The mixing zone

The feed mixing zone is a single vapour volume in which the three pure feeds, the compressor recycle and the stripper overhead combine before entering the reactor. It is the simplest of the four vessels: one phase, a fixed volume, no reaction, no heat duty.

Source: teprob.f:428 and 434 for its states, teprob.f:465-466 for its temperature, teprob.f:492 for its pressure, teprob.f:576-579 for its outlet flow, and teprob.f:783-788 for its energy balance.

Equations

All eight components are vapour and the volume is fixed at VTV, so the equilibrium block needs only the ideal gas law applied to the mixture (teprob.f:492):

\[ P_v = \frac{N_v R T_K}{V_{tv}} \]

The temperature comes from the specific internal energy, not from a state directly. The block totals the holdups, forms the mole fractions and the energy per mole, and then solves for whatever temperature makes the mixture's specific internal energy equal to it (teprob.f:465-466):

\[ N = \sum_i n_i, \qquad x_i = \frac{n_i}{N}, \qquad e = \frac{E}{N} \]

That solve is Newton's method in TESUB2 (teprob.f:1415-1442), warm-started from the previous evaluation's answer, which is why TCV is state rather than a derived quantity. See The plant.

Flow out of the mixing zone is not valve-driven. It is a square-root resistance across the pressure difference to the reactor, converted from mass to moles by the stream's mean molecular weight (teprob.f:576-579):

\[ F_6 = \frac{1937.6 \, \sqrt{\max(P_v - P_r,\, 0)}}{\overline{M}_6} \]

The clamp at zero is what stops a reversed pressure gradient from producing a NaN out of the square root, and it is reachable from an adversarial state though not from the nominal trajectory.

The component and energy balances have five inlets and one outlet (teprob.f:762-770 and 783-788):

\[ \frac{dn_i}{dt} = \dot n_{i,1} + \dot n_{i,2} + \dot n_{i,3}

• \dot n_{i,5} + \dot n_{i,9} - \dot n_{i,6} \]

\[ \frac{dE}{dt} = h_1 F_1 + h_2 F_2 + h_3 F_3 + h_5 F_5 + h_9 F_9 - h_6 F_6 \]

There is no Q term: the mixing zone is adiabatic.

Variables

Three things the source settles

The mixed A/C feed does not pass through here. Stream 4 goes directly to the stripper, and it appears in the stripper's energy balance at teprob.f:778-782 and in the stripper's feed at teprob.f:614-662, never in the mixing zone's. The three feeds that do enter are streams 1, 2 and 3, the D, E and A feeds.

Stream 7 is an alias of stream 6, made in the stripper block. teprob.f:656-661 copies flow, enthalpy, temperature, composition and component flows from 6 to 7 wholesale. There is no mixing, no pressure drop and no heat loss between them; stream 7 exists so that the reactor's balance at teprob.f:763-772 can name its own inlet.

The pressure published as stripper pressure is this vessel's. teprob.f:694 reports PTV as XMEAS(16), which Downs and Vogel's measurement table names stripper pressure. The model carries no separate stripper vapour space: the stripper's overhead discharges into the mixing zone as stream 5, and PTV is the pressure of that shared vapour node. The mixing zone's own outlet flow is reported as XMEAS(6), the reactor feed rate (teprob.f:684).