2.3 Batch vs Continuous and Steady vs Unsteady Operation

Before writing a material or energy balance, you must decide what kind of process you are analyzing. The same chemistry can run in a batch autoclave, a semi-batch polymerizer, or a continuous reactor–separator train. On the UPDA/MMUP Chemical exam, mode selection determines whether you work with amounts, molar rates, or differential accumulation terms—and whether “steady state” is a valid shortcut.

Batch, semi-batch, and continuous

Batch process: Charge raw materials, close the vessel (or operate as a closed system for mass), run the process for a batch time $t_b$, then discharge product. No continuous feed or product flow during the main reaction period (except possibly vents). Production rate equals batch size divided by total cycle time (reaction + charge + discharge + clean).

Continuous process: Feed and product streams flow while the unit operates. After start-up, many continuous units approach a steady state where inventories and outlet compositions stop changing with time. Refineries, gas plants, and large utility systems in Qatar are predominantly continuous.

Semi-batch (fed-batch): One or more streams are added or removed during the batch. Example: slow addition of a reactant to control exotherm, or continuous gas feed to a liquid batch reactor with no liquid outflow until the end. Inventory of at least one component changes throughout the run by design.

Steady state vs unsteady state

The general conservation statement for any quantity (mass, moles of species $i$, energy) is: $\text{In} - \text{Out} + \text{Generation} - \text{Consumption} = \text{Accumulation}.$

Steady state means accumulation = 0. Properties inside the system and outlet flows do not change with time. For total mass with no reaction mass defect (ordinary chemical processes): $\sum \dot{m}_{\mathrm{in}} = \sum \dot{m}_{\mathrm{out}}.$ For species $i$ with reaction, generation/consumption terms remain even at steady state; only the $d n_i / dt$ inventory term drops.

Unsteady (transient) state means accumulation ≠ 0. Classic exam situations:

• Filling or draining a tank
• Start-up of a continuous stirred tank reactor (CSTR) from empty or from a different composition
• Shut-down and purge of a process unit
• Grade transition when product specification changes
• Batch reaction progress (composition changes until the batch ends)

How mode changes the balance equations (preview)

You will formalize these equations in Chapters 3–4; here is the structural preview.

1. Continuous, steady, no reaction (mixer, splitter, heat exchanger on mass basis) $\dot{m}_{\mathrm{in}} = \dot{m}_{\mathrm{out}}, \qquad \dot{n}_{i,\mathrm{in}} = \dot{n}_{i,\mathrm{out}}.$ Algebraic equations only—no time derivatives.

2. Continuous, steady, with reaction $\dot{n}_{i,\mathrm{in}} - \dot{n}_{i,\mathrm{out}} + \nu_i \dot{\xi} = 0,$ where $\nu_i$ is the stoichiometric coefficient (negative for reactants) and $\dot{\xi}$ is the molar extent rate. Extent links all species so you do not invent independent “reaction rates” for each component inconsistently.

3. Batch reactor (constant volume liquid, well mixed) $\frac{d n_i}{dt} = \nu_i V r,$ where $r$ is reaction rate. Integrated over batch time with conversion definitions from Section 2.2.

4. Tank filling (unsteady, no reaction) $\frac{d m}{dt} = \dot{m}_{\mathrm{in}} - \dot{m}_{\mathrm{out}}.$ If outlet is closed, $m(t) = m_0 + \dot{m}_{\mathrm{in}} t$ (constant feed rate).

Recognizing which of these four structures applies is half the exam problem; writing the algebra is the other half.

Plant examples tied to Qatar-style process thinking

Batch reactor (specialty chemicals, catalysts, some polymer grades): A 10 m³ jacketed reactor is charged with 6000 kg monomer and initiator, heated, held for 4 h, then dumped to a product tank. Material balance is per batch. Annual capacity ≈ (kg product per batch) × (batches per year). Energy balance must include the dynamic heat-up—not a steady $Q$ load alone.

Continuous distillation (NGL fractionation, refining): Feed, distillate, and bottoms flow continuously. At steady state, $F = D + B$ (mass) and component balances close without accumulation. Unsteady behavior appears during feed composition swings or start-up when tray holdups change—operators watch level and composition controllers until inventories stabilize.

