Study on temperature distribution simulation during cementing of hot dry rock (HDR) geothermal well is rare. It has important guiding significance to simulate the construction process of temperature distribution of hot dry rock on site construction. Based on numerical simulation of HDR considering heat-fluid-solid coupling, the influence of temperature distribution on well cementing is analyzed when the drilling fluid cycles and reaches stable state, respectively, and when the cement slurry is injected during the cementing process. It is found that the seepage at the well bottom accelerates the flow velocity of wellbore; the stable temperature change is less than the cyclic temperature change; and the upper and lower temperature variation of the stratum is greater when the cement slurry is injected. Therefore, as to cement retarder involved, the influence of temperature variation on concretion should be considered during cementing of the hot dry rock geothermal well.
Currently, articles on the simulation of downhole temperature field during well cementing are in a limited number, and especially those on simulating the temperature field of hot dry rock (HDR) well cementing are comparatively rare. By simulating the horizontal and vertical distribution of the HDR downhole temperature field, we investigated the distributing characteristics and influential factors of HDR downhole temperature field, aiming at guiding operation of HDR well cementing.
When the depth of hot dry rock (HDR) well is reaching 1000 m, heat-fluid-solid coupling should be considered for HDR numerical simulation, where both stratum thickness and radius are 1 m; the borehole diameter and length are 0.25 m and 1 m, respectively; the relevant wall thickness and length of drill pipe are 0.015 m and 0.9 m, respectively; and the length of drill bit is 0.05 m, as shown in
1) Flow equation
Flow in free and porous media is applied, which should satisfy the continuity equation:
where
2) Temperature distribution
In the present model, heat transfer within HDR stratum, fluid, drill stem and drill bit in the borehole is considered. Assume that no heat was generated from drill bit, and then the continuity equation of the relevant heat circulation is as follows:
where,
3) Convection heat transfer
The governing equation of convection heat transfer between drilling fluid and well wall is given below,
where
normal vector of solid surface;
The drilling fluid flows in from the entrance and flows out from the exit as for seepage field. Boundaries
As for temperature field, considering heat transfer in the porous media, the values for boundaries a, b, exit and entrance boundaries are all 293.15 K, while those of the borehole wall and boundaries
HDR stratum parameters [
Mesh division of the geometric model is shown in
Well depth | 1000 m | Pore water heat conductivity coefficient | 0.5 W/(m∙K) |
---|---|---|---|
Geothermal gradient | 3˚C/100 m | Slurry density | 1300 kg/m3 |
Rock density | 2700 kg/m3 | Specific heat capacity of slurry | 2800 J/(kg∙K) |
Specific heat capacity of rock | 1400 J/(kg∙K) | Surface heat transfer coefficient | 200 W/(m3∙K) |
Rock heat conductivity coefficient | 10 W/(m∙K) | Slurry heat conductivity coefficient | 1 W/(m∙K) |
Porosity | 0.1 | Drill pipe heat conductivity coefficient | 17 W/(m∙K) |
Permeability | 1e-14(D) | Drill pipe density | 7800 kg/m3 |
Internal friction angle | 30˚ | Drill pipe atmospheric heat capacity | 460 J/(kg∙K) |
Poisson’s ratio | 0.3 | Drill bit density | 3200 kg/m3 |
Biot coefficient | 1 | Drill bit heat conductivity coefficient | 1500 W/(m∙K) |
Pore water density | 1000 kg/m3 | Drill bit atmospheric heat capacity | 400 J/(kg∙K) |
Pore water specific heat capacity | 4200 J/(kg∙K) | Heat transfer coefficient | 200 W/(m2∙K) |
1) Flow field simulation of HDR stratum
Four individual seepage velocities under the well of 10−4 m/s, 10−8 m/s, 10−12 m/s and 0 m/s are used for simulation and calculation, among which the simulation result corresponding to 10−4 m/s is shown in
Clearly, the permeability of the well bottom can affect the flow of drilling fluid. The flow velocity at the bottom of the well increases with better well bottom permeability. However, the influence is generally very small, and thus can be ignored.
