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Entropy–Percolation Coupling as the Hidden Law of Drilling-Fluid Behaviour.

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Title: Entropy–Percolation Coupling as the Hidden Law of Drilling-Fluid Behaviour.
Authors: Rasool, Muhammad Hammad1,2,3 (AUTHOR) Hammad.rasool@utp.edu.my
Source: Arabian Journal for Science & Engineering (Springer Science & Business Media B.V. ). Jun2026, Vol. 51 Issue 12, p15459-15480. 22p.
Subjects: Drilling fluids, Thermodynamics, Water filtration, Shear (Mechanics), Dimensionless numbers, Percolation theory, Microstructure
Abstract: Conventional rheological models describe how drilling fluids respond to shear but do not explain why their properties emerge from molecular interactions. This study introduces a novel Entropy-Regulated Percolation (ERP) (interpretive) conceptual framework; a first-principles theory linking thermodynamics, microstructure, and drilling fluid behaviour. ERP treats rheology and filtration as outcomes of a single entropy–energy balance that governs reversible bond networks. Two new dimensionless parameters are introduced: the entropy–power ratio (Ψ), capturing the balance between structural reorganization and shear energy input, and the bond-lifetime number (Λ), describing how long mud-network bonds endure relative to the deformation timescale. Together, Ψ and Λ form a universal map that classifies drilling fluids as shear-dominated, balanced, or network-dominated. In addition to the engineering-level quantitative interpretation of the ERP framework, a citric acid:glycerine NADES-based drilling fluid study is re-examined as a conceptual case study showing that its position near the balanced-to-network regime explains its stable viscosity, reversible thixotropy, and low permeability. By connecting bond free energy (ΔGb), bond lifetime (τb), and structural order (Ω) to measurable flow and filtration data, ERP provides a thermodynamic interpretive framework that rationalizes empirical rheological and filtration behaviour. The framework shifts drilling-fluid design toward an interpretive, physics-based approach, unifying chemistry, structure, and performance. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:Conventional rheological models describe how drilling fluids respond to shear but do not explain why their properties emerge from molecular interactions. This study introduces a novel Entropy-Regulated Percolation (ERP) (interpretive) conceptual framework; a first-principles theory linking thermodynamics, microstructure, and drilling fluid behaviour. ERP treats rheology and filtration as outcomes of a single entropy–energy balance that governs reversible bond networks. Two new dimensionless parameters are introduced: the entropy–power ratio (Ψ), capturing the balance between structural reorganization and shear energy input, and the bond-lifetime number (Λ), describing how long mud-network bonds endure relative to the deformation timescale. Together, Ψ and Λ form a universal map that classifies drilling fluids as shear-dominated, balanced, or network-dominated. In addition to the engineering-level quantitative interpretation of the ERP framework, a citric acid:glycerine NADES-based drilling fluid study is re-examined as a conceptual case study showing that its position near the balanced-to-network regime explains its stable viscosity, reversible thixotropy, and low permeability. By connecting bond free energy (ΔGb), bond lifetime (τb), and structural order (Ω) to measurable flow and filtration data, ERP provides a thermodynamic interpretive framework that rationalizes empirical rheological and filtration behaviour. The framework shifts drilling-fluid design toward an interpretive, physics-based approach, unifying chemistry, structure, and performance. [ABSTRACT FROM AUTHOR]
ISSN:2193567X
DOI:10.1007/s13369-026-11207-z