https://github.com/felipearocha/integrity-code-series-week9-cui
Coupled thermohygro-electrochemical CUI simulator with DFOS-informed inverse problem (Integrity Code Series, Week 9). Three-PDE physics, Strang splitting, 154 tests, full CI/CD.
https://github.com/felipearocha/integrity-code-series-week9-cui
api-579 api-rp-583 butler-volmer corrosion-under-insulation cui dfos fitness-for-service inverse-problem monte-carlo philip-de-vries physics-simulation pipeline-integrity scientific-python strang-splitting
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Coupled thermohygro-electrochemical CUI simulator with DFOS-informed inverse problem (Integrity Code Series, Week 9). Three-PDE physics, Strang splitting, 154 tests, full CI/CD.
- Host: GitHub
- URL: https://github.com/felipearocha/integrity-code-series-week9-cui
- Owner: felipearocha
- License: other
- Created: 2026-04-28T14:46:56.000Z (about 2 months ago)
- Default Branch: main
- Last Pushed: 2026-04-28T15:20:55.000Z (about 2 months ago)
- Last Synced: 2026-04-28T17:18:28.727Z (about 2 months ago)
- Topics: api-579, api-rp-583, butler-volmer, corrosion-under-insulation, cui, dfos, fitness-for-service, inverse-problem, monte-carlo, philip-de-vries, physics-simulation, pipeline-integrity, scientific-python, strang-splitting
- Language: Python
- Size: 65.4 KB
- Stars: 0
- Watchers: 0
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: CHANGELOG.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
Awesome Lists containing this project
README
# ICS2 Week 9 — CUI Coupled Thermohygro-Electrochemical Simulation
[](https://doi.org/10.5281/zenodo.20172508)
[](https://github.com/felipearocha/integrity-code-series-week9-cui/actions/workflows/ci.yml)
[](https://www.python.org/)
[](#testing)
[](LICENSE)
Three-way coupled physics-first simulator for **Corrosion Under Insulation (CUI)**
on insulated carbon-steel process piping. Simulates moisture ingress through a
cladding holiday, hygrothermal transport to the hot pipe surface, and Butler-
Volmer corrosion kinetics — all solved together via Strang operator splitting.
Includes a DFOS-informed inverse problem to recover holiday source magnitude
from outer-cladding temperature observations.
## Integrity Code Series
Part of an ongoing series of physics-first integrity simulators by Felipe Rocha:
| # | Repo | Domain |
|---|---|---|
| Week 3 | [Integrity-code-series-3](https://github.com/felipearocha/Integrity-code-series-3) | F1 lap simulation (six coupled ODEs) |
| Week 6 | [Integrity-code-series-week6-smartphone-galvanic](https://github.com/felipearocha/Integrity-code-series-week6-smartphone-galvanic) | Smartphone galvanic corrosion (Laplace + Butler-Volmer) |
| Week 7 | [integrity_code_series_week7_h2_lferw](https://github.com/felipearocha/integrity_code_series_week7_h2_lferw) | LF-ERW H2 conversion (B31.12 + NACE TM0316) |
| Week 8 | [integrity-code-series-week8-creep-fatigue-heater](https://github.com/felipearocha/integrity-code-series-week8-creep-fatigue-heater) | Creep-fatigue 9Cr-1Mo (Norton/Omega + Coffin-Manson) |
| Week 9 | [integrity-code-series-week9-cui](https://github.com/felipearocha/integrity-code-series-week9-cui) | CUI thermohygro-electrochemical (3 PDEs, Strang) |
| Week 10 | [integrity-code-series-week-10_nnph_scc](https://github.com/felipearocha/integrity-code-series-week-10_nnph_scc) | NNpHSCC full-physics (Chen-Sutherby-Xing + BS 7910) |
| Bonus | [Vibration-Accelerated-Corrosion-Coupled-Mechano-Electrochemical-Simulation](https://github.com/felipearocha/Vibration-Accelerated-Corrosion-Coupled-Mechano-Electrochemical-Simulation) | Vibration-accelerated corrosion (SDOF + Butler-Volmer + Archard) |
| Bonus | [synthetic-integrity-digital-twin-piml](https://github.com/felipearocha/synthetic-integrity-digital-twin-piml) | Physics-informed neural-network surrogate |
| Bonus | [integrity-data-foundation](https://github.com/felipearocha/integrity-data-foundation) | Engineering data validation baseline |
## Quickstart
```bash
git clone https://github.com/felipearocha/integrity-code-series-week9-cui.git
cd REPO
python -m venv .venv && source .venv/bin/activate # Windows: .venv\Scripts\activate
pip install -r requirements.txt
python run_all.py # ~70 s on a laptop; produces 7 figures + 1 GIF + audit_chain.json
pytest tests/ -v # 151 tests
python validation/benchmarks.py # 5 analytical benchmarks
```
## Problem Statement
Corrosion Under Insulation (CUI) on carbon steel process piping causes ~60% of pipe
leaks in documented refinery case studies (AMPP 2022). It progresses unseen beneath
insulation systems for years. PHMSA Docket 2026-1520 (April 24, 2026) places external
corrosion threats on hazardous liquid pipelines under active regulatory scrutiny.