In
2) HDR temperature field simulation
In
In
As for HDR geothermal well, the well surface and bottom temperatures are 20˚C and
Seepage velocity (m/s) | 10−4 | 10−8 | 10−12 | 0 |
---|---|---|---|---|
Flow velocity of drilling fluid (m/s) | 4.9616 | 4.9607 | 4.9606 | 4.9606 |
220˚C respectively, and the well depth is 2000 m. Well structure is shown in
Simulation results of temperature distribution of circulating drilling fluid at 0 h, 1 h, 5 h, 10 h, 24 h, 48 h and 96 h are presented in
time. The temperature at different stopping time of upper part decreases while that of lower part increases. Comparison of temperature distribution at different stopping time reveals that temperature variation of upper and lower parts are 5˚C and 16˚C, respectively, and temperature difference of upper annular space is far smaller than that of lower part. Meanwhile, regarding comparison between
After being stable for 96 h, the ahead fluid and cement slurry will be injected successively, and then the relevant temperature variation of the annular space is shown in
Well depth | Earth temperature | Standing 96 h | Ahead fluid injection | Cement slurry injection (1 h) | Cement slurry injection (2 h) | Cement slurry injection (3 h) | Cement slurry injection (4 h) | Cement slurry injection (5 h) | Subsequent liquid injection | Waiting on cement setting (1 h) | Waiting on cement setting (10 h) | Waiting on cement setting (24 h) | Waiting on cement setting (48 h) | Waiting on cement setting (96 h) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0.0 | 20.00 | 21.32 | 26.69 | 36.17 | 37.72 | 38.67 | 39.31 | 39.77 | 27.34 | 26.23 | 24.44 | 23.17 | 22.17 | 21.37 |
6.1 | 20.61 | 22.00 | 27.09 | 36.48 | 38.01 | 38.95 | 39.59 | 40.04 | 27.80 | 26.75 | 25.06 | 23.84 | 22.87 | 22.09 |
29.4 | 22.94 | 24.40 | 29.69 | 38.59 | 39.99 | 40.87 | 41.46 | 41.89 | 30.64 | 29.59 | 27.67 | 26.34 | 25.30 | 24.48 |
35.5 | 23.55 | 24.89 | 30.77 | 39.46 | 40.81 | 41.65 | 42.23 | 42.65 | 31.81 | 30.30 | 27.95 | 26.59 | 25.62 | 24.90 |
300.0 | 50.00 | 50.73 | 53.82 | 61.86 | 62.57 | 63.03 | 63.36 | 63.60 | 55.27 | 54.14 | 52.74 | 51.92 | 51.30 | 50.84 |
304.8 | 50.48 | 51.38 | 54.80 | 62.41 | 63.10 | 63.55 | 63.87 | 64.10 | 56.21 | 54.95 | 53.45 | 52.62 | 51.98 | 51.47 |
306.1 | 50.61 | 51.61 | 55.37 | 62.72 | 63.40 | 63.84 | 64.16 | 64.39 | 56.91 | 55.84 | 53.98 | 52.96 | 52.24 | 51.67 |
609.6 | 80.96 | 81.06 | 81.58 | 87.73 | 87.66 | 87.65 | 87.65 | 87.64 | 81.92 | 81.57 | 81.55 | 81.44 | 81.29 | 81.17 |
914.4 | 111.44 | 111.29 | 111.10 | 115.95 | 114.94 | 114.31 | 113.86 | 113.53 | 109.37 | 109.39 | 110.52 | 110.97 | 111.17 | 111.29 |
1219.2 | 141.92 | 141.37 | 139.64 | 141.91 | 140.02 | 138.70 | 137.88 | 137.30 | 135.63 | 136.11 | 138.80 | 140.03 | 140.73 | 141.19 |
1300.0 | 150.00 | 150.17 | 151.25 | 149.76 | 147.53 | 146.14 | 145.29 | 144.66 | 146.11 | 145.95 | 147.90 | 148.89 | 149.43 | 149.74 |
1306.1 | 150.61 | 150.97 | 152.67 | 150.24 | 147.98 | 146.59 | 145.75 | 145.11 | 147.50 | 147.36 | 148.95 | 149.74 | 150.17 | 150.43 |
1524.0 | 172.40 | 172.12 | 171.58 | 169.39 | 165.37 | 162.51 | 160.39 | 158.68 | 165.24 | 165.77 | 168.76 | 170.20 | 171.05 | 171.62 |
1706.9 | 190.69 | 189.51 | 185.87 | 186.09 | 182.53 | 179.61 | 177.27 | 175.33 | 178.67 | 180.02 | 184.92 | 187.05 | 188.32 | 189.21 |
