This study addresses the diffusion coefficient of CO2 into light-hydrocarbons. Experiments were done under nonisothermal and nonisobaric conditions, using dynamic pendant drop volume analysis to measure the change in hydrocarbon drop volume due to CO2 diffusion, for 25–45 °C and 25–65 bar. A new numerical model was developed, where a spherical drop was used rather than the actual pendant shaped drop, which enabled sensitivity studies. The approach showed 3–6% difference in the surface area of the spherical drop compared to experimental drop. This is translated to less than 6% difference when compared to the published data. Interfacial tension investigations showed a change from a negative (decreasing) to positive (increasing) trend with temperature for pressures 30–60 bar. A suggested explanation was based on the density difference between the drop (CO2+hydrocarbon) and the surrounding CO2. Further, the observed higher diffusion coefficient of n-hexane compared to n-decane may be attributed to viscosity.

Graphical abstract

A numerical study on the effect of complex fracture aperture geometry on propagation of thermal front in a coupled single fracture-matrix system has been carried out. Sinusoidal and logarithmic functions have been used to capture the variation in fracture aperture. Modifications have been made to existing coupled partial differential governing equations to consider the variation of fracture aperture. Effect of temperature on the thermal and physical properties of rock have been incorporated. A fully implicit finite difference scheme has been used to discretize the coupled governing equations. Thermal convection, dispersion and conduction are the major transport processes within fracture, while conduction is the major transport process within rock matrix. The results suggest that variation of fracture aperture increases the heat transfer rate at the fracture-matrix interface. Sensitivity analysis on rock thermal conductivity and fracture aperture have been carried out. The results suggest that the heat transfer from rock matrix to fracture for the case of the parallel plate model is greatly dependent on the rock thermal conductivity (λ m ) as compared to variable aperture model. Further, the thermal front propagation for both parallel plate model and variable aperture model is sensitive to changes in fracture aperture. The heat transfer rate at the interface is greater at smaller fracture apertures and decreases with increase in aperture.

An implicit finite difference numerical model has been developed to investigate the influence of fracture heterogeneity on the propagation of thermal front in a single horizontal fracture-matrix system. Instead of depending on a complex and data-demanding geostatistical method for a precise representation of fracture aperture, a statistical linear congruential generator (LCG) method was applied in the present study to replicate the unpredictable nature of fracture aperture morphology. The results have been compared with the parallel plate model and simple sinusoidal model. Finally, sensitivity analysis of fracture aperture size and fluid flow rate has been carried out to identify the conditions at which fracture heterogeneity is critical. The results indicate that LCG-aperture enhances the heat transfer between fracture and hot rock matrix compared to the parallel and sinusoidal fractures. Further, the temperature profiles in hot rock indicate that there was a greater loss of heat for the case of LCG-aperture (25% loss) compared to sinusoidal (16%) and parallel plate (8%) apertures. It was found that heterogeneity does not play a major role at small fracture aperture size (≤50 µm) and at low flow rates. However, as fracture aperture size increases, the heterogeneity plays a vital part even at low flow rates.

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