Flux-Decline Modelling in Membrane Filtration of Textile Effluent: Hermia Models and Critical Flux on Published Data

FD-Bench is a declared-protocol modelling study of flux decline in membrane filtration of textile dye effluent, executed entirely on published experimental data — no bench runs, no membrane rig, but with the statistical rigour those experiments deserve.

Textile clusters such as Tirupur in Tamil Nadu discharge dye-laden effluent under Central Pollution Control Board norms, and membrane processes are among the main treatment routes; in every such plant the operating question is the same — why and how fast does permeate flux fall? The classical answer is Hermia's four constant-pressure blocking laws (complete pore blocking, standard blocking, intermediate blocking and cake filtration), distinguished by the exponent n, plus the critical-flux concept of Field et al. Yet most published studies fit one mechanism, report one R² and move on; the exponent is rarely tested for physical plausibility, competing models are rarely compared formally, and digitisation error is almost never acknowledged.

This study assembles published flux–time and flux-step datasets for dye/effluent membrane filtration (curves digitised with WebPlotDigitizer under a logged, triplicate-digitisation protocol), fits all four Hermia mechanisms and combined variants by non-linear least squares (SciPy curve_fit), compares them by RMSE and AIC with confidence intervals on fitted parameters, checks each exponent against its theoretical value, and estimates critical flux from published flux-step data.

The deliverable is a paper-style study with a reproducible Python pipeline: mechanism-atlas tables, digitisation-uncertainty statements and an operational recommendation on how far above critical flux a textile-effluent membrane plant can afford to run.

Membrane treatment of Indian textile effluent is limited by flux decline, and the fouling-mechanism models that should guide plant operation — Hermia's blocking laws and the critical-flux concept — are usually applied without the statistical discipline that makes them useful: one mechanism fitted per study, linearised-transform R² reported instead of honest curve fits, fitted exponents accepted whatever their physical plausibility, and digitisation error from published curves never propagated. There is no reproducible, declared-protocol re-analysis that fits all Hermia mechanisms and combined variants to published textile-effluent flux data, compares them formally by information criteria, tests exponents against theoretical values with confidence intervals, and estimates critical flux from published step experiments under declared criteria. This dissertation fills that gap with a fully scripted pipeline, triplicate digitisation with propagated uncertainty, and model-selection tables that regenerate from a versioned data store — turning scattered published curves into an evidence-based mechanism atlas for dye-effluent membrane operation.

Abstract

This dissertation models permeate-flux decline in membrane filtration of textile dye effluent using published experimental data under a pre-declared analysis protocol. Published curves are extracted under a logged, triplicate WebPlotDigitizer protocol whose uncertainty propagates into every fit. Four Hermia constant-pressure blocking mechanisms (complete, standard, intermediate, cake) and combined variants are fitted to each dataset by non-linear least squares; model selection uses RMSE, AIC and physical-plausibility checks on the fitted exponent n against theoretical values (2, 1.5, 1, 0). Critical flux is estimated from published flux-step experiments by declared change-point analysis. The study reports which mechanism each operating regime exhibits, how the exponent shifts with crossflow velocity and transmembrane pressure, and the operating margin above critical flux.

Introduction

Dye-house effluent carries colour, suspended solids and salinity at concentrations that foul membranes quickly; Indian textile clusters treat it under CPCB discharge norms. Membrane plant economics are governed by flux decline: a fouling run that halves flux doubles the membrane area or the cleaning frequency. The classical models — Hermia's blocking laws and the critical-flux concept — are cheap to evaluate; the intellectual work lies in disciplined fitting and honest model selection, not hardware.

Existing system and literature gap

The membrane-fouling literature is vast, but its modelling practice is uneven: single-mechanism fits reported without competing-model comparison, R² quoted on linearised transforms that distort error structure, exponents accepted whatever their value, and no statement of how digitising published curves perturbs the conclusions. What is missing is a declared-protocol re-analysis of published textile-effluent data: every mechanism fitted to every dataset, formal model comparison, exponent-plausibility testing and propagated digitisation uncertainty.

Proposed work

• Select and document published flux–time and flux-step datasets for dye and textile-effluent membrane filtration, recording membrane type, operating conditions and source figure per point.
• Digitise curves with WebPlotDigitizer under a declared protocol — triplicate digitisation, axis-calibration checks, a digitisation log — and propagate the spread into fitted-parameter uncertainty.
• Implement the four Hermia mechanisms plus combined cake–blocking variants; fit all of them to every dataset by bounded non-linear least squares from common declared initialisations.
• Compare models per dataset by RMSE and AIC; test fitted exponents against theoretical values with confidence intervals; analyse how the dominant mechanism shifts with operating conditions.
• Estimate critical flux from published flux-step data under declared change-point criteria and compare it with each experiment's operating flux.

