Understanding the Impact of Temperature-Dependent Thermal Conductivity on the Steam-Assisted Gravity-Drainage (SAGD) Process. Part 1: Temperature Front Prediction

2014 ◽  
Author(s):  
Mazda Irani ◽  
Marya Cokar
Keyword(s):  
Thermal Conductivity ◽  
Gravity Drainage ◽  
Temperature Dependent ◽  
Steam Assisted Gravity Drainage ◽  
Temperature Front ◽  
The Impact ◽  
Temperature Dependent Thermal Conductivity

Discussion on the Effects of Temperature on Thermal Properties in the Steam-Assisted-Gravity-Drainage (SAGD) Process. Part 1: Thermal Conductivity

SPE Journal ◽  
2013 ◽  
Vol 21 (02) ◽  
pp. 334-352 ◽  
Author(s):  
Mazda Irani ◽  
Marya Cokar
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Temperature Profile ◽  
Conductive Heat Transfer ◽  
Gravity Drainage ◽  
Conductive Heat ◽  
Temperature Dependent ◽  
Steam Chamber ◽  
Steam Assisted Gravity Drainage ◽  
Temperature Dependent Thermal Conductivity

Summary Steam-assisted gravity drainage (SAGD) is the preferred thermal-recovery method used to produce bitumen from Athabasca deposits in Alberta, Canada. In SAGD, steam injected into a horizontal injection well is forced into the reservoir, losing its latent heat when it comes into contact with cold bitumen at the edge of a depletion chamber. Heat energy is transferred from steam to reservoir, resulting in reduced bitumen viscosity that enables the bitumen to flow toward the horizontal production well under gravity forces. Conduction is the main heat-transfer mechanism at the edge of the steam chamber in SAGD, and reservoir thermal conductivity is a key parameter in conductive-heat transfer. Conductive-heat transfer occurs at higher rates across reservoirs with higher thermal conductivity, which in turn affects the temperature profile ahead of the steam interface. Consequently, a reservoir with higher thermal conductivity will result in higher reservoir-heating rates, which lead to higher oil rates. However, when oil-sand reservoirs are heated from reservoir temperature to steam-chamber temperature, the thermal conductivity can decrease up to 25%, which affects the temperature profile and conductive heating at the edge of the steam-saturated zone known as the steam chamber. This study provides an analytical model that includes a temperature-dependent thermal-conductivity value. This novel approach is the first of its kind to incorporate a temperature-dependent thermal-conductivity value within an analytical SAGD model to predict temperature front, oil production, and steam/oil ratio (SOR). Furthermore, if Butler's (1985) model is used, the results reveal that the arithmetic average thermal-conductivity values at reservoir and steam temperatures could be used for temperature-profile prediction, which would result in an error of less than 1% for the range of SAGD applications. The results of this study suggest that the minimum error for oil rates depends on the viscosity/temperature correlation. The optimum thermal conductivity should be calculated at the temperature that gives dimensionless temperatures [i.e., (T−Tr)/(Tst−Tr)] varying between 0.75 to 0.85 for m-values [Butler-suggested power constants (Butler 1985, 1991; Butler and Stephens 1981)] between 3 and 5.6. This study also investigates the effect of including temperature-dependent thermal conductivity on SOR variation and suggests that for both laterally expanding and angularly expanding reservoirs the SOR is independent of the thermal conductivity.

Stagnant lid convection with temperature-dependent thermal conductivity and the thermal evolution of icy worlds

2020 ◽  
Vol 224 (3) ◽  
pp. 1870-1889
Author(s):  
Frédéric Deschamps
Keyword(s):  
Thermal Conductivity ◽  
Thermal Evolution ◽  
Heat Fluxes ◽  
The Body ◽  
Temperature Dependent ◽  
Temperature Dependent Conductivity ◽  
Icy Bodies ◽  
Main Component ◽  
The Impact ◽  
Temperature Dependent Thermal Conductivity

SUMMARY Convection is an efficient process to release heat from planetary interiors, but its efficiency depends on the detailed properties of planetary mantles and materials. A property whose impact has not yet been studied extensively is the temperature dependence of thermal conductivity. Because thermal conductivity controls heat fluxes, its variations with temperature may alter heat transfer. Here, I assess qualitatively and quantitatively the influence of temperature-dependent thermal conductivity on stagnant lid convection. Assuming that thermal conductivity varies as the inverse of temperature $(k \propto 1/T)$, which is the case for ice Ih, the main component of outer shells of solar System large icy bodies, I performed numerical simulations of convection in 3-D-Cartesian geometry with top-to-bottom viscosity and conductivity ratios in the ranges 105 ≤ Δη ≤ 108 and 1 ≤ Rk ≤ 10, respectively. These simulations indicate that with increasing Rk, and for given values of the Rayleigh number and Δη, heat flux is reduced by a factor Rk0.82, while the stagnant lid is thickening. These results have implications for the structures and thermal evolutions of large icy bodies, the impact of temperature-dependent conductivity being more important with decreasing surface temperature, Tsurf. The heat fluxes and thermal evolutions obtained with temperature-dependent conductivity are comparable to those obtained with constant conductivity, provided that the conductivity is fixed to its value at the bottom or in the interior of the ice shell, that is, around 2.0–3.0 W m−1 K−1, depending on the body. By contrast, temperature-dependent conductivity leads to thicker stagnant lids, by about a factor 1.6–1.8 at Pluto (Tsurf = 40 K) and a factor 1.2–1.4 at Europa (Tsurf = 100 K), and smaller interior temperatures. Overall, temperature-dependent thermal conductivity therefore provides more accurate descriptions of the thermal evolutions of icy bodies.

Flow and thermal analysis of Jeffrey nanofluid in a microchannel: Buongiorno's Model

2021 ◽  
pp. 095440892110501
Author(s):  
D.O. Soumya ◽  
B.J. Gireesha ◽  
P. Venkatesh ◽  
Abdulmohsen Alsaiari
Keyword(s):  
Thermal Conductivity ◽  
Brownian Motion ◽  
Thermal Energy ◽  
Energy Concentration ◽  
Physical Parameters ◽  
Temperature Dependent ◽  
Jeffrey Nanofluid ◽  
The Impact ◽  
Temperature Dependent Thermal Conductivity ◽  
Irreversibility Ratio

The present consideration explores the thermal energy and mass transfer process in conducting Jeffrey nanofluid flows through a microchannel. The slip boundary conditions, Brownian motion and temperature-dependent thermal conductivity were considered. The dimensionless governing models have been solved to the best possible investigative solutions using the Runge-Kutta-Fehlberg 4 −5th order numerical procedure. The impact of physical parameters on the momentum, energy, concentration, irreversibility and irreversibility ratio was revealed graphically in detail. It is concluded that the resultant momentum profile is augmented with the relaxation and retardation times parameter all over the flow region. The temperature-dependent thermal conductivity contributes to the resulting thermal energy of the flow system ever-growing to high. The concentration profile was diminutions through growing in the Brownian motion parameter. The irreversibility and irreversibility ratio were obtained mathematically and explained concerning the notable parameters. The magnetic parameter was to diminish the irreversibility rate, but it was augmented by increasing the parameter for the relaxation and retardation times ratio. Effect of thermal radiation, variable thermal conductivity, pressure gradient, buoyancy force and thermophoresis on the Jeffery nanofluid in a microchannel by the Buongiorno model have been inspected for the first time. The effects of this works are innovative and original.

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