Mathematical Model and Application of Spontaneous and Forced Imbibition in Shale Porous Media-Considered Forced Pressure and Osmosis

Abstract

The energized hydraulic fracturing technology of “energizing, hydraulic fracturing, shut-in, and flowback” has achieved good development results in some shale oil fields. The mechanisms of forced imbibition (FI) under forced pressure (the difference between hydraulic fluid pressure and original pore pressure) need to be further studied; especially, the difference and boundary of various mechanisms in forced soaking are still unclear. The wettability of pores is different, the reservoir shows strong mixed wettability, and the permeability of clay mineral pores has osmotic pressure. This paper analyzes the imbibition forces in distinct types of pores, and the dynamic models of spontaneous imbibition (SI) and FI in a single capillary tube are established. Based on the fractal theory and capillary bundle model, the mathematical models of SI and FI at the core scale are established, and semi-analytical solution models considering different forces are proposed, especially considering forced pressure and osmosis. In addition, the above mathematical models are fitted and verified by imbibition experiments and NMR, which ensured the accuracy and validity of the mathematical models. In this paper, the sensitivity analysis of different factors to oil displacement rate and oil recovery by imbibition is quantitatively evaluated. The research shows that the imbibition rate of FI is faster than that of SI, and the ultimate oil recovery is also higher. Smaller pores mainly control the imbibition rate, which increases with oil–water interfacial tension and forced pressure. However, the imbibition rate decreases with increasing water-phase viscosity and fractal dimension.

Experimental study on the influence of pore structure on spontaneous imbibition in marine black shale

“…When the direction of imbibition is consistent with that of shale gas production, capillary force becomes the driving force of shale gas migration; otherwise, it creates resistance causing the retention of fracturing fluid, known as the water blocking effect, which can negatively impact shale gas production (Holditch, 1978;Lu et al, 2022). Therefore, water imbibition in shale is considered as a key factor affecting shale gas recovery, and understanding the transport mechanism of the water imbibition process in shale is of great importance for shale gas production (Roychaudhuri et al, 2013;Zhao et al, 2017;Meng et al, 2020;Li et al, 2022a). Spontaneous imbibition, also known as capillary filling, occurs naturally without external pressure differences (Cai et al, 2014;Dou et al, 2021).…”

Imbibition Mechanisms of Fracturing Fluid in Shale Oil Formation: A Review from the Multiscale Perspective

“…The imbibition length and pore imbibition volume of these two types of imbibitions have been established. Li et al 119 proposed a model considering the capillary imbibition, forced pressure, and osmosis-dependent fracturing fluid loss in shale formations. As shown in Figure 9(III), compared with the capillaries in brittle minerals, osmosis occurs during imbibition in clay minerals.…”

“…Various capillary bundle models for the imbibition characterization: (I) curved capillary; (II) capillary bundle model including the organic and inorganic matter; and (III) spontaneous imbibition and forced imbibition in (a) clay and (b) brittle minerals . Panel (I) has been reproduced with permission from ref .…”

“…Copyright 2019, Elsevier. Panel (III) has been reproduced with permission from ref . Copyright 2022, American Chemical Society.…”

Correlation between Natural Seepage and Ionic Diffusion in Shales

“…Another aspect is to complement the results of the research core experiments through modeling . As well as carrying out explorations of the combined nature of experiments and mathematical models. , For example, Qu (2022) supplemented the modified proppant settling velocity model based on the original wellhead pressure calculation model through experiments to achieve the accurate calculation of the critical backflow velocity of proppant. The average errors of this model in field tests were 11.9 and 11.6%, respectively .…”