_{1}

The wellbore temperature has an important effect on design and drilling of deep well.
** **Based on energy conservation equations and actual drilling data of one deep well, the wellbore temperature distribution was simulated and the influence of different parameters on the wellbore temperature was revealed
using the software of Hydraulics Analysis System. The results show that, while drilling, the mud temperature in wellbore gradually decreases from the formation temperature to the stable temperature, and it is higher than the mud
inlet temperature on ground, the annular temperature is higher than the temperature in drill string, and the bottom hole temperature is higher than the ground temperature. The effect of geothermal gradient on wellbore temperature is great, while the mud density is negligible. The bottom hole temperature increases with the increase of mud inlet temperature, geothermal gradient, mud thermal conductivity and decrease of mud flow rate, mud specific heat and mud density.

With the increase of world energy demand and the development of petroleum industry, deep and ultra-deep wells have become an important way of oil-gas development [

In 1962, Ramey proposed the classical method of predicting wellbore fluid temperature distribution [

The well structure and heat transfer diagram in deep well is shown in

The energy conservation equations of various media in the wellbore system [

∂ ( ρ c T ) ∂ t + ∂ ( ρ c v T ) ∂ z = 1 r ∂ ∂ r ( r k c ∂ ( c T ) ∂ r ) + ∂ ∂ z ( k c ∂ ( c T ) ∂ z ) + S (1)

S = ρ T d c d t − ∇ ( k c T ∇ c ) + q f + q t (2)

In the above equations, t is time, z is the axial position along wellbore, r is the radial position in borehole, T is the temperature in drill string or annular, ρ is the density of drilling fluid, c is the specific heat of drilling fluid, v is the drilling fluid flow velocity, T is the temperature of drilling fluid, k is the convective heat transfer coefficient, q f is the heat generated by mechanical energy loss of rotary drilling tool, pressure drop of bit nozzle or fluid circulating pressure loss in per volume, q t is the heat transfer quantity in per volume between the tube

string and the annular space, or between the annular space and the formation.

Apparently the temperature distribution is related not only with heat conduction but also with fluid pressure transfer. Due to the complexity the model cannot be calculated directly. HAS solves the equations to get the temperature distribution in deep well using full implicit difference and Gauss-Seidel iteration methods.

To calculate borehole pressure loss accurately, HAS uses different mud rheological modes (powerlaw, binham, carson and H-B) and a variety of rheological parameter calculation and optimization methods to descript the mud rheological properties. The effects of drill pipe rotation, eccentricity, joints and the downhole motor pressure drop are also taken into account as well as the different hole cleaning conditions, which are the flow with single-phase fluid, the flow with full suspension of cuttings, the flow with general cleaning condition and the flow with poor cleaning condition in the calculation of borehole pressure loss, based on the advanced three-layer cuttings dynamic transport theoretical model of ERW, empirical calculation model of cuttings transport in whole section of ERW under multiple working conditions [

Coupling the above model of pressure loss and calculation model [

Based on these models, HAS can be also used for hydraulics design before drilling, hydraulics monitoring during drilling and hydraulics analysis and optimization before or after drilling. It can be used for hydraulics analysis, monitoring, design and optimization of complex structural wells drilling such as conventional directional wells, horizontal wells, sidetrack wells, small wellbore wells, deep wells, ultra-deep wells, HTHP wells, deepwater wells, etc.

The temperature analysis module of HAS is shown in

A vertical deep well of 7000m was drilled with Φ215.9 mm bit, Φ139 mm drill pipe. The oil-based mud density was 1.75 g/cm^{3}, mud inlet temperature was 27˚C, mud flow rate was 30 L/s, nozzle combination was Φ22 mm + Φ22 mm + Φ33 mm, the specific heat of mud, steel and formation were 1675, 400 and 837 J/(Kg·˚C) respectively, and the thermal conductivity was 1.73, 44 and 2.25 W/(m·˚C) respectively, the geothermal gradient was 3˚C/100m.

with time when drilling to 7000 m. It can be seen from the figures that with the progress of drilling, the mud temperature in wellbore gradually decreases from the geothermal temperature to a stable temperature. After 16 hours, the temperature change begins to slow down whether in annular or drill string. The bottom hole temperature is about 118˚C, which is 91˚C higher than the mud inlet temperature, and the annular temperature is greater than the temperature in drill string. If the geothermal gradient is higher, for example 5˚C/100m in Southwest oil and gas field in China, the bottom hole temperature will become a big problem for drilling.

In general, the temperature in annular is always higher than drill string. Therefore, the sensitivity analysis is performed with the annular temperature distribution when drilling to 7000 m after 16 hours. The factors affecting the temperature distribution include mud inlet temperature (tin), geothermal gradient (tg), mud specific heat (Cf), mud thermal conductivity (Kf), mud density (ρf) and mud flow rate (Qf). The influence of each factor on the annulus temperature is shown in Figures 4-6. It can be seen from these figures that the bottom hole temperature increases with the increase of mud inlet temperature, geothermal gradient and mud thermal conductivity, and decreases with the increase of mud flow rate, mud specific heat and mud density. Geothermal gradient and mud specific heat have a greater impact on the annulus temperature field than mud thermal conductivity, mud inlet temperature and mud flow rate, while mud density has negligible impact.

1) Based on the theory of fluid mechanics and heat transfer, considering the characteristics of deep well drilling, a wellbore temperature model was proposed in drilling of deep wells. Using full implicit difference and Gauss-Seidel iteration

methods, the model was solved and the distribution of wellbore temperature can be calculated and analyzed.

2) With the progress of drilling, the mud temperature in wellbore gradually decreases from the geothermal temperature to a stable temperature. The mud temperature in wellbore is higher than the mud inlet temperature on the ground, the annulus temperature is higher than the temperature in the drill string, and the bottom hole temperature is higher than the ground temperature.

3) The factors affecting the temperature field include mud inlet temperature, geothermal gradient, mud specific heat, mud thermal conductivity, mud density and mud flow rate, etc. The bottom hole temperature increases with the increase of mud inlet temperature, geothermal gradient and mud thermal conductivity, and decreases with the increase of mud flow rate, mud specific heat and mud density.

4) Geothermal gradient and mud specific heat have a greater impact on the annulus temperature field than mud thermal conductivity, mud inlet temperature and mud flow rate, while mud density has negligible impact.

The author declares no conflicts of interest regarding the publication of this paper.

Xia, B.Y. (2021) Research on Temperature Distribution in Wellbore of Deep Well Drilling. Open Journal of Applied Sciences, 11, 1269-1276. https://doi.org/10.4236/ojapps.2021.1112096