Geothermal energy is clean and independent to the weather and seasonal changes. In China, the huge demanding of clean energy requires the geothermal energy exploitation in the reservoir with depth larger than 1000 m. Before the exploitation, it is necessary to estimate the potential geothermal energy production from deep reservoirs by numerical modeling, which provides an efficient tool for testing alternative scenarios of exploitation. We here numerically assess the energy production in a liquid-dominated middle-temperature geothermal reservoir in the city of Tianjin, China, where the heat and fluid transport in the heterogeneous reservoir and deep wellbores are calculated. It is concluded that the optimal injection/production rate of the typical geothermal doublet well system is 450 m3/h, with the distance between geothermal doublet wells of 850 m. The outflow temperature and heat extraction rate can reach 112°C and 43.5 MW, respectively. Through decreasing injection/production rate lower than 450 m3/h and optimizing layout of the injection well and production well (avoiding the high permeability zone at the interwell sector), the risk of heat breakthrough can be reduced. If the low permeability zone in the reservoir is around injection well, it usually leads to abnormal high wellhead pressure, which may be solved by stimulation technique to realize stable operation. The methodology employed in this paper can be a reference for a double-well exploitation project with similar conditions.
In China, coal burning contributes 70% of CO2 emissions, 80% of SO2 emissions, and 70% of soot emissions [
Most of the geothermal resources in China are of middle and low temperature. Among 2700 geothermal wells and thermal springs, only 700 spots have the temperature higher than 80°C [
The HT processes relating to the cold water injection into the geothermal reservoir environment have been evaluated by analytical and numerical methods. Gringarten and Sauty [
In contrast, the numerical models can address the complex conditions in the field, such as irregular boundary conditions and heterogeneous distribution of hydraulic and thermal parameters. These numerical models include TOGUH2 and FEFLOW, which can simulate two-dimensional [
We here employed T2WELL to simulate the HT processes in a typical geothermal reservoir in Tianjin, where the fluid processes in the wellbore are described by 1D non-Darcy flow, while in the reservoir 3D fluid and heat transport processes are calculated. We compared the energy production under 5 scenarios of geothermal exploitation in the heterogeneous geothermal reservoir. As a result, the potential production rate in this geothermal field is determined.
The Shanlingzi Geothermal Field in the eastern Tianjin, China, is located in the Panzhuang Uplift, surrounded by the Cangdong Fault, Tianjin Fault, Hangu Fault, and Haihe Fault (Figure
(a) Location of the Wumishan geothermal reservoir, Tianjin, China, (b) stratigraphy in the research area, and (c) the position of existing boreholes in the model domain.
This geothermal reservoir is composed of carbonate rocks. The downhole logs in well DL-4 and aquifer tests in 9 wells yield that the porosity in the reservoir ranges from 1.9% to 9.4% and permeability from 1.0 × 10−16 m2 to 1.25 × 10−12 m2 (Table
Permeability and porosity measured in 9 wells.
Well number | Start buried depth | End buried depth | Thickness of exposed Wumishan Formation | Permeability (m2) | Porosity (%) |
---|---|---|---|---|---|
DL-1 | 1800 | 2328 | 528 | 3.65 × 10−13 | 5%–6% |
DL-2 | 1798 | 2100 | 302 | 1.0 × 10−12 | |
DL-3 | 3481 | 3634 | 153 | 2.09 × 10−13 | |
DL-4 | — | 2122 | — | 1.25 × 10−12 | |
DL-5 | 1846 | 2384 | 538 | 4.89 × 10−13 | |
DL-6 | — | 2533 | — | 4.88 × 10−13 | |
DL-7 | 1655 | 2327 | 672 | 3.07 × 10−13 | |
DL-8 | — | 2373 | — | 2.77 × 10−13 | |
DL-9 | — | 2495 | — | 2.63 × 10−13 | |
DL-4 (well logging data) | 1938.7 | 2314.9 | — | 1.0 × 10−16-4.7 × 10−15 | 1.9%–9.4% |
Following the geological conditions in the Shanlingzi Geothermal field, we selected an area of 48 km2 to investigate the penitential heat production potential based on a double well heat extraction method: one well for injection and another for extraction. The maximum depth of the model reaches 4000 m, corresponding to the bottom of the Wumishan geothermal reservoir. Within this depth, there are seven layers of formations and lithology logs in seven deep boreholes (Figures
Lithology structure of the study area (rectangular area of the dotted line in Figure
TOUGH2-WELL [
For the fluid flow,
For the heat transport,
In the wellbore, the fluid flow is described by
It is noted that the
The heat exchange between wellbore and reservoir is determined by
Due to the heavy cost of drilling, limited data are available regarding the temperature and pressure measurement at the depth from 3300 m to 4000 m. In this study area, temperature and pressure are measured in four boreholes, within the maximum depth of 2750 m (Figures
The temperature (a) and pressure (c) measured in the shallow aquifers extended to the deep geothermal reservoir by a 1D natural state model. The steady temperature distribution (b) of cases (N1–N6) with calibrated heat conductivity. Temperature variation with time (d) of 5 points in (b).