API RP 583 identifies 50-175 C as the critical temperature window for CUI on carbon steel.
This package simulates three-way coupled physics: heat conduction through the insulation
annulus, hygrothermal moisture transport driven by capillary and thermal gradients, and
Butler-Volmer electrochemical corrosion at the steel surface — all solved together via
Strang operator splitting. A DFOS-informed inverse problem recovers moisture source
locations from outer cladding temperature measurements.
---
## Governing Equations
### Field 1 — Fourier Heat Conduction (Eq. 1)
```
rho_eff(theta_w)*cp_eff(theta_w)*dT/dt = div(lambda_eff(theta_w)*grad(T)) + Q_corr
```
Boundary conditions:
```
T(r_i) = T_process (1a) inner wall Dirichlet
-lambda*dT/dr|_outer = h_conv*(T-T_inf) + eps*sigma*(T^4-T_inf^4) (1b) Robin outer
dT/dz|_ends = 0 (1c) adiabatic axial ends
```
### Field 2 — Philip-de Vries Hygrothermal Moisture Transport (Eq. 2)
```
d(theta_w)/dt = div(D_theta(theta_w)*grad(theta_w)) + div(D_T(theta_w,T)*grad(T))
```
Where:
```
D_theta(theta_w) = D_theta0 * exp(beta_theta * theta_w) (2a)
D_T(theta_w, T) = D_vap_atm * xi(theta_w) * f(theta_w, T) (2b)
theta_w|_holiday = f * THETA_SAT + (1 - f) * THETA_INIT (2c) partial-holiday Dirichlet
with f = min(S_mag / S_ref, 1)
J_w.n|_intact = 0 (2d) zero-flux
theta_w|_t=0 = THETA_INIT [ASSUMED] (2e)
```
The partial-holiday BC (2c) models the cladding defect as a fraction `f`
of the outer circumference at saturation; `S_mag = S_ref` (default
`S_REF_DEFAULT = 1e-6 m^3/m^3/s`) is a fully wet holiday, `S_mag = 0` is
intact cladding. Above `S_ref` the BC saturates and S_mag is non-
identifiable from T_clad alone, so the inverse problem (Eq. 6) is
restricted to the unique-recovery range `S ∈ [0, S_ref]`.
### Field 3 — Butler-Volmer Electrochemical Kinetics (Eq. 3)
```
i_corr = i0(T) * [exp(alpha_a*F*eta/(RT)) - exp(-alpha_c*F*eta/(RT))] if theta_w > theta_crit
= 0 if theta_w <= theta_crit
i0(T) = i0_ref * exp(-Ea/R * (1/T - 1/T_ref)) (3a)
```
### Wall Loss — Faraday's Law (Eq. 4)
```
dWT/dt = -M_Fe/(n*F*rho_steel) * i_corr(T, theta_w)
```
### Strang Operator Splitting (Eq. 5)
```
u^{n+1} = L_EC(dt/2) o L_HY(dt/2) o L_TH(dt) o L_HY(dt/2) o L_EC(dt/2) u^n
```
### Tikhonov Inverse Problem (Eq. 6)
```
min_S J(S) = (T_obs - T_model(S))^2 + lambda_reg * S^2 S in [0, S_ref]
```
Single-parameter 1D inverse for `S_mag`, solved by golden-section line
search on `J(S)` in `src/inverse_problem.py`. Recovery error is <1% on
the identifiable range `S in [0, S_ref]` for synthetic DFOS cases with
0.03 K measurement noise (see `[6/9]` in `run_all.py`). Above S_ref the
model BC saturates and the inverse is non-injective by construction.
A full adjoint formulation is out of scope.
