CN116738113A - Construction method of mathematical model for predicting scaling position in geothermal well bore - Google Patents
Construction method of mathematical model for predicting scaling position in geothermal well bore Download PDFInfo
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Abstract
The invention discloses a construction method of a mathematical model for predicting a scaling position in a geothermal well bore, which comprises the following steps: (1) Measuring flow, temperature, pressure and fluid characteristics of geothermal fluid at a wellhead in a geothermal well; (2) calculating a gas compression factor in the geothermal fluid; (3) Calculating corrected liquid phase density and gas phase density in geothermal fluid; (4) Determining a flow pattern in a depth at which the geothermal fluid is calculated to be located; (5) Determining the Reynolds number and the relative roughness of the primary supercharging well depth position; (6) calculating the friction between the geothermal fluid and the wellbore; (7) calculating a flash depth of the geothermal fluid in the wellbore; (8) The relative error in the position of the fouling of the geothermal fluid prediction is calculated. The construction method of the mathematical model for predicting the scaling position of the geothermal fluid in the well bore is simple, does not need complex mathematical derivation, can predict the flash evaporation position of the geothermal fluid in the well bore more quickly, and is suitable for industrial application.
Description
Technical Field
The invention relates to a mathematical model, in particular to a construction method of a mathematical model for predicting the scaling position of geothermal fluid in a well bore.
Background
The storage of geothermal energy is quite abundant and is one of important new energy sources (Cai Yihan)Direct utilization of geothermal energy [ M ]]Tianjin, tianjin university Press, 2014. Geothermal energy can be used in the fields of power generation, heating, aquaculture, chemical industry, etc. (Ingvar B, fridleifsson. Geothermal energy for the benefit of the people, geothermal energy benefits people), renewable&Sustainable Energy Reviews (review of renewable and sustainable energy), 2001,5 (3): 299-312.). The geothermal system in China is mainly divided into a high-temperature granite reservoir represented by a sheep-eight well, a medium-low-temperature sandstone reservoir represented by a salty yang and a medium-low-temperature carbonate reservoir represented by a county (Chen Junguang. Design and research of a sheep-eight well geothermal double-working-medium power generation management system [ D)]The preparation method comprises the following steps: university of electronics, 2021.). Various problems have been encountered while exploiting geothermal energy, wherein scaling of geothermal fluids in the well bore is a serious problem (Boch R, leis A, haslinger E, et al Scale-fragment formation impairing geothermal energy production: interaction H) 2 S corrosion and CaCO 3 Crystal growth (scale formation detrimental to geothermal energy production: H) 2 S corrosion and CaCO 3 Crystal growth interactions). Geothermal Energy (geothermal energy), 2017,5 (1): 1-19.). The scaling position of geothermal fluid in the well bore is modeled based on the principles of conservation of mass, conservation of momentum and conservation of energy to a certain extent (Arn's S.Depositon of calcium carbonate minerals from geothermal waters-theoretical considerations (theoretical thinking of the deposition of calcium carbonate minerals in geothermal water.) Geothermics (geothermal), 1989,18 (1/2): 33-39.) and coupled with the correlation equations of chemical thermodynamics to solveD, kohl T.coupled thermal-hydro-aulic-chemical modelling of enhanced geothermal systems (modeling of thermo-hydro-chemical coupling of enhanced geothermal systems). Geophysical Journal International (J.International geophysics), 2005,161 (2): 533-548.). In turn, many software and related programs have been developed to simulate the scaling process of geothermal fluids in wellbores (Bankoff S G.A variable density single-fluid model for two-phase flow with particular reference to steam-water flow (two-phase flow variable density single fluid model, in particular)Reference steam-water flow). Journal of Heat Transfer (journal of heat transfer), 1960,82 (4): 265-272.). The temperature gradient and the pressure gradient of the geothermal fluid in the well bore can be calculated through the temperatures and the pressures of the well head and the well bottom, and when the temperature gradient and the pressure gradient are obviously suddenly changed, the geothermal fluid is flashed at the obviously changed position, and then scaling is generated. Therefore, the position of the flash point and thus the scale formation position can be obtained from the temperature gradient and the abrupt position of the pressure gradient of the geothermal fluid in the well bore.