Key thermal properties of the western thermal reservoir of Cangdong Fault (the solid rectangular zone as shown in Figure
Properties | Thickness (m) | Porosity | Permeability (m2) | Rock gain density (kg/m3) | Specific heat (J/kg °C) |
---|---|---|---|---|---|
Q | 520 | 0.25 | 2.37 × 10−17 | 2232 | 920 |
Nm | 1078 | 0.29 | 4.65 × 10−13 | 1930 | 958 |
Ng | 78 | 0.32 | 6.6 × 10−13 | 2012 | 909 |
Qn | 114 | 0.05 | 2.09 × 10−13 | 2600 | 909 |
Jxw | 2110 | 0.05 | 3.65 × 10−13 | 2677 | 838 |
Bottom boundary | 100 | 0.05 | 3.65 × 10−13 | 2677 | 2000 |
The rational of using a 1D model to describe the heat transport processes in the natural status is that the geothermal energy and groundwater in the deep thermal reservoir have not yet been extensively exploited and the groundwater flow velocity in the aquifer is extremely low (1–10 m/yr) [
The temperature and pressure logging data are collected about 1–1.5 months before the exploitation season. The equilibration time can be at least 6 months, for the heating period in Tianjin is from November 15th to March 15th of the following year. The test data can represent the temperature and pressure distribution of the reservoir after the thermal-hydraulic conduction process between water and rock matrix is fully balanced under the hydrostatic condition.
In order to obtain thermal-physical parameters of geological layers, a 1D model based on real geological conditions is established. The cases from N1 to N6 is set up with different heat conductivity, and other properties are the same (summarized in Table
Heat conductivity setting of each case (N1–N6) (Q: Quaternary caprock; Nm: Minghuazhen group of Neogene; Ng: Guantao group of Neogene; Qn: Qingbaikou system; Jxw: Wumishan group of Jixian).
Cases | N1 | N2 | N3 | N4 | N5 | N6 | |
---|---|---|---|---|---|---|---|
Heat conductivity W/m °C | Q | 2.5 | 2.0 | 1.48 | 1.48 | 1.48 | 1.48 |
Nm | 2.5 | 2.0 | 2.0 | 2.00 | 2.00 | 2.00 | |
Ng | 2.5 | 2.5 | 2.5 | 2.50 | 2.50 | 2.50 | |
Qn | 2.5 | 2.5 | 2.5 | 2.50 | 2.50 | 2.50 | |
Jxw | 2.5 | 2.5 | 2.5 | 2.85 | 3.20 | 3.80 | |
Bottom boundary | 2.5 | 2.5 | 2.5 | 2.85 | 3.20 | 3.80 |
The thickness of each layer is given as the average values according to the downhole logs in seven boreholes (Figure
In the sedimentary basin, the heat transfer speed of the caprock with low heat conductivity (caprock) is low, which leads to the high gradient of geothermal temperature. With the same heat flux, the bedrock usually has high heat conductivity and high heat transfer speed, which leads to the low temperature gradient. When all the layers in the model have the same heat conductivity, the temperature in the steady state has changed a little, compared with the initial temperature (Figure
Based on the heat conductivity and hydrogeological parameters in case N5 (best fitting), the different specific heat of the Wumishan Formation (808 J/kg °C, 838 J/kg °C (N5), 868 J/kg °C, 898 J/kg °C) is set up to determine the influence on temperature distribution in the steady state. When the natural state model reaches the steady state, temperature distribution almost does not change with different specific heat of bed rock. At present, the measured data of the specific heat capacity of the rock is still limited. In the future, the influence of specific heat of caprock and bedrock on the heat transfer mechanism of the steady-state model will be explored.
