Theory

Reverse vapor flow would occur (for most tray designs) if the pressure gradient reverses and the liquid level on a tray fall below the downcomer clearance height. In this case, there would be no downcomerbackup, and the vapor from the tray above would freely flow through the downcomer to equalize the pressures. However, when the liquid level on the tray is above the bottom of the downcomer, reverse vapor flow can still occur when the reverse pressure pushes the downcomer backup below the bottom edge. This would occur when (P1 - P2) >= (level - x)*rho*g.

Coulson and Richardson, Volume 6 (1991), page 469 state that the bottom of the downcomer apron is usually 5 to 10mm below the weir height. In the simple tray model we have assumed x = 0.

The vapor flow/pressure equation for trays and packing was previously:

P_diff = vapin.P – P

Vapin.P is the pressure in the stage below. P_diff is therefore the pressure drop across the tray/packing section.

For trays, the orifice equation calculates the vapor flow through the holes in the tray. The pressure drop across the holes, P_diffv, is:

P_diffv = P_diff - Rhoml*g*Level

(because the downstream pressure is not P, but P+ Rhoml*g*Level because of the liquid head on the tray.)

For packing, P_diffv = P_diff.

Therefore the vapor flow equation is:

P_diffv *Rhovin = Fv_inp*(Fv_inp + eps)*C0 .................(1)

Where:

Rhovin (kmol/m3) is the vapor density from the tray below

Fv_inp (kmol/hr) is the vapor molar flow rate

C0 is the orifice coefficient for flow through the holes in the tray (this is back-calculated from Aspen HYSYS calculated vapor flow and pressure profile).

For reverse flow, the vapor flow equation must use the vapor density from the tray above and the pressure

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gradient reverses. We have implemented reverse vapor flow for simple trays/packing as follows:

dp_rho = max(0,P_diffv)*Rhovin/C0 + min(0,P_diff + C1*Rhoml*g*Level)*Rhov/(C0*Rev_cof); ……............. (2)

dp_rho/(abs(vapin.f)+eps) = vapin.f ; .................................(3)

dp_rho is an intermediate term which is then used in the flow equation below. The equation is written in this way so that it continuously handles forward and reverse flow with run-time conditionals (that can lead to robustness issues).

The max term in the dp_rho equation handles the normal case of vapor flowing up. When P_diffv is negative, this term is zero. Likewise, when the vapor is flowing up, the second min term is zero because (P_diff + C1*Rhoml*g*Level) is positive. Vapor will only reverse when (P_diff + C1*Rhoml*g*Level) is negative.

For packing, C1 is set to zero, so vapor reverses when P_diff is negative.For trays, C1=1 and the flow equation becomes:

(P_diff + C1*Rhoml*g*Level)*Rhov = Fv_inp*(Fv_inp + eps)*C0 ..........(4)

As you can see, this looks almost identical to equation (1) except it uses Rhov instead of Rhovin.

Rev_cof is a multiplier to take into account the different flow coefficient, C0, for reverse flow. Rev_cof would be = 1 for packing, but for trays it would have to take into account the flow under the downcomer and could be calculated based upon the area. For now it is a fixed variable allowing users to manipulate it.

There is one simplification we have made in the model - the Level in equation (4) should be the level of the tray below. This is difficult to obtain so we are approximating by using the level on the tray instead.

Overview- Reverse Vapor Flow in ColumnsUsing Reverse Vapor Flow in Columns

See Also

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