Abstract
A numerical model is investigated representing counter-current spontaneous imbibition of water to displace oil or gas from a core plug. The model is based on mass and momentum conservation equations in the framework of the theory of mixtures. We extend a previous imbibition model that included fluid–rock friction and fluid–fluid drag interaction (viscous coupling) by including fluid compressibility and Brinkman viscous terms. Gas compressibility accelerated recovery due to gas expansion from high initial non-wetting pressure to ambient pressure at typical lab conditions. Gas compressibility gave a recovery profile with two characteristic linear sections against square root of time which could match tight rock literature experiments. Brinkman terms decelerated recovery and delayed onset of imbibition. Experiments where this was prominent were successfully matched. Both compressibility and Brinkman terms caused recovery deviation from classical linearity with the square root of time. Scaling yielded dimensionless numbers when Brinkman term effects were significant.Article HighlightsSpontaneous imbibition with viscous coupling, compressibility and Brinkman terms.Viscous coupling reduces spontaneous imbibition rate by fluid–fluid friction.Brinkman terms delay early recovery and explain seen delayed onset of imbibition.Gas compressibility accelerates recovery and can be significant at lab conditions.Gas compressibility gives recovery with two root of time lines as seen for shale.
Highlights
Fractured reservoirs contribute to around 20% of the hydrocarbon reserves discovered worldwide
In this paper we have studied counter-current spontaneous imbibition driven by capillary forces
The model was formulated based on mass balance and momentum balance equations which account for fluid–rock interactions, fluid–fluid interaction, fluid compressibility and Brinkman terms
Summary
Fractured reservoirs contribute to around 20% of the hydrocarbon reserves discovered worldwide. Water injection has been applied successfully in naturally fractured reservoirs, but is most effective when the matrix is water-wet and capillary forces can take up the injected water spontaneously (from the fractures) This process is referred as spontaneous imbibition and can recover as much oil or gas at matrix level as by forced imbibition if the matrix is strongly water-wet, but less under other wetting conditions (Zhou et al 2000). Spontaneous imbibition can occur counter-currently, where the wetting and non-wetting fluids flow in opposite direction This usually happens when all open sides of the matrix are exposed to wetting phase and gravity is negligible (Morrow and Mason 2001). Spontaneous imbibition is regarded as a crucial driving mechanism for oil recovery from naturally fractured reservoirs (Morrow and Mason 2001; Andersen et al 2014; Abd et al 2019). Numerous works have modeled this phenomenon with analytical and numerical approaches (Mattax and Kyte 1962; Ma et al 1997; Mason et al 2012; Schmid and Geiger 2012)
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