Feasibility

• Technical: all fitting runs in Python (NumPy, SciPy curve_fit, pandas) on a 16 GB laptop; each dataset is a few hundred points, so fitting takes minutes.
• Data: published literature is the data source, accessible through the institute library; digitisation is logged and reproducible; no lab access required.
• Economic: zero cost beyond WebPlotDigitizer (free for academic use).
• Operational (research): the protocol — model forms, initialisations, bounds, selection criteria — is frozen before fitting; every table regenerates from the digitised store and fixed configuration, which is the audit trail an M.Tech viva demands.

In scope

• Published constant-pressure/constant-flux flux–time datasets and flux-step datasets for dye and textile-effluent filtration on UF/NF/MD-class membranes, selected with documented inclusion criteria.
• All four Hermia mechanisms plus combined variants; non-linear least-squares fitting with bounds; RMSE/AIC model selection; exponent-plausibility testing; triplicate-digitisation uncertainty.
• Critical-flux estimation from published step data under declared change-point criteria; operating-margin analysis against source experiments.
• Synthesis into a mechanism atlas: which mechanism dominates which operating regime, and what that implies for plant practice.

Out of scope

• New laboratory experiments: no membrane rig, no synthetic or real effluent runs — the study is a re-analysis of published data by declared design.
• Full CFD or molecular-dynamics fouling simulation; the scope is classical engineering models fitted with statistical discipline.
• Membrane-cleaning protocol design and long-term ageing economics (future scope).
• Novel fouling-theory development: existing mechanisms are compared, not new ones proposed.

The work follows a quantitative, model-comparative research design in six phases over 26 weeks, with the analysis protocol (model forms, bounds, initialisations, selection criteria, digitisation rules) frozen at the end of Phase 1 — before the first fit.

Validation inside the study: synthetic flux-decline generation with known exponents recovered by the fitter within tolerance; digitisation repeatability quantified from the triplicate protocol; fitting-routine checks on hand-computable decay curves; and a full re-run reproducing every table from the frozen configuration and versioned store.

The pipeline separates data acquisition from model fitting, with the digitisation log and frozen protocol as first-class artefacts, so every fitted number carries its provenance and uncertainty.

flowchart TD
  A["Published membrane studies\nflux-time and flux-step figures"] --> B["WebPlotDigitizer\ntriplicate, logged, calibrated"]
  B --> C[("Versioned data store\npoints + provenance + spread")]
  C --> D["Hermia model library\nn = 2, 1.5, 1, 0 + combined forms"]
  D --> E["Non-linear least-squares fitter\nSciPy curve_fit, bounded"]
  E --> F["Model selection\nRMSE, AIC, plausibility flags"]
  C --> G["Digitisation uncertainty\npropagated to parameters"]
  G --> F
  C --> H["Critical-flux estimator\ndeclared change-point criteria"]
  F --> I["Mechanism atlas\nregime vs mechanism tables"]
  H --> I
  I --> J["Results tables, figures\nand operational recommendation"]

Three design decisions matter at the viva. First, digitisation is triplicate and logged because published curves are the study's raw material: the spread across three independent digitisations is propagated into parameter confidence intervals, so conclusions carry their measurement error explicitly instead of pretending curve-reading is exact. Second, all mechanisms are fitted to every dataset from common declared initialisations — selecting one mechanism per dataset in advance would convert model selection into assumption; the AIC/RMSE comparison over the full model set is the study's evidence. Third, the exponent-plausibility check is separate from model selection: a mechanism can win on RMSE while its fitted exponent is physically implausible, and the atlas reports both facts rather than silently privileging one, which is exactly the honest-reporting discipline 22RMI16 teaches.

• Add a bench validation phase on a college membrane rig with a synthetic dye solution, closing the loop between published-data re-analysis and fresh measurement.
• Extend the model library with resistance-in-series and pore-blocking–cake two-stage models for long runs.
• Re-run the atlas restricted to one membrane class (e.g. MD only) with deeper operating-condition stratification.
• Study cleaning-recovery curves (flux restoration after chemical cleaning) under the same declared-fitting discipline.
• Build a plant-side flux-decline calculator that recommends operating margin above the estimated critical flux for a given effluent class.