CN116738779B - Method for calculating supercritical geothermal fluid conductivity - Google Patents
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- FAPWRFPIFSIZLT-UHFFFAOYSA-M Sodium chloride Chemical compound [Na+].[Cl-] FAPWRFPIFSIZLT-UHFFFAOYSA-M 0.000 claims description 59
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Abstract
The invention discloses a method for calculating the conductivity of supercritical geothermal fluid, which comprises the following steps: by multi-physical process coupling of heat transfer, flow and chemistry, corresponding considerations rely on temperature, density, and fluid salinity to build a fluid conductivity model; the invention quantitatively analyzes the evolution law and the control mechanism of the conductivity of the fluid from the high-temperature high-pressure geochemical action process.
Description
Technical Field
The invention relates to the technical field of new energy, in particular to a method for calculating the conductivity of supercritical geothermal fluid.
Background
The geothermal energy is used as non-carbon-based clean energy, has the characteristics of good stability, high energy utilization coefficient, convenient development and utilization and the like, and is a renewable energy with very competitive advantages. Currently, geothermal resources can be divided into shallow geothermal resources, hydrothermal geothermal resources and dry rock geothermal resources according to the endowment conditions of the geothermal resources, wherein the hydrothermal geothermal resources are the main battlefield for development and utilization at present. The acquisition of high-grade heat energy is always the power pursued by the research of geothermal energy. In recent years, supercritical geothermal fluids having ultra-high temperatures (> 374 ℃) have become hot spots for hydrothermal type geothermal exploration and development. Supercritical geothermal fluids are multicomponent fluids with high temperature and high pressure (critical point, pure water: t=374 ℃, p=22.1 MPa; sea water: t=406 ℃, p=29.8 MPa), most commonly present in basalt, the formation of which is closely related to shallow magma activity. The supercritical geothermal fluid has the advantages of high enthalpy (-3200 kJ/kg), low dynamic viscosity, high geothermal energy productivity (50 MW for single well installation), etc., wherein the installed capacity of the supercritical geothermal well can reach 10 times of that of a conventional geothermal well with high temperature (about 200-350 ℃). Supercritical geothermal fluid development has significant technological and economic value in coping with climate change and achieving energy structure adjustment.
The scale and the space spreading characteristics of the supercritical geothermal fluid are accurately identified, and the supercritical geothermal fluid is a premise for promoting the supercritical geothermal fluid to realize efficient development. Because of the significant differences in rock and fluid conductivity, the Magnetotelluric (MT) method is an effective geophysical tool for detecting underground fluids, and currently the electro (magnetic) method has a wide range of application scenarios and achieves significant results when detecting conventional high temperature geothermal reservoirs (depth <3km, conductivity typically greater than 100S/m) and deep magma melts (depth >5km, conductivity typically less than 5S/m). The electric method detects the conductivity model of the melt and the water-rich rock mass established by means of the indoor conductivity experiment, and the spatial conductivity characteristics of the underground medium can be established by collecting field current and voltage data and combining mathematical model inversion, so that the magma room and the conventional high-temperature geothermal fluid can be identified efficiently. However, the current electric method has larger ambiguity when detecting the supercritical geothermal fluid (depth is 2-6km, conductivity is generally 0.1-100S/m), and particularly the identification of the scale and space spread characteristics of the supercritical geothermal fluid is very difficult, and the main constraint factor is that the three-element structure of the supercritical geothermal system is not clearly depicted, and the knowledge of the evolution rule of the conductivity of the supercritical geothermal fluid is not clear.
Fluid composition (salt content), fluid temperature and fluid pressure are the main parameters controlling their own conductivity, in other words, supercritical geothermal fluid conductivity is the result of a heat transfer-flow-chemical multiphysics coupling. At present, different conductivity models are established in terms of fluid pressure, fluid temperature, fluid salinity and the like by using a NaCl-H2O system.
The supercritical fluid conductivity is currently mainly a result of considering the simple action of a few physical fields, and a series of (semi) empirical models are established. According to the experimental test results of the density and viscosity correlation of the supercritical fluid under the influence of temperature, pressure and salinity, a fluid conductivity (semi-) empirical model which depends on the density, viscosity, temperature and pressure of the fluid is established through data statistics and correlation fitting. These models are mainly used in geological environments within specific temperature, pressure, salinity ranges. However, these models are difficult to use in geological environments with salinity above 6wt% NaCl, temperatures above 350℃and pressures below 200 MPa; recently Watanabe et al established a semi-empirical model of fluid conductivity with maximum salinity of 24.6wt% nacl at 20-525 ℃ and pressure in the range 25-200 MPa; the conductivity experimental data of different ages may be contradictory due to its reliance on Bannard et al.