Wellbore physics models are generally described as vertical circular pipes with liquid flow in the deeper regions, and as geothermal fluid rises along the wellbore, both the momentum and heat of the geothermal fluid are lost, so accurate estimation of heat loss is important to simulate flow in a geothermal well. The geothermal fluid flashes in the upper zone due to the pressure and temperature decrease in the geothermal well bore. From the flash location, a two-phase flow (liquid-vapor) is produced as the mixing speed and vapor mass increase. The continuous increase of vapor in the gas phase can easily dilute the carbon dioxide in the gas phase, so that the dissolved carbon dioxide in the geothermal fluid in the liquid phase is quickly released into the gas phase, and the alkalinity in the geothermal fluid is increased, and the scaling phenomenon is easy to generate. According to this law, the fouling position can be predicted, and in fact can be obtained indirectly by predicting the flash point position. During upward flow, depending on the relative amounts or phase velocities of the vapor and liquid, several flow patterns (e.g., bubble flow, slugging flow, churning flow or semi-annular flow, dispersed annular flow and annular flow) may occur. The phase distribution in the upward vertical and inclined pipes is quite complex due to the sliding between the vapor (gas phase) and the liquid phase. When the mixture rises to the wellhead, the steam is separated and used to generate electricity, while the remaining liquid (or brine) is reinjected into the ground. Analysis of two-phase flow within a geothermal well requires calculation of production process parameters (e.g., pressure, temperature, enthalpy, heat flux, and velocity profile) and fluid thermophysical characteristics. There is a problem in that some two-phase flow parameters (e.g., void fraction, phase content, and coefficient of friction) are determined using an unsuitable relationship. The specific flow patterns of geothermal fluid in a wellbore are as follows:
(1) A bubble flow; the gas exists in the form of small bubbles, which are randomly distributed and whose diameters also change randomly. The bubbles move at different speeds depending on their respective diameters and the liquid flows up the pipe at a very uniform speed. Apart from density, the gas has little effect on the pressure gradient. The pipe is almost completely filled with liquid and the free gas phase is very small.
(2) A bullet-like flow; the liquid phase is still continuous and the small bubbles begin to coalesce and form stable bubbles of nearly the same size and shape, having nearly the same diameter as the tube, separated by a mass of liquid. The bubble velocity is greater than the liquid velocity. A thin film of liquid is around the bubble, the liquid velocity begins to be unstable, and both the gas phase and the liquid phase have a significant impact on the pressure gradient.
(3) A transitional flow; in this region a transition from a continuous liquid phase to a continuous gas phase takes place. The liquid phase is entrained in the gas phase, which begins to dominate.
(4) A mist flow; the gas phase is continuous, the liquid phase is entrained and carried by the gas phase, which is the primary controlling factor.
Hughmark and Pressburg were first to apply phase content to geothermal well reservoir simulators In 1961 (Hughmark GA, pressburg b.s. hold up and pressure drop with GAs-liquid flow In a vertical pipe (liquid holdup and pressure drop of GAs-liquid stream In vertical tubing). AIChE (american society of chemical engineers). 1961,7 (4): 677-682.), after which Duns and Ros designed a pattern of fluid flow In vertical well bores (Duns H, ros N c.vertical flow of GAs and liquid mixtures In wells (vertical flow of GAs-liquid mixture In well). In: proceedings 6th World Petroleum Congress,Section II,Paper 22-PD 6,Frankfurt am Main,Germany,pp (attached: sixth meeting notes of the world conference of petroleum, second section, paper 22-PD 6, germany frankfurt). 1963:451-465), P tzay et al developed a method for CaCO using Davies and Pitzer activity coefficient calculation methods 3 -H 2 O-CO 2 Balancing simulation algorithm and computer program for calcite scale formation in a system (P.tzay G, st.hl G, K.rmn FH, et al modeling of scale formation and corrosion from geothermal water (modeling geothermal water scale and corrosion). Electrochimica Acta (journal of electronics chemistry), 1998,43 (1-2): 137-147.) for determining different gases (e.g., CO) in geothermal wellheads 2 、CH 4 And N 2 ) The point of flash evaporation of the geothermal fluid at the concentration and the distribution of the partial pressure of the gas in the well bore. After the model is built, the location of the flash point in the geothermal well bore can be calculated by software programs such as HOLA (Bjornsson G.A multi-feedzone geothermal wellbore simulator (Multi-make-up geothermal well bore simulator), technical Report LBL-23546,Berkeley:Lawrence Berkeley Laboratory (technical report LBL-23546, berkeley: lorenter Keril laboratory), 1987:1-102.) and WELLSIM (Gunn C, freston D.an integrated steady-state wellbore simulation and analysis package (Integrated steady state well bore simulation and analysis software package), proceedings of the 13th New Zealand Geothermal Workshop.Auckland,NZ:New Zealand Geothermal Workshop (thirteenth New Zealand Kogynecomastia, new Zealand Kogynecomastia), 1991:161-166). The difference between these two types of software is that HOLA does not take into account the effect of the salt content and the non-condensable gas content in the geothermal fluid on the location of the flash point, whereas WELLSIM requires consideration of the effect of both parameters. Garg et al then uses the newly established empirical correlation of phase fractions to simulate analysis of the temperature and pressure in geothermal wellbores as a function of wellbore depth to determine the location of the flash point (Garg S K, pritchett J W, alexander J H.A new liquid hold-up correlation for geothermal wells, a new correlation of geothermal well liquid holdup.) Geothermics, 2004,33 (6): 795-817.) and optimize parameters to best represent field data. Akin et al calculated that calcium carbonate from Kizildere geothermal fields of Turkish produced scale about 80 meters above the flash point using PHREEQC software (Akin T, guney A, kargi H.modeling of calcite scaling and estimation of gas breakout depth in a geothermal well by using PHREEQC (use PHREEQC to model calcite scale and estimate gas leak depth in geothermal wells). Fortieth Workshop on Geothermal Reservoir Engineering (forty-set geothermal reservoir engineering society). Stanford University, stanford, california, 2015:1-8.).
