CN105160056B - High temperature and pressure oil gas straight well two phase flow perforation completion parameter and production capacity optimization method - Google Patents
High temperature and pressure oil gas straight well two phase flow perforation completion parameter and production capacity optimization method Download PDFInfo
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Abstract
The invention belongs to development of oil and gas reservoir administrative skill fields, specially a kind of high temperature and pressure oil gas straight well two phase flow perforation completion parameter and production capacity optimization method, it is related to the structure of high temperature and pressure oil gas straight well Two-phase flow's separation, flow through oil reservoir steady-state model, pit shaft Two-phase flow's separation, liquid holdup is analyzed, the optimization of two phase flow production capacity and algorithm flow design etc.；This approach includes the following steps：A, petrol-gas permeation fluid steady-state model is built；B, pit shaft two phase flow model is built；C, analysis meter fluid operator liquid holdup；D, two phase flow production capacity Optimized model is built；E, two phase flow production capacity Optimized model is solved.The present invention accurately predicts the distribution of optimal perforation, and is optimized to parameter, the raising of oil gas production equipment design level can be greatly facilitated, to be conducive to Reservoir Development.
Description
Technical field
The invention belongs to development of oil and gas reservoir administrative skill field, specially a kind of high temperature and pressure oil gas straight well two phase flow
Perforation completion parameter and production capacity optimization method, are related to high temperature and pressure oil gas straight well Two-phase flow's separation, flow through oil reservoir stable state mould
The structure of type, pit shaft Two-phase flow's separation, liquid holdup analysis, the optimization of two phase flow production capacity and algorithm flow design etc..
Background technology
Since there is liquids and gases the feature of flowing, the two to be commonly referred to collectively as fluid.So-called two phase flow or multiphase flow are
Refer to the flowing for existing simultaneously two or more different phase substances, for example, the mixed flow of gas and liquid, gas and solid it is mixed
Collaborate dynamic, liquid and solid mixed flow and oil gas water mixed flow.Multiphase flow can according to the number for participating in flowing each phase
It is divided into two phase flow and three-phase flow, wherein especially most common with two phase flow.In petroleum works, the key problem of oil gas well mining is exactly
Research to fluid flowing law in pipeline.Oil/gas well is when entering the middle and later periods of exploitation, fluid in most of oil gas well conduits
Mainly two-phase flow, it is also possible to being flowed for oil gas water three phase.
Research to two phase flow in pipeline mainly uses various energy equations, by experimental analysis, obtains corresponding half and passes through
Semi-theoretical model is tested, common model mainly has shunting model, uniform flow model, drift-flux model etc..Divergent die therein
Type and uniform flow model formulation are fairly simple, but production required precision is not achieved in engineer application, and uniform flow model is only applicable to
Part flow pattern, shunting model cannot be used for straight well pipe stream suitable for flow in horizontal pipe.Comparatively, drift-flux model considers
Flow behavior between two phase flow is easy to get its mathematical model, is the common processing method of current two-phase flow problem.
Biphase gas and liquid flow mainly discusses flowing law of the gas with liquid two-phase medium under the conditions of common flowing, in oil gas
In well engineering, two-phase flow phenomenon often occurs.Two-phase medium is different from single-phase medium, and there are boundaries, are flowed in fluid
In the process, two-phase medium is other than the active force between two-phase, and there is also active forces between medium and pipeline wall surface.Even
Under the conditions of afterflow is dynamic, the active force between two-phase interface is in equilibrium state, but there are the exchanges of energy；Moreover, in gas-liquid two-phase
In flowing, the flowing velocity of each phase is different, and this sliding phenomenon is known as slipping.
Invention content
The technical problem to be solved by the present invention is to：It is proposed a kind of high temperature and pressure oil gas straight well two phase flow perforation completion parameter
With production capacity optimization method, accurate prediction is made to perforating parameter, to improve Oil & Gas Productivity ratio.
The technical solution adopted by the present invention to solve the technical problems is：High temperature and pressure oil gas straight well two phase flow perforation completion
Parameter and production capacity optimization method, include the following steps：
A, petrol-gas permeation fluid steady-state model is built；
B, pit shaft two phase flow model is built；
C, analysis meter fluid operator liquid holdup；
D, two phase flow production capacity Optimized model is built；
E, two phase flow production capacity Optimized model is solved.