Disclosure of Invention
In order to solve the problems in the prior art, the invention aims to provide a calculation method of the supercritical geothermal fluid conductivity, which quantitatively analyzes the evolution rule and the control mechanism of the fluid conductivity in the high-temperature high-pressure geochemical action process.
In order to achieve the above purpose, the invention adopts the following technical scheme: a method for calculating the conductivity of a supercritical geothermal fluid, comprising:
corresponding considerations rely on temperature T, density ρ, and fluid salinity Θ to establish fluid conductivity σ by multiphysics coupling of heat transfer, flow, and chemistry l The model, control equation, is as follows:
log(σ l )＝-1.706-93.78/T+0.8075log(Θ)+3.0781log(ρ)+log(Λ(T,p))
wherein Λ (T, p) is the molar conductivity controlled by temperature and pressure, and is related to the solution viscosity mu, and the formula is:
Λ＝A+Bμ -1 +Cμ -2
wherein the coefficients A, B, C are functions of the molar concentrations m, respectively, of:
C＝c 1 +c 2 m
wherein a is 1 、a 2 、a 3 、a 4 ，b 1 、b 2 、b 3 、b 4 ，c 1 、c 2 Are all coefficients;
the solution viscosity mu is controlled by salinity Θ, temperature T and pressure P, and the equation is as follows:
wherein,is the viscosity of pure water under a given temperature and pressure state, +.>Melt viscosity at 800 ℃;
the solution density is:
wherein reference density at 1 bar pressure:
solution compressibility coefficient:
λ NaCl,l ＝m 4 +m 5 T
wherein m is 0 、m 1 、m 2 、m 3 、m 4 、m 5 Are all coefficients;
the total rock conductivity was estimated by the alchi formula:
wherein sigma r Is the conductivity of the rock containing fluid, phi is the porosity of the rock, s l Is brine saturation, m is a rock related parameter, n is a saturation index, and α is a coefficient factor.
As a further improvement of the present invention, by multi-physical process coupling of heat transfer, flow and chemistry, the corresponding considerations rely on temperature T, density ρ, and fluid salinity Θ to build a fluid conductivity model comprising: processing the conductivity model into NaCl-H 2 O system, consider the conductivity characteristic under the heat transfer, flow, chemical coupling action in the porous medium, realize the coupling of many physical fields; the method comprises the following steps:
multiphase fluid flow darcy equation:
where u is the fluid velocity, κ is the total rock permeability, κ r,i Is the relative permeability, μ is the solution viscosity, ρ is the density, g is the gravitational acceleration, p is the phase partial pressure, l is the liquid phase, v is the weather, r is the relative permeability;
the relative permeability relationship of the liquid phase, the gas phase and the solid phase is as follows:
κ rv +κ rl ＝1-S h
wherein S is i I phase volume saturation (i=l, v, h), solid phase precipitation is mainly rock salt NaCl, h is solid phase;
fluid mass conservation equation:
where phi is the porosity of the rock,is a fluid mass source [ kg/s ]]T is the time s]；
Rock salt NaCl mass conservation equation:
wherein Q is NaCl Is the source term, xi is the mass fraction of NaCl in the fluid;
energy conservation equation:
wherein the subscript r represents rock, hi is the enthalpy of the i phase, Q e Is the internal energy, K is the effective thermal conductivity of the saturated medium, and T is the temperature;
the mass fraction of total NaCl in the multiphase fluid in the conductivity model is as follows:
when rock salt is precipitated, the solid phase saturation Sh is increased, the permeability of the whole rock is reduced, and the mutual relations are as follows:
wherein, kappa 0 And κ permeabilities are sh=0 and Sh, respectively>0, phi * =0.8 is the ratio of liquid phase to gas phase when all pore spaces are filled, i.e. permeability is 0; the constant ψ=0.8; in addition, when Sh<0.2 time κ>0, when Sh is greater than or equal to 0.2＝0；
In addition, fluid salinity:
the beneficial effects of the invention are as follows:
1. theory of: the formation of the underground supercritical geothermal fluid is a special fluid formed by long-term action in complex physical and chemical processes such as high-temperature heat transfer, fluid flow, water-rock gasification reaction and the like, the physical properties of the special fluid are controlled by the action of multiple physical fields, the conductivity of the supercritical geothermal fluid is calculated by means of heat transfer-flow-chemical multiple physical field coupling, and the main control mechanism of the conductivity of the supercritical geothermal fluid can be explored from the basic physicochemical law, so that the conductivity characteristics of the supercritical geothermal fluid can be analyzed theoretically.
