J. Hydrol. Hydromech., Vol. 74, No. 4 - Early view, 2026, p. 1 - 10, doi: .
Scientific Paper, English

Katsutoshi Seki, Martinus Th. van Genuchten, Wolfgang Durner, Luwen Zhuang, Silvia L. B. Bermudez: Trimodal hydraulic models for unsaturated flow: Coupling triple-porosity water retention with general conductivity functions

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• We present trimodal hydraulic models that couple a triple-porosity water retention function (WRF) with a general hydraulic conductivity function (HCF) to predict unsaturated flow from saturation to dry conditions. The WRF is a linear combination of subfunctions representing macro-, meso-, and micro-pores such as, for example, tri-VG (VG+VG+VG), BVV (BC+VG+VG), or VVP (VG+VG+film flow) formulations, where VG and BC present the van Genuchten and Brooks-Corey type functions. The general HCF links K(h) to the measured WRF with only two additional parameters. Applied to soils, construction materials, and a trimodal sandstone, the models reproduce θ(h) and K(h) data across capillary and film-flow regimes and capture the sharp conductivity drop often observed just below saturation without ad hoc interpolation. The tri-VG and BVV models resolve three pore domains and match observed pore-size distributions where trimodality is evident, with VVP offering a compact alternative. The WRF, in practice readily measured over a wide pressure-head range, robustly identifies triple-porosity parameters, while only limited K data can calibrate the HCF. A limitation is that representing the near-saturated K drop requires a corresponding decrease in θ; without accompanying retention data, macropore parameters should not be over-interpreted. Overall, explicit macroporosity within a trimodal WRF plus a parsimonious HCF provides an efficient, unified framework for modeling unsaturated flow.
  
  KEY WORDS: Soil water retention; Unsaturated hydraulic conductivity; Triple-porosity model; Macroporosity; Film flow; General hydraulic conductivity function.
  
  Address:
  - Katsutoshi Seki, Natural Science Laboratory, Toyo University, 5-28-20 Hakusan, Bunkyo-ku, Tokyo 112-8606, Japan. (Corresponding author. Tel.: Fax.: Email: seki_k@toyo.jp)
  - Martinus Th. van Genuchten, Department of Earth Sciences, Utrecht University, Princetonlaan 8a, 3584 CB Utrecht, Netherlands. Department of Nuclear Engineering, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil.
  - Wolfgang Durner, Soil Science and Soil Physics Division, Institute of Geoecology, Technische Universität Braunschweig, 38092 Braunschweig, Germany.
  - Luwen Zhuang, Center for Water Resources and Environment, and Guangdong Key Laboratory of Marine Civil Engineering, School of Civil Engineering, Sun Yat-sen University, Guangzhou 510275, China.
  - Silvia L. B. Bermudez, Department of Civil Engineering, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil.

J. Hydrol. Hydromech., Vol. 74, No. 4 - Early view, 2026, p. 11 - 21, doi: .
Scientific Paper, English

Bernardo Gehlen, Ricardo Leite Martins Bazarin, Rafael Augusto Bastos Rodrigues Alves, Diogo Nardelli Siebert: An REV analysis of capillary pressure curves using the Full Morphology Method and the van Genuchten model

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• A Representative Elementary Volume (REV) analysis is fundamental to guarantee that simulations are performed in a representative domain. While the literature presents approaches to determine the REV of scalar properties, especially single-phase ones, identifying the REV for full capillary pressure curves remains challenging due to the computational costs of direct simulations and limited convergence metrics. This study proposes a hierarchical framework to evaluate the REV of drainage capillary pressure curves of digital rocks imaged via micro-computed tomography (micro-CT) using the Full Morphology Method (FM) and the van Genuchten model. Instead of adapting standard convergence criteria to the fitted parameters, whose non-linearity complicates a stability analysis, we introduce a statistical Mean Absolute Error (MAE) metric to quantify the convergence of the entire curve shape. The methodology was validated using four sandstone micro-CT samples. Results establish a preliminary hierarchy to identify the REV for the full curve at sizes at least double of the statistical REV for residual saturation. Crucially, the MAE-based approach diagnosed the lack of convergence of more heterogeneous samples for which a coefficient-of-variation-based metric failed. The framework provides a robust and physically representative criterion for defining simulation domain sizes, thereby preventing the use of non-representative data in reservoir characterization.
  
  KEY WORDS: Digital rock physics; Representative elementary volume; Full morphology method; van Genuchten model; Capillary pressure curves.
  
  Address:
  - Bernardo Gehlen, Federal University of Santa Catarina, Rua Dona Francisca, 8300, Joinville, Santa Catarina, 89219-600, Brazil. (Corresponding author. Tel.: Fax.: Email: b.gehlen@posgrad.ufsc.br)
  - Ricardo Leite Martins Bazarin, Federal University of Santa Catarina, Rua Dona Francisca, 8300, Joinville, Santa Catarina, 89219-600, Brazil.
  - Rafael Augusto Bastos Rodrigues Alves, Federal University of Santa Catarina, Rua Dona Francisca, 8300, Joinville, Santa Catarina, 89219-600, Brazil.
  - Diogo Nardelli Siebert, Federal University of Santa Catarina, Rua Dona Francisca, 8300, Joinville, Santa Catarina, 89219-600, Brazil.

J. Hydrol. Hydromech., Vol. 74, No. 4 - Early view, 2026, p. 22 - 31, doi: .
Scientific Paper, English

Felipe Eler, Martinus Th. van Genuchten, Paulo Couto: Uncertainty Assessment of Capillary Pressure Curves Measured Using Centrifuge Methods

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• The centrifuge technique (CT) is widely used across hydrology, petrophysics, and related disciplines to measure the water retention/capillary pressure curves, but standard data inversion methods lack uncertainty quantification and often cannot guarantee solution uniqueness. To address this, we present a novel Bayesian framework for inverting CT data that explicitly accounts for experimental uncertainties, provides confidence intervals, quantifies parameter covariance, and analyzes solution uniqueness. The framework was validated against synthetic first-drainage data (the desorption curve) across various curve shapes and noise levels, successfully recovering true capillary pressure curves. Application to experimental core samples of Indiana Limestone, Silurian Dolomite, and Upper Gray Berea yielded highly consistent results, demonstrating the framework’s practical reliability. The approach also facilitates crucial non-uniqueness analyses, identifies parameter correlations, and offers strategies for improved solution stability. To promote transparency, reproducibility, and cross-disciplinary collaboration, the complete framework is publicly available as an open-source code on GitHub.
  
  KEY WORDS: Capillary Pressure Curve; Centrifuge Method; Uncertainty Quantification; Solution Uniqueness; Bayesian Inference.
  
  Address:
  - Felipe Eler, Department of Civil Engineering, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, RJ, Brazil. (Corresponding author. Tel.: Fax.: Email: felipe.eler@petroleo.ufrj.br)
  - Martinus Th. van Genuchten, Department of Nuclear Engineering, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, RJ, Brazil. Department of Earth Sciences, Utrecht University, Utrecht, The Netherlands.
  - Paulo Couto, Department of Civil Engineering, Federal University of Rio de Janeiro, UFRJ, Rio de Janeiro, RJ, Brazil.