Specifically, in step A, the method for the structure petrol-gas permeation fluid steady-state model includes：
Assuming that perforated interval is a length of lperf, the cylinder that radius is rperf, the perforated interval in entire straight well pit shaft includes N
A preforation tunnel, since bottom, the position of the i-th perforation is xi (i=1,2 ..., N)；By i-th of preforation tunnel into becoming a mandarin
Measure qImiGenerated pressure p ii can be described as
QIm is the mixed traffic in unit preforation tunnel in formula (1)；
qIm=qIL+qIG (2)
QIG and qIL indicates that the air-liquid in unit preforation tunnel becomes a mandarin flow respectively in formula (2)：
QIG=AIVISL (3)
qIL=AIVISG (4)
Wherein, AI indicates the cross-sectional area of eyelet, VISL and VISG be respectively Perforation ocular fluids superficial liquid velocity and
Superficial gas velocity；Point sink radius rpeq of equal value based on perforation and its fracture area damage epidermis sp can be described as：
If the spacing between perforation is fully big, point sink flow qIm, j at preforation tunnel j will produce pressure at eyelet i,
Eyelet j can be described as steady state pressure caused by eyelet j：
Gross pressure at eyelet i becomes a mandarin generation for pressure and other perforations of the generation that becomes a mandarin of eyelet i itself
The sum of pressure
It brings formula (1) and formula (6) into formula (7), can obtain：
The position of perforation j is x=xj, x1Indicate first perforating site since perforated interval bottom；Perforating site xiFor
Known variables, pressure and inbound traffics of the non-linear dependence at each perforation；
By at N number of eyelet pressure and flow be expressed as N-dimensional vector, can obtain：
P=(p1, p2..., pN)T, q=(qIm,1, qIm,2..., qIm,N)2 (9)
Formula (9) is expressed as matrix form：
P=Bq (10)
Coefficient matrix B is determined by perforating parameter and cloth hole site in formula (10), gives the distribution of perforation pressure and Perforation
Eye distribution can be become a mandarin flow if the coefficient matrix B in formula (10) is reversible by asking N × N rank inverse matrixs to calculate perforation：
Q=B-1p (11)。
Specifically, the method for building pit shaft two phase flow model described in step B includes：
If downhole well fluid is gas-liquid two-phase fluid, the overall presure drop of the perforated interval of Δ x long can be obtained：
Δpw=Δ pf+ Δs pg+Δpaw+ΔpaE (12)
Equal sign right end first item Δ pf indicates the pressure drop caused by wall friction in formula (12)：
Wall friction shear stress τ w are defined as：
Wherein ftp indicates that two phase flow Fanning friction factor, Vtp indicate the true average speed of the two phase flow fluid in pit shaft
Degree；The total mass flow rate Mtp of two phase flow is defined as flowing through the gross mass of the gas-liquid mixed stream of any cross section, root in the unit interval
According to mass balance, can obtain
Mtp=AVtpρtp (15)
Or it is expressed as
Mtp=ML+MG=AVSLρL+AVSGρG (16)
Wherein ML and MG indicates that liquid phase stream and gas phase stream flow, ρ L and ρ G indicate that liquid phase stream and gas phase stream are close respectively respectively
Degree；According to the equation of gas state
Combined type (15) and (16), can obtain
In homogeneous phase model, two phase flow density p tp is defined as gas, liquid fluid density and is with liquid holdup HL
The weighted average of weight,
ρtp=ρLHL+ρG(1-HL) (19)
During gas liquid two-phase flow, the flow section area AL of liquid phase accounts for the ratio of total area of passage A, as holds liquid
Rate：
AG indicates the flow section area of gas phase in formula；
Void fraction is defined as
The Section 2 Δ pg of formula (12) equal sign right end is pressure drop caused by fluid gravity：
Δpg=-g ρtpΔx cos α (22)
The Section 3 of formula (12) equal sign right end is to become a mandarin to accelerate pressure drop according to quality and momentum balance to be added caused by flowing
Ram compression drop can be described as：
In formula Vm indicate two-phase mixtures fluid speed, QItp indicate unit pit shaft length in two-phase integrated flux and
QIm indicates the mixing integrated flux in unit pit shaft；
QIm=QIL+QIG≠QItp (25)
Vm=VSL+VSG (26)
Wherein QIG and QIL is the liquid and gas accumulation inbound traffics in unit pit shaft respectively；By analyzing predicted value and reality
Test data, the weighted average of Δ paW1 and Δ paW2 can obtain accelerating the optimum prediction of pressure drop
Δpaw=ωΔpaWI+(1-ω)ΔpaW2 (27)
It brings formula (23) into, can obtain
Best weight coefficient is ω=0.8；
Last expression of formula (12) equal sign right end, which becomes a mandarin, accelerates pressure drop caused by fluid expansion, can by total pressure drop with
The coefficient of expansion is multiplied to obtain：
β aE are the coefficient of expansion in formula, can be estimated with following formula
Along perforation straight well, pressure p w, i at i-th of eyelet meet following formula：
Wherein pd is the pressure at the starting position x1 of downstream bottom end；
About discrete type (31), the discrete scheme of friction pressure drop is
Accelerate pressure drop discrete scheme be
For biphase gas and liquid flow, gas phase, liquid phase accumulation inbound traffics in unit pit shaft are
The discrete scheme of position pressure drop is again
Δpg=-q ρtp|xi+1-xi|cos α (36)
Wherein α i are the inclination angle of the i-th perforation；
The discrete scheme of formula (29) is
Association type (30)-(36), wellbore fluids pressure drop are represented by matrix form
P=F [q] (38).
Specifically, the method for analysis meter fluid operator liquid holdup described in step C includes：
For the speed VG of gas phase, described using the empirical constitutive relation containing two-phase mixtures fluid speed Vm：
VG=C0Vm+Vd(39)
C0 and Vd is drift parameter in formula, and C0 indicates that distributed constant in pipeline section, Vd indicate being averaged relative to liquid phase
Speed, the rate of climb of bubble：
Vc indicates characteristic velocity, the rate of climb of characterization bubble in a liquid in formula (40)
Wherein σ GL show that tension, parameter Ku are Kutateladze numbers between gas phase and liquid phase：
Cw is friction factor in formula (42), and Cku is constant and NB is Bond number numbers
According to formula (39), void fraction HG and liquid holdup HL are expressed as
Specifically, the method for building two phase flow production capacity Optimized model described in step D includes：
Petrol-gas permeation fluid and wellbore pressure loss coupling model are established according to formula (8) and formula (31)：
For one include N number of eyelet straight well, above-mentioned coupling model is 2N side for including 2N unknown function
The suitable of journey composition determines mathematical problem, is solved using following iterative formula：
