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Frontiers in Energy

ISSN 2095-1701

ISSN 2095-1698(Online)

CN 11-6017/TK

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Front. Energy    2019, Vol. 13 Issue (3) : 439-449    https://doi.org/10.1007/s11708-019-0612-4
RESEARCH ARTICLE
A numerical study of non-Darcy flow in EGS heat reservoirs during heat extraction
Wenjiong CAO1, Wenbo HUANG1, Guoling WEI2, Yunlong JIN2, Fangming JIANG1()
1. Laboratory of Advanced Energy Systems, Guangdong Key Laboratory of New and Renewable Energy Research and Development, CAS Key Laboratory of Renewable Energy, Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou 510640, China
2. Guangdong Hydrogeology Battalion, Guangzhou 510510, China
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Abstract

Underground non-Darcy fluid flow has been observed and investigated for decades in the petroleum industry. It is deduced by analogy that the fluid flow in enhanced geothermal system (EGS) heat reservoirs may also be in the non-Darcy regime under some conditions. In this paper, a transient 3D model was presented, taking into consideration the non-Darcy fluid flow in EGS heat reservoirs, to simulate the EGS long-term heat extraction process. Then, the non-Darcy flow behavior in water- and supercritical CO2 (SCCO2)-based EGSs was simulated and discussed. It is found that non-Darcy effects decrease the mass flow rate of the fluid injected and reduce the heat extraction rate of EGS as a flow resistance in addition to the Darcy resistance which is imposed to the seepage flow in EGS heat reservoirs. Compared with the water-EGS, the SCCO2-EGS are more prone to experiencing much stronger non-Darcy flow due to the much larger mobility of the SCCO2. The non-Darcy flow in SCCO2- EGSs may thus greatly reduce their heat extraction performance. Further, a criterion was analyzed and proposed to judge the onset of the non-Darcy flow in EGS heat reservoirs. The fluid flow rate and the initial thermal state of the reservoir were taken and the characteristic Forchheimer number of an EGS was calculated. If the calculated Forchheimer number is larger than 0.2, the fluid flow in EGS heat reservoirs experiences non-negligible non-Darcy flow characteristic.
Keywords enhanced geothermal system      non-Darcy flow      heat extraction      Reynolds number      Forchheimer number     
Corresponding Author(s): Fangming JIANG   
Online First Date: 25 February 2019    Issue Date: 04 September 2019
 Cite this article:   
Wenjiong CAO,Wenbo HUANG,Guoling WEI, et al. A numerical study of non-Darcy flow in EGS heat reservoirs during heat extraction[J]. Front. Energy, 2019, 13(3): 439-449.
 URL:  
https://academic.hep.com.cn/fie/EN/10.1007/s11708-019-0612-4
https://academic.hep.com.cn/fie/EN/Y2019/V13/I3/439
Fig.1  Model geometry and numerical mesh system
B correlation B value/cm-1
β=4.1 ×109 K1.5 [20] 1.3 × 108
β=1.82 ×108 K1.25ε0.75 [21] 3.2 × 108
β=4.8 ×1010K1.176 [22] 3.2 × 109
Tab.1  Correlations for the non-Darcy coefficient b
Group # Case # Working fluid b/cm-1
1 Case 1 H2O Darcy
Case 2 H2O 1.3 × 108
Case 3 SCCO2 Darcy
Case 4 SCCO2 1.3 × 108
2 Case 5 H2O 3.2 × 108
Case 6 H2O 3.2 × 109
Case 7 SCCO2 3.2 × 108
Case 8 SCCO2 3.2 × 109
Tab.2  Simulated cases
Fig.2  Fluid pressure distribution in the heat reservoir (The plots from left to right correspond to time instants of 1, 5, and 10 years, respectively)
Fig.3  Seepage speed distribution in the heat reservoir (The plots from left to right correspond to time instants: 1, 5, and 10 years, respectively)
Fig.4  Fluid temperature fields in the heat reservoir (The plots from left to right correspond to time instants of 1, 5, and 10 years, respectively)
Fig.5  Mass flow rate as a function of EGS operation time in water- and SCCO2-based EGS
Fig.6  Non-Darcy effect on the production temperature curve for water- and SCCO2-based EGSs
Fig.7  Non-Darcy effects on the real-time heat extraction rate versus EGS operation time for water- and SCCO2-based EGSs
Fig.8  Relative velocity reduction in the heat reservoir due to non-Darcy flow after 5 years of EGS operation
Case # Heat transfer fluid β/cm−1 Foch γ Re Fo
Point A Point B Point C Point A Point B Point C Point A Point B Point C
2 H2O 1.3 × 108 0.03 2.0% 1.1% 2.1% 0.14 5.8 × 10−4 0.13 0.03 1.3 × 10−4 0.03
5 H2O 3.2 × 108 0.07 2.5% 1.7% 2.6% 0.08 3.3 × 10−4 0.07
6 H2O 3.2 × 109 0.74 13.1% 10.1% 14.9% 0.78 3.2 × 10−3 0.74
4 SCCO2 1.3 × 108 0.35 11.0% 7.2% 11.1% 2.25 5.4 × 10−3 1.51 0.51 1.2 × 10−3 0.35
7 SCCO2 3.2 × 108 0.85 21.1% 13.6% 21.8% 1.27 3.1 × 10−3 0.85
8 SCCO2 3.2 × 109 8.54 53.9% 49.7% 59.1% 12.70 3.1 × 10−2 8.54
Tab.3  Relative velocity reduction, Reynolds number, and Forchheimer number at the three monitoring points after 5 years of EGS operation
A Area/m2
cp Specific heat capacity/(J·kg -1·K-1)
Fo Forchheimer number
Foch Characteristic Forchheimer number
g Acceleration of gravity/(m·s -2)
ha Volumetric heat exchange coefficient/(W·m-3·K-1)
k Thermal conductivity/(W·m-1·K-1)
K Permeability/m2
p Pressure/Pa
Q Mass flow rate/(kg·s-1)
Re Reynolds number
t Time/s
SND Non-Darcy term
T Temperature/K
Tg Ground temperature/K
u Velocity vector/(m·s-1)
x, y, z Cartesian coordinates
Greek symbols
ρ Density/(kg·m-3)
ε Porosity
μ Dynamic viscosity/(Pa·s)
β Non-Darcy coefficient
γ Relative velocity reduction
Subscripts/superscripts
ch Characteristic
eff Effective
f Fluid
H2O Water
inj Injection
ini Initial
out Production, outlet
ref Reference
s Solid or rock
SCCO2 Supercritical carbon dioxide
  
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