The 5 spots with different depths (Figure
The double well geothermal system is established in the Wumishan reservoir. One well is used for heat extraction and another well for fluid injection, to maintain the water balance. A 3D conceptual model with the domain size of 6000 m × 8000 m × 700 m is established (Figure
(a) Lateral 2D cross section of the model and (b) well placement in the model domain and discretization.
Geological and thermophysical parameters of wellbore.
Wellbore parameter | |
---|---|
Roughness (mm) | 0.046 |
Diameter (m) | 0.15 |
The distance between wells (m) | 850 |
Range of buried depth (m) | 3300–4000 |
Reinjection temperature | 30 |
Temperature (°C) | 111–120°C |
Pressure (MPa) | 32.6–38.3 |
In the model domain, the injection and extraction via two wells interrupt the fluid and heat transport near the wells, but does not affect the lateral boundaries that are far enough from the wells, where constant pressure and temperature boundary conditions are employed. The heat transfer between wellbore and surrounding rock is calculated by
Parameter setting of the modeling cases.
Cases | Injection/production rate (m3/h) | Porosity | Permeability (m2) | Homogenization or heterogeneity |
---|---|---|---|---|
Reference case simulation (RCS) | 450 | 0.05 | 3.65 × 10−13 | Homogenization |
H1 | 150 | 0.05 | 3.65 × 10−13 | Homogenization |
H2 | 300 | 0.05 | 3.65 × 10−13 | Homogenization |
H3 | 600 | 0.05 | 3.65 × 10−13 | Homogenization |
H4 | 750 | 0.05 | 3.65 × 10−13 | Homogenization |
H5 | 900 | 0.05 | 3.65 × 10−13 | Homogenization |
C1–C5 | 450 | 0.01–0.09 | 3.65 × 10−15–3.65 × 10−11 | Heterogeneity |
There is no such a deep geothermal well with completion depth more than 4000 m finished in Dongli District, which brings a difficulty in sample gathering, including groundwater samples and rock samples. In real strata, density, porosity, permeability, heat conductivity, and specific heat can vary a lot from different rock types. When the fluids flow through the aquifer, it may give priority to the high porosity and permeability zone. As for the above thermophysical parameters of the reservoir, the permeability and porosity have the largest effect on flow field and heat extraction [
In this paper, 5 scenarios were designed for comparison in which the permeability and porosity of the subdomain are heterogeneous. There will be a great difference in the distribution of porosity and permeability in the actual reservoir, but the correlation of porosity and permeability has facilitated the study of the heterogeneity of the reservoir.
Bryant et al. [
Compared with clastic rock, different kinds of the relationship between porosity and permeability of carbonate reservoirs are much more complex [
The logging interpretation of the geothermal reservoir at DL-6 well.
Sequence number | Start depth (m) | End depth (m) | Thickness (m) | Porosity (%) | Permeability (m2) |
---|---|---|---|---|---|
1 | 1938.7 | 1944.9 | 6.2 | 9.36 | 4.71 × 10−15 |
2 | 1959.4 | 1965.5 | 6.1 | 3.69 | 5.00 × 10−16 |
3 | 1972.7 | 1977.6 | 4.9 | 4.64 | 4.10 × 10−16 |
4 | 1982.5 | 1989.5 | 7.0 | 2.70 | 1.10 × 10−16 |
5 | 1998.6 | 2004.8 | 6.2 | 7.25 | 2.63 × 10−15 |
6 | 2011.7 | 2030.4 | 18.7 | 6.36 | 1.66 × 10−15 |
7 | 2048.0 | 2055.7 | 7.7 | 4.01 | 4.70 × 10−16 |
8 | 2090.5 | 2105.4 | 14.9 | 4.49 | 4.50 × 10−16 |
9 | 2119.1 | 2132.0 | 12.9 | 7.74 | 2.76 × 10−15 |
10 | 2132.0 | 2138.5 | 6.5 | 3.63 | 1.40 × 10−16 |
11 | 2147.0 | 2150.1 | 3.1 | 7.35 | 1.67 × 10−15 |
12 | 2153.2 | 2157.7 | 4.5 | 6.55 | 9.70 × 10−16 |
13 | 2159.5 | 2161.7 | 2.2 | 3.02 | 1.2 × 10−16 |
14 | 2166.9 | 2182.1 | 15.2 | 1.85 | 1.00 × 10−16 |
15 | 2192.7 | 2199.4 | 6.7 | 6.90 | 1.72 × 10−15 |
16 | 2212.2 | 2216.7 | 4.5 | 3.57 | 1.50 × 10−15 |
17 | 2221.5 | 2224.8 | 3.3 | 3.54 | 1.30 × 10−16 |
18 | 2255.4 | 2267.9 | 12.5 | 5.19 | 6.80 × 10−16 |
19 | 2274.9 | 2278.4 | 3.5 | 4.48 | 4.60 × 10−16 |
20 | 2292.4 | 2297.0 | 4.6 | 4.34 | 6.00 × 10−16 |
21 | 2314.9 | 2317.3 | 2.4 | 4.21 | 4.80 × 10−16 |
The relationship between permeability and porosity of dolomite in Wumishan Formation of typical geological conditions.