2. Intuitiveness: supercritical geothermal fluids are typically present in the ground for 3-6km and are difficult to observe directly. Solving partial differential equation of flow process, conservation of material and conservation of energy by finite element method, and further calculating conductivity value of supercritical fluid. The distribution characteristics of the conductivity in the underground can be intuitively displayed, and the change characteristics of the supercritical fluid conductivity along with the changes of flow, heat transfer and chemical reaction can be displayed.
3. Predictability: supercritical geothermal fluids are formed by long term action through complex physicochemical processes in the subsurface, the scale and time of intrusion of magma, the depth and path of circulation of groundwater, and the water-gas action process and range, which affect the formation of supercritical geothermal fluids and also affect their conductivity characteristics. By solving the mathematical equation of the physicochemical process, the formation of the supercritical geothermal fluid conductivity under the conditions of temperature, pressure, salinity and density can be explored, and the change of the supercritical geothermal fluid conductivity along with the evolution of the geological process can be calculated and predicted by means of the mathematical equation.
4. Economy: previously, the conductivity of supercritical geothermal fluid mainly depends on indoor high-temperature high-pressure experiment test and monitoring. By means of the evolution rule of the conductivity of the supercritical geothermal fluid through heat transfer, flow and chemical coupling, the high cost caused by the high-temperature and high-pressure supercritical fluid conductivity experiment can be greatly reduced, and the personnel waste caused by long-time operation of the experiment can be avoided. Meanwhile, the method can be compared with the test results of different laboratories in the world, and corresponding standards and corresponding characteristic rule templates are established.
Drawings
Fig. 1 is a schematic diagram of a multi-physical field coupling structure in an embodiment of the invention.
Detailed Description
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
Examples
When the temperature and pressure of the supercritical geothermal fluid water-rock interaction change, the physical properties of the underground medium can be changed by mineral dissolution and precipitation, so that the explanation of the conductivity of the geological structure by electric detection is affected. Therefore, it is necessary to quantitatively analyze the evolution law and control mechanism of the fluid conductivity from the high-temperature high-pressure geochemical action process.
A calculation method of supercritical geothermal fluid conductivity further establishes a numerical model of a water rock action process and a fluid conductivity evolution rule by means of experimental test results, so that the model is treated as NaCl-H in the embodiment 2 O system, considering conductivity characteristics under the actions of heat transfer, flow and chemical coupling in porous medium, realizes multi-physical field coupling, as shown in figure 1. The method comprises the following steps:
multiphase fluid flow darcy equation:
where u is the fluid velocity [ m/s ]]Kappa is the total rock permeability [ m ] 2 ]，κ r, i is the relative permeability [ ]]Mu is the dynamic viscosity [ Pa.s ]]ρ is the density [ kg/m ] 3 ]G is gravity [ m/s ] 2 ]P is the phase partial pressure [ Pa]。
Relative permeability relationship of liquid phase (l), gas phase (v) and solid phase (h, rock salt NaCl):
κ rv +κ rl ＝1-S h
wherein S is i Is different phase volume saturation, and the solid phase precipitation is mainly rock salt (NaCl).
Fluid mass conservation equation:
wherein phi is the porosity of the rock [ ]]，Is a fluid mass source [ kg/s ]]T is the time s]。
Rock salt (NaCl) mass conservation equation:
wherein Q is NaCl Is the source item [ kg/s ]]，X i Is the mass fraction of NaCl in the fluid [ ]]。
Energy conservation equation:
wherein the subscript r represents rock, h i Is the enthalpy value of the i phase [ kJ/kg ]]，Q e Is the internal energy [ kJ]K is the effective thermal conductivity of the saturated medium [ W/(m.K)]T is the temperature [ DEGC ]]。
The total NaCl mass fraction in the multiphase fluid in the model is as follows:
when rock salt precipitates, the solid phase saturation S is increased h Reduce the permeability of the whole rock and the mutual relation is that
S h ≤1-φ *
Wherein, kappa 0 And kappa permeabilities are S respectively h =0 and S h >0, phi * =0.8 is the ratio of liquid phase to gas phase when all pore spaces are filled, i.e. permeability is 0. The constant ψ=0.8. In addition, when S h <0.2 time κ>0, when S h κ=0 at 0.2.