U.S. Philippines, italyThe development and utilization of geothermal energy are earlier than in turkish and other countries, and thus a rich wellbore flow and scale simulation related experience (Fujii y caco) is accumulated 3 scale problems in the Nigorikawa geothermal area Hokkaido (Hokkaido Nigorikawa geothermal zone CaCO) 3 Scaling problem). Japan geothermal association (japan geothermal institute), 1988,25 (4): 54-65.). The established geothermal fluid scaling position prediction model generally includes a dissolution-precipitation law of calcium carbonate in geothermal fluid, a dissolution law of non-condensable gases such as carbon dioxide, a pressure drop determination of single-phase and two-phase flows in a well bore, scaling mechanism analysis, flash position prediction, etc. (range G, perera V, ponte C, et al, return calcite deposits of well PV8 while discharging: a successful operation at Riberia Grande geothermal field, s.a. Miguel Island, azo res (a calcite deposit of digging PV8 wells while draining water: successful operation of the hot field of the armia Grande, australia Island), european Geothermal Congress 2019Den Haag,The Netherlands (the netherlands de Haag, 2019, european geothermal institute, 11-14june 2019).
Our country has relatively late development and utilization in geothermal fluid scaling simulations and has less build-up for this problem (Bo Xianbiao, guo Zhipeng, wang Lingbao. Geothermal fluid flow in the wellbore and calcium carbonate scaling process simulation. New energy evolution, 2021,9 (5): 434-442.). Currently, two methods are adopted for solving the built geothermal fluid scaling position prediction model, namely, according to the known bottom hole parameters (pressure, temperature, total mass flow, carbon dioxide content and the like) of a thermal storage or geothermal well shaft, the thermal storage or the bottom hole is gradually solved towards the wellhead direction of the geothermal well, and the parameters of each section are determined, namely, a Down-Top algorithm; secondly, the well head parameters (pressure, temperature, dryness, total flow and carbon dioxide content) are known, and the well head is used for solving the well head gradually to the bottom of the well and the thermal storage direction, so that the algorithm is called Top-Down algorithm.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a construction method of a mathematical model for predicting the scaling position in a geothermal well bore, which can predict the flash evaporation position of geothermal fluid in the well bore more quickly and can determine the scaling position of the geothermal fluid.
The invention discloses a construction method of a mathematical model for predicting scaling positions in a geothermal well bore, which comprises the following steps:
measuring the flow, temperature, pressure and fluid characteristics of geothermal fluid at a wellhead in a geothermal well; the fluid characteristics include gas solubility, standard critical pressure, critical temperature and viscosity of the geothermal fluid at the wellhead, wherein:
solubility of gas: r is R s ＝20.481；
Standard critical pressure:
critical temperature:
viscosity: μ=1.0×10 -3 Pa·s；
The gas compression coefficient in the geothermal fluid is obtained through calculation, and the specific process is as follows:
step 201, setting an initial value of pressure gradient in the well depth range according to the pressure value of geothermal fluid at the well head, and calculating to obtain a primary boost pressure value p 1 The position which is a certain distance away from the wellhead and corresponds to the primary supercharging pressure value is recorded as a primary supercharging well depth position;
in p 0 For the pressure value at the wellhead, Δp is the initial value of the assumed pressure gradient;
step 202, correcting the measured value of the temperature and the pressure of the geothermal fluid at the wellhead by using the comparison temperature and the comparison pressure, and calculating to obtain the dimensionless temperature T of the geothermal fluid at the wellhead r And dimensionless pressure drop p r ；
Dimensionless temperature:
dimensionless pressure drop:
wherein:t is a geothermal fluid temperature measurement at the wellhead pe Is the critical temperature of geothermal fluid, +.>P is a measurement of geothermal fluid pressure drop at the wellhead pe Is the critical pressure of the geothermal fluid;
step 203, according to the dimensionless temperature T of the geothermal fluid at the wellhead r And dimensionless pressure drop p r Searching in the dimensionless gas compression coefficient diagram to obtain a gas compression coefficient Z in geothermal fluid at a wellhead;
correcting the liquid volume flow and the gas volume flow in the geothermal fluid at the wellhead; then correcting the liquid mass flow and the gas mass flow of the geothermal fluid according to the empirical parameters; and finally, calculating the corrected liquid phase density and gas phase density in the geothermal fluid, wherein the specific formulas are as follows:
the liquid volume flow rate of the geothermal fluid at the wellhead corrected according to the empirical parameters is:
q L ＝6.49×10 -5 q 0
wherein q L For the corrected liquid volume flow rate of the geothermal fluid at the wellhead according to the empirical parameters, q 0 Is the actual volumetric flow at the geothermal fluid wellhead;