Given initial valueAccording to the iterative algorithm of coupling model, the pressure of the flow and pit shaft at each eyelet is calculated
Distribution；When pi and qi increments are less than given control error, above-mentioned iterative formula convergence；
When building production capacity Optimized model, using total output as object function, the aggregated capacity of gas well is maximized
The variable of optimization problem is perforating site, meets condition：
0≤x1≤…≤xi≤…≤xN≤Hp(48)
Perforated interval is divided into J sections using J-1 nodes X j (j=1,2 ..., J-1), every section includes I perforation unit (N
=I × J), i.e., the Kong Mi in each segmentation limit interval is constant, but the Kong Mi being often segmented is not necessarily identical；N number of point of straight well section
Section section is：
[Xj, Xj+1], j=0,1 ..., J-1, X0=0, XJ=Hp (49)
The each upper coordinate of I eyelet on that segment of segmentation is represented by：
XI×j+i=Xj+(Xj+1-Xj) i/I, i=0,1 ..., I, j=0,1 ..., J-1 (50)
As the eyelet number I > 1 in each segmentation, then workload can be reduced by being segmented calculating, and decision variable is reduced to by N number of
J-1；
According to the relational expression that becomes a mandarin (45) of optimization strategy (47) and perforation straight well, the optimization of perforation straight well production capacity is obtained
Object function is
If considering water, gas coning problem, it is required that it is equal as possible in the upper inbound traffics of each perforation segmentation, to slow down water, gas
The time burst of cone
Due to qIm and unknown, formula (52) is the equation group comprising J-1 equation and J-1 unknown quantitys；
Consider that infinite fluid diversion well, i.e. pi=pd obtain the straight well capacity Optimized model of infinite fluid diversion perforation：
Consider that limited fluid diversion well, the pressure drop of straight well pit shaft cannot be ignored, i.e. pi=pwi obtains limited fluid diversion perforation straight well
Production capacity Optimized model：
Specifically, in step E, the method solved to two phase flow production capacity Optimized model includes：
1) initial value is givenWith allowable error ε=10-3；
2) inclination angle at each point is calculated
I indicates the number of perforation waypoint, s in formulakIndicate inclined angle alphakAnd αk-1Between measurement length, Δ siExpression is inclined
The material calculation at oblique angle；
3) the Reynolds number Retp of two-phase fluid is calculated：
μ in formulatp=μLHL+μG(1-HL), wall surface thunder Lip river coefficients R w is calculated with following formula
Wherein μIm=μLFIL+μG(1-FIL), ρIm=ρLFIL+ρG(1-FIL) andAnd FIG=1-CIL；
4) two-phase pit shaft stream Fanning friction factor is calculated, for Axial Laminar：
For axial turbulence：
Wherein Colebrook-White equations can be used to estimate without wall flow Fanning friction factor f0：
5) pressure and perforation for applying the uniform cloth hole straight well of iterative formula (46) calculating enter flow distribution；
6) the best perforation distribution of infinite fluid diversion well is calculated in solving model (53)；
7) the best perforation distribution of limited fluid diversion well is calculated in solving model (54).
The beneficial effects of the invention are as follows：Accurate prediction is made to perforating parameter, is conducive to optimize straight well design, to improve oil gas
Well capacity ratio.
Description of the drawings
Fig. 1 is high temperature and pressure oil gas straight well two phase flow perforation completion parameter of the present invention and production capacity optimization method flow chart；
Fig. 2 is preforation tunnel arrangement architecture figure；
Fig. 3 is pit shaft unit section figure；
Fig. 4 is pressure drop distribution figure；
Fig. 5 (a), 5 (b) are respectively the apparent velocity distribution map changed with well depth for infinite fluid diversion well, limited fluid diversion well；
Fig. 6 (a), 6 (b) are respectively to scheme with the current capacity contrast that well depth changes for infinite fluid diversion well, limited fluid diversion well；
Fig. 7 (a), 7 (b) are respectively the wellbore fluids flow velocity pair changed with well depth for infinite fluid diversion well, limited fluid diversion well
Than figure；
Fig. 8 is the liquid holdup distribution map changed with well depth；
Fig. 9 (a), 9 (b) are respectively the shot density comparison diagram changed with well depth for infinite fluid diversion well, limited fluid diversion well.
Specific implementation mode
The present invention is directed to propose a kind of high temperature and pressure oil gas straight well two phase flow perforation completion parameter and production capacity optimization method, right
Perforating parameter makees accurate prediction, to improve Oil & Gas Productivity ratio.
As shown in Figure 1, this method includes：1. building petrol-gas permeation fluid steady-state model；2. building pit shaft two phase flow mould
Type；3. analysis meter fluid operator liquid holdup；4. building two phase flow production capacity Optimized model；5. a pair two phase flow production capacity Optimized model is asked
Solution.
The embodiment of each step is illustrated below：
Pressure drop in pit shaft is the important parameter of gas well design, and optimization design, the stable yields of gas well parameter are increased production and tried
The design of well is significant.The pressure drop relationships of biphase gas and liquid flow in following discussion perforation straight well.If in system being air-liquid two-phase
Fluid, the fluid in pit shaft are one-dimensional constant temperature, steady-flow, oil reservoir homogeneous, do not have mass exchange between gas-liquid two-phase fluid.
(1) flow through oil reservoir steady-state model is established：
Regard perforated interval as a length of lperf, radius rperfCylinder.Perforated interval in entire straight well pit shaft includes N number of
The arrangement architecture of preforation tunnel, perforated hole is as shown in Figure 2.If formation damage is ignored, since bottom, the position of the i-th perforation
It is set to xi(i=1,2 ..., N).For easy analysis, biphase gas and liquid flow is considered as pseudo- single-phase flow, works as ratioWhen very little, according to
The average pressure of uniform line source, by i-th of preforation tunnel into inbound traffics qImiGenerated pressure piiIt can be described as
Q in formulaImFor the mixed traffic in unit preforation tunnel
qIm=QIL+qIG(2)
Q in formulaIGAnd qILIndicate that the gas-liquid in unit preforation tunnel becomes a mandarin flow, is represented by respectively
qIG=AIVISL(3)
qIL=AIVISG(4)
Wherein, AIIndicate the cross-sectional area of eyelet, VISLAnd VISGThe respectively superficial liquid velocity and table of Perforation ocular fluids
See gas velocity.
