CN104847314B - HTHP oil gas straight well single-phase flow perforation completion parameter optimization method - Google Patents

Abstract

The present invention relates to belong to development of oil and gas reservoir administrative skill field, specially a kind of HTHP oil gas straight well single-phase flow perforation completion parameter optimization method, it is related specifically to the single-phase flow model of HTHP oil gas straight well, structure and the algorithm flow design of flow through oil reservoir and Wellbore Flow coupling model etc..The invention discloses a kind of HTHP oil gas straight well single-phase flow perforation completion parameter optimization method, make accurate prediction to perforating parameter, to improve Oil ＆ Gas Productivity ratio.It comprises the following steps：A, structure Wellbore Flow Pressure Drop Model；B, structure petrol-gas permeation fluid and Wellbore Flow coupling model；C, structure perforating parameter Optimized model；D, perforating parameter Optimized model solved.The present invention is applied to Reservoir Development.

Description

HTHP oil gas straight well single-phase flow perforation completion parameter optimization method

Technical field

The present invention relates to development of oil and gas reservoir administrative skill field is belonged to, specially a kind of HTHP oil gas straight well list Mutually stream perforation completion parameter optimization method, is related specifically to the single-phase flow model of HTHP oil gas straight well, flow through oil reservoir and pit shaft Structure and algorithm flow design of Coupled with Flow model etc..

Background technology

Perforation is one of main completion method at present, be with special perforating gun by sleeve pipe and cement sheath partial penetrating, Make to set up passage between pit shaft and stratum, reach that oil gas flows into the purpose of pit shaft.Perforating gun is the equipment for perforating oil gas well And its assembly of auxiliary equipment.Most widely used at present is jet perforating rifle, and perforating process is exactly the cumulative by perforating bullet Principle is come what is completed, and perforating bullet produces HTHP metal jet squeezing bushing, cement sheath and stratum after being detonated, when jet pressure Power exceedes the yield strength of formation rock, and duct will be formed in stratum.

Perforation completion is a kind of most popular Well completion method in domestic and international oil field, and this completion mode is given birth to oil well The influence for producing effect is very big, has done substantial amounts of research work to it both at home and abroad, main purpose is exactly to study perforating parameter to improve Productivity ratio.Usually, the performance of Oil/gas Well is influenceed by its geometry.According to geometry, perforated hole can be divided into perforation straight well, Perforated horizontal wells and perforation inclined shaft.Perforation straight well performance depends on the fluid and the fluid on vertical cross-section flowed into pit shaft. Change of fluid in Oil/gas Well is mainly influenceed by overall presure drop, therefore, and the overall presure drop being better understood from straight well contributes to optimization straight Well is designed.

Perforating parameter is related to hole depth, phase, Kong Mi, aperture etc., and the selection of these parameters has important to improving straight well production capacity Influence, meanwhile, in order to suppress water, gas coning, delay water, gas break through, it is necessary to improve the inflow profile along straight well pit shaft, make The inflow profile distribution in well depth direction is as far as possible uniform.Therefore, the reasonable selection of perforating parameter is to improving production capacity, and improvement, which becomes a mandarin, weight Want meaning.

Oil-gas reservoir single-phase flow perforation steady-state model：Consider half unbounded oil-gas reservoir, eyelet is considered as cylinder, fluid passes through hole Eye enters pit shaft from stratum, and becoming a mandarin for perforation can produce influence to the pressure at other eyelets, using the characteristic of stratum filtration, The pressure drop correlations that can be set up at each eyelet.Fluid in pit shaft is influenceed by factors such as gravity, frictional force and fluid acceleration, Wellbore fluids flow model is set up using conservation of mass physical principle.Before model is set up, basic assumption is first described below：

(1) oil reservoir is uniform and isotropic.It is constant in reservoir permeability, not with change in location, also not Orientation differences are measured with reservoir.

(2) reservoir is Unbounded Domains, is constant in the pressure of unlimited distance.

(3) downhole well fluid is constant temperature single-phase flow, and fluid is incompressible fluid.

Regard perforated interval as a length of l_perf, radius is r_perfCylinder.Perforated interval in whole straight well pit shaft is comprising N number of Preforation tunnel, structure is as shown in Figure 2.

Assuming that formation damage is ignored, since bottom, the position of the i-th perforation is x_i(i=1,2 ..., N) work as ratioDuring very little, according to the average pressure of uniform line source, inbound traffics q is entered by i-th of preforation tunnel_iProduced pressure p_iiCan It is described as

If the spacing between perforation is fully big, the point sink intensity Q at perforation j_jThere can be following formula table to pressure influence at perforation i State

It is the inlet pressure and other perforation inlet pressure sums of the i-th perforation itself in the perforation i gross pressures produced

Bring formula (1) into and formula (2) is arrived in formula (3), then

Perforation j position is x=x_j, x₁Represent first perforating site since perforated interval bottom.Perforating site x_iFor Known variables, pressure and inbound traffics of the non-linear dependence at each perforation.

Using vector representation：Formula (4) is represented by：

Wherein coefficient matrices A is distributed dependent on perforation size and perforation.

