CN105184061B - The method for numerical simulation of gas-producing well temperature, pressure distribution - Google Patents
The method for numerical simulation of gas-producing well temperature, pressure distribution Download PDFInfo
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Abstract
The present invention relates to development of oil and gas reservoir administrative skill fields, and it discloses a kind of method for numerical simulation of gas-producing well temperature, pressure distribution, accurate simulation are carried out to the temperature, pressure parameter distribution situation of gas-producing well, to provide guidance foundation for production.This approach includes the following steps：A, temperature, pressure coupled-differential equations model is established；B, estimate differential equation group relevant parameter；C, algorithm design is carried out using calculus of finite differences；D, C# development platforms are based on and build simulation softward；E, primary data is inputted in simulation softward, obtains temperature, pressure distribution simulation result.The present invention can accurately predict the Temperature and pressure distribution of gas-producing well, the raising of oil gas production equipment design level is greatly facilitated, to be conducive to Reservoir Development.
Description
Technical field
The present invention relates to development of oil and gas reservoir administrative skill fields, the specially Numerical-Mode of gas-producing well temperature, pressure distribution
Quasi- method is related to the temperature, pressure coupling mechanism analysis of gas-producing well, and mathematical model is established, method for numerical simulation design etc..
Background technology
Produce gas well usually along with high temperature, high flow rate, high pressure, this is because friction, pit shaft deformation, heat transfer etc.
Reason.With the evolution of production environment, including deep water and high-temperature pressure condition, design, hydrate in petroleum works facility
Prevent optimization, producing well dynamic analysis, it is necessary to accurate prediction is carried out to temperature, pressure.
When liquid is initially generated from a region, temperature may think that the same in shaft bottom.This can not be gas
Vertical.If Joule-Thompson effects are appropriately considered, gasinlet temperature can be estimated with formation temperature.Therefore,
The temperature of wellbore bottom can be reliably estimated.However, with the rising of fluid, its temperature is significantly higher than surrounding formation
Temperature, this is because formation temperature with depth reduce and decline.
There is temperature difference with fluid when stratum, heat transfer phenomenon will occur.In any depth, formation temperature not only with radiation away from
It is also related with the production time from related.When reaching stationary flow, turbulent flow ensure that the temperature of fluid is normal in certain depth
Number.Then, the thermal loss in fluid is reduced with the time, and the heat different from surrounding formation depending on pit shaft red heat liquid
Resistance.
Complete system is by fluid, annular gap, casing, setting and stratum containing low-pressure air, as shown in Figure 1：
Catheter diameter is rti, outer diameter is rt0, the internal diameter of casing is rci, outer diameter is rc0, heat by the air in ring into
Row conduction.Radiation also occurs with convection current.When tube body is heated, the conduction velocity of radiation energy depends on the temperature of tube body.Conduit with
The conduction of radiation energy between casing sends out depending on interface and absorbs the feature of heat.In many cases, between conduit and hole
Gap blocked.Since the conductibility of cement is likely lower than the stratum on periphery, calculating by pit shaft stage, gradually to
On.Using the air inlet of gas well as the intersection point of reference axis, pit shaft is the positive direction of reference axis downwards.Fig. 2 shows pit shaft infinitesimal
Pressure deduction analysis, P is Fluid pressure, and v is gas velocity, and l is depth, and dv is the speed increment on dl, and dp is the pressure on dl
Increment, θ are the inclinations angle of pit shaft.
Invention content
The technical problem to be solved by the present invention is to：It is proposed a kind of method for numerical simulation of gas-producing well temperature, pressure distribution,
Accurate simulation is carried out to the temperature, pressure parameter distribution situation of gas-producing well, to provide guidance foundation for production.
Scheme is used by the present invention solves above-mentioned technical problem：The numerical simulation side of gas-producing well temperature, pressure distribution
Method includes the following steps：
A, temperature, pressure coupled-differential equations model is established；
B, estimate differential equation group relevant parameter；
C, algorithm design is carried out using calculus of finite differences；
D, C# development platforms are based on and build simulation softward；
E, primary data is inputted in simulation softward, obtains temperature, pressure distribution simulation result.