Because not considering pit shaft damage factor, based on perforation and its fracture area damage epidermis spPoint sink radius of equal value
rpeqIt can be described as
If the spacing between perforation is fully big, the point sink flow q at preforation tunnel jIm,jPressure is will produce at eyelet i,
Eyelet j can be described as steady state pressure caused by eyelet j：
Gross pressure at eyelet i becomes a mandarin generation for pressure and other perforations of the generation that becomes a mandarin of eyelet i itself
The sum of pressure
It brings formula (1) and formula (6) into formula (7), can obtain
The position of perforation j is x=xj, x1Indicate first perforating site since perforated interval bottom.Perforating site xiFor
Known variables, pressure and inbound traffics of the non-linear dependence at each perforation.
By at N number of eyelet pressure and flow be expressed as N-dimensional vector
P=(p1, p2..., pN)T, q=(qIm, 1, qIm, 2..., qIm, N)T (9)
Then the matrix representation forms of formula (9) are
P=Aq (10)
Coefficient matrices A is determined by perforating parameter and cloth hole site in formula, gives the distribution of perforation pressure and preforation tunnel point
Cloth can be become a mandarin flow if the coefficient matrices A in formula (10) is reversible by asking N × N rank inverse matrixs to calculate perforation
Q=A-1p (11)
(2) pit shaft Two-phase flow's separation is established：
To establish the flow model of downhole well fluid, if downhole well fluid is gas-liquid two-phase fluid, the perforation of Δ x long is chosen
Well section is analyzed, and cross-section structure is as shown in Figure 3.The overall presure drop of perforated interval includes following four parts：Weight position pressure drop Δ
pg, friction pressure drop Δ pfAnd pit shaft becomes a mandarin and accelerates pressure drop Δ p caused by fluid expansionaWWith Δ paE。
Δpw=Δ pf+Δpg+ΔpaW+ApaE (12)
Under normal circumstances, accelerate pressure drop very little compared with friction pressure drop, weight position pressure drop, often eyelet is ignored.Only
Have in the case of high heat load, accelerates pressure drop that can just increase to the degree comparable with friction pressure drop.
Equal sign right end first item Δ p in formula (12)fIndicate the pressure drop caused by wall friction, be in two-phase pressure drop most
It is important
One component part reflects the interaction effect between two-phase and between two-phase mixtures fluid and borehole wall wall surface
It answers.In homogeneous flow model, two phase flow is considered as a kind of single-phase flow, and physical parameter is by the corresponding parameter folding of gas-liquid two-phase
Obtained from conjunction.According to quality and momentum balance, can obtain：
Wall surface fricting shearing stress τ in formulawIt is defined as
Wherein ftpIndicate peaceful (Fanning) friction coefficient of two phase flow model, VtpIndicate the true of the two phase flow fluid in pit shaft
Average speed.
The total mass flow rate M of two phase flowtpIt is defined as flowing through total matter of the gas-liquid mixed stream of any cross section in the unit interval
Amount, can obtain according to mass balance：
Mtp=AVtpρtp (15)
Also referred to as
Mtp=ML+MG=AVSLρL+AVSGρG (16)
Wherein MLAnd MGLiquid phase stream and gas phase current mass flow, ρ are indicated respectivelyLAnd ρGLiquid phase stream and gas phase stream are indicated respectively
Density.According to the equation of gas state
Combined type (15) and (16), can obtain
In homogeneous phase model, two phase flow density ptpGas, liquid fluid density is defined as with liquid holdup HLFor adding for weight
Weight average
ρtp=ρLHL+ρG(1-HL)(19)
During gas liquid two-phase flow, the flow section area A of liquid phaseLThe ratio for accounting for total area of passage A, as holds liquid
Rate, also known as true liquid holdup or liquid holdup
A in formulaGIndicate the flow section area of gas phase, since density of liquid phase changes with well depth, therefore liquid holdup is not one
Constant also changes with well depth.Likewise, void fraction is defined as：
The Section 2 Δ p of formula (12) equal sign right endgFor pressure drop caused by fluid gravity.
Δpg=-g ρtpΔx cos α (22)
For vertical well, weight position pressure drop accounts for sizable proportion, and the actual density ratio of two-phase fluid in overall presure drop
The averag density of fluid split-phase stream is very big greatly, and result of calculation differs greatly.
The acceleration pressure drop of two phase flow is usually made of two parts；Change caused acceleration pressure drop along well depth by circulation area A
Change acceleration caused by (such as heating, cooling, expansion or shrinkage caused by pressure change) along well depth with by two-phase current density
Pressure drop.The Section 3 of formula (12) equal sign right end is to become a mandarin to accelerate pressure drop caused by flowing, according to quality and momentum balance, acceleration pressure
Drop can be described as following two formula.
V in formulamIndicate the speed of two-phase mixtures fluid, QItpIndicate unit pit shaft length in two-phase integrated flux and
QImIndicate the mixing integrated flux in unit pit shaft
QIm=QIL+QIG≠QItp (25)
Vm=VSL+VSG (26)
Wherein QIGAnd QILIt is the liquid and gas accumulation inbound traffics in unit pit shaft respectively.By analyzing predicted value and reality
Test data, Δ paW1With Δ paW2Weighted average can obtain accelerate pressure drop optimum prediction
ΔpaW=ω Δs paWI+(1-w)ΔpaW2 (27)
It brings formula (23) into, can obtain
Best weight coefficient is ω=0.8.
Last expression of formula (12) equal sign right end, which becomes a mandarin, accelerates pressure drop caused by fluid expansion, usually can be by total pressure
Drop is multiplied to obtain with the coefficient of expansion
β in formulaaEFor the coefficient of expansion, can be estimated with following formula
Along perforation straight well, the pressure p at i-th of eyeletw,iMeet following formula
Wherein pdFor downstream bottom end starting position x1The pressure at place.
