Pre-Darcy Flow and Klinkenberg effect in Dense, Consolidated Carbonate Formations

Experimental studies on pre-Darcy flow generally focus on unconsolidated porous media with high permeability. In this work, pre-Darcy flow is studied in consolidated carbonate rocks from different formations of Zagros basin. The core samples are calcite, dolomite and chalk-salt characterized by low-porosity (12.33–28.21%) and low permeability (0.011–18.53 md). Digital rock images were obtained using dental CT-scan with a resolution of 200 pixels per μm. A series of single-phase flooding experiments were conducted to evaluate the onset of pre-Darcy flow in different cores using N₂ as gas phase. Superficial velocity versus pressure gradient was measured and different onset values were reported. Results indicate the presence of pre-Darcy flow in single phase gas experiments. The minimum observed Darcy velocity was 0.445 × 10⁻⁰⁵ m/s, below which pre-Darcy flow prevails. In addition, different flow regimes such as pre-Darcy, Darcy and non-Darcy flow regimes were determined using reduced pressure drop analysis and Reynolds number analysis. The range of Reynolds number were reported for different flow regimes and different core permeabilities. The pre-Darcy regime was observed at velocities in the range of (0.445–5.88) × 10⁻⁰⁵ m/s for all cores. For a carbonate core with k = 0.01 md, pre-Darcy flow was observed in the range of \(Re_{\sqrt k }\) < 2.1 × 10⁻⁰⁷, Re_d < 0.168 and Re_p < 0.025. It was also found that pre-Darcy flow arises due to Klinkenberg effect at low gas pressure in different core samples which show different behavior depending on their permeability.