1767.8 | 196.78 | 195.15 | 189.75 | 190.21 | 186.68 | 183.72 | 181.31 | 179.30 | 182.22 | 183.90 | 189.78 | 192.31 | 193.81 | 194.87 |
1793.9 | 199.39 | 197.84 | 192.75 | 192.86 | 189.31 | 186.31 | 183.84 | 181.78 | 184.88 | 186.48 | 192.41 | 194.98 | 196.49 | 197.56 |
1800.0 | 200.00 | 198.69 | 194.53 | 193.96 | 190.40 | 187.38 | 184.88 | 182.78 | 186.42 | 187.84 | 193.49 | 195.94 | 197.37 | 198.37 |
1806.1 | 200.61 | 199.30 | 195.43 | 194.40 | 190.84 | 187.81 | 185.29 | 183.18 | 187.35 | 188.91 | 194.25 | 196.53 | 197.90 | 198.91 |
1828.8 | 202.88 | 201.44 | 197.17 | 195.37 | 191.79 | 188.73 | 186.18 | 184.05 | 188.92 | 190.70 | 196.18 | 198.53 | 199.96 | 201.02 |
1889.8 | 208.98 | 206.72 | 199.58 | 197.08 | 193.41 | 190.26 | 187.64 | 185.44 | 191.05 | 193.41 | 200.24 | 203.20 | 205.04 | 206.44 |
1950.7 | 215.07 | 211.88 | 201.22 | 197.67 | 193.85 | 190.58 | 187.87 | 185.60 | 192.45 | 195.43 | 203.85 | 207.54 | 209.85 | 211.63 |
1981.7 | 218.17 | 214.47 | 201.73 | 196.76 | 192.82 | 189.47 | 186.70 | 184.39 | 192.85 | 196.16 | 205.50 | 209.63 | 212.26 | 214.29 |
1987.8 | 218.78 | 214.99 | 201.75 | 195.91 | 191.93 | 188.55 | 185.76 | 183.45 | 192.84 | 196.22 | 205.75 | 209.98 | 212.67 | 214.76 |
1993.9 | 219.39 | 215.46 | 201.71 | 195.56 | 191.57 | 188.17 | 185.38 | 183.07 | 192.79 | 196.26 | 206.00 | 210.34 | 213.10 | 215.24 |
2000.0 | 220.00 | 215.95 | 201.61 | 195.17 | 191.16 | 187.75 | 184.96 | 182.65 | 192.71 | 196.29 | 206.27 | 210.73 | 213.56 | 215.76 |
It can be observed from
When conditions are ripe, we can test how the simulations correspond to the real experimental data.
1) The seepage at the bottom of the well can accelerate the velocity of flow in the wellbore, but the impact is negligible.
2) The temperature of upper stratum increases with the increase of circulation time, but the temperature variation of lower stratum has an opposite trend.
3) At stable circulation state, the temperature of upper part decreases, while that of lower part increases. The temperature variation of upper annular space is far lower than that of lower part in stable state. The temperature variation in stable state is less than
that in cyclic state.
4) During injection of cement slurry, the temperature variation of upper and lower stratum is greater. During waiting on the cement setting period, the subsequent annular space temperature will return to stratum temperature gradually. Generally, the control agent of cement slurry solidification is very sensitive to temperature, so the influence of stratum temperature variation on cement slurry solidification should be considered during circulation of drilling fluid and injection of cement slurry, aiming at ensuring construction safety and increasing well cementing quality.
This research was supported by NSFC project “Study on the evolution mechanism of composite materials with high temperature resistance, high pressure resistance, and low elastic modulus”, No. 51474192; and “Basic research funding of central universities”, No. 2652015067.
Yang, H. and Shao, Y. (2017) Numerical Simulation for Hot Dry Rock Geothermal Well Temperature Field. Advances in Chemical Enginee- ring and Science, 7, 34-44. http://dx.doi.org/10.4236/aces.2017.71004