the mass flow of the gas of the geothermal fluid at the wellhead corrected according to the empirical parameters is:
wherein q g For the well head corrected according to the experience parameterVolumetric gas flow in geothermal fluid; r is the gas solubility, z is the gas compression coefficient in the geothermal fluid at the wellhead;
q t ＝q L +q g
wherein: q t The total volumetric flow of the geothermal fluid at the wellhead is corrected according to the empirical parameters;
corrected mass flow rate w of liquid phase in geothermal fluid at wellhead L The method comprises the following steps:
w L ＝q 0 (4.05×10 -8 γ 0 +8.85×10 -7 γ g R s )
wherein: gamma ray 0 For geothermal fluid water to oil fluid specific gravity, gamma g Is the gas content in the geothermal fluid;
corrected mass flow of gas w in geothermal fluid at wellhead g And total liquid mass flow w in geothermal fluid t The method comprises the following steps:
w g ＝8.85×10 -7 q 0 γ g (R-R s )
w t ＝w L +w g
corrected density ρ of liquid phase in geothermal fluid at wellhead L And gas phase density ρ g The method comprises the following steps of:
determining a flow pattern in the depth of the calculated geothermal fluid, wherein the flow pattern comprises the following specific processes:
step 401, calculating a test variable v of the geothermal fluid at the depth of the primary pumping well t Delta and v gD The test variables are used for determining boundary conditions of geothermal fluid:
wherein: v t The geothermal fluid velocity at the well depth position is pressurized for one time, m/s; v gD Is the non-dimensional gas velocity at the well depth position of the primary pressure boost; sigma is the surface tension of the fluid at the position of the primary booster well depth, N; a is that p Is the shaft cross-section of geothermal shaft;
the boundary constraints are:
wherein: (L) B The overall dimensionless number, d, of velocity for bubble flow-slug boundary h Equivalent diameter for geothermal fluid flow; (L) S The overall dimensionless number of velocity for the slug-transition flow boundary; (L) M The overall dimensionless number of velocity for the transition flow-mist flow boundary;
step 402, comparing delta, v respectively gD ，(L) S Sum (L) M The method comprises the steps of carrying out a first treatment on the surface of the Make the following judgment if delta < (L) B The flow pattern of the geothermal fluid at the well depth position corresponding to the pressure value is bubble flow; if delta > (L) B ，v gD ＜(L) S The flow pattern of the geothermal fluid at the well depth position corresponding to the pressure value is a bullet-shaped flow; if (L) M ＞v gD ＞(L) S The flow pattern of the geothermal fluid at the well depth position corresponding to the pressure value is transition flow; if v gD ＞(L) M The flow pattern of the geothermal fluid at the well depth position corresponding to the pressure value is mist flow; if delta < (L) B If so, executing the next step; otherwise, executing step 201, and adjusting the pressure gradient value to be smaller on the basis of the original pressure gradient initial value; then executing the second to fourth steps;
fifthly, determining the Reynolds number of the geothermal fluid at the position of the primary pressurizing well depth, the Reynolds number of bubbles in the geothermal fluid and the relative roughness of the geothermal well bore;
wherein the Reynolds number N of the geothermal fluid Re ：
Wherein mu L Hydrodynamic viscosity coefficient for geothermal fluid;
by v pair b Performing iterative solution on bubble Reynolds number N in geothermal fluid b The formula is as follows:
average gas rise velocity v of geothermal fluid bf ：
The relative roughness of the geothermal fluid in the wellbore is:
wherein: ζ is the absolute roughness of the geothermal well bore, d is the inner diameter of the well bore;
step six, calculating the friction force f between the geothermal fluid and the well bore corresponding to the primary pressurized well depth position and the average density of the geothermal fluidThe specific formula is as follows:
when N is Re ＜2400，
When N is Re ≥2400，So the average density of geothermal fluid->The method comprises the following steps:
calculating the friction loss gradient tau of geothermal fluid f The method comprises the following steps:
wherein: g c Is a constant of attraction force;
step seven, calculating the flash evaporation depth D of the geothermal fluid in the well bore, namely, the position of the primary pressurizing well depth:
step eight, calculating the relative error of the predicted scaling position of the geothermal fluid as follows:
wherein: psi phi type 1 The flash depth D of the geothermal fluid in the well bore is calculated as a predicted value, namely by the steps;
ψ 2 the actual value, namely the scaling position of the geothermal fluid in the well bore, which is obtained through actual measurement;
omega is the depth of the submersible pump, i.e., the depth of the submersible pump in the geothermal wellbore.
The invention has the beneficial effects that:
(1) The mathematical model is simple and does not need complex mathematical deduction, the flow patterns of the geothermal fluid at different positions of the shaft are judged mainly through the different flow patterns of the gas-liquid two-phase flow in the geothermal shaft, and then the flash evaporation point position of the geothermal fluid in the shaft is calculated to judge the scaling position of the geothermal fluid in the shaft.
