicit none |
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| 189 | include "microphys.h" |
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| 190 | |
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| 191 | c arguments: INPUT |
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| 192 | c ---------------- |
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| 193 | REAL P |
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| 194 | real T |
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| 195 | REAL*8 S |
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| 196 | double precision rc |
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| 197 | REAL Matm !g.mol-1 ( = mmean(ig,l) ) |
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| 198 | |
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| 199 | c local: |
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| 200 | c ------ |
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| 201 | DOUBLE PRECISION Cpatm,Cpn2,Cpco2 |
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| 202 | DOUBLE PRECISION psat, xinf, pco2 |
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| 203 | DOUBLE PRECISION Dv |
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| 204 | DOUBLE PRECISION l0,l1,l2,l3,l4 |
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| 205 | DOUBLE PRECISION knudsen, a, lambda ! F and S correction |
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| 206 | DOUBLE PRECISION Ak ! kelvin factor |
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| 207 | DOUBLE PRECISION vthatm,lpmt,rhoatm, vthco2 ! for Kn,th |
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| 208 | |
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| 209 | c arguments: OUTPUT |
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| 210 | c ---------- |
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| 211 | DOUBLE PRECISION C0,C1,C2 |
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| 212 | DOUBLE PRECISION kmix,Lsub |
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| 213 | |
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| 214 | c DEFINE heat cap. J.kg-1.K-1 and To |
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| 215 | |
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| 216 | data Cpco2/0.7e3/ |
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| 217 | data Cpn2/1e3/ |
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| 218 | |
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| 219 | kmix = 0d0 |
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| 220 | Lsub = 0d0 |
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| 221 | |
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| 222 | C0 = 0d0 |
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| 223 | C1 = 0d0 |
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| 224 | C2 = 0d0 |
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| 225 | |
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| 226 | c Equilibirum pressure over a flat surface |
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| 227 | psat = 1.382 * 1.00e12 * exp(-3182.48/dble(T)) ! (Pa) |
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| 228 | c Compute transport coefficient |
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| 229 | pco2 = psat * dble(S) |
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| 230 | c Latent heat of sublimation if CO2 co2 (J.kg-1) |
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| 231 | c version Azreg_Ainou (J/kg) : |
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| 232 | l0=595594. |
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| 233 | l1=903.111 |
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| 234 | l2=-11.5959 |
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| 235 | l3=0.0528288 |
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| 236 | l4=-0.000103183 |
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| 237 | Lsub = l0 + l1 * dble(T) + l2 * dble(T)**2 + l3 * |
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| 238 | & dble(T)**3 + l4 * dble(T)**4 ! J/kg |
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| 239 | c atmospheric density |
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| 240 | rhoatm = dble(P*Matm)/(rgp*dble(T)) ! g.m-3 |
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| 241 | rhoatm = rhoatm * 1.00e-3 !kg.m-3 |
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| 242 | call KthMixNEW(kmix,T,pco2/dble(P),rhoatm) ! compute thermal cond of mixture co2/N2 |
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| 243 | call Diffcoeff(P, T, Dv) |
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| 244 | |
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| 245 | Dv = Dv * 1.00e-4 !!! cm2.s-1 to m2.s-1 |
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| 246 | |
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| 247 | c ----- FS correction for Diff |
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| 248 | vthco2 = sqrt(8d0*kbz*dble(T)/(dble(pi) * mco2/nav)) ! units OK: m.s-1 |
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| 249 | knudsen = 3*Dv / (vthco2 * rc) |
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| 250 | lambda = (1.333+0.71/knudsen) / (1.+1./knudsen) ! pas adaptée, Dahneke 1983? en fait si (Monschick&Black) |
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| 251 | Dv = Dv / (1. + lambda * knudsen) |
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| 252 | c ----- FS correction for Kth |
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| 253 | vthatm = sqrt(8d0*kbz*dble(T)/(pi * 1.00e-3*dble(Matm)/nav)) ! Matm/nav = mass of "air molecule" in G , *1e-3 --> kg |
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| 254 | Cpatm = Cpco2 * pco2/dble(P) + Cpn2 * (1d0 - pco2/dble(P)) !J.kg-1.K-1 |
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| 255 | lpmt = 3 * kmix / (rhoatm * vthatm * (Cpatm - 0.5*rgp/ |