Further, in step A, the temperature, pressure coupled-differential equations model of establishing specifically includes：
Based on the assumption that model construction condition obtain energy conservation equation, mass-conservation equation, momentum conservation equation respectively：
Wherein, energy conservation equation：
Mass-conservation equation：
Momentum conservation equation：
On infinitesimal dl, the radiant heat conducted from fluid to setting-bed boundary is
The radiant heat conducted from setting-bed boundary to surrounding formation is：
Convolution (4) and formula (5) obtain the differential equation of fluid and surrounding formation heat transfer：
(1) and (6) is integrated, following ODE is obtained：
When fluid flows in the wellbore, due to caliber change very little, Joule-Thomson coefficients can be ignored not
Meter, therefore dh=CpDT, the enthalpy change amount for formula (7) entirety are：
The differential prescription of Fluid pressure in the natural gas well, temperature, density and rate can be obtained by formula (1), (2), (3), (8)
Journey：
Use yi(i=1,2,3,4) replaces ρ, v, P, T, then equation group can be reduced to
Further, the model construction condition of the hypothesis includes：
The flowing of natural gas is one way stable；The heat transfer of pit shaft is stable state；Stratum heat transfer is unstable；Conduit and
Casing is concentric.
Further, in step B, estimation differential equation group relevant parameter specifically includes：
B1. the coefficient of heat conduction is estimated：
B2. specific heat at constant pressure C is calculatedP：
Cp=1243+3.14T+7.931 × 10-4T2-6.881×10-7T3 (12)
B3. stratum heat diffusion equation：
B4. friction coefficient f is calculated：
Further, described to carry out algorithm to design including to temperature, pressure coupled differential using calculus of finite differences in step C
The solution of group model：
Gas-producing well is divided into n section, j (j=1,2 ..., n) is node, and n is shaft bottom, step-length h；
The boundary condition of temperature, pressure coupled-differential equations is：
In order to calculate the correlative of each node, following iterative equation is used：
To use above equation, need to estimate a [i], b [i], c [i] and d [i]:
Further, in step D, the simulation softward include subscriber interface module, output output module, algoritic module and
Chart module；
The subscriber interface module is used to provide the initial information of gas well, these information can be divided into static data, fluid
Data and creation data：
Static data：The static lower gas well feature of description；
Fluid data：The state of fluid is described；
Creation data：The parameter that production phase gives；
The input/output module is used to read in memory, preserves data；
The algoritic module is used to carry out mathematical computations according to the algorithm of design；
The data result that the chart module is used to simulate carries out pictorialization displaying.
The beneficial effects of the invention are as follows：The Temperature and pressure distribution of gas-producing well is accurately predicted, oil gas is greatly facilitated
The raising of winning apparatus design level, to be conducive to Reservoir Development.
Description of the drawings
Fig. 1 is well section structural schematic diagram；
Fig. 2 is that conduit internal pressure deduction analyses schematic diagram；
Fig. 3 is the method for numerical simulation flow chart of gas-producing well temperature, pressure of the present invention distribution；
Fig. 4 is simulation software construction schematic diagram；
Fig. 5 is program circuit schematic diagram；
Fig. 6 is to simulate the pressure distribution curve figure come；
Fig. 7 is to simulate the temperature distributing curve diagram come.
Specific implementation mode
The present invention is directed to propose a kind of method for numerical simulation of gas-producing well temperature, pressure distribution, to the temperature, pressure of gas-producing well
Parameter distribution situation carries out accurate simulation, to provide guidance foundation for production.
The parameter paraphrase likely related in the present invention is as follows：
A:Inner tube area, m2；
CP:Specific heat at constant pressure, J/Kg.K；
f:Friction coefficient；
f(TD):Stratum transient heat conduction equation of time；
g:Acceleration of gravity；
h:Specific enthalpy；
kang:Gas heat conductivity in ring, J/m.K；
kcem:Setting heat conductivity, J/m.K；
ke:Stratum heat conductivity, J/m.K；
l:Pit shaft length, l；
M:The molar average weight of gas, g/mol；
P:Fluid pressure, pa；
PPe:Critical pressure, pa；
rcem：Setting outer diameter, m
Re:Reynolds number；
t:Production time, s；
T:Fluid temperature (F.T.), K；
Te:Surrounding formation temperature, K；
Uti:Overall heat-transfer coefficient, W/m.K；
v:Natural gas rate, m/s；
w:Total mass velocity；
z:Compressibility factor；
α：The thermal diffusivity on stratum, m2/s。
The solution of the present invention is described in further detail with reference to the accompanying drawings and embodiments：
As shown in figure 3, the method for numerical simulation of gas-producing well temperature, pressure distribution of the present invention includes：
A, temperature, pressure coupled-differential equations model is established；
B, estimate differential equation group relevant parameter；
C, algorithm design is carried out using calculus of finite differences；
D, C# development platforms are based on and build simulation softward；
E, primary data is inputted in simulation softward, obtains temperature, pressure distribution simulation result.