(2) And (3) establishing a mathematical model to predict the scaling position of the geothermal fluid, and finally forming a set of calculation method for briefly determining the scaling position through wellhead parameters. According to the calculation method, the flow patterns of the geothermal fluid from the wellhead of the geothermal well to the bottom of the geothermal well at different depths can be established, the flash evaporation position of the geothermal fluid can be finally determined, and the scaling position of the geothermal fluid can be determined.
(3) The mathematical model can predict the flash evaporation position of geothermal fluid in the well bore more quickly without considering the complex influencing factors.
(4) The mathematical model is simple and feasible, and is suitable for industrial application.
(5) The method solves the problem of black box in the prior software calculation, and builds a theoretical model for generating sediment by flash evaporation of geothermal fluid in a well bore.
Detailed Description
The present invention will be described in further detail with reference to examples. The specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the present invention.
The invention discloses a construction method of a mathematical model for predicting scaling positions in a geothermal well bore, which comprises the following steps:
measuring the flow, temperature, pressure and fluid characteristics of geothermal fluid at a wellhead in a geothermal well; the fluid characteristics include gas solubility, standard critical pressure, critical temperature, and viscosity of the geothermal fluid at the wellhead, wherein,
solubility of gas: r is R s ＝20.481；
Standard critical pressure:
critical temperature:
viscosity: μ=1.0×10 -3 Pa·s；
The gas compression coefficient in the geothermal fluid is obtained through calculation, and the specific process is as follows:
step 201, setting an initial value of a pressure gradient in a well depth range according to a pressure value of geothermal fluid at a well head, and calculating a primary boost pressure value p by a formula (1) 1 The position which is a certain distance away from the wellhead and corresponds to the primary supercharging pressure value is recorded as a primary supercharging well depth position; the greater the pressure of the geothermal fluid at the wellhead, the greater the pressure gradient, and the initial value of the pressure gradient may be set to 0.05-2.0MPa, with either too large or too small a gradient affecting the final predicted result.
The formula is as follows:
in p 0 For the pressure value at the wellhead, Δp is the initial value of the assumed pressure gradient;
step 202, correcting the measured value of the temperature and the pressure of the geothermal fluid at the wellhead by using the comparison temperature and the comparison pressure according to formulas (2) and (3) to obtain the dimensionless temperature T of the geothermal fluid at the wellhead r And dimensionless pressure drop p r ；
Dimensionless temperature:
dimensionless pressure drop:
wherein:t is a geothermal fluid temperature measurement at the wellhead pe Is the critical temperature of geothermal fluid, +.>P is a measurement of geothermal fluid pressure drop at the wellhead pe Is the critical pressure of the geothermal fluid.
Step 203, according to the dimensionless temperature T of the geothermal fluid at the wellhead r And dimensionless pressure drop p r Searching a dimensionless gas compression coefficient diagram (see chemical industry thermodynamics published by chemical industry publishers 2009) to obtain a gas compression coefficient Z in geothermal fluid at a wellhead;
correcting the liquid volume flow and the gas volume flow in the geothermal fluid at the wellhead; then correcting the liquid mass flow and the gas mass flow of the geothermal fluid according to the empirical parameters; and finally, calculating the corrected liquid phase density and gas phase density in the geothermal fluid, wherein the specific formulas are as follows:
the liquid volume flow rate of the geothermal fluid at the wellhead corrected according to the empirical parameters is:
q L ＝6.49×10 -5 q 0 (4)
wherein q L For the corrected liquid volume flow rate of the geothermal fluid at the wellhead according to the empirical parameters, q 0 Is the actual volumetric flow at the geothermal fluid wellhead.
The mass flow of the gas of the geothermal fluid at the wellhead corrected according to the empirical parameters is:
wherein q g The gas volume flow in the geothermal fluid at the wellhead is corrected according to the empirical parameters; r is the gas solubility, which may be taken herein as 100-120, and z is the gas compression coefficient in the geothermal fluid at the wellhead.
The correction parameters of the formulas (4) and (5) are 6.49×10, respectively -5 And 3.27X10 -7 Can be found in the literature "prediction wo-phase pressure drops in vertical pipe for two-phase pressure drop prediction in vertical wells" (journal Journal of Petroleum Technology,1967 edition, publication number 829-838).
q t ＝q L +q g (6)
Wherein: q t The total volumetric flow of the geothermal fluid at the wellhead is corrected according to the empirical parameters.
Corrected mass flow rate w of liquid phase in geothermal fluid at wellhead L (kg/s) is:
w L ＝q 0 (4.05×10 -8 γ 0 +8.85×10 -7 γ g R s ) (7)
wherein: gamma ray 0 For geothermal fluid water to oil fluid specific gravity, gamma g Is the gas content in the geothermal fluid.
