Bioprocess Engineering & Downstream Purification
Tangential-Flow Diafiltration Diavolume Formula
Calculate Constant-Volume Diafiltration Residual Impurity C_end = C_0 * EXP(-N_dv * S), Required Diavolumes LN(C_0 / C_target) / S with Non-Ideal Sieving S, Buffer Volume, and Spec Gate.
Account for Donnan and steric sieving S < 1 when sizing mAb diafiltration buffer exchange!
During downstream Monoclonal Antibody (mAb) and viral-vector Tangential-Flow Filtration (TFF), Constant-Volume Diafiltration (CVD) feeds fresh formulation buffer at the exact permeate flow rate so retentate volume V_ret stays constant across N_dv = V_permeate / V_ret Diavolumes! Differential mass balance d(V_ret * C) = -C_permeate * dV_permeate = -(S * C) * V_ret * dN_dv integrates to C_end = C_0 * EXP(-N_dv * S), where S = C_permeate / C_retentate (0 < S <= 1) is the Membrane Sieving Coefficient! Assuming ideal S = 1.0 when electrostatic Donnan exclusion lowers salt sieving to S = 0.80 leaves 3.3x higher residual excipient at 6 diavolumes—requiring Required_DV = LN(C_0 / C_target) / S!
Verify on Retentate_Batch_Volume = 50.0 L (B2), Initial_Elution_Salt C_0 = 100.0 mM (B3), Target_Formulation_Spec C_target = 0.10 mM (1,000-fold clearance, B4), Applied_Diavolumes N_dv = 6.0 (B5), and Sieving_Coefficient S = 1.00 (B6): Residual Salt Concentration after 6 DV is 100 * EXP(-6.0) = 0.2479 mM (E2); Exact Diavolumes Required for 0.10 mM is LN(100 / 0.10) / 1.0 = 6.91 DV (E3); Buffer Consumed at 6 DV is 50 * 6 = 300.00 L (E4); and Batch Status warns "Continue Diafiltration (Exceeds Target)" (E5) until N_dv reaches 7.0 DV (0.0912 mM <= 0.10 mM)!
| TFF Diafiltration Metric (Vret=50L, C0=100mM, Target=0.10mM, Ndv=6, S=1.00) | Formula | Verified Output |
|---|---|---|
| Residual Impurity C_end (mM) | C_0 * EXP(-N_dv * S) | 0.2479 mM (0.8230 mM @ S=0.80) |
| Required Diavolumes for Spec | LN(C_0 / C_target) / S | 6.91 DV (8.63 DV @ S=0.80) |
| Diafiltration Buffer Volume (L) | V_retentate * N_dv | 300.00 L (350.00 L @ 7 DV) |
| GMP Buffer-Exchange Release Gate | C_end <= C_target | Continue Diafiltration (Exceeds Target) |
Constant-Volume Diafiltration Residual Concentration Formula
Validate V_ret > 0, C_0 > C_target > 0, N_dv >= 0, and 0 < S <= 1!
=LET(v_rt, B2, c_in, B3, c_tg, B4, n_dv, B5, sv_c, B6, IF(OR(v_rt <= 0, c_tg <= 0, c_in <= c_tg, n_dv < 0, sv_c <= 0, sv_c > 1), "Invalid TFF Parameter", ROUND(c_in * EXP(-n_dv * sv_c), 4)))Donnan Exclusion Sieving Check (S = 0.80) & 7-Diavolume Pass Check
Test S = 0.80 in cell B6: Residual Salt jumps to 0.823 mM and Required DV rises to 8.63! Test N_dv = 7 at S = 1.0: C_end drops to 0.0912 mM ("Pass: Impurity <= Target")!
=IF(ISTEXT(E2), E2, IF(E2 <= B4, "Pass: Impurity <= Target", "Continue Diafiltration (Exceeds Target)"))Try the example
Use the original values or change them to test your understanding.