### Monte Carlo / PoF (Eq. 9-10)
```
xi = {S_mag, theta_crit, i0_ref, E_a, lambda_eff, L_defect} N_MC = 10,000 (LHS)
PoF(t*) = (1/N) * sum( 1[WT_k(t*) > 0.20 * t_nom] )
```
### FAD — API 579-1 Level 2 Option B (Eq. 12-13)
```
f(Lr) = [1 + 0.5*Lr^2]^(-1/2) * [0.3 + 0.7*exp(-0.65*Lr^6)]
Lr_max = 0.5*(1 + UTS/SMYS)
```
---
## Repository Structure
```
integrity_code_series_week9_cui_thermohygro/
├── run_all.py
├── requirements.txt
├── README.md
├── EXECUTION_ORDER.md
├── conftest.py
├── src/
│ ├── constants.py Physical constants, [ASSUMED] flags
│ ├── geometry.py 2D axisymmetric FDM mesh
│ ├── thermal_field.py Fourier PDE solver (Crank-Nicolson)
│ ├── moisture_field.py Philip-de Vries solver (explicit, sub-stepped)
│ ├── electrochemistry.py Butler-Volmer + Faraday wall loss
│ ├── coupled_solver.py Strang operator splitting, baseline runner
│ ├── inverse_problem.py Tikhonov inverse, DFOS synthetic tests
│ ├── monte_carlo.py LHS sampling, MC propagation, Spearman
│ ├── surrogate_gbr.py GBR surrogate, parity metrics
│ ├── fad_assessment.py API 579-1 Level 2 FAD
│ └── audit_chain.py SHA-256 hash-linked run log
├── validation/
│ └── benchmarks.py
├── visualization/
│ ├── plot_fields.py
│ ├── plot_mc_dist.py
│ ├── plot_analysis.py
│ └── generate_gif.py
├── tests/
│ ├── test_geometry_thermal.py
│ ├── test_moisture_electrochemistry.py
│ └── test_remaining.py
├── assets/figures/ 8 static PNG panels (300 DPI)
├── assets/animations/ cui_moisture_front.gif
├── assets/audit_chain.json
└── notebooks/
```
---
## [ASSUMED] Parameter Flags
| Parameter | Value | Basis |
|-----------|-------|-------|
| D_theta0 (mineral wool) | 6.0e-11 m^2/s | Literature porous media, mineral wool [ASSUMED] |
| beta_theta | 5.0 | D_theta exponential slope [ASSUMED] |
| theta_crit | 0.05 vol fraction | API RP 583 qualitative guidance [ASSUMED] |
| i0_ref at 25 C | 1.0e-5 A/m^2 | General Fe dissolution literature [ASSUMED] |
| E_a Fe dissolution | 50 kJ/mol | General electrochemistry literature [ASSUMED] |
| eta_mixed | 0.15 V | Mixed potential anodic overpotential [ASSUMED] |
| K_mat X52 | 70 MPa sqrt(m) | Sweet service estimate [ASSUMED] |
| D_T coupling | 0.05 * D_theta0 * theta_w * T_norm | Philip-de Vries simplified [ASSUMED] |
| Holiday source S | 1.0e-6 m^3/m^3/s | Continuous wetting rate [ASSUMED] |
---
## Escalation Table (vs. Week 8)
| Dimension | Week 8 | Week 9 |
|-----------|--------|--------|
| PDE count | 1 (PR EOS + chemistry, algebraic) | 3 coupled PDEs (Fourier + PdV + BV) |
| Geometry | 1D spatial pipeline | 2D axisymmetric annulus |
| Inverse problem | None | DFOS-informed Tikhonov inversion |
| Operator method | Sequential | Strang splitting (2nd order) |
| Sensor integration | None | DFOS noise model + synthetic tests |
---
## Cybersecurity Summary
STRIDE threat model applied to DFOS sensor network feeding inverse solver:
| Threat | Mitigation |
|--------|-----------|
| Spoofing (DFOS fiber injection) | Cryptographic signing at acquisition unit |
| Tampering (inverse solver input) | Hash-verified I/O; audit_chain.json |
| Repudiation | Immutable SHA-256 chain per run |
| Information Disclosure | OT-segment VLAN for DFOS network |
| Denial of Service | Rate limiting + GBR surrogate fallback |
| Elevation of Privilege | Surrogate out-of-bounds triggers human review |
| Data Poisoning | Physics residual validation before GBR retraining |
---
## License
Research and educational use only. Not for operational fitness-for-service decisions
without independent engineering review and site-specific validation.
API RP 583, API 579-1, PHMSA regulations take precedence over model output.
[ASSUMED] parameters must be validated against site-specific inspection data.
---
Integrity Code Series — ICS2 | Week 9 | Physics-first. Verification over visibility.
---
## How to Cite
If this software contributes to your work, please cite both the software (this repository) and the underlying methods it implements.
**Software (archived release):**
> Rocha, F. (2026). *Integrity Code Series - Week 9 - CUI Coupled Thermohygro-Electrochemical Simulation* (Version 1.1.1) [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.20172508
**BibTeX:**
```bibtex
@software{rocha_2026_week9,
author = {Rocha, Felipe},
title = {{Integrity Code Series - Week 9 - CUI Coupled Thermohygro-Electrochemical Simulation}},
year = 2026,
publisher = {Zenodo},
version = {v1.1.1},
doi = {10.5281/zenodo.20172508},
url = {https://doi.org/10.5281/zenodo.20172508}
}
```
The two DOIs Zenodo provides are:
| DOI | What it points to |
|--------------------------------------|--------------------------------------------------------------------|
| `10.5281/zenodo.20172508` (concept) | Always resolves to the latest version - use this for citation. |
| `10.5281/zenodo.20172509` (version) | Pinned to v1.1.1 specifically - use when reproducibility matters. |
A machine-readable citation file is also available in [`CITATION.cff`](CITATION.cff) - GitHub will display a "Cite this repository" widget at the top right of the repo page that exports BibTeX / APA / RIS automatically.