In specific implementation, in step A, based on the assumption that model construction condition obtain energy conservation equation, quality respectively
Conservation equation, momentum conservation equation；
The case where to meet practical gas-producing well, makes the following assumptions：
(1) flowing of natural gas is one way stable；
(2) heat transfer of pit shaft is considered as stable state；
(3) it is based on dimensionless transient heat conduct equation of time, stratum heat transfer is unstable；
(4) conduit and casing are concentric；
Energy conservation equation：
Mass-conservation equation：
Momentum conservation equation：
Coupled-differential equations model：On infinitesimal dl, the radiant heat conducted from fluid to setting-bed boundary is
The radiant heat conducted from setting-bed boundary to surrounding formation is
By on (4) and (5), obtaining the differential equation of fluid and surrounding formation heat transfer：
(1) and (6) is integrated, the following differential equation is obtained
When fluid flows in the wellbore, due to caliber change very little, Joule-Thomson coefficients can be ignored not
Meter.Therefore, dh=CpDT, whole enthalpy change amount are
(1) (2) (3) (8) are put together, are arranged, Fluid pressure, temperature, density in the natural gas well can be obtained
With the differential group equation of rate：
Use yi(i=1,2,3,4) replaces ρ, v, P, T, then equation group can be reduced to
Estimate that differential equation group relevant parameter includes described in step B：
B1. the coefficient of heat conduction is estimated：
Above formula shows that in wellbore system, material (gas, oil, water or mixture) is determining heat between casing/conduit annular space
It is played an important role during conduction.
B2. specific heat at constant pressure C is calculatedP：
Cp=1243+3.14T+7.931 × 10-4T2-6.881×10-7T3 (12)
B3. stratum heat diffusion equation：
B4. friction coefficient f is calculated：
In step C algorithm design is carried out using calculus of finite differences；Due to CPIt is not constant with θ, pit shaft must be divided into several length
Spend section, step-length h.Assuming that well can be divided into n section, j (j=1,2 ..., n) is node, and n is shaft bottom.According to shaft bottom
Temperature and pressure, the density and fluid velocity of corresponding natural gas can be calculated.The boundary condition of the above-mentioned differential equation is：
In order to calculate the correlative of each node, following iterative equation is used；
To use above equation, need to estimate a [i], b [i], c [i] and d [i]:
In step D, simulation softward is built based on C# development platforms；Software configuration is as shown in Figure 4 comprising user interface mould
Block, input/output module, algoritic module and icon module；
(1) subscriber interface module：The main initial information for providing gas well, these information can be divided into static data, fluid
Data and creation data：
(i) static data：The static lower gas well feature of description, is abbreviated as S.
(ii) fluid data：The state of fluid is described, Ru Shui, oil or gas are abbreviated as F.
(iii) creation data：The parameter that production phase gives, is abbreviated as P.
(2) input/output module：The module reads in memory, preserves data.Use Microsoft SQL
Server2000 establishes the database of pit shaft.
(3) algoritic module：The module will be applied to all mathematical computations.It can calculate and arbitrarily be saved from shaft bottom to well head
The temperature and pressure of point.
(4) chart module：The module is by data drawing list.Temperature, pressure distribution can be drawn by CrystalReports
Curve and export result.
After the completion of simulation softward designs, so that it may using primary data is inputted in simulation softward, to obtain temperature, pressure
Distribution simulation is as a result, specific algorithm flow is as shown in Figure 5.
