Effect Of Variable Thermal Conductivity Of The Formations On The Fluid Temperature Distribution In The Wellbore

A mathematical model has been developed to study the effect of variable thermal conductivity of the formations and wellbore characteristics on the fluid temperature behavior inside the wellbore during injection or production and after shut-in. Curing the injection or production period, the wellbore fluid temperature is controlled mainly by the flow rate and heat lost to the formation. Variable thermal conductivities of the formation have little effect on the fluid temperature profile. However, the change with the time of fluid temperature in the wellbore is related to the formation thermal via heat lost from the fluid to the formation. During early shut-in times, the wellbore fluid temperature is a function of the rate of heat conduction and convection in the fluid and the rate of heat lost which is a complex function of the formation thermal conductivity. There exist negative gradients in the wellbore fluid temperature profile where the formation thermal conductivity changes abruptly from a smaller value to alarger value. As the shut-in time increases, the fluid temperature inside the well bore is strongly affected by differences in formation thermal conductivities. This effect is very apparent after a few hours of shut in. The rate of return of the fluid temperature to the geothermal is proportional to the magnitude of the formation thermal conductivity.