In addition, fluid volume salinity:
x is not used here NaCl The ratio score serves two purposes. First, fluid volume salinity is an indicator of conductivity, and whole rock conductivity is high when fluid salinity is high. The total salinity of the fluid multiplied by the porosity allows an estimate of the conductivity characteristics of the whole rock, since the fluid occupies only the pore portion of the unit volume of the medium. Second, the volume salinity is an estimate of the cumulative amount of sodium chloride in a unit volume of rock in the fluid. Thus, the volume salinity is a useful metal mineral distribution profile tracer because the distribution of metal minerals in the fluid is controlled by chloride ligands, rather than solid NaCl.
The present example represents the simulation results in terms of fluid volume salinity per unit volume of saturated rock, i.e. the combined mass fraction of NaCl in liquid and gas phases (excluding rock salts) times the porosity. This method in turn enables the calculation of conductivity distribution in the model geometry domain for direct comparison with magnetotelluric imaging images under the geothermal zone. The method is also an innovation point of the technical method for realizing quantitative evaluation of the control mechanism of the electrical detection supercritical fluid in the water rock action process.
To be in multi-physical with heat transfer-flow-chemistryThe path coupling takes into account the dependence on temperature (TK]) Density (ρ [ kg/m ] 3 ]) Fluid salinity (Θ [ wt ]]) Is (sigma) l [S/m]) Model, control equation is
log(σ l )＝-1.706-93.78/T+0.8075log(Θ)+3.0781log(ρ)+log(Λ(T,p))
Wherein Λ (T, p) [ S.m ] 2 /mol]The molar conductivity is controlled by temperature and pressure, and is related to the viscosity of the fluid, and the formula is as follows:
Λ＝A+Bμ -1 +Cμ -2
wherein the coefficients A, B, C are the molar concentrations m [ mol/kgH, respectively 2 O]Is the function of (1), respectively:
C＝c 1 +c 2 m
wherein the coefficient a 1 ＝4.16975E-3,a 2 ＝-5.08206E-3,a 3 ＝0.575588,a 4 ＝1.00422,b 1 ＝25.5008,b 2 ＝6.04911E-2,b 3 ＝2.51861E6，b 4 ＝0.430952,c 1 ＝-4.89245E-10,c 2 ＝-1.75339E-11。
In the model, the solution viscosity μ is controlled by salinity Θ' [ wt% ], temperature TK, pressure P [ MPa ], and its equation is:
wherein mu H2O (T, P) is the viscosity of pure water at a given temperature and pressure,is melt viscosity at 800 ℃.
The solution density is:
wherein the reference density is 1 bar pressure
Solution compressibility coefficient:
λ NaCl,l ＝m 4 +m 5 T
wherein the coefficient m 0 ＝58443；m 1 ＝23.772；m 2 ＝0.018639；m 3 ＝-1.9687E-6；m 4 ＝-1.5259E-5；m 5 ＝5.5058E-8。
The total rock conductivity was estimated by the alchi formula:
wherein sigma r Is the conductivity of the rock containing fluid, s l Is the brine saturation, m is the rock related parameter (=1.9), n is the saturation index (≡2), and α is the coefficient factor (=0.6).
The model of this example was examined:
the simulation platform COMSOL Multiphysics is a commercial multi-physical field coupling simulation platform, and has reliability and stability in numerical calculation of energy equations, mass equations and darcy flow equations. In addition, naCl-H 2 The O system multiphase flow simulation is widely applied to a magma hot liquid system and an ore-forming system, and the observation data is verified. The porous medium and fluid property parameters in the model are adjusted mainly by experimental results and comparison verification of the section of the field electrical structure.
In order to evaluate the identification effect of the conductivity characteristics on the detection of the supercritical geothermal fluid by an electric method, the conductivity characteristic section calculated by gridding multiple physical field coupling is adopted, and is compared and analyzed with the magnetotelluric observation electric structure section of the geothermal region, the root mean square deviation (RMSE) between the observed value (O) and the simulated value (M) is established as a standard for judging the goodness of fit, and the calculation formula is as follows:
the foregoing examples merely illustrate specific embodiments of the invention, which are described in greater detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention.
