Revisiting Thomson equation for accurate modeling of pore scale thermodynamics of hydrocarbon solvents

Abstract

As stated by the classical Thomson equation, the pore scale thermodynamics of a solvent is different from bulk conditions, being critically controlled by capillary characteristics. This equation shows that the boiling point temperatures decrease remarkably as the pore size becomes smaller, after a threshold value. This paper experimentally investigates this phenomenon for hydrocarbon solvents and compares the results with the values, obtained from the Thomson equation, to test its applicability in modeling heavy-oil recovery by solvents under nonisothermal conditions. As an initial step, the boiling point temperatures of two single-component solvents (heptane and decane) were measured by saturating Hele-Shaw type cells with variable apertures (ranging from 0.04 mm to 5 mm) and monitoring the boiling process. One experiment was run with a thickness of 12 mm to represent the bulk case. As the aperture (pore size) became smaller, the boiling point temperature decreased. For example, the measured boiling temperatures of heptane and decane were approximately 58 °C and 107 °C for the aperture values less than 0.15 mm, which were considerably lower than the “bulk” values (around 40%). In the next step, the same experiments were repeated using micromodels, representing porous media. Using the Thomson equation, the boiling points of the selected liquids were mathematically computed and compared with the experimental results from Hele-Shaw and micromodel experiments. Finally, modifications to the Thomson equation and alternative formulations were suggested.

Thermodynamics of liquids in capillary medium

“…To test the theory presented in the previous section and determine the boiling points of solvents at pore scale (capillaries from nanoscale to macroscale), experiments were performed using microfluidic chips. In a series of works, the investigation was initiated using Hele-Shaw glass cells to visualize the nucleation (Al-Kindi & Babadagli 2018, 2019 b ) and vaporization (Al-Kindi & Babadagli 2019 a ) of several liquids in confined spaces with capillary sizes ranging between 0.04 and 12 mm. All the experiments with Hele-Shaw cells and microfluidic chips were conducted under atmospheric pressure (1 atm).…”

“…To achieve precise measurements, a heat transfer study was implemented using the Fourier's law of heat conduction (Al-Kindi & Babadagli 2019 b ). In the microfluidic and Hele-Shaw cell experiments, the temperature was sensed on the exterior surface of the chips.…”

“…Such analysis was repeated with every experiment to calculate the actual fluid temperature within the Hele-Shaw and microfluidic models.

Figure 2.Schematic of a Hele-Shaw/microfluidic chip placed on a heating plate (Al-Kindi & Babadagli 2019 b ).

…”

“…The thermodynamics and phase behaviour in capillary media are different from those of the bulk condition (Al-Kindi & Babadagli 2019 a , b ). This was first formulated by Lord Kelvin (Thomson 1872) indicating that the saturation pressure and temperature are inversely proportional to the capillary size.…”

“…This was first formulated by Lord Kelvin (Thomson 1872) indicating that the saturation pressure and temperature are inversely proportional to the capillary size. This yields lower temperatures for boiling (Al-Kindi & Babadagli 2018, 2019 b ) or lower pressures for condensation (Tsukahara et al . 2012; Bao et al .…”