Tank filling (feed storage, intermediate surge): A methanol day tank starts at 2 m liquid height. Transfer pump feeds 15 m³/h while a process draw of 5 m³/h runs. Net fill rate 10 m³/h; time to reach a high-level trip depends on cross-sectional area and trip height. This is a pure accumulation problem—no reaction required.

Semi-batch gas–liquid reactor: Air or oxygen is sparged into a liquid batch for oxidation while liquid product is not withdrawn until the end. Oxygen may be limiting in the gas phase even though liquid inventory dominates the mass of the vessel; balances must track both phases and accumulation of dissolved/reacted oxygen products.

Decision tree for UPDA-style stems

1. Does the problem mention continuous flows (kg/h, kmol/h) with no time variation? → Continuous steady balances.
2. Does it give a cycle time, charge recipe, or “per batch”? → Batch amounts; productivity = batch result / cycle time.
3. Does level, inventory, or concentration change with time? → Keep accumulation; may need integration or $m(t)$ formulas.
4. Is a reactant added slowly while product stays in the vessel? → Semi-batch; do not force a steady-state equal-in-out assumption on the liquid.
5. Start-up/shut-down language? → Unsteady; steady-state shortcuts fail.

Worked example 1 — Batch productivity

A batch crystallizer produces 800 kg of product per batch. Charge, reaction/crystallization, and clean-out total 5 h per cycle. The plant runs 7200 h/year. What is the annual production capacity?

Solution. Batches per year = $7200 / 5 = 1440$. Annual product = $1440 \times 800 = 1{,}152{,}000,\mathrm{kg/year}$ (1152 t/y). If someone divides 800 kg by 5 h and multiplies by 7200 incorrectly as if continuous 160 kg/h without recognizing the same arithmetic, they get the same number—but for continuous plants the “batch size” concept does not apply. The conceptual difference matters when availability, turnaround, or parallel batch trains appear in word problems.

Worked example 2 — Continuous steady mixer

Two continuous streams mix at steady state: Stream 1 is 2000 kg/h pure water; Stream 2 is 500 kg/h of 20 wt% NaOH. Find product mass flow and NaOH mass fraction.

Solution. No accumulation, no reaction: $\dot{m}_P = 2000 + 500 = 2500\,\mathrm{kg/h}.$ NaOH mass in = $0.20 \times 500 = 100,\mathrm{kg/h}$ → $w_{\mathrm{NaOH}} = 100/2500 = 0.04$ (4 wt%). This is the default continuous steady structure from Chapter 3.

Worked example 3 — Unsteady tank fill

A cylindrical tank (cross-sectional area 4 m²) contains 6 m³ of liquid. Inlet flow is 0.02 m³/s; outlet is closed. How long until the volume reaches 12 m³?

Solution. $\frac{dV}{dt} = 0.02,\mathrm{m}^3/\mathrm{s}$ → $\Delta V = 6,\mathrm{m}^3$ needs $t = 6 / 0.02 = 300,\mathrm{s}$ (5 min). Height rises from $h = V/A = 6/4 = 1.5,\mathrm{m}$ to $12/4 = 3.0,\mathrm{m}$. Steady-state thinking (“in = out”) would wrongly predict no change because it ignores the closed outlet.

Worked example 4 — Spotting the wrong assumption

A CSTR is being started with pure solvent inside; reactant feed starts at $t = 0$. Can you use the steady-state design equation $V = F_{A0} X_A / (-r_A)$ immediately at $t = 0^+$?

Solution. No. That algebraic design equation assumes steady state (no accumulation of A). During start-up, $dC_A/dt \neq 0$ until the outlet composition settles. Using the steady formula at early times underpredicts or misrepresents holdup requirements. After long operation at constant feeds, the steady equation becomes valid.

Link forward

Section 2.1 gave you units, compositions, and bases. Section 2.2 added stoichiometry and conversion. This section tells you which balance skeleton to load before you solve. Chapter 3 develops steady material balances without and with reaction, then recycle, bypass, and purge—almost always under continuous steady assumptions unless the stem says otherwise. Chapter 4 adds energy. Reaction engineering later revisits batch vs CSTR vs PFR as reactor types, which is a kinetics/design specialization of the same mode ideas.

For UPDA success: circle the process mode in every word problem before writing equations. That five-second habit prevents applying continuous steady templates to tank-filling or batch-charge questions.