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| 256 | & (dble(Matm)*1.00e-3))) ! mean free path related to heat transfer |
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| 257 | knudsen = lpmt / rc |
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| 258 | lambda = (1.333+0.71/knudsen) / (1.+1./knudsen) ! pas adaptée, Dahneke 1983? en fait si (Monschick&Black) |
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| 259 | kmix = kmix / (1. + lambda * knudsen) |
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| 260 | c --------------------- ASSIGN coeff values for FUNCTION |
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| 261 | xinf = dble(S) * psat / dble(P) |
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| 262 | Ak = exp(2d0*sigco2*mco2/(rgp* dble(rho_ice_co2*T* rc) )) |
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| 263 | C0 = mco2*Dv*psat*Lsub/(rgp*dble(T)*kmix)*Ak*exp(-Lsub*mco2/ |
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| 264 | & (rgp*dble(T))) |
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| 265 | C1 = Lsub*mco2/(rgp*dble(T)**2) |
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| 266 | C2 = dble(T) + dble(P)*mco2*Dv*Lsub*xinf/(kmix*rgp*dble(T)) |
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| 267 | RETURN |
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| 268 | END |
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| 269 | |
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| 270 | |
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| 271 | c====================================================================== |
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| 272 | subroutine Diffcoeff(P, T, Diff) |
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| 273 | c Compute diffusion coefficient CO2/N2 |
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| 274 | c cited in Ilona's lecture - from Reid et al. 1987 |
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| 275 | c====================================================================== |
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| 276 | IMPLICIT NONE |
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| 277 | |
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| 278 | include "microphys.h" |
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| 279 | |
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| 280 | c arguments |
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| 281 | c ----------- |
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| 282 | |
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| 283 | REAL P |
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| 284 | REAL Pbar !!! has to be in bar for the formula |
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| 285 | REAL T |
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| 286 | |
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| 287 | c output |
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| 288 | c ----------- |
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| 289 | |
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| 290 | DOUBLE PRECISION Diff |
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| 291 | |
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| 292 | c local |
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| 293 | c ----------- |
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| 294 | |
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| 295 | DOUBLE PRECISION dva, dvb, Mab ! Mab has to be in g.mol-1 |
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| 296 | |
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| 297 | Pbar = P * 1d-5 |
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| 298 | |
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| 299 | Mab = 2. / ( 1./mn2 + 1./mco2 ) * 1000. |
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| 300 | |
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| 301 | dva = 26.9 ! diffusion volume of CO2, Reid et al. 1987 (cited in Ilona's lecture) |
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| 302 | dvb = 18.5 ! diffusion volume of N2 |
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| 303 | |
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| 304 | Diff = 0.00143 * dble(T)**(1.75) / (dble(Pbar) * sqrt(Mab) |
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| 305 | & * (dble(dva)**(1./3.) + dble(dvb)**(1./3.))**2.) !!! in cm2.s-1 |
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| 306 | |
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| 307 | RETURN |
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| 308 | |
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| 309 | END |
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| 310 | |
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| 311 | |
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| 312 | c====================================================================== |
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| 313 | |
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| 314 | subroutine KthMixNEW(Kthmix,T,x,rho) |
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| 315 | |
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| 316 | c Compute thermal conductivity of CO2/N2 mixture |
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| 317 | c (***WITHOUT*** USE OF VISCOSITY) |
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| 318 | |
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| 319 | c (Mason & Saxena, 1958 - Wassiljeva 1904) |
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| 320 | c====================================================================== |
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| 321 | |
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| 322 | implicit none |
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| 323 | |
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| 324 | include "microphys.h" |
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| 325 | c arguments |
