<p>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 (ΔG<sub>b</sub>), bond lifetime (<i>τ</i><sub>b</sub>), 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.</p>

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

  • Muhammad Hammad Rasool

摘要

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.