# A numerical model for wet steam circulating in horizontal wellbores during starting stage of the steam-assisted-gravity-drainage process

## Abstract

Steam-assisted-gravity-drainage (SAGD) has been proved effective in heavy oil recovery. Preheating of the wellbore-surrounding reservoir is to circulate steam in the injector and producer so that heat can be conducted into surrounding oil layer. At this stage, the amount of steam injected into the reservoir is neglected. As a result, creating a large temperature difference between wellbore and annuli is key during the preheating process. A model is established for estimating steam properties in the wellbores so that the highest steam temperature in wellbores can be achieved. The model is comprised of mass, energy and momentum balance equations and the model is solved with numerical method. It is found that: (a) rich heat energy reflected in high steam quality does little effect on heat absorption rate of oil layer. The only effective method for temperature increase in oil layer is to increase the steam temperature in wellbores; (b) in order to increase the heat conduction rate to oil layer, a lower steam quality, a higher steam pressure and a lower mass flow rate is recommended.

## Nomenclature

*w*The mass flow rate (kg/s)

*r*The radius (m)

*L*The length of the long tube or annuli (m)

*v*The flow velocity (m/s)

*p*The wet steam pressure (Pa)

*τ*_{f}The shear force of steam flow in long tube and annuli (N)

*h*The enthalpy of wet steam (J/kg)

*T*The temperature of the wet steam under a certain pressure (K)

*f*_{wall}The friction coefficient of the long tube

*U*The heat transfer factor (W/(m

^{2}·K))*h*_{fITi}The forced convection heat transfer factor (W/(m

^{2}·K))*h*_{fITo}The forced convection heat transfer factor (W/(m

^{2}·K))*L*_{v}The latent heat of vaporization (kJ/kg)

*h*_{w}The enthalpy of water (kJ/kg)

*T*_{h}The temperature at the interface between cement sheath and oil layer (K)

*f*_{wi}The convective heat transfer coefficient (W/(m

^{2}·K))*T*_{ei}The formation temperature (K)

## Greek alphabet

*ω*Annuli/oil-layer heat capacity radio (dimensionless)

*θ*The angle between wellbore and the horizontal line (rad)

*ρ*The density of wet steam at the cross-section (kg/m

^{3})*Q*The heat conduction (transfer) rate (J/s)

*λ*The thermal conductivity (W/(m·K))

## Notes

### Acknowledgements

The authors wish to thank the National Basic Research Program of China (2015CB250900), the Program for New Century Excellent Talents in University (Grant No.NCET-13-1030) and the National Natural Science Foundation of China (Grant No.40974055).

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