The permeability is generated randomly following the log-normal distribution [
Five representative distributions of permeability and porosity are selected and discussed (Figure
Five hypothetical heterogeneous permeability distributions ((a) C1, (c) C2, (e) C3, (g) C4, and (i) C5) and the corresponding two-dimensional cross sections (b, d, f, h, j) at east 3000 m. Red dashed lines and blue dashed lines indicate the location of production well and injection well, respectively.
The heat production is under a constant rate of 450 m3/h for 50 years, the bottom pressure in injection well increases to 38.64 MPa (increased by 1.10% when compared to the initial pressure), and the bottom pressure in production well decreases to 38.11 MPa (reduced by 0.28%) (Figure
Temperature (a) and pressure (c) field distributions at the injection/production rate of 450 m3/h, and temperature (b) and pressure (d) field distributions at the injection/production rate of 900 m3/h along a 2D SW-NE trending cross section of the reservoir (50 years). Black dotted lines represents the location of injection well and production well.
Temperature of outlet water (a) and heat extraction rate (b) variation for different constant production rates.
The wellhead temperature, under the constant rate of 150 m3/h and 300 m3/h, increases to about 1.65°C and 0.65°C after 50 years, compared with the base case of 450 m3/h (Figure
Fluid temperature, pressure, enthalpy, and operating cost should be considered when evaluating the productivity of geothermal extraction engineering. Due to negligible effect of the pressure on energy balance, the heat extraction rate (
It is illustrated in Figure
As shown in Figure
The temperature distribution along a 2D SW-NE trending cross section of the reservoir after 50 years in the reference case simulation ((a) RCS) and five cases in the heterogeneity of permeability ((b) C1, (c) C2, (d) C3, (e) C4, and (f) C5). Black dotted lines represents the location of injection well and production well.
The temperature profile (a) and flow rate variation (b) along open-hole section of production well after 50 years. Heat extraction rate variation (c) and output temperature variation (d) over time. Different cases including the RCS and five cases (C1, C2, C3, C4, and C5) in the heterogeneity of permeability are analyzed.
In the actual application, the injection and production rate is controlled by wellhead pressure of both wells. The different geological conditions and flow rates lead to the variation of wellhead pressure (Figure
Wellhead pressure of production well (a) and injection well (b) over time by contrasting the RCS and five heterogeneous cases (C1, C2, C3, C4, and C5).
In summary, when the high permeability zone exists between the wells, heat breakthrough may occur and the lifetime is approximately lower than 20 years. However, the existence of the high permeability zone also reduces the reinjection costs of the doublet well at some extent. Low permeability zone at the interwell sector may prolong the lifetime of the heat extraction system and promote stability, and it can also retard injection of tail water when the low permeability zone is at the vicinity of injection well. Thus, it is necessary to determine subsurface heterogeneity in a high resolution based on such as a tracer test and geophysical prospecting before sitting the extraction and injection segment in a deep geothermal reservoir. When the optimized layout of doublet well system is considered, the high permeability zone at the interwell sector should be avoided.
Thermal hydraulic coupling process, as the basis, should be first taken into the research of the doublet well geothermal system, especially for a planar fracture in the hot dry rock reservoir [
Almost all the ways of geothermal exploitation encounter scaling problems of wellbores. The process of mineral dissolution and precipitation [
This study optimized the injection/production rate and evaluated the energy productions in the deep geothermal reservoir in Tianjin, China, in a lifespan of 50 years. The temperature and pressure distribution under unexploited conditions is evaluated by a 1D heat conduction model. Furthermore, an integrated 1D–3D wellbore-reservoir model is established by the T2WELL simulator.