Corrected mass flow of gas w in geothermal fluid at wellhead g And total liquid mass flow w in geothermal fluid t The method comprises the following steps:
w g ＝8.85×10 -7 q 0 γ g (R-R s ) (8)
w t ＝w L +w g (9)
correction parameter 8.85×10 -7 And 4.05X10 -8 Can be found in the literature, "predictive wo-phase pressure drops in vertical pipe" (journal Journal of Petroleum Technology, 1967)Version, number of publications 829-838).
Corrected density ρ of liquid phase in geothermal fluid at wellhead L And gas phase density ρ g The method comprises the following steps of:
determining a flow pattern in the depth of the calculated geothermal fluid, wherein the flow pattern comprises the following specific processes:
step 401, calculating the test variable of the geothermal fluid at the depth of the primary pumping well, namely the variable v involved in formulas (12), (13) and (14) t Delta and v gD The test variables are used for determining boundary conditions of geothermal fluid:
wherein: v t Geothermal fluid velocity (m/s) at the primary booster well depth location; v gD Is the non-dimensional gas velocity at the well depth position of the primary pressure boost; sigma is the surface tension (N) of the fluid at the position of the primary pressure boosting well depth, and can be obtained from a table look-up in chemical engineering principle published by higher education press in 2017. A is that p Is the shaft cross-sectional area of a geothermal shaft.
The boundary constraints are:
wherein: (L) B The overall dimensionless number, d, of velocity for bubble flow-slug boundary h Is the equivalent diameter of the geothermal fluid flow. (L) S The overall dimensionless number of velocity for the slug-transition flow boundary; (L) M The overall dimensionless number of velocity for the transition flow-mist flow boundary;
step 402, comparing delta, v respectively gD ，(L) S Sum (L) M . Make the following judgment if delta < (L) B The flow pattern of the geothermal fluid at the well depth position corresponding to the pressure value is bubble flow; if delta > (L) B ，v gD ＜(L) S The flow pattern of the geothermal fluid at the well depth position corresponding to the pressure value is a bullet-shaped flow; if (L) M ＞v gD ＞(L) S The flow pattern of the geothermal fluid at the well depth position corresponding to the pressure value is transition flow; if v gD ＞(L) M The flow pattern of the geothermal fluid at the well depth position corresponding to the pressure value is mist flow; if delta < (L) B If so, executing the next step; otherwise, step 201 is executed to reduce the pressure gradient value based on the original pressure gradient initial value. And then performing the second to fourth steps.
(L) B 、(L) S Sum (L) M Is a parameter reported by Orkiszewski according to Griffith and Wallis, duns and Ross for the boundary between bubble and slugs proposed by the remaining three flow regimes, (L) S Overall dimensionless number of velocities for slug-transition flow boundary, (L) M The overall dimensionless number of velocity for the transition flow-mist flow boundary; see, publication, "predictive wo-phase pressure drops in vertical pipe" (journal Journal of Petroleum Technology,1967 edition, pages 829-8)38)。
TABLE 2 boundary conditions of flow patterns in geothermal fluids
The contents of Table 2 are derived from the literature "Predicting two-phase pressure drops in vertical pipe" (journal Journal of Petroleum Technology,1967 edition, pages 829-838).
X in table 2 is the steam quality, also called steam quality, or steam dryness (measured by in situ sampling) of the geothermal fluid.
Fifthly, determining the Reynolds number of the geothermal fluid at the position of the primary pressurizing well depth, the Reynolds number of bubbles in the geothermal fluid and the relative roughness of the geothermal well bore;
wherein the Reynolds number N of the geothermal fluid Re
Wherein mu L The viscosity coefficient of the geothermal fluid hydrodynamic force can be obtained through table lookup, and the table is shown in chemical engineering principle published by higher education press in 2017;
by v pair b Performing iterative solution on bubble Reynolds number N in geothermal fluid b Formulas such as (19), (20), (21):
average gas rise velocity v of geothermal fluid bf ：
Bubble Reynolds numberNumber N b Since the rising speed of the bubbles in the geothermal fluid is nonlinear in the solving process, iteration is necessary to iterate the rising speed of the bubbles, and the initial rising speed of the bubbles in the geothermal fluid can be assumed to be v in the iteration process b ＝1.7。
The relative roughness of the geothermal fluid in the wellbore is:
wherein: ζ is the absolute roughness of the geothermal wellbore and d is the wellbore inner diameter.
The formula derivation process of the relative roughness is as follows:
determining a liquid partition coefficient Γ and a friction coefficient f of a geothermal fluid
The final rising velocity of the bubbles in the geothermal fluid is known from the calculated distribution coefficient as:
further, the Reynolds number of the water in the geothermal fluid is
N is obtained through calculation w The relative roughness of the geothermal fluid in the wellbore is:
wherein: ζ is the absolute roughness of the geothermal wellbore and d is the wellbore inner diameter.
