A fractal model for obtaining spontaneous imbibition capillary pressure curves based on 2D image analysis of low-permeability sandstone

Spontaneous imbibition (SI) is the principal production mechanism in naturally fractured reservoirs produced by waterflooding and is essential for fluid flow characterization to predict their future performance. As an alternative to the expensive, time-consuming laboratory measurements, 2D images render a different prospect to obtain SI capillary pressure curves, especially for tight reservoirs. This paper introduces a unique approach to infer SI capillary pressure curves from 2D images through integrating image analysis and fractal theory. Using pore-related information obtained from image analysis, we properly represent the pore structure as bundles of tortuous square and triangular tubes with sinusoidally varying radii to imitate cross-sectional variation between pore bodies and throats. Moreover, we simulate the piston-like and snap-off displacement mechanisms to derive an innovative fractal SI capillary pressure model. The developed model considers the contact angle hysteresis caused by surface roughness and heterogeneity of reservoir rocks. The Mayer-Stowe-Princen (MSP) approach is implemented to compute the entry capillary pressure of piston-like displacement. The laboratory-measured porosity and permeability are utilized to determine the model's 3D-related parameters that cannot be inferred from 2D images. The model reliability is verified with the good accuracy of the predicted capillary pressure curves versus laboratory-measured data of five samples from the Liushagang and Huangliu in the South China Sea. Finally, the fundamental parameters influencing the developed SI capillary pressure model are investigated with sensitivity analysis.