About discrete type (31), the discrete scheme of friction pressure drop is
Accelerate pressure drop discrete scheme be
For biphase gas and liquid flow, gas phase, liquid phase accumulation inbound traffics in unit pit shaft are
The discrete scheme of position pressure drop is again
Δpg=-g ρtp|xi+1-xi|cos α (36)
Wherein αiFor the inclination angle of the i-th perforation.
The discrete scheme of formula (29) is
Association type (30)-(36), wellbore fluids pressure drop are represented by matrix form
P=F [q] (38)
(3) liquid holdup is analyzed：
For two phase flow, the quantity of the monophasic fluid often not ratio in it in total flow in pipeline.Upwards at one
The biphase gas and liquid flow of flowing, gas are fast compared to the speed of liquid phase flowing.Therefore, there is trapping phenomena, the volume in situ of liquid phase will be big
In the volume that liquid phase flows into, i.e., relative to gas phase, liquid phase is in the duct by " interception ".
In order to calculate the sliding in homogeneous model between liquids and gases phase, drift model flux is used for describing in pit shaft
Multiphase Flow.The model flux that drifts about is that Zuber and Findlay are put forward for the first time in nineteen sixty-five.Its basic thought is by gas-liquid
Stereoscopic Two-phase mixture fluids are monophasic fluid, and the drift between gas, liquid fluid is precisely due to speed heterogeneous between gas phase and liquid phase
Degree distribution.The speed V of gas phaseG, can use and contain two-phase mixtures fluid speed VmEmpirical constitutive relation describe：
VG=C0Vm+Vd (39)
C in formula0And VdFor drift parameter, C0Indicate distributed constant in pipeline section, when flow velocity increases, velocity contour
More and more uniform and C0Tend to be unified.VdIndicate that the average speed relative to liquid phase, the rate of climb of bubble can be described as
V in formulacIndicate characteristic velocity, the rate of climb of characterization bubble in a liquid
Wherein σGLShow tension, parameter K between gas phase and liquid phaseuFor Kutateladze numbers, there is following formula expression
C in formulawFor friction factor, CkuFor constant and NBFor Bond number numbers
According to formula (39), void fraction H in situGWith liquid holdup HLIt is expressed as
The structure of two phase flow production capacity Optimized model：Notice that straight well pit shaft and reservoir are included in identical pressure system,
Therefore, at same position, the pressure drop of downhole well fluid is equal to the pressure drop of reservoir fluid, and the downhole well fluid flow at this is equal to
The integrated flow that downstream perforation flows into.To which oil reservoir and pit shaft meet coupling condition, by formula (8) and formula (31), obtain coupled mode
Type
For one include N number of eyelet straight well, coupling model is 2N equation structure for including 2N unknown function
At suitable determine mathematical problem.Coupled problem is solved, using following iterative formula：
Given initial valueThe pressure and perforation stream of downhole well fluid can be gone out with step by step calculation with the Iteration
Amount.Work as piAnd qiIncrement is less than given control error, above-mentioned Iteration convergence.Perforation distribution optimization be related to it is many because
Element, such as the flow that becomes a mandarin, eyelet radius, pit shaft length, eyelet etc..Make herein using total output as the factors above of object function
For constraints.
Maximize the aggregated capacity of gas well
The variable of optimization problem is perforating site, meets condition：
0≤x1≤…≤xi≤…≤xN≤Hp (48)
In actual generating process, in order to reduce calculation amount, the general method for using segmentally numerical calculation is subtracted with reaching
Few optimized variable number.With J-1 nodes XjPerforated interval is divided into J sections by (j=1,2 ..., J-1), and every section includes I perforation
Unit (N=I × J), i.e., the Kong Mi in each segmentation limit interval is constant, but the Kong Mi being often segmented is not necessarily identical.Straight well
The N number of piecewise interval of section is：
[XjXj+1], j=0,1 ..., J-1, X0=0, XJ=Hp (49)
The each upper coordinate of I eyelet on that segment of segmentation is represented by
XI×j+i=Xj+(Xi+1-Xj) i/I, i=0,1 ..., I, j=0,1 ..., J-1 (50)
As the eyelet number I > 1 in each segmentation, then workload can be reduced by being segmented calculating, and decision variable is reduced to by N number of
J-1.
According to the relational expression that becomes a mandarin (45) of optimization strategy (47) and perforation straight well, the optimization of perforation straight well production capacity is obtained
Object function is:
If considering water, gas coning problem, it is required that it is equal as possible in the upper inbound traffics of each perforation segmentation, to slow down water, gas
The time burst of cone
Due to qImIt is also unknown, formula (52) is the equation group comprising J-1 equation and J-1 unknown quantitys.Consideration is infinitely led
Flow well, i.e. pi=pd, obtain perforating parameter optimization problem:
The straight well capacity Optimized model (53) of infinite fluid diversion perforation established above is that constraint becomes with the position of perforated interval
It measures, includes J-1 bound variable in model, which is nonlinear optimal problem, and numerical optimisation algorithms is selected to solve.
Solving model, the hole position distribution situation of perforated interval when optimal production capacity both can be obtained.Infinite fluid diversion well is not related to the shadow of pressure drop
It rings, therefore, gives pit shaft with end pressure, can both obtain best hole position by Optimized model and perforation becomes a mandarin flow, it can
For analyzing influence of the flow to best Kong Mi, to improve straight well production capacity.
Consider that limited fluid diversion well, the pressure drop of straight well pit shaft cannot be ignored, i.e. pi=pwi, perforating parameter optimization problem
For:
Limited fluid diversion perforation straight well production capacity Optimized model (54) established above using the position of perforated interval as bound variable,
Include J-1 bound variable in each model, model is nonlinear optimal problem, equally with production capacity Optimized model (53), choosing
It selects numerical optimisation algorithms and solves the optimization problem.Limited fluid diversion well considers pressure drop considerations in pit shaft, and solution obtains best eyelet
Pressure and perforation when position become a mandarin flow, can be used for analyzing the influence of pressure and flow to best Kong Mi, and improve
Straight well production capacity improves inflow profile, flow-after-flow test.