Step six, the speed of the geothermal fluid along the shaft can be changed obviously in a short distance and guidedResulting in variable frictional losses between the geothermal fluid and the wellbore. It is necessary to calculate the friction between the geothermal fluid and the wellbore at the reynolds numbers of the different geothermal fluids. Knowing the Reynolds number of the geothermal fluid and the relative roughness of the geothermal well bore according to formulas (18) and (25), calculating the friction force f between the geothermal fluid and the well bore corresponding to the position of the primary pressurized well depth and the average density of the geothermal fluidThe specific formula is as follows:
when N is Re ＜2400，
When N is Re ≥2400，So the average density of geothermal fluid->The method comprises the following steps:
calculating the friction loss gradient tau of geothermal fluid f The method comprises the following steps:
wherein: g c Is a constant of attraction force;
step seven, calculating the flash depth D of the geothermal fluid in the wellbore (i.e., at the primary pressurized well depth location), a second flash of the geothermal fluid may also occur after the flash of the geothermal fluid in the wellbore, but this is not considered in the present method,
such as: assuming that the depth at the wellhead is 0m, when the calculated result meets the boundary condition (i.e. the condition in table 2) of the bubble flow pattern, the depth value is the depth value at which the bubble flow occurs, i.e. the position at which the geothermal fluid flashes:
step eight, finally, considering that the scaling position of the geothermal well usually occurs above the submersible pump, and adopting the depth of the submersible pump as the denominator of the formula (31), calculating the relative error of the scaling position of the geothermal fluid as follows:
wherein: psi phi type 1 The depth D of the flash evaporation of the geothermal fluid in the well bore calculated by the above steps is a predicted value.
ψ 2 Is the actual value, i.e. the position of the fouling of the geothermal fluid in the well bore, obtained by actual measurements.
Omega is the depth of the submersible pump, i.e., the depth of the submersible pump in the geothermal well bore, which can be measured by the field geothermal well.
Example 1
The wellhead parameters of the first geothermal well in a county are:
according to the wellhead parameters in the first geothermal well in a certain county in the table, the wellhead parameters of the geothermal well are substituted into a mathematical model established in the specific embodiment to be calculated, the position of the geothermal fluid in the geothermal well, which is subjected to flash evaporation, can be predicted to be 6.3m, and the relative error of the geothermal fluid is calculated to be 5.7% according to the actual scaling position of 0 m.
Example 2
The wellhead parameters of the second geothermal well in a county are:
according to the wellhead parameters in the geothermal well of the second port in a certain county in the table, the wellhead parameters of the geothermal well are substituted into a mathematical model established in the specific embodiment for calculation, the position of the geothermal fluid in the geothermal well bore where flash evaporation occurs can be predicted to be 34.6m, and the relative error is calculated to be 1.5% according to the actual scaling position of 30 m.
It should be noted that while the above describes in detail preferred embodiments of the present invention, the present invention is not limited to the above-mentioned embodiments, which are merely illustrative and not restrictive, and that many forms can be made by those skilled in the art without departing from the spirit of the present invention and the scope of the appended claims.
Claims (1)
1. A method of constructing a mathematical model for predicting the location of scale in a geothermal wellbore, comprising the steps of:
measuring the flow, temperature, pressure and fluid characteristics of geothermal fluid at a wellhead in a geothermal well; the fluid characteristics include gas solubility, standard critical pressure, critical temperature and viscosity of the geothermal fluid at the wellhead, wherein:
solubility of gas: r is R s ＝20.481；
Standard critical pressure: p is p pe ＝22.055kPa；
Critical temperature: t (T) pe ＝374.15；
Viscosity: μ=1.0×10 -3 Pa·s；
The gas compression coefficient in the geothermal fluid is obtained through calculation, and the specific process is as follows:
step 201, setting an initial value of pressure gradient in the well depth range according to the pressure value of geothermal fluid at the well head, and calculating to obtain a primary boost pressure value p 1 The position which is a certain distance away from the wellhead and corresponds to the primary supercharging pressure value is recorded as a primary supercharging well depth position;
in p 0 For the pressure value at the wellhead, Δp is the initial value of the assumed pressure gradient;
step 202, correcting the measured value of the temperature and the pressure of the geothermal fluid at the wellhead by using the comparison temperature and the comparison pressure, and calculating to obtain the dimensionless temperature T of the geothermal fluid at the wellhead r And dimensionless pressure drop p r ；
Dimensionless temperature:
dimensionless pressure drop:
wherein:t is a geothermal fluid temperature measurement at the wellhead pe Is the critical temperature of geothermal fluid, +.>P is a measurement of geothermal fluid pressure drop at the wellhead pe Is the critical pressure of the geothermal fluid;
step 203, according to the dimensionless temperature T of the geothermal fluid at the wellhead r And dimensionless pressure drop p r Searching in the dimensionless gas compression coefficient diagram to obtain a gas compression coefficient Z in geothermal fluid at a wellhead;
