Element Distribution

The Element Distribution unit operation splits the elements in its inlet stream(s) across multiple outlet streams, then constrains how each outlet's available elements are allocated to the outlet's molecules. It is useful for modeling high-temperature processes where standard vapor–liquid equilibrium does not apply — for example, carbothermic silicon production, where carbon, oxygen, and silicon redistribute among gas and liquid outlets.

How it works

The calculation has two layers:

1. Outlet allocation — for each element (e.g. C, O, Si), you specify what fraction of the total inlet flow goes to each outlet.
2. Molecule constraints — within each outlet, you specify how the available elements are consumed by molecules (e.g. CO, SiO, Si). Molecules are grouped by their basis element: the element whose flow determines how much of that molecule forms.

After both layers resolve, residuals show how much of each element remains unconsumed in each outlet, and the grid also shows a total residual row that summarizes the overall element balance. A well-specified distribution has zero residuals.

Distribution modes

Each cell in the outlet allocation grid and each molecule fraction cell has a mode that controls how its value is determined.

Fixed

The user enters an explicit percentage (0–100%). Fixed values are taken as-is and contribute directly to the balance. All fixed values in a row must sum to at most 100%.

Remainder

The cell's value is inferred as whatever is left over after all fixed (and float) values in the same row are accounted for:

$\text{Remainder} = 100\% - \sum \text{Fixed}$

At most one cell per row can be set to Remainder. Remainder is available for both outlet allocation rows and molecule fraction rows.

Float

Float is available for outlet allocation rows only. Instead of specifying a percentage directly, Float means: pull exactly as much of this element as the outlet's molecules demand.

For example, if outlet 1 contains the molecule CO on oxygen basis at 100%, and 200 mol of O is routed to outlet 1, then Float on C for outlet 1 will pull exactly 200 mol of C — one carbon atom per CO molecule.

Float is useful when you know the molecule stoichiometry but don't want to manually calculate the element split. The percentage is derived automatically and displayed as a read-only value in the grid.

Rules:

• Multiple Float cells are allowed in the same element row (unlike Remainder, which is limited to one).
• Float demand must not exceed the available inlet flow for that element.
• A Float cell cannot depend on another Float element's outlet flow (no circular dependencies). If element C is Float and its molecules need the outlet flow of element O, then O must be Fixed or Remainder — not Float.

Example: carbothermic silicon production

Consider a process with inlet elements C, O, and Si, and two outlets:

Outlet 1 molecules (basis element in parentheses):

Outlet 2 molecules:

In this setup:

• All oxygen goes to the gas outlet, where 92.5% feeds CO and 7.5% feeds SiO.
• Silicon splits 15/85 between gas and liquid. The gas portion goes into SiO; the liquid portion becomes elemental Si.
• Carbon is Float on outlet 1: it pulls exactly as much C as CO demands (one C per CO molecule, scaled by the oxygen flow). The leftover C goes to outlet 2 as Remainder.

Heat and direct work input

Direct work input is power supplied directly to the unit, such as electricity entering an arc furnace. It is available in every heat mode and defaults to zero. Positive values supply work; negative values export work.

Heat and work contribute separately to the energy balance:

$\dot{H}_{\mathrm{out}} - \dot{H}_{\mathrm{in}} = \dot{Q} + \dot{W}$

Here, $\dot{H}$ is the enthalpy carried by the material streams per unit time, $\dot{Q}$ is heat input, and $\dot{W}$ is direct work input. Positive heat enters the unit; negative heat represents heat loss.

• In Heat Ingress mode, the model uses heat plus direct work to solve the common outlet temperature.
• In N-1 outlet temperatures mode, it uses heat plus direct work to solve the one unspecified outlet temperature. Omitted heat ingress means zero heat, even when electrical work is supplied.
• In Isothermal and All outlet temperatures modes, the outlet temperatures are specified. The model calculates the required heat input as the material enthalpy increase minus direct work input.

For example, to model an arc furnace receiving 100 MW of electricity and losing 10 MW of heat, select Heat Ingress, set Direct work input to 100 MW, and set Heat Ingress to −10 MW. The outlet streams carry 90 MW more enthalpy than the inlet streams.

Using with Adjust

When an Adjust operation is used with Element Distribution, leave the value you want Adjust to drive as a calculated, not fixed, result.

For example, if Adjust varies a carbon inlet flow to make a pure carbon outlet go to zero, keep that carbon outlet as Remainder and target the calculated outlet flow. Do not set the carbon outlet to Fixed 0% at the same time.

The reason is that Fixed 0% forbids any flow from going to that outlet. If the current Adjust trial value leaves even a small amount of carbon unused, the element balance has nowhere to put it, so the specification becomes invalid before Adjust can continue iterating. Remainder gives the leftover flow a legal place to go, and Adjust can then drive that calculated leftover to zero.

Inputs

• Fluid package: Fluid package supplying compositions for the inlet stream.
• Heat Mode: Choose how outlet thermal conditions are specified. Isothermal uses one temperature for every outlet. All outlet temperatures specifies one temperature per outlet. N-1 outlet temperatures lets you leave one outlet temperature blank so it is solved by enthalpy balance, with optional heat ingress. Heat Ingress specifies heat input instead of direct outlet temperatures. Both energy-driven modes include direct work in the balance.
• Direct work input: Signed power crossing the unit boundary, with a power-unit selector. Defaults to zero. For an electric furnace, enter its electrical power here.
• Outlet Pressure: Common pressure used for all outlet streams.
• Elements: The elements to distribute (e.g. C, O, Si). Populated from positive inlet element flow when available.
• Outlet molecule table: Per-outlet list of molecules, each with a formula, basis element, mode, and fraction.

Outputs

• Total Work input: The specified direct work input.

• Total Heat input: The specified heat ingress in energy-driven modes, or the calculated remaining heat duty when outlet temperatures are specified.

• Multiple outlet streams whose elemental make-up follows the specified distribution.

• A total residual row showing the overall element balance across all outlets.

• Per-outlet residuals showing unconsumed element amounts (should be zero for a balanced specification).