Calculadora de volumen de reactor de lixiviación por tiempo de residencia

Qué responde: convierte el caudal de pulpa y el tiempo de residencia requerido en volumen de trabajo, y de ahí en el volumen geométrico del reactor, el volumen por tanque para la cantidad de tanques en serie que se elija, el diámetro y la altura de cada uno y el tiempo de residencia real por tanque. Es el cálculo que traduce una cinética medida en laboratorio a un número de tanques y a un tamaño de agitador.

Leaching Equipment

Residence time is the parameter most often traded away to raise throughput, and it is usually the wrong thing to trade. This calculator works the sizing in the practical direction: give it the slurry flow and the residence time your leach kinetics need, and it returns the total working volume, the volume per tank for the number of tanks you choose, and the physical dimensions for a stated height-to-diameter ratio.

Inputs

Volumetric slurry flow through the leach circuit.
Time the slurry must stay in contact with the lixiviant to reach your target extraction. Establish it from batch leach kinetics rather than from a rule of thumb — it varies enormously with particle size and temperature.
Fraction of the vessel's geometric volume occupied by slurry at operating level. A freeboard is needed for aeration, foam and surge.
Splitting the volume across several tanks in series narrows the residence time distribution towards plug flow, which raises recovery for a given total volume.
Vessel aspect ratio. Taller vessels use less floor area but need more agitator shaft length and more air for a given power input.
How to use it

Runs entirely in your browser — nothing you enter is sent anywhere. Defaults are typical lab/pilot values so you can see the arithmetic move; replace them with your own numbers before you rely on the result.

Results

Total working volume—m³
Total geometric volume—m³
Working volume per tank—m³
Tank diameter—m
Tank height—m
Actual residence time per tank—min

The results appear here and update as you type. Each result is followed by the conditions under which it holds.

    Read the assumptions before you use a number. A sizing figure without its conditions is not a result — it is a guess with a decimal point. The assumptions listed below are part of this calculator's output, not small print.

    How to use it

    1. Establish the kinetics, not the rule of thumb

      Run a batch leach at your intended temperature, pulp density and lixiviant concentration, and plot extraction against time. The residence time you need is the point where the curve flattens towards your target — anything beyond it is reactor volume you have paid for but do not use.

    2. Convert flow and time into working volume

      Working volume is slurry flow multiplied by residence time. This is the volume the slurry must actually occupy, and it is independent of how you divide it among vessels.

    3. Add freeboard to get geometric volume

      Vessels need freeboard for aeration, foam, and surge during flow changes. Working fraction is the share of the vessel that is slurry at normal operating level.

    4. Choose the number of tanks in series

      The same total volume split across several tanks in series behaves closer to plug flow, so recovery rises without spending more volume. It also costs more vessels, more agitators and more interconnecting pipework.

    5. Fix the aspect ratio and read off dimensions

      Height-to-diameter ratio trades floor area against agitator shaft length and air requirements. A very tall, slender vessel is harder to agitate evenly and is more prone to solids settling in the base.

    Formulas used

    Total working volume V = Q × (τ / 60) Geometric volume = V / (working fraction) Volume per tank = V / N N = tanks in series For volume of one tank: V_tank = π (D/2)² × (H/D × D) solve D = ( 4 V_tank / (π × (H/D)) )^(1/3) , H = D × (H/D)

    Assumptions & applicability

    • Ideal mixing within each tank, with tanks in series to model the residence time distribution. Real vessels have dead zones, short-circuiting and stagnant corners, so the effective volume is normally less than the geometric volume.
    • The required residence time is an input that must come from batch leach kinetics on your own material. Leach rates vary by orders of magnitude with particle size, mineralogy, temperature and lixiviant strength, so a generic figure is not usable for design.
    • Constant slurry density and flow. In reality pulp density changes along the circuit as solids dissolve and as wash water is added.
    • No allowance is made for solids settling out in the vessel, for agitator power limits, or for the increase in viscosity and the fall in mixing quality at high pulp density.
    • Heat input and temperature control are not modelled, although leach kinetics depend strongly on temperature.
    • The scaling and abrasion behaviour of the vessel and agitator material is not considered.

    FAQ

    Why use several tanks in series instead of one large tank?

    Because the total residence time is the same but the distribution is much narrower. Part of the slurry cannot short-circuit straight through, so more of it actually receives the full contact time. That translates into higher recovery for the same total volume, which is why leach circuits are almost always built as a series of agitated tanks rather than one large vessel.