Algorithm flow designs:Based on discussed above, steps are as follows for the specific algorithm that model calculates：
Step 1：Given initial valueWith allowable error ε=10-3。
Step 2：Calculate the inclination angle at each point
I indicates the number of perforation waypoint, s in formulakIndicate inclined angle alphakAnd αk-1Between measurement length, Δ siExpression is inclined
The material calculation at oblique angle.
Step 3：Calculate the Reynolds number Retp of two-phase fluid：
μ in formulatp=μLHL+μG(1-HL), wall surface thunder Lip river coefficients RwIt is calculated with following formula：
Wherein μtp=μLHL+μG(1-HL), ρIm=ρLFIL+ρG(1-FIL) ρ andAnd FIG=1-CILF。
Step 4：Two-phase pit shaft stream Fanning friction factor is calculated, for Axial Laminar
For axial turbulence：
Wherein without wall flow Fanning friction factor f0Colebrook-White equations can be used to estimate：
Step 5：The pressure of uniform cloth hole straight well is calculated using iterative formula (46) and perforation enters flow distribution.
Step 6：Solve the best perforation distribution that Parametric optimization problem (53) calculates infinite fluid diversion well.
Step 7：Solve the best perforation distribution that Parametric optimization problem (54) calculates limited fluid diversion well.
By taking the YB-X gas well at HTHP of western part of China as an example, using Optimized model established above, perforated hole is analyzed
Optimal perforation distribution and parameter optimization.As described in above-mentioned model analysis and solution procedure, perforated interval is opened from bottom
Beginning is split into several perforation units.It is calculated to simplify, perforated interval, which is divided into many perforations, to be segmented, and each perforation segmentation includes
Perforation unit it is not necessarily identical, calculated according still further to above-mentioned calculating step.
Model parameter and measurement data：About oil pipe data, casing data and wellbore depth measurement, hole deviation in real case simulation
The data such as angle, azimuth and wellbore vertical depth are shown in Table 1- tables 3.In addition to this, it is also necessary to partial data is supplemented, including：Straight well
Perforation ranging from 6600-7100m, the pressure of downstream base portion is 39.8949MPa, and perforated hole relevant parameter is shown in Table 4.
Table 1
Table 2
Table 3
Table 4
Simulation calculates analysis：Numerical simulation is carried out to high-temperature high-pressure perforation well, has obtained a series of numerical result, including
The optimal perforation of pressure drop, each phase flow rate, speed and perforated interval is distributed.Uniform shot density is taken as 5 holes/rice in simulation, simulation
Pressure drop as shown in figure 3, perforation becomes a mandarin, the superficial velocity of flow is shown in Fig. 4.Perforation well capacity optimal solution and uniform inflow are excellent
Neutralizing is as schemed
Shown in 5 (a), 5 (b), and compared with uniform cloth hole analog result.Analog result is shown, for uniform cloth
Hole, infinite fluid diversion well capacity are 34450m3/ d and limited fluid diversion well capacity are 30070m3/d。
Fig. 6 (a) shows that the high density eyelet of infinite fluid diversion well is distributed in the bottom and top position of perforated interval more.Most
Excellent production capacity is 34661m3/ d increases by 3.19% than uniform cloth hole well capacity.And uniform inflow to the improvement effect of production capacity not
Greatly, production capacity 34431m3/ d reduces by 5.52% than uniform cloth hole well capacity.Limited fluid diversion well capacity optimizes and uniformly enters
Shown in flow-optimized result such as Fig. 6 (b), the results showed that perforation is distributed comparatively dense in the high well section that becomes a mandarin.Optimal production capacity is 30151m3/
D, more uniform perforated hole volume increase 2.69%.Uniform inflow constraint to perforation distribution be in adverse effect, i.e., height become a mandarin well section cloth hole compared with
Sparse, to ensure becoming a mandarin as possible uniformly for pit shaft, optimal production capacity is 29973m3/ d, than the uniform perforated hole underproduction 3.23%.Figure
7 (a), 7 (b) show the flowing velocity of two-phase wellbore fluids, with eyelet and the increase that becomes a mandarin of accumulation perforation, wellbore fluids
Flow velocity increases with the well depth of straight well.Fig. 8 shows that the liquid holdup of two phase flow changes with perforation depth, and range is in 0.6823 He
Between 0.7114.
Optimal perforation is distributed as shown in figure 9, since oil reservoir improves larger supply range, the bottom and top of perforated interval
There are higher inbound traffics in portion, and the supply range in the middle part of perforated interval is small, to which inbound traffics are smaller.For infinite fluid diversion well, pit shaft
In fluid have the influence of pressure drop, perforation, which becomes a mandarin, to be symmetric, and shot density is also in symmetrical distribution.In uniform inflow
Constraint under, the well section that the shot density of limited fluid diversion well becomes a mandarin in height gradually decreases, and increases in the low well section to become a mandarin；And it is unlimited
Water conservancy diversion well both ends and grazing shot hole become a mandarin well section cloth hole it is closeer.Due to the factor of pressure drop, limited fluid diversion well compares infinite fluid diversion
There is well higher bottom pressure drop and height to become a mandarin flow.