It is concluded that the optimal (maximum) injection/production rate for typical geothermal doublet well system studied here with a reservoir thickness of 700 m and a well distance of 850 m is 450 m3/h. Under the production rate of 450 m3/h, the maximum outflow temperature can basically remain stable of 112°C and thermal energy extraction rate can reach average of 43.5 MW.
The high-permeability channels at the interwell sector should be avoided, when the optimization layout of the doublet well system is considered. The heterogeneous distribution of porosity and permeability causes significant changes in the outflow temperature. In the case that a high permeability zone exists between injection and production wells, the outflow temperature can decrease by 4–8°C when compared to the homogeneous case. When a low permeability zone occurs between two wells, the outflow temperature can basically keep stable and lifetime of the heat extraction system can reach 50 years at least.
The wellhead pressures of injection well and production well can be intensely influenced by the distribution of a low permeability zone. If the low permeability zone in the reservoir is around injection well, it usually leads to higher wellhead pressure than that in the homogeneous strata. When the low permeability zone is around production well, the wellhead pressure needs to be depressurized to maintain the profitable output of geothermal water. The existence of low permeability zone around the wellbores does not benefit the stable operation and cost saving and may be solved by the technique of formation acidizing to increase production or lower operation costs.
Further, the detailed geochemistry of water, geology of reservoir, and geophysical parameters are needed to run the T- (thermal-) H- (hydraulic-) C- (chemical-) M (mechanics) model to evaluate the influence of thermal stress and wellbore scaling on the heat breakthrough. The effect of economic parameters (electricity price, heat price, and discount rate) should be considered to optimize the cost of reservoir exploitation in combination with numerical results in further study. More accurate main parameters, related coupling processes, and cost analysis should be updated and added into the model to get accurate results to achieve optimum performance.
Mass accumulation term, kg m−3
Mass or heat flux, W m−1
An arbitrary subdomain of the flow system
The saturation of phase
Darcy velocity in phase
Mass fraction of component
Absolute permeability to phase
Relative permeability, m2
The pressure of a reference phase and usually taken to be the gas phase, Pa
Sinks and sources, kg m−3 s−1
The internal energy of phase
The velocity of phase
The kinetic energy per unit mass
Well cross-sectional area, m2
Distance along-wellbore coordinate (can be inclined), m
Specific heat of rock, J kg−1°C−1
Specific enthalpy of fluid phase
Gravitational acceleration, m s−2
The wellbore heat loss/gain per unit length of wellbore, kg m−3 s−1
The lateral area between wellbore and surrounding formation, for grid cell
The overall heat transfer coefficient of wellbore and formation, W−1 K−1 m−1
The temperature of
Ambient temperature, °C
Radium of the wellbore, m
Ramey’s well heat loss function
The velocity of mixture (liquid water in our model), m s−1
Permeability
Fitting parameter
Fitting parameter.
Porosity
The density of phase
Heat conductivity, W−1 K−1 m−1
Grain density, kg m−3
Viscosity, kg m−1 s−1
The area-averaged heat conductivity of the wellbore (contains the fluids and possible solid portion), W−1 K−1 m−1
Incline angle of wellbore, °
Area of closed surface, m2
The thermal dispersivity of the surrounding formation, m2 s−1
Perimeter of wellbore, m
The wall shear tress, MPa
The mixture density (liquid water), kg m−3.
Refers to liquid water in this paper
The index for the components, 1 for H2O, 4 for energy.
We can directly link the dataset in this manuscript by providing the relevant information. The data in this manuscript is available and can be found in the database linking page.
The authors declare that they have no conflicts of interest.
This study is supported by the National Key Research and Development Program of China (no. 2016YFB0600804), National Natural Science Foundation of China (no. 41572215, 41402205, and 41502222), Center for Hydrogeology and Environmental Geology Survey, China Geological Survey (DD20179621 and DD20189113), Special Project for New Energy, Jilin Province (SXGJSF2017-5), Graduate Innovation Found of Jilin University (no. 101832018C052), and the Major Project of China National Science and Technology (no. 2016ZX05016-005).