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OpenPNM Extracted-Network Cross-Check

This report documents a controlled verification study of voids against OpenPNM on the same extracted pore network. The purpose is narrower than the XLB benchmark: here the goal is to verify representation consistency, boundary-condition handling, and single-phase solver agreement, not to compare different geometric reductions of the same image.

The reproducible artifact for this report is notebook notebooks/12_mwe_synthetic_volume_openpnm_benchmark.ipynb.

Goal

The benchmark answers the following question:

Given the same segmented image and the same extracted spanning network, do voids and OpenPNM return the same absolute permeability when the OpenPNM side is given the exact same throat hydraulic conductances?

That is the correct verification target for this comparison. If the agreement stops being essentially exact, the likely causes are:

  • a change in PoreSpy extraction or boundary labeling
  • an import/export bug between voids and OpenPNM-style data
  • a regression in solver assembly or sign conventions
  • an OpenPNM API change that breaks the adapter assumptions

Governing Formulations

voids Solve

For each segmented image, voids:

  1. extracts a network with snow2
  2. prunes to the axis-spanning subnetwork
  3. solves the steady pressure system
\[ \mathbf{A}\,\mathbf{p} = \mathbf{b}, \]

with throat fluxes

\[ q_t = g_t (p_i - p_j), \]

and apparent permeability from Darcy's law,

\[ K = \frac{|Q|\,\mu\,L}{A\,|\Delta p|}. \]

For this benchmark, the voids side uses:

  • conductance_model = "valvatne_blunt"
  • solver = "direct"
  • \(\mu = 1.0 \times 10^{-3}\) Pa s

OpenPNM Reference Solve

This benchmark does not ask OpenPNM to reconstruct its own conductances from geometry. Instead, the wrapper exports the extracted voids network to an OpenPNM-compatible structure, injects the voids throat hydraulic conductances, and runs OpenPNM StokesFlow with the same pressure boundary conditions.

Scientifically, that means:

  • geometry is shared
  • conductance closure is shared
  • only network representation, BC application, and linear-solver path differ

This is why machine-precision agreement is the expected result. It is a strong regression test for the interoperability layer, but it is not an independent constitutive-model validation.

Synthetic Benchmark Setup

All cases in this report use:

  • synthetic spanning binary volumes generated with generate_spanning_blobs_matrix
  • shape (32, 32, 32)
  • flow axis x
  • voxel size 2.0e-6 m
  • fluid viscosity 1.0e-3 Pa s
  • preferred benchmark input delta_p = 1 Pa
  • synthetic grayscale observations followed by Otsu thresholding

The five-case set is:

Case Target porosity Blobiness Seed used
phi032_b14 0.32 1.4 401
phi035_b16 0.35 1.6 501
phi038_b18 0.38 1.8 601
phi040_b18 0.40 1.8 901
phi041_b20 0.41 2.0 701

The synthetic grayscale model is intentionally simple and high-contrast. It is used here only to exercise the image-to-segmentation-to-network workflow under controlled conditions.

Figures

Representative segmentation workflow

Representative mid-plane slices for case phi038_b18: binary truth, synthetic grayscale observation, and the Otsu-segmented image passed to the benchmark.

OpenPNM permeability scatter

voids permeability against OpenPNM permeability. The identity line is expected because both sides solve the same extracted network with the same hydraulic conductances.

Porosity from image to extracted network

Porosity traced through the workflow: binary truth, segmented image, absolute network porosity, and effective network porosity.

Results

The full CSV generated by the notebook is available here: openpnm_5_case_results.csv.

Case Segmentation mismatch Np Nt K_voids [m^2] K_openpnm [m^2] Rel. diff.
phi032_b14 3.05e-05 53 150 6.097e-15 6.097e-15 1.16e-15
phi035_b16 0.00e+00 26 79 1.702e-14 1.702e-14 9.27e-16
phi038_b18 0.00e+00 36 106 2.092e-14 2.092e-14 1.51e-15
phi040_b18 0.00e+00 45 134 2.033e-14 2.033e-14 1.09e-15
phi041_b20 6.10e-05 37 106 3.928e-14 3.928e-14 8.03e-16

Summary statistics for this five-case set:

  • maximum relative permeability difference: 1.51e-15
  • mean relative permeability difference: 1.10e-15
  • maximum relative total-flow difference: 1.47e-15
  • mean segmentation mismatch: 1.83e-05
  • OpenPNM version in this run: 3.6.1

Those numbers are in the machine-precision regime and are exactly what this benchmark should show when the adapter is working correctly.

Interpretation

These results support the following conclusions:

  1. The current voids OpenPNM interoperability path is numerically consistent for the tested cases.
  2. The benchmark is sensitive enough to catch future regressions in BC labels, solver assembly, or OpenPNM API adaptation because the present baseline is effectively exact.
  3. The small nonzero values in the error columns are not physically meaningful; they are floating-point roundoff.

The practical interpretation is straightforward: if this benchmark starts to show visible scatter away from the identity line, treat that as a likely bug until proven otherwise.

Limits Of This Verification

This report is intentionally narrow.

Important limits and assumptions:

  • OpenPNM is not used here as an independent physics reference
  • the OpenPNM side receives voids throat conductances directly
  • the images are small synthetic cases, not real rock volumes
  • the grayscale model is synthetic and should not be interpreted as scanner realism
  • agreement here does not imply agreement with independent extracted-network or direct-image references