Claims (1)
1. high temperature and pressure oil gas straight well two phase flow perforation completion parameter and production capacity optimization method, which is characterized in that including following step
Suddenly：
A, petrol-gas permeation fluid steady-state model is built；
B, pit shaft two phase flow model is built；
C, analysis meter fluid operator liquid holdup；
D, two phase flow production capacity Optimized model is built；
E, two phase flow production capacity Optimized model is solved；
In step A, the method for the structure petrol-gas permeation fluid steady-state model includes：
Assuming that perforated interval is a length of lperf, radius rperfCylinder, the perforated interval in entire straight well pit shaft includes N number of perforation
Eyelet, since bottom, the position of the i-th perforation is xi, i=1,2 ..., N；By i-th of preforation tunnel into inbound traffics qIm, iInstitute
The pressure p of generationiiIt can be described as
Q in formula (1)ImFor the mixed traffic in unit preforation tunnel, qIm, iFor by the unit preforation tunnel of i-th of perforation
Mixed traffic；μ is the viscosity of fluid；K is the permeability of fluid；
qIm=qIL+qIG (2)
Q in formula (2)IGAnd qILThe air-liquid inbound traffics in unit preforation tunnel are indicated respectively：
qIG=AIVISG (3)
qIL=AIVISL (4)
Wherein, AIIndicate the cross-sectional area of eyelet, VISLAnd VISGThe respectively superficial liquid velocity of Perforation ocular fluids and apparent gas
Speed；Based on perforation and its fracture area damage epidermis spPoint sink radius r of equal valuepeqIt can be described as：
If the spacing between perforation is fully big, the mixed traffic q at preforation tunnel jIm, jIt will produce pressure, eyelet j at eyelet i
Steady state pressure caused by eyelet i can be described as：
Gross pressure at eyelet i becomes a mandarin the pressure of generation for pressure and other perforations of the generation that becomes a mandarin of eyelet i itself
The sum of
Formula (1) and formula (6) are substituted into formula (7), can be obtained：
The position of perforation j is x=xj, x1Indicate first perforating site since perforated interval bottom；Perforating site xiIt is unknown
Variable, pressure and inbound traffics of the non-linear dependence at each perforation；
By at N number of eyelet pressure and flow be expressed as N-dimensional vector, can obtain：
P=(p1, p2..., pN)T, q=(qIm, 1, qIm, 2..., qIm, N)T (9)
Formula (9) is expressed as matrix form：
P=Bq (10)
Coefficient matrix B is determined by perforating parameter and cloth hole site in formula (10), gives the distribution of perforation pressure and preforation tunnel point
Cloth can be by asking N × N rank inverse matrixs to calculate perforation inbound traffics if the coefficient matrix B in formula (10) is reversible：
Q=B-1p (11)；
Described in step B build pit shaft two phase flow model method include：
If downhole well fluid is gas-liquid two-phase fluid, the overall presure drop of the perforated interval of differential element of volume Δ x can be obtained：
Δpω=Δ pf+Δpg+Δpaw+ΔpaE (12)
Equal sign right end first item △ p in formula (12)fIndicate the pressure drop caused by wall friction：
S is the skin factor of pit shaft；
Wall friction shear stress τwIt is defined as：
Wherein ftpIndicate two phase flow Fanning friction factor, VtpIndicate the true average speed of the two phase flow fluid in pit shaft；Two-phase
The total mass flow rate M of streamtpIt is defined as flowing through the gross mass of the gas-liquid mixed stream of any cross section in the unit interval, it is flat according to quality
Weighing apparatus, can obtain
Mtp=AVtpρtp (15)
Or it is expressed as
Mtp=ML+MG=AVSLρL+AVSGρG (16)
Wherein, A indicates total area of passage；ML and MG indicates liquid phase stream and gas phase current mass flow, V respectivelySLIndicate liquid phase levelling
Equal flow velocity, VSGIndicate gas phase stream mean flow rate, ρLAnd ρGLiquid phase stream and gas phase current density are indicated respectively；According to the equation of gas state
In formula (17), ZgIndicate that the compressed coefficient of gas phase stream, R indicate that ideal gas constant, T indicate the thermodynamics of perfect gas
Temperature, M indicate the quality of gas phase stream；
Combined type (15) and (16), can obtain
In homogeneous phase model, two phase flow density ptpGas, liquid fluid density is defined as with liquid holdup HLIt is flat for the weighting of weight
,
ρtp=ρLHL+ρG(1-HL) (19)
During gas liquid two-phase flow, the flow section area A of liquid phaseLAccount for the ratio of total area of passage A, as liquid holdup：
A in formulaGIndicate the flow section area of gas phase；
The Section 2 Δ p of formula (12) equal sign right endgFor pressure drop caused by fluid gravity：
Δpg=-g ρtpΔx cosα (22)
In formula (22), g is acceleration of gravity, and α is the inclination angle of perforation, and Δ x indicates the differential element of volume of fluid；
The Section 3 of formula (12) equal sign right end is to become a mandarin to accelerate pressure drop caused by flowing, according to quality and momentum balance, acceleration pressure
Drop can be described as：
V in formulamIndicate the speed of two-phase mixtures fluid, QItpIndicate the two-phase integrated flux and Q in unit pit shaft lengthImTable
Show the mixing integrated flux in unit pit shaft；
QIm=QIL+QIG≠QItp (25)
Vm=VSL+VSG (26)
Wherein QIGAnd QILIt is the gas phase and liquid phase accumulation inbound traffics in unit pit shaft respectively；By analyzing predicted value and experiment number
According to,
Δpaw1With Δ paw2Weighted average can obtain accelerate pressure drop optimum prediction
Δpaw=ω Δs paw1+(1-ω)Δpaw2 (27)
Substitution formula (23), can obtain
Best weight coefficient is ω=0.8；Δ z is the infinitesimal length of perforated interval；
Last expression of formula (12) equal sign right end, which becomes a mandarin, accelerates pressure drop caused by fluid expansion, can be by total pressure drop and expansion
Multiplication obtains：
β in formulaaEFor the coefficient of expansion, can be estimated with following formula
Wherein, P is the pressure of fluid；
Along perforation straight well, the pressure p at i-th of eyeletW, iMeet following formula：