correcting the liquid volume flow and the gas volume flow in the geothermal fluid at the wellhead; then correcting the liquid mass flow and the gas mass flow of the geothermal fluid according to the empirical parameters; and finally, calculating the corrected liquid phase density and gas phase density in the geothermal fluid, wherein the specific formulas are as follows:
the liquid volume flow rate of the geothermal fluid at the wellhead corrected according to the empirical parameters is:
q L ＝6.49×10 -5 q 0
wherein q L For the corrected liquid volume flow rate of the geothermal fluid at the wellhead according to the empirical parameters, q 0 Is the actual volumetric flow at the geothermal fluid wellhead;
the mass flow of the gas of the geothermal fluid at the wellhead corrected according to the empirical parameters is:
wherein q g The gas volume flow in the geothermal fluid at the wellhead is corrected according to the empirical parameters; r is the gas solubility, z is the gas compression coefficient in the geothermal fluid at the wellhead;
q t ＝q L +q g
wherein: q t The total volumetric flow of the geothermal fluid at the wellhead is corrected according to the empirical parameters;
corrected mass flow rate w of liquid phase in geothermal fluid at wellhead L The method comprises the following steps:
w L ＝q 0 (4.05×10 -8 γ 0 +8.85×10 -7 γ g R s )
wherein: gamma ray 0 For geothermal fluid water to oil fluid specific gravity, gamma g Is the gas content in the geothermal fluid;
corrected mass flow of gas w in geothermal fluid at wellhead g And total liquid mass flow w in geothermal fluid t The method comprises the following steps:
w g ＝8.85×10 -7 q 0 γ g (R-R s )
w t ＝w L +w g
corrected density ρ of liquid phase in geothermal fluid at wellhead L And gas phase density ρ g The method comprises the following steps of:
determining a flow pattern in the depth of the calculated geothermal fluid, wherein the flow pattern comprises the following specific processes:
step 401, calculating a test variable v of the geothermal fluid at the depth of the primary pumping well t Delta and v gD The test variables are used for determining boundary conditions of geothermal fluid:
wherein: v t The geothermal fluid velocity at the well depth position is pressurized for one time, m/s; v gD Is the non-dimensional gas velocity at the well depth position of the primary pressure boost; sigma is the surface tension of the fluid at the position of the primary booster well depth, N; a is that p Is the shaft cross-section of geothermal shaft;
the boundary constraints are:
wherein: (L) B The overall dimensionless number, d, of velocity for bubble flow-slug boundary h Equivalent diameter for geothermal fluid flow; (L) S The overall dimensionless number of velocity for the slug-transition flow boundary; (L) M The overall dimensionless number of velocity for the transition flow-mist flow boundary;
step 402, comparing delta, v respectively gD ，(L) S Sum (L) M The method comprises the steps of carrying out a first treatment on the surface of the Make the following judgment if delta < (L) B The flow pattern of the geothermal fluid at the well depth position corresponding to the pressure value is bubble flow; if delta > (L) B ，v gD ＜(L) S The flow pattern of the geothermal fluid at the well depth position corresponding to the pressure value is a bullet-shaped flow; if (L) M ＞v gD ＞(L) S The flow pattern of the geothermal fluid at the well depth position corresponding to the pressure value is transition flow; if v gD ＞(L) M The flow pattern of the geothermal fluid at the well depth position corresponding to the pressure value is mist flow; if delta < (L) B If so, executing the next step; otherwise, executing step 201, and adjusting the pressure gradient value to be smaller on the basis of the original pressure gradient initial value; then executing the second to fourth steps;
fifthly, determining the Reynolds number of the geothermal fluid at the position of the primary pressurizing well depth, the Reynolds number of bubbles in the geothermal fluid and the relative roughness of the geothermal well bore;
wherein the Reynolds number N of the geothermal fluid Re ：
Wherein mu L Hydrodynamic viscosity coefficient for geothermal fluid;
by v pair b Performing iterative solution of bubble Reynolds in geothermal fluidNumber N b The formula is as follows:
average gas rise velocity v of geothermal fluid bf ：
The relative roughness of the geothermal fluid in the wellbore is:
wherein: ζ is the absolute roughness of the geothermal well bore, d is the inner diameter of the well bore;
step six, calculating the friction force f between the geothermal fluid and the well bore corresponding to the primary pressurized well depth position and the average density of the geothermal fluidThe specific formula is as follows:
when N is Re ＜2400，
When N is Re ≥2400，
So the average density of geothermal fluidThe method comprises the following steps:
calculating the friction loss gradient tau of geothermal fluid f The method comprises the following steps:
wherein: g c Is a constant of attraction force;
step seven, calculating the flash evaporation depth D of the geothermal fluid in the well bore, namely, the position of the primary pressurizing well depth:
step eight, calculating the relative error of the predicted scaling position of the geothermal fluid as follows:
wherein: psi phi type 1 The flash depth D of the geothermal fluid in the well bore is calculated as a predicted value, namely by the steps;
ψ 2 the actual value, namely the scaling position of the geothermal fluid in the well bore, which is obtained through actual measurement;
omega is the depth of the submersible pump, i.e., the depth of the submersible pump in the geothermal wellbore.
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