mass-transfer-separations

Mass Transfer And Separations

Engineering-science skill for transport-driven separation problems. It is aimed at tutoring and first-pass design calculations rather than full process simulation.

Units: SI by default. Keep concentration basis explicit: mole fraction, partial pressure, mol/m3, or mass fraction.

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Module 1 - Diffusion

def fick_flux_1d(diffusivity_m2_s, c1, c2, length_m):
    """
    Fick's first law in 1D:
    N_A = -D * dc/dz
    Returns positive flux from point 1 to point 2 when c1 > c2.
    """
    if length_m <= 0:
        return None
    return diffusivity_m2_s * (c1 - c2) / length_m

def characteristic_diffusion_time(length_m, diffusivity_m2_s):
    """Order-of-magnitude diffusion time scale."""
    if diffusivity_m2_s <= 0:
        return None
    return length_m**2 / diffusivity_m2_s

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Module 2 - Convective Mass Transfer

def sherwood_number(k_m_s, length_m, diffusivity_m2_s):
    """Sherwood number."""
    if diffusivity_m2_s <= 0:
        return None
    return k_m_s * length_m / diffusivity_m2_s

def mass_transfer_flux(k_overall, area_m2, driving_force):
    """
    Overall mass-transfer rate.
    Rate = K * A * driving force
    Driving force must match the coefficient basis.
    """
    return k_overall * area_m2 * driving_force

def volumetric_mass_transfer_rate(kla_s_inv, volume_m3, c_star, c_bulk):
    """
    Gas-liquid transfer rate with kLa.
    """
    return kla_s_inv * volume_m3 * (c_star - c_bulk)

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Module 3 - Packed Towers

def htu_ntu_height(htu_m, ntu):
    """Packed height from transfer units."""
    return htu_m * ntu

def absorption_factor(L_over_mV):
    """
    Absorption factor A = L / (m V)
    A > 1 generally favors absorption.
    """
    return L_over_mV

def stripping_factor(mV_over_L):
    """
    Stripping factor S = m V / L
    S > 1 generally favors stripping.
    """
    return mV_over_L

Interpretation

Metric	Meaning
Large HTU	Poor mass-transfer efficiency
Large NTU	Difficult separation or tight outlet spec
A > 1	Absorption usually feasible
S > 1	Stripping usually feasible

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Module 4 - Distillation Screening

def fenske_min_stages(xd_light, xb_light, alpha_avg):
    """
    Minimum equilibrium stages at total reflux for binary distillation.
    """
    import math
    numerator = xd_light / (1.0 - xd_light)
    denominator = xb_light / (1.0 - xb_light)
    if alpha_avg <= 1.0 or denominator <= 0:
        return None
    return math.log(numerator / denominator) / math.log(alpha_avg)

def relative_volatility(k_light, k_heavy):
    """Relative volatility alpha = K_light / K_heavy."""
    if k_heavy == 0:
        return None
    return k_light / k_heavy

Use Fenske for a lower bound only. Actual stages require reflux and efficiency considerations.

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Module 5 - Process Selection Logic

Problem	Likely separation route
Remove dissolved gas from liquid	Stripping / flash
Remove acid gas from gas stream	Absorption
Split close-boiling liquids	Distillation if relative volatility allows
Recover dilute solute from liquid	Extraction, adsorption, or membranes
Slow species transport through stagnant film	Diffusion-limited process

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Output Format

When using this skill, structure the answer as:

1. Separation target and basis
2. Governing transfer mechanism
3. Equations used and coefficient basis
4. Calculated stages, height, flux, or rate
5. Whether the process looks transfer-limited or equilibrium-limited

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Learning Resources

Resource	Notes
Geankoplis	Standard transport and separation reference
Treybal	Strong absorption / extraction treatment
Wankat	Good distillation and separations text
LearnChemE separations content	Short worked examples