Wherein pdFor downstream bottom end starting position x1The pressure at place；ΔpF, iFor the friction pressure drop of i-th of perforation；ΔpG, iIt is i-th
The heavy position pressure drop of perforation；ΔpAW, iFor i-th of perforation pit shaft become a mandarin caused by accelerate pressure drop；ΔpAE, iFor the stream of i-th of perforation
Accelerate pressure drop caused by body expansion；
About discrete type (31), the discrete scheme of friction pressure drop is
Accelerate pressure drop discrete scheme be
VM, iFor the speed of the two-phase mixtures fluid of i-th of perforation；VIm, iFor the two-phase mixtures in i-th of perforation unit pit shaft length
The speed of fluid；QItp, iFor the integrated flux of the two-phase mixtures fluid in i-th of perforation unit pit shaft length；UTp, iIt is i-th
The theoretical average speed of the two phase flow fluid of perforation；VTp, iFor the true average speed of the two phase flow fluid of i-th of perforation；
For biphase gas and liquid flow, gas phase, liquid phase accumulation inbound traffics in unit pit shaft are
Wherein, qIG, jFor the gas phase integrated flux in i-th of perforation jth section unit pit shaft；qIL, jFor i-th of perforation jth section unit
Liquid phase in pit shaft accumulates inbound traffics；
The discrete scheme of position pressure drop is again
Δpg=-g ρtp|xi+1-xi|cosα (36)
The discrete scheme of formula (29) is
Association type (30)-(36), wellbore fluids pressure drop are represented by matrix form
P=F [q] (38)；
The method of analysis meter fluid operator liquid holdup described in step C includes：
For the speed V of gas phaseG, using containing two-phase mixtures fluid speed VmEmpirical constitutive relation describe：
VG=C0Vm+Vd (39)
C in formula0Indicate distributed constant in pipeline section, VdIndicate the average speed relative to liquid phase：
In formula (40), KμFor Kutateladze numbers；VcIndicate characteristic velocity,
Wherein σGLSurface tension between gas phase and liquid phase, parameter Ku are Kutateladze numbers：
C in formula (42)wFor friction factor, CkuFor constant and NBFor Bond number numbers
D indicates bubble diameter；
According to formula (39), void fraction HGWith liquid holdup HLIt is expressed as
Described in step D build two phase flow production capacity Optimized model method include：
Petrol-gas permeation fluid and wellbore pressure loss coupling model are established according to formula (11) and formula (38)：
For one include N number of eyelet straight well, above-mentioned coupling model is 2N equation structure for including 2N unknown function
At it is suitable determine mathematical problem, solved using following iterative formula：
Given initial valuepd, whereinFor the pressure of the first time iterative calculation at i-th of perforation；According to coupling model
Iterative algorithm, calculate the flow and pit shaft at each eyelet pressure distribution；Work as piAnd qiIncrement is less than given control error,
Above-mentioned iterative formula convergence；
When building production capacity Optimized model, using total output as object function, the aggregated capacity of gas well is maximized
The variable of optimization problem is perforating site, meets condition：
0≤x1≤…≤xi≤…≤xN≤Hp (48)
HpIndicate pit shaft height；
Using J-1 nodes XjPerforated interval is divided into J sections by (j=1,2 ..., J-1), and every section includes I perforation unit (N=I
× J), i.e., the Kong Mi in each segmentation limit interval is constant, but the Kong Mi being often segmented is not necessarily identical；The N number of segmentation of straight well section
Section is：
[Xj, Xj+1], j=0,1 ..., J-1, X0=0, XJ=Hp (49)
The each upper coordinate of I eyelet on that segment of segmentation is represented by：
XI×j+i=Xj+(Xj+1-Xj) i/I, i=0,1 ..., I, j=0,1 ..., J-1 (50)
As the eyelet number I > 1 in each segmentation, then workload can be reduced by being segmented calculating, and decision variable is reduced to J-1 by N number of
It is a；
According to the relational expression that becomes a mandarin (45) of optimization strategy (47) and perforation straight well, the target of perforation straight well production capacity optimization is obtained
Function is
If considering water, gas coning problem, require to go up inbound traffics in the segmentation of each perforation it is equal as possible, to slow down water, gas coning
Time burst
Due to qImIt is also unknown, formula (52) is the equation group comprising J-1 equation and J-1 unknown quantitys；
Consider infinite fluid diversion well, i.e. pi=pd, obtain the straight well capacity Optimized model of infinite fluid diversion perforation：
Consider that limited fluid diversion well, the pressure drop of straight well pit shaft cannot be ignored, i.e. pi=pwi, obtain the straight well capacity of limited fluid diversion perforation
Optimized model：
In step E, the method solved to two phase flow production capacity Optimized model includes：
1) initial value is givenpdWith allowable error ε=10-3；
2) inclination angle at each point is calculated
I indicates the number of perforation, Δ S in formulakIndicate inclined angle alphakAnd αk-1Between measurement length, Δ siIndicate the meter at inclination angle
Calculate step-length；
3) the Reynolds number Re of two-phase fluid is calculatedtp：
μ in formulatp=μLHL+μG(1-HL), μLIndicate the dynamic viscosity of liquid phase fluid, μGIndicate the dynamic viscosity of gaseous fluid, wall
Face thunder Lip river coefficients R ewIt is calculated with following formula
Wherein μIm=μLFIL+μG(1-FIL), ρIm=ρLFIL+ρG(1-FIL) andAnd FIG=1-FIL；VImIndicate two-phase
The mean flow rate of fluid-mixing；
4) two-phase pit shaft stream Fanning friction factor is calculated, for Axial Laminar：
For axial turbulence：
Wherein without wall flow Fanning friction factor f0Colebrook-White equations can be used to estimate：
K indicates wellbore tubulars inner wall roughness；
5) pressure and perforation for applying the uniform cloth hole straight well of iterative formula (46) calculating enter flow distribution；
6) the best perforation distribution of infinite fluid diversion well is calculated in solving model (53)；
7) the best perforation distribution of limited fluid diversion well is calculated in solving model (54).
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