Claims (2)
1. A method for calculating the conductivity of a supercritical geothermal fluid, comprising:
corresponding considerations rely on temperature T, density ρ, and fluid salinity Θ to establish fluid conductivity σ by multiphysics coupling of heat transfer, flow, and chemistry l The model, control equation, is as follows:
log(σ l )＝-1.706-93.78/T+0.8075log(Θ)+3.0781log(ρ)+log(Λ(T,p))
wherein Λ (T, p) is the molar conductivity controlled by temperature and pressure, and is related to the solution viscosity mu, and the formula is:
Λ＝A+Bμ -1 +Cμ -2
wherein the coefficients A, B, C are functions of the molar concentrations m, respectively, of:
C＝c 1 +c 2 m
wherein a is 1 、a 2 、a 3 、a 4 ，b 1 、b 2 、b 3 、b 4 ，c 1 、c 2 Are all coefficients;
the solution viscosity mu is controlled by salinity Θ, temperature T and pressure P, and the equation is as follows:
wherein,is the viscosity of pure water under a given temperature and pressure state, +.>Melt viscosity at 800 ℃;
the solution density is:
wherein reference density at 1 bar pressure:
solution compressibility coefficient:
λ NaCl,l ＝m 4 +m 5 T
wherein m is 0 、m 1 、m 2 、m 3 、m 4 、m 5 Are all coefficients;
the total rock conductivity was estimated by the alchi formula:
wherein sigma r Is the conductivity of the rock containing fluid, phi is the porosity of the rock, s l Is the saturation of the brine,m is a rock related parameter, n is a saturation index, and α is a coefficient factor.
2. The method of calculating the conductivity of a supercritical geothermal fluid according to claim 1, wherein establishing a fluid conductivity model by means of multiple physical process coupling of heat transfer, flow and chemistry, corresponding considerations in dependence on temperature T, density ρ, and fluid salinity Θ comprises: processing the conductivity model into NaCl-H 2 O system, consider the conductivity characteristic under the heat transfer, flow, chemical coupling action in the porous medium, realize the coupling of many physical fields; the method comprises the following steps:
multiphase fluid flow darcy equation:
where u is the fluid velocity, κ is the total rock permeability, κ r,i Is the relative permeability, μ is the solution viscosity, ρ is the density, g is the gravitational acceleration, p is the phase partial pressure, l is the liquid phase, v is the weather, r is the relative permeability;
the relative permeability relationship of the liquid phase, the gas phase and the solid phase is as follows:
κ rv +κ rl ＝1-S h
wherein S is i I phase volume saturation (i=l, v, h), solid phase precipitation is mainly rock salt NaCl, h is solid phase;
fluid mass conservation equation:
where phi is the porosity of the rock,is a fluid mass source [ kg/s ]]T is the time s]；
Rock salt NaCl mass conservation equation:
wherein Q is NaCl Is the source term, xi is the mass fraction of NaCl in the fluid;
energy conservation equation:
wherein the subscript r represents rock, hi is the enthalpy of the i phase, Q e Is the internal energy, K is the effective thermal conductivity of the saturated medium, and T is the temperature;
the mass fraction of total NaCl in the multiphase fluid in the conductivity model is as follows:
when rock salt precipitates, the solid phase saturation S is increased h The permeability of the whole rock is reduced, and the interrelationship is as follows:
S h ≤1-φ *
wherein, kappa 0 And kappa permeabilities are S respectively h =0 and S h >0, phi * =0.8 is the ratio of liquid phase to gas phase when all pore spaces are filled, i.e. permeability is 0; the constant ψ=0.8; in addition, anotherIn addition, when S h <0.2 time κ>0, when S h Kappa=0 at ∈0.2;
in addition, fluid salinity:
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| CN109840388A (en) * | 2019-03-06 | 2019-06-04 | 中国石油大学(华东) | A kind of numerical simulation evaluation method of geothermal system heat wave and degree |
| WO2021180189A1 (en) * | 2020-03-13 | 2021-09-16 | 重庆科技学院 | Multi-element thermal fluid thermal recovery oil reservoir numerical simulation method |
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| CN109840388A (en) * | 2019-03-06 | 2019-06-04 | 中国石油大学(华东) | A kind of numerical simulation evaluation method of geothermal system heat wave and degree |
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| yingchun wang,等.Geochemical evidence for the nonexistence of supercritical geothermal fluids at the yangbajing geothermal field, southern tibet.Journal of Hydrology.2022,全文. * |
| 羊八井地热田地热地质条件及其对超临界地热资源勘探的启示;王迎春 等;天然气工业;第42卷(第4期);35-45 * |
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