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| 326 | c ----------- |
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| 327 | |
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| 328 | REAL T |
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| 329 | DOUBLE PRECISION x |
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| 330 | DOUBLE PRECISION rho !kg.m-3 |
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| 331 | |
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| 332 | c outputs |
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| 333 | c ----------- |
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| 334 | |
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| 335 | DOUBLE PRECISION Kthmix |
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| 336 | |
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| 337 | c local |
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| 338 | c ------------ |
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| 339 | |
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| 340 | DOUBLE PRECISION x1,x2 |
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| 341 | |
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| 342 | DOUBLE PRECISION Tc1, Tc2, Pc1, Pc2 |
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| 343 | |
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| 344 | DOUBLE PRECISION A12, A11, A22, A21 |
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| 345 | |
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| 346 | DOUBLE PRECISION Gamma1, Gamma2, M1, M2 |
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| 347 | DOUBLE PRECISION lambda_trans1, lambda_trans2,epsilon |
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| 348 | |
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| 349 | DOUBLE PRECISION kco2, kn2 |
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| 350 | |
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| 351 | x1 = x |
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| 352 | x2 = 1d0 - x |
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| 353 | |
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| 354 | M1 = mco2 |
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| 355 | M2 = mn2 |
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| 356 | |
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| 357 | Tc1 = 304.1282 !(Scalabrin et al. 2006) |
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| 358 | Tc2 = 126.192 ! (Lemmon & Jacobsen 2003) |
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| 359 | |
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| 360 | Pc1 = 73.773 ! (bars) |
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| 361 | Pc2 = 33.958 ! (bars) |
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| 362 | |
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| 363 | Gamma1 = 210.*(Tc1*M1**(3.)/Pc1**(4.))**(1./6.) |
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| 364 | Gamma2 = 210.*(Tc2*M2**(3.)/Pc2**(4.))**(1./6.) |
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| 365 | |
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| 366 | c Translational conductivities |
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| 367 | |
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| 368 | lambda_trans1 = ( exp(0.0464 * T/Tc1) - exp(-0.2412 * T/Tc1) ) |
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| 369 | & /Gamma1 |
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| 370 | |
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| 371 | lambda_trans2 = ( exp(0.0464 * T/Tc2) - exp(-0.2412 * T/Tc2) ) |
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| 372 | & /Gamma2 |
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| 373 | |
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| 374 | c Coefficient of Mason and Saxena |
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| 375 | epsilon = 1. |
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| 376 | |
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| 377 | A11 = 1. |
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| 378 | |
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| 379 | A22 = 1. |
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| 380 | |
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| 381 | A12 = epsilon * (1. + sqrt(lambda_trans1/lambda_trans2)* |
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| 382 | & (M1/M2)**(1./4.))**(2.) / sqrt(8*(1.+ M1/M2)) |
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| 383 | |
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| 384 | A21 = epsilon * (1. + sqrt(lambda_trans2/lambda_trans1)* |
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| 385 | & (M2/M1)**(1./4.))**(2.) / sqrt(8*(1.+ M2/M1)) |
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| 386 | |
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| 387 | c INDIVIDUAL COND. |
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| 388 | |
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| 389 | call KthCO2Scalab(kco2,T,rho) |
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| 390 | call KthN2LemJac(kn2,T,rho) |
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| 391 | |
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| 392 | c MIXTURE COND. |
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| 393 | Kthmix = kco2*x1 /(x1*A11 + x2*A12) + kn2*x2 /(x1*A21 + x2*A22) |
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| 394 | Kthmix = Kthmix*1e-3 ! from mW.m-1.K-1 to W.m-1.K-1 |
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| 395 | RETURN |
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| 396 | |
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| 397 | END |
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| 398 | |
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| 399 | c====================================================================== |