Embodiment：
For certain a bite gas-producing well, input data is shown in Table 1：
Table 1:Gas-producing well correlated inputs tables of data
It is simulated by software, obtains series of results.Such as Fig. 6 and Fig. 7, temperature and pressure is from shaft bottom to well head, increasingly
It is small.This is because the heat transfer of gravity, friction and pit shaft to stratum.Temperature declines very much, but then become at 0 to 3000 meters
In stabilization, temperature is then with depth linear change.Fig. 6 shows that, in same well depth, gas production is bigger, since frictional resistance volume increases
Pressure is smaller, and since flow velocity increases, temperature increases.
Claims (3)
1. the method for numerical simulation of gas-producing well temperature, pressure distribution, which is characterized in that include the following steps：
A, temperature, pressure coupled-differential equations model is established；
B, estimate differential equation group relevant parameter；
C, algorithm design is carried out using calculus of finite differences；
D, C# development platforms are based on and build simulation softward；
E, primary data is inputted in simulation softward, obtains temperature, pressure distribution simulation result；
In step A, the temperature, pressure coupled-differential equations model of establishing specifically includes：
Based on the assumption that model construction condition obtain energy conservation equation, mass-conservation equation, momentum conservation equation respectively：
Wherein, energy conservation equation：
Mass-conservation equation：
Momentum conservation equation：
On infinitesimal dl, the radiant heat conducted from fluid to setting-bed boundary is
The radiant heat conducted from setting-bed boundary to surrounding formation is：
Convolution (4) and formula (5) obtain the differential equation of fluid and surrounding formation heat transfer：
(1) and (6) is integrated, following ODE is obtained：
When fluid flows in the wellbore, due to caliber change very little, Joule-Thomson coefficients are ignored, therefore
Dh=CpDT, the enthalpy change amount for formula (7) entirety are：
The differential group equation of Fluid pressure in the natural gas well, temperature, density and rate can be obtained by formula (1), (2), (3), (8)：
Use yi, i=1,2,3,4 replace ρ, v, P, T, then equation group can be reduced to
In step B, estimation differential equation group relevant parameter specifically includes：
B1. the coefficient of heat conduction is estimated：
B2. specific heat at constant pressure C is calculatedP：
Cp=1243+3.14T+7.931 × 10-4T2-6.881×10-7T3 (12)
B3. stratum heat diffusion equation：
B4. friction coefficient f is calculated：
In step C, described to carry out algorithm design using calculus of finite differences include solution to temperature, pressure coupled-differential equations model：
Gas-producing well is divided into n section, j is node, and j=1,2 ..., n, n is shaft bottom, step-length h；
The boundary condition of temperature, pressure coupled-differential equations is：
In order to calculate the correlative of each node, following iterative equation is used：
To use above equation, need to estimate a [i], b [i], c [i] and d [i]:
2. the method for numerical simulation of gas-producing well temperature, pressure distribution as described in claim 1, which is characterized in that the hypothesis
Model construction condition includes：
The flowing of natural gas is one way stable；The heat transfer of pit shaft is stable state；Stratum heat transfer is unstable；Conduit and casing
It is concentric.
3. the method for numerical simulation of gas-producing well temperature, pressure distribution as described in claim 1, which is characterized in that in step D, institute
It includes subscriber interface module, input/output module, algoritic module and chart module to state simulation softward；
The subscriber interface module is used to provide the initial information of gas well, these information be divided into static data, fluid data and
Creation data：
Static data：The static lower gas well feature of description；
Fluid data：The state of fluid is described；
Creation data：The parameter that production phase gives；
The input/output module is used to read in memory, preserves data；
The algoritic module is used to carry out mathematical computations according to the algorithm of design；
The data result that the chart module is used to simulate carries out pictorialization displaying.
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| CN104453861A (en) * | 2014-11-11 | 2015-03-25 | 中国石油天然气股份有限公司 | Method and system for determining temperature distribution of high-pressure gas well shaft |
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| CN104453861A (en) * | 2014-11-11 | 2015-03-25 | 中国石油天然气股份有限公司 | Method and system for determining temperature distribution of high-pressure gas well shaft |
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| An Optimal Model for Predicting the Productivity of Perforated Vertical HTHP Wells;Jiancheng Hu等;《THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING》;20140731(第92期);第1247-1259页 * |
| 气井压力温度预测综合数值模拟;郭春秋等;《石油学报》;20010515;第22卷(第3期);第100-105页 * |
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