﻿ Function flash_calculation.m

## MRST - MATLAB Reservoir Simulation Toolbox

Function flash_calculation.m

## Flash calculation

Given the total concentration of each component C and the pressure p, compute

• the concentrations in the gas phase, cg,
• the concentrations in the liquid phase, cl,
• the liquid saturation, s,
• the total water concentration, Cw and
• the water concentration in the liquid, cw.

In the case we are considering, the flash equation when both phases are present can be reduced to a scalar equation, see Bravo tutorial note.

```function [cg, cl, cw, s, Cw] = flash_calculation(C, p, system, init_sL)
```
```   [nComp, k, R, Temp, vp] = deal(system.nComp, system.k, system.R, system.Temp, system.vp);

tol = 1e-14;

omega_g = R*Temp*ones(nComp, 1);
min_pressure = sum(bsxfun(@times, omega_g', C), 2) + vp;
```

There is a minimum pressure, min_pressure, under which no liquid phase exists. The cells where this is the case are indexed with ind_g_unsat.

```   ind_g_unsat = p < min_pressure;
```

There is a maximum pressure above which the liquid phase is unsaturated and no gas phase is present. The cells where this is the case are indexed with ind_l_unsat.

```   ind_l_unsat = sum(bsxfun(@times, C, k') + vp, 2) <= p;

nc = size(p, 1);
```

If no initial guess for the liquid saturation is given, we start with sL=0.5.

```   if nargin < 4
init_sL = 0.5*ones(nc, 1);
end

s = zeros(nc, 2);
cg = zeros(nc, nComp);
cl = zeros(nc, nComp);
cw = zeros(nc, 2);
Cw = zeros(nc, 1);
```

We set the concentrations in the cells where the gas phase is unsaturated. The concentrations in the liquid phase are set to NaN.

```   if any(ind_g_unsat)
s(ind_g_unsat, 1)  = 1;
s(ind_g_unsat, 2)  = 0;
cg(ind_g_unsat, :) = C(ind_g_unsat, :);
cl(ind_g_unsat, :) = NaN(nnz(ind_g_unsat), 3);
Cw(ind_g_unsat)    = zeros(nnz(ind_g_unsat), 1);
cw(ind_g_unsat, :) = zeros(nnz(ind_g_unsat), 2);
end
```

We set the concentrations in the cells where the liquid phase is unsaturated. The concentrations in the gas phase are set to NaN. We use computeWaterComp.m to compute the water concentrations.

```   if any(ind_l_unsat)
s(ind_l_unsat, 1)  = 0;
s(ind_l_unsat, 2)  = 1;
cg(ind_l_unsat, :) = NaN(nnz(ind_l_unsat), 3);
cl(ind_l_unsat, :) = C(ind_l_unsat, :);
[Cw(ind_l_unsat), cwg, cwl] = computeWaterComp(p(ind_l_unsat), C(ind_l_unsat, :), cl(ind_l_unsat, ...
:), s(ind_l_unsat, 2), system);
cw(ind_l_unsat, 1) = cwg;
cw(ind_l_unsat, 2) = cwl;
end
```

We compute the liquid saturation by the solving the scalar saturation equation using Newton iterations. Then the functions computeComposition.m and computeWaterComp.m are used to compute the concentrations in the gas and liquid phases.

```   ind_sat = ~ind_l_unsat & ~ind_g_unsat;
if any(ind_sat)
converged = false;
seq = @(sL)(sat_eq(C(ind_sat, :), p(ind_sat), vp, sL, k, Temp, R, nComp));
ssat = init_sL(ind_sat);
while ~converged
eqs = seq(ssat);
dssat = -eqs.val./diag(eqs.jac{1});
ssat = ssat.val + dssat;
ssat = min(max(ssat, 0), 1);
plot(ssat)
converged = all(abs(eqs.val) <= tol) | all(abs(dssat) < 1e-14);
end
s(ind_sat, 1) = 1 - ssat;
s(ind_sat, 2) = ssat;
[cg_sat, cl_sat] = computeComposition(C(ind_sat, :), p(ind_sat), ssat, system);
[Cwsat, cwgsat, cwlsat] = computeWaterComp(p(ind_sat), C(ind_sat, :), cl_sat, ssat, system);
Cw(ind_sat) = Cwsat;
cw(ind_sat, 1) = cwgsat;
cw(ind_sat, 2) = cwlsat;
cg(ind_sat, :) = cg_sat;
cl(ind_sat, :) = cl_sat;
end
```
```end
```

This is the scalar equation for the liquid saturation when both phases are present, see Bravo tutorial note

```function y = sat_eq(C, p, vp, s, k, Temp, R, nComp)
y= -(p/vp - 1);
for ic = 1:nComp
y = y + 1/vp*(R*Temp*C(:,ic)./(1 + (R*Temp/k(ic) - 1).*s));
end
end
```

Published October 10, 2014