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| 400 | subroutine KthN2LemJac(kthn2,T,rho) |
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| 401 | c Compute thermal cond of N2 (Lemmon and Jacobsen, 2003) |
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| 402 | cWITH viscosity |
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| 403 | c====================================================================== |
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| 404 | |
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| 405 | implicit none |
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| 406 | |
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| 407 | include "microphys.h" |
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| 408 | c include "microphysCO2.h" |
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| 409 | |
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| 410 | |
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| 411 | c arguments |
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| 412 | c ----------- |
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| 413 | |
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| 414 | REAL T |
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| 415 | DOUBLE PRECISION rho !kg.m-3 |
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| 416 | |
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| 417 | c outputs |
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| 418 | c ----------- |
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| 419 | |
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| 420 | DOUBLE PRECISION kthn2 |
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| 421 | |
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| 422 | c local |
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| 423 | c ------------ |
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| 424 | |
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| 425 | DOUBLE PRECISION g1,g2,g3,g4,g5,g6,g7,g8,g9,g10 |
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| 426 | DOUBLE PRECISION h1,h2,h3,h4,h5,h6,h7,h8,h9,h10 |
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| 427 | DOUBLE PRECISION n1,n2,n3,n4,n5,n6,n7,n8,n9,n10 |
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| 428 | DOUBLE PRECISION d4,d5,d6,d7,d8,d9 |
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| 429 | DOUBLE PRECISION l4,l5,l6,l7,l8,l9 |
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| 430 | DOUBLE PRECISION t2,t3,t4,t5,t6,t7,t8,t9 |
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| 431 | DOUBLE PRECISION gamma4,gamma5,gamma6,gamma7,gamma8,gamma9 |
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| 432 | |
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| 433 | DOUBLE PRECISION Tc,rhoc |
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| 434 | |
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| 435 | DOUBLE PRECISION tau, delta |
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| 436 | |
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| 437 | DOUBLE PRECISION visco |
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| 438 | |
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| 439 | DOUBLE PRECISION k1, k2 |
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| 440 | |
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| 441 | N1 = 1.511d0 |
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| 442 | N2 = 2.117d0 |
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| 443 | N3 = -3.332d0 |
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| 444 | |
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| 445 | N4 = 8.862 |
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| 446 | N5 = 31.11 |
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| 447 | N6 = -73.13 |
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| 448 | N7 = 20.03 |
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| 449 | N8 = -0.7096 |
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| 450 | N9 = 0.2672 |
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| 451 | |
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| 452 | t2 = -1.0d0 |
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| 453 | t3 = -0.7d0 |
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| 454 | t4 = 0.0d0 |
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| 455 | t5 = 0.03 |
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| 456 | t6 = 0.2 |
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| 457 | t7 = 0.8 |
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| 458 | t8 = 0.6 |
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| 459 | t9 = 1.9 |
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| 460 | |
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| 461 | d4 = 1. |
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| 462 | d5 = 2. |
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| 463 | d6 = 3. |
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| 464 | d7 = 4. |
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| 465 | d8 = 8. |
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| 466 | d9 = 10. |
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| 467 | |
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| 468 | l4 = 0. |
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| 469 | gamma4 = 0. |
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| 470 | |
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| 471 | l5 = 0. |
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| 472 | gamma5 = 0. |
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| 473 | |
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| 474 | l6 = 1. |
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| 475 | gamma6 = 1. |
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| 476 | |
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| 477 | l7 = 2. |
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| 478 | gamma7 = 1. |
