GeoDict Upscaling MICP GeoApp

The Upscaling MICP GeoApp is a custom GeoDict application developed for upscaling mercury injection capillary pressure (MICP) information from small-scale measurements to larger, more representative porous material models. Its core functionality is not simply enlarging small-scale MICP curves, but rather: distinguishing resolved pores from unresolved porous materials in large-scale models; importing small-scale GeoDict simulation or experimental capillary pressure data for unresolved materials; assigning pressure, saturation, porosity, and displacement pressure to these materials; using SatuDict to directly compute MICP for resolved pores; and integrating information across different scales to obtain a complete upscaled MICP capillary pressure curve for the entire sample. This method is particularly suitable for digital rock and whole-core analysis, as well as for materials with明显的跨尺度 pore structures such as fuel cell GDL+MPL. With the optional SatuDict-Thomeer Model support, it can further characterize unresolved porosity, displacement pressure, and pore geometry factor.

Why Upscale MICP?

Porous materials often have pore structures spanning multiple orders of magnitude. High-resolution µCT and FIB-SEM can resolve fine pores but typically have small fields of view. Medical CT and other large-field imaging can cover entire cores or large samples but cannot directly resolve micron or nanometer-scale pores. Therefore, a large-scale 3D model typically contains both resolved pores (which can be directly identified in the current image) and unresolved porosity (existing within certain porous material regions but below the current image resolution). If MICP is computed only for resolved pores, the pore volume hidden inside fine porous materials is not fully considered, and the resulting capillary pressure–saturation relationship may not represent the real sample.

The Upscaling MICP GeoApp addresses this by: importing small-scale capillary pressure data for unresolved porous materials, having GeoDict perform MICP simulations on resolved pores in the large-scale model, and finally integrating both parts into a complete upscaled capillary pressure curve.

Core Workflow

The GeoApp establishes a typical cross-scale workflow:

Large-scale 3D scan → Image segmentation to identify pores, dense solids, and unresolved porous materials → Extract representative sub-samples from different porous regions → Perform higher-resolution µCT scans or obtain experimental MICP data on sub-samples → Obtain capillary pressure curves for each unresolved porous material → GeoDict computes MICP for resolved pores in the large-scale model → Integrate contributions from resolved and unresolved pores → Obtain the upscaled MICP curve for the entire sample

This enables researchers to account for both large-scale heterogeneity and fine pore characteristics without having to scan the entire large sample at the highest resolution.

Key Features

Flexible Data Import – Capillary pressure curves for unresolved porous materials can be imported from either GeoDict simulations or user-provided experimental measurements. The pore structure of unresolved materials does not need to be explicitly displayed voxel by voxel in the large-scale model; instead, their预先 obtained capillary pressure characteristics can be used as effective porous medium properties in the overall calculation.

Material Property Assignment – For each unresolved porous material, users can specify pressure, saturation, porosity, and displacement pressure. These parameters describe the behavior of the unresolved pore system during mercury intrusion, allowing it to be incorporated into the MICP calculation together with explicitly resolved pores in the large-scale model.

MICP Simulation for Resolved Pores – For pores that can be clearly resolved in the current 3D model, the GeoApp directly uses GeoDict's MICP analysis capabilities via SatuDict. SatuDict uses the Pore Morphology Method (PMM) to simulate the distribution of two immiscible fluids under capillary-dominated conditions and calculates capillary pressure curves based on the Young–Laplace relationship.

Complete Upscaled MICP Curve – The final output is the complete capillary pressure curve for the entire sample, integrating both pores resolved in the large-scale scan and fine pores that exist within porous materials but cannot be resolved by large-scale imaging.

Application Examples

Whole Core MICP Upscaling

In a Petrobras case study, a medical CT scan of a whole core was performed with a model size of 156×205×1404 voxels at a resolution of 488 µm. While medical CT can cover large core scales, the 488 µm resolution means many fine pores cannot be directly resolved. The core was segmented into pore space, solid matrix, and three different porous matrix regions. Sub-samples were extracted from different porous matrix regions for higher-resolution µCT scanning, and MICP curves were obtained for each fine-scale porous material. These were then combined with the resolved structure from the medical CT to obtain the upscaled MICP capillary pressure curve of the whole core. This workflow enables digital core analysis to span the巨大的 spatial scale gap from local micropore structures to the entire core scale.

Fuel Cell GDL + MPL

MICP upscaling is also applicable to fuel cells and other materials with multi-scale pore structures. In PEM fuel cells, the GDL (Gas Diffusion Layer) and MPL (Microporous Layer) are important structures affecting mass transport and water management. Relevant structural scales range from nanometers to hundreds of micrometers, and a single imaging scale cannot resolve all these structures simultaneously. In a GDL+MPL combined model, larger pores in the GDL can be explicitly resolved, while fine pores in the MPL and other regions cannot be directly resolved in the overall model. The Upscaling MICP GeoApp can combine capillary pressure data from these unresolved materials with resolved structures such as the GDL, saturate the hidden pores, and obtain the complete MICP capillary pressure curve for the GDL+MPL sample.

Comparison with Traditional Digital MICP

Traditional single-scale digital MICP primarily analyzes pores that are resolved in the current image. The key extension of Upscaling MICP is that it considers both resolved and unresolved pores simultaneously. Traditional MICP operates at a single image scale, while Upscaling MICP supports cross-scale data. Traditional MICP is directly based on the 3D pore structure of the current image, while Upscaling MICP combines 3D direct computation with external capillary pressure data. Traditional MICP is suitable for relatively homogeneous single-scale structures, while Upscaling MICP is more appropriate for complex, multi-scale, heterogeneous materials. Traditional MICP yields the MICP curve of the current model, while Upscaling MICP yields the upscaled MICP curve of the entire representative sample.

Required GeoDict Modules

According to Math2Market's licensing requirements:

SatuDict – Required. Responsible for capillary pressure, two-phase fluid distribution, MICP/MECP calculations. Its MICP simulation is based on the pore morphology method and the Young–Laplace relationship.

Upscaling MICP GeoApp – Required.

SatuDict – Thomeer Model – Optional. Used to further characterize unresolved porosity, displacement pressure, and pore geometry factor.

Depending on the specific digital rock workflow, ImportGeo-Vol for CT/µCT image import, processing, and segmentation, as well as PoroDict and MatDict for structure analysis, are also commonly used in combination.