    What pulp density can I run?

    The practical ceiling is usually set by mixing, not by chemistry. As pulp density rises, slurry viscosity rises sharply, the power needed to keep solids in suspension rises, and the driving force for dissolution falls because the liquid-to-solid ratio drops. Establish the achievable density in an agitated test vessel at your intended geometry before committing to a reactor design.

    Should I use an agitated tank or a column or autoclave?

    It depends on the kinetics and on why you are leaching. Atmospheric agitated tanks suit slow kinetics and coarse solids, autoclaves are needed when the chemistry requires elevated temperature and oxygen overpressure, and columns or heaps suit very low-grade material where long residence times are acceptable because the cost per tonne is low. The decision is normally made by kinetics together with the required oxygen or pressure, not by tank volume.

    Equipment sized with this calculation

    Pilot-Scale PP ReactorLab-Scale PP ReactorElectric Heating PP Reactor

    Further reading

    How to scale up from Pilot-Scale PP Reactors?Alkali Resistant PP Reactor Stirring Systems and Agitation Types

    Reference entry TL-LEACHING-REACTOR-RESIDENCE-TIME. The calculator returns a pre-feasibility number. For a quotation we need the feed assay, throughput, medium and temperature — and, where the result hinges on it, test data from your own material.

    Send the campaign results — we return the configuration, the calculation and what we would change in the next test round.

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    Qué calcula

    El volumen de trabajo total es simplemente caudal por tiempo. Dividiéndolo por la fracción de volumen útil se obtiene el volumen geométrico que hay que construir. Repartiendo el volumen de trabajo entre N tanques en serie sale el volumen por tanque, y con la relación altura:diámetro elegida se resuelve el diámetro y de ahí la altura. La última salida devuelve el tiempo de residencia efectivo por tanque con el volumen realmente calculado, que sirve para comprobar que el redondeo a dimensiones constructivas no cambió la cinética.

    Datos de entrada

    • Caudal de pulpa en m³/h, con el reciclo que tenga el circuito.
    • Tiempo de residencia requerido en minutos, proveniente de la cinética de lixiviación del material.
    • Fracción de volumen útil en %, es decir qué parte del volumen geométrico es pulpa en operación.
    • Tanques en serie y relación altura:diámetro.

    Cómo se calcula

    El volumen de trabajo total sale del caudal y del tiempo, con el tiempo pasado a horas:

    V = Q × (τ / 60)

    El volumen geométrico es volumen geométrico = V / fracción de volumen útil y el volumen de trabajo por tanque, V_tank = V / N. Con la relación altura:diámetro se resuelve el diámetro de un tanque cilíndrico:

    D = (4 V_tank / (π × (H/D)))^(1/3) y H = D × (H/D)

    El tiempo de residencia real por tanque se recalcula con el volumen resultante, de modo que se vea el efecto de haber ajustado el diámetro y la altura a valores constructivos.

    Cómo leer el resultado

    Revise primero la cantidad de tanques: con el mismo volumen total, más tanques en serie dan una distribución de tiempos más estrecha y por lo tanto más recuperación, pero también más agitadores, más instrumentación y más puntos de mantenimiento. Después mire el volumen geométrico contra el de trabajo: la diferencia es el espacio que no reacciona, y en tanques reales suele ser mayor de lo previsto por zonas muertas, esquinas estancadas y caminos preferenciales. Por último, el diámetro y la altura no son intercambiables: un tanque muy alto con el mismo volumen exige más potencia de agitación por unidad de volumen y complica la suspensión de sólidos.

    Errores frecuentes

    • Usar un tiempo de residencia genérico de biblioteca. Las velocidades de lixiviación varían en órdenes de magnitud con el tamaño de partícula, la mineralogía, la temperatura y la fuerza del lixiviante.
    • Olvidar que la densidad de pulpa cambia a lo largo del circuito, porque los sólidos se disuelven y porque se añade agua de lavado.
    • Suponer mezcla ideal. Los recipientes reales tienen zonas muertas y cortocircuitos, así que el volumen efectivo suele ser menor que el geométrico.
    • Ignorar que el tiempo de residencia requerido depende de la temperatura y no modelar el aporte de calor, que es lo que muchas veces decide la cinética.

    Si la cinética todavía no está medida, el paso previo es una serie de ensayos por lotes a la temperatura y la densidad de pulpa previstas. Con esas curvas el volumen deja de ser una estimación y se convierte en una decisión de diseño.