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| 479 | |
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| 480 | l8 = 2. |
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| 481 | gamma8 = 1. |
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| 482 | |
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| 483 | l9 = 2. |
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| 484 | gamma9 = 1. |
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| 485 | |
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| 486 | c---------------------------------------------------------------------- |
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| 487 | call viscoN2(T,visco) !! v given in microPa.s |
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| 488 | |
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| 489 | Tc = 126.192d0 |
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| 490 | rhoc = 11.1839 * 1000 * mn2 !!!from mol.dm-3 to kg.m-3 |
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| 491 | |
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| 492 | tau = Tc / T |
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| 493 | delta = rho/rhoc |
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| 494 | |
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| 495 | k1 = N1 * visco + N2 * tau**t2 + N3 * tau**t3 !!! mW m-1 K-1 |
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| 496 | c--------- residual thermal conductivity |
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| 497 | |
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| 498 | k2 = N4 * tau**t4 * delta**d4 * exp(-gamma4*delta**l4) |
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| 499 | & + N5 * tau**t5 * delta**d5 * exp(-gamma5*delta**l5) |
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| 500 | & + N6 * tau**t6 * delta**d6 * exp(-gamma6*delta**l6) |
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| 501 | & + N7 * tau**t7 * delta**d7 * exp(-gamma7*delta**l7) |
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| 502 | & + N8 * tau**t8 * delta**d8 * exp(-gamma8*delta**l8) |
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| 503 | & + N9 * tau**t9 * delta**d9 * exp(-gamma9*delta**l9) |
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| 504 | |
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| 505 | kthn2 = k1 + k2 |
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| 506 | |
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| 507 | RETURN |
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| 508 | |
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| 509 | END |
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| 510 | |
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| 511 | |
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| 512 | c====================================================================== |
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| 513 | |
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| 514 | subroutine viscoN2(T,visco) |
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| 515 | |
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| 516 | c Compute viscosity of N2 (Lemmon and Jacobsen, 2003) |
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| 517 | |
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| 518 | c====================================================================== |
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| 519 | |
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| 520 | implicit none |
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| 521 | |
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| 522 | include "microphys.h" |
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| 523 | c include "microphysCO2.h" |
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| 524 | c arguments |
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| 525 | c ----------- |
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| 526 | |
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| 527 | REAL T |
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| 528 | |
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| 529 | c outputs |
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| 530 | c ----------- |
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| 531 | |
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| 532 | DOUBLE PRECISION visco |
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| 533 | |
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| 534 | |
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| 535 | c local |
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| 536 | c ------------ |
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| 537 | |
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| 538 | DOUBLE PRECISION a0,a1,a2,a3,a4 |
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| 539 | DOUBLE PRECISION Tstar,factor,sigma,M2 |
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| 540 | DOUBLE PRECISION RGCS |
|---|
| 541 | |
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| 542 | |
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| 543 | c---------------------------------------------------------------------- |
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| 544 | |
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| 545 | |
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| 546 | factor = 98.94 ! (K) |
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| 547 | |
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| 548 | sigma = 0.3656 ! (nm) |
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| 549 | |
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| 550 | a0 = 0.431 |
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| 551 | a1 = -0.4623 |
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| 552 | a2 = 0.08406 |
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| 553 | a3 = 0.005341 |
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| 554 | a4 = -0.00331 |
