P as follows: 1 vap liq liq HUj = vap Vj – HUj m (12) m two.two. downcomer To decide the dynamic behavior on the liquid flow through the downcomer and towards the next segment, the downcomer backup desires to become predicted. Thus, the downcomerChemEngineering 2021, five,6 ofis modelled separately. The following equations represent the composition and energy balances also because the molar fraction summation inside the downcomer: d HUj d HUjdc,liq dc xi,jdtdc,liq dc,liq hj= Ldc 1 xi,j-1 + Ltodc xi,j – L j j- j = Ldc 1 h j-1 + Ltodc h j – L j j- jNC dc xi,j = 1 liq liqtostage dc xi,jdc Lside xi,j j(13)dttostage dc,liq hjLside h j jdc,liq(14) (15)i =The vapor volumes with the tray and downcomer are combined and thus, vapor holdup within the downcomer is neglected. The liquid hold-up is calculated as a Cyanine5 NHS ester medchemexpress function with the downcomer geometry plus the incoming and outgoing flows. In the equations on the downcomer, the molar side streams Lside to and in the adjacent segment are regarded. j 2.three. Connection in between Downcomer and Stage To account for downcomer dynamics, the model requirements to include things like equations to connect the equilibrium stage as well as the downcomer. Commonly, the liquid backup within the downcomer is calculated straight from a steady-state momentum balance Equation (16) [40]. hcl,jdc,steadystate dc,steadystate= ht + hw + how + hda(16)where hcl,j , ht , hw , how and hda would be the steady-state clear liquid height, the total stress drop, the weir height, the height of crest more than weir and the head loss as a consequence of liquid flow below the downcomer apron. Nonetheless, this Carbendazim Fungal approach is not always correct for the duration of start-up. As gas flows by way of the holes in the trays, the solution from the equation predicts a rise inside the backup on the downcomer. Nevertheless, the liquid does not rise inside the downcomer when there is a pressure drop around the stage. Rather, it rises as quickly as there is a significant backflow, and the downcomer apron is sealed. We assume a flow from and to the downcomer that is certainly depending on Torricelli’s law plus the derived discharge equation of a submerged rectangular orifice. The method considers the discharge of liquid in the downcomer for the stage, as well as the resistance against the discharge induced by the two-phase flow on the stage as follows: Ljtostage= res,jtostageAda m,jdc,liq2g hdc – hcl,j cl,j(17)exactly where hdc and hcl,j would be the actual clear liquid heights inside the downcomer and around the stage. cl,j The flow from the stage for the downcomer is calculated similarly as follows: Ltodc = todc Ada m,j j res,jliq2g hcl,j – hdc cl,j(18)exactly where Ada describes the region beneath the downcomer apron. The resistance coefficient for the flow towards the downcomer todc only accounts for the friction under the apron res tostage and is, consequently, set to 0.6. The resistance coefficient for the flow for the stage res is calculated considering the steady-state momentum balance. By rearranging Equation (17) tostage and employing the stationary values from Equation (16), the resistance coefficient res is obtained as follows: res,jtostage=dc,liq Ada m,jLjtostage,steadystate(19)dc,steadystate hcl,j2g- hcl,jIt is assumed that the liquid height around the stage and in the downcomer is almost equal till the liquid reaches the height of the weir as well as a significant backflow happens fromtained as follows:tostage ,=dc,liq ,tostage,steadystate dc,steadystate ,-(19),ChemEngineering 2021, five,7 ofIt is assumed that the liquid height on the stage and inside the downcomer is nearly equal until the liquid reaches the h.
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