bubble point pressre and temperature

[branch171]

when using GERG2008 at 250 K for a 0.95,0.05 mixture of CO2 and N2 the bubble point calculation fails, returns nans.

The reason appears to be a function called bubbledew_check.

The bubble point convergence above this call is converge to 1e-11 error. However, bubbledew_check returns false and the result is ignored.

commenting out and making the converged to true always. Allows the correct bubble point line to be generated all the way the the critical point.

**There is some wrong in bubbledew_check it is returning false for what appears to be converge solutions.

function bubble_pressure(model::EoSModel, T, x, method::ThermodynamicMethod)
    x = x/sum(x)
    T = float(T)
    model_r,idx_r = index_reduction(model,x)
    if length(model_r)==1
        (P_sat,v_l,v_v) = saturation_pressure(model_r,T)
        return (P_sat,v_l,v_v,x)
    end
    x_r = x[idx_r]
    if has_a_res(model)
        bubble_pressure_result_primal = bubble_pressure_impl(primalval(model_r),primalval(T),primalval(x_r),index_reduction(method,idx_r))
        bubble_pressure_result = bubble_pressure_ad(model_r,T,x_r,bubble_pressure_result_primal)
    else
        bubble_pressure_result = bubble_pressure_impl(model_r,T,x_r,index_reduction(method,idx_r))
    end
    (P_sat, v_l, v_v, y_r) = bubble_pressure_result
    y = index_expansion(y_r,idx_r)
#    converged = bubbledew_check(model,P_sat,T,v_v,v_l,y,x)
    converged = true
    if converged
        return (P_sat, v_l, v_v, y)
    else
        nan = zero(v_l)/zero(v_l)
        y = y*nan
        return (nan,nan,nan,y)
    end
end

[longemen3000]

the problem is one level deeper:

julia> volume(model,4.739379837118585e6,T,z,phase = :v)
9.377608555918565e-5

that is a false root.

[branch171]

Are OK, thanks I specifically wrote the volume solver in HELD to over come this issue with GERG2008. The multiple maxwell loops periodically caused the current Clapeyrom volume solver to find them. This is fatal for HELD as you need to start off feasible in your solution. My volume solver is robust but maybe slow as a results, it systematically brackets all volume roots and rejects those that are false. This takes a bit of bookkeeping but so far its worked well. I will test this bubble point with HELD and confirm the roots is correctly found.