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| 555 | |
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| 556 | M2 = mn2 * 1.00e3 !!! to g.mol-1 |
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| 557 | |
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| 558 | Tstar = T*1./factor |
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| 559 | |
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| 560 | RGCS = exp( a0 + a1 * log(Tstar) + a2 * (log(Tstar))**2. + |
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| 561 | & a3 * (log(Tstar))**3. + a4 * (log(Tstar))**4. ) |
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| 562 | |
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| 563 | |
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| 564 | visco = 0.0266958 * sqrt(M2*T) / ( sigma**2. * RGCS ) !!! microPa.s |
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| 565 | |
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| 566 | |
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| 567 | RETURN |
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| 568 | |
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| 569 | END |
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| 570 | |
|---|
| 571 | |
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| 572 | c====================================================================== |
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| 573 | |
|---|
| 574 | subroutine KthCO2Scalab(kthco2,T,rho) |
|---|
| 575 | |
|---|
| 576 | c Compute thermal cond of CO2 (Scalabrin et al. 2006) |
|---|
| 577 | |
|---|
| 578 | c====================================================================== |
|---|
| 579 | |
|---|
| 580 | implicit none |
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| 581 | |
|---|
| 582 | |
|---|
| 583 | |
|---|
| 584 | c arguments |
|---|
| 585 | c ----------- |
|---|
| 586 | |
|---|
| 587 | REAL T |
|---|
| 588 | DOUBLE PRECISION rho |
|---|
| 589 | |
|---|
| 590 | c outputs |
|---|
| 591 | c ----------- |
|---|
| 592 | |
|---|
| 593 | DOUBLE PRECISION kthco2 |
|---|
| 594 | |
|---|
| 595 | c LOCAL |
|---|
| 596 | c ----------- |
|---|
| 597 | |
|---|
| 598 | DOUBLE PRECISION Tc,Pc,rhoc, Lambdac |
|---|
| 599 | |
|---|
| 600 | DOUBLE PRECISION Tr, rhor, k1, k2 |
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| 601 | |
|---|
| 602 | DOUBLE PRECISION g1,g2,g3,g4,g5,g6,g7,g8,g9,g10 |
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| 603 | DOUBLE PRECISION h1,h2,h3,h4,h5,h6,h7,h8,h9,h10 |
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| 604 | DOUBLE PRECISION n1,n2,n3,n4,n5,n6,n7,n8,n9,n10 |
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| 605 | |
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| 606 | Tc = 304.1282 !(K) |
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| 607 | Pc = 7.3773e6 !(MPa) |
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| 608 | rhoc = 467.6 !(kg.m-3) |
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| 609 | Lambdac = 4.81384 !(mW.m-1K-1) |
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| 610 | |
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| 611 | g1 = 0. |
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| 612 | g2 = 0. |
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| 613 | g3 = 1.5 |
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| 614 | g4 = 0.0 |
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| 615 | g5 = 1.0 |
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| 616 | g6 = 1.5 |
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| 617 | g7 = 1.5 |
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| 618 | g8 = 1.5 |
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| 619 | g9 = 3.5 |
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| 620 | g10 = 5.5 |
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| 621 | |
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| 622 | h1 = 1. |
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| 623 | h2 = 5. |
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| 624 | h3 = 1. |
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| 625 | h4 = 1. |
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| 626 | h5 = 2. |
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| 627 | h6 = 0. |
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| 628 | h7 = 5.0 |
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| 629 | h8 = 9.0 |
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| 630 | h9 = 0. |
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| 631 | h10 = 0. |
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| 632 | |
|---|
| 633 | n1 = 7.69857587 |
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| 634 | n2 = 0.159885811 |
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| 635 | n3 = 1.56918621 |
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| 636 | n4 = -6.73400790 |
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| 637 | n5 = 16.3890156 |
|---|
| 638 | n6 = 3.69415242 |
|---|
| 639 | n7 = 22.3205514 |
|---|
| 640 | n8 = 66.1420950 |
|---|
| 641 | n9 = -0.171779133 |
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| 642 | n10 = 0.00433043347 |
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| 643 | |
|---|
| 644 | Tr = T/Tc |
|---|
| 645 | rhor = rho/rhoc |
|---|
| 646 | |
|---|
| 647 | k1 = n1*Tr**(g1)*rhor**(h1) + n2*Tr**(g2)*rhor**(h2) |
|---|
| 648 | & + n3*Tr**(g3)*rhor**(h3) |
|---|
| 649 | |
|---|
| 650 | k2 = n4*Tr**(g4)*rhor**(h4) + n5*Tr**(g5)*rhor**(h5) |
|---|
| 651 | & + n6*Tr**(g6)*rhor**(h6) + n7*Tr**(g7)*rhor**(h7) |
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| 652 | & + n8*Tr**(g8)*rhor**(h8) + n9*Tr**(g9)*rhor**(h9) |
|---|
| 653 | & + n10*Tr**(g10)*rhor**(h10) |
|---|
| 654 | |
|---|
| 655 | k2 = exp(-5.*rhor**(2.)) * k2 |
|---|
| 656 | |
|---|
| 657 | kthco2 = (k1 + k2) * Lambdac ! mW |
|---|
| 658 | |
|---|
| 659 | RETURN |
|---|
| 660 | |
|---|
| 661 | END |
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