If given pressure distribution and perforation along pit shaft is distributed, if coefficient matrices A is, it is known that its inverse presence, formula (5) is also It can be write as the form of calculation of vector：

The content of the invention

The technical problems to be solved by the invention are：Propose a kind of HTHP oil gas straight well single-phase flow perforation completion parameter Optimization method, makees accurate prediction to perforating parameter, to improve Oil ＆ Gas Productivity ratio.

The technical solution adopted for the present invention to solve the technical problems is：

HTHP oil gas straight well single-phase flow perforation completion parameter optimization method, comprises the following steps：

A, structure Wellbore Flow Pressure Drop Model；

B, structure petrol-gas permeation fluid and Wellbore Flow coupling model；

C, structure perforating parameter Optimized model；

D, perforating parameter Optimized model solved.

Further, in step A, the structure Wellbore Flow Pressure Drop Model is specifically included：

If the uniform perforated interval in straight well pit shaft, which is split into N number of isometric perforation unit, each unit, only includes one Individual preforation tunnel, the length of pit shaft unit, p are represented with Δ x₁, U₁, A₁End pressure, speed and cross section on difference representative unit Product, p₂, U₂, A₂End pressure, speed and cross-sectional area under difference representative unit；

The law of conservation of momentum is applied in control volume elements in the axial direction, that is, controls the summation of the external force suffered by volume elements CV to be equal to and leads to Control volume elements surface C S fluid momentum and the fluid momentum increment rate sum in control volume elements is crossed, the equation of momentum can be obtained：

ρ is fluid density in formula, and A is the area in any section of pit shaft.

For stable state pit shaft stream

One-Dimensional flows problem will be considered as along the two-dimensional flow problem in section, the mean flow rate for taking section is U, utilizes quality Conservation equation, formula (7) is expanded into：

Formula (9) equal sign left side is the power sum that control volume surface is in downward direction acted on along pit shaft axis

Mass flow in formula

Section 1 represents the net pressure acted in control volume elements on the right of formula (9) equal sign；Section 2 represents to act on well casing The shear stress of wall：

τ_ω(π D Δs x)=Δ p_wallA (12)

The right Section 3 represents Action of Gravity Field, and gravitational pressure drop is

Δp_g=ρ g Δ x cos θ (13)

Convolution (9)-(13) can be obtained

Section 1 represents net momentum on the right of formula (14) equal sign, is due to that more fluids cause axle by perforation into pipeline Caused by changing to flow velocity, the pressure drop is due to acceleration effect Δ p_accProduce, can be described as：

The overall presure drop of perforation downhole well fluid includes friction pressure drop Δ p_wall, accelerate pressure drop Δ p_accWith gravitational pressure drop Δ p_g

Δp_w=Δ p_wall+Δp_acc+Δp_g (16)

The pressure drop as caused by wall friction depends on perforation mean flow rate U in perforation unit₂, Darcy-Weisbach can be used Equation is calculated：

Along the direction of perforation depth, the pressure representative at perforation unit i is p_wi, then according to formula (16), can obtain The calculation of pressure relational expression of the corresponding pit shaft shaft position of preforation tunnel

P in formula_dFor position x₁The downstream at place is with end pressure, Δ p_{Wall, i}, Δ p_{Acc, i}, Δ p_{G, i}Wall friction pressure is represented respectively Drop, accelerate pressure drop and gravitational pressure drop in the pressure drop of the corresponding pit shaft axial positions of perforation i；

Consider perforation unit i, the discrete scheme of formula (17) is：

Mean flow rate U in formula_iAvailable expressionCalculated, the integrated flow at this is

Accelerate pressure drop be as more fluids by perforation into pipeline cause axial flow velocity change caused by, depend on Fluid density and mean flow rate.

Gravitational pressure drop is that the gravity for having fluid is produced, and is represented by

Δp_{G, i}=ρ g cos α_i|x_i+1-x_i| (22)

α in formula_iRepresent perforation unit i inclination angle；

Bring formula (19), (21) and (22) into formula (18), both can obtain the Pressure Drop Model of Wellbore Flow：

Further, in step B, the petrol-gas permeation fluid of straight well and the flowing of straight well wellbore fluids are considered as a phase interaction Entirety, while pressure and discharge relation between comprehensive oil reservoir and pit shaft, pressure, in the continuity of boundary, are set up with flow Oil-gas reservoir and the coupling model of pit shaft, specific method include：

By formula (23), the vector form that the pressure drop correlations of downhole well fluid are expressed as：

The vector expression of vector expression and Wellbore Flow Pressure Drop Model based on petrol-gas permeation fluid model is coupled Model：

Further, in step B, also solved including the coupling model to acquisition, method is as follows：

For there is a pit shaft of N number of perforation, coupling model is include that 2N equation of 2N unknown function constitute suitable fixed Mathematical problem, for the nonlinear coupling model, is solved using following iterative formula：

Given initial valuep_d, according to the iterative algorithm of coupling model, by iterative formula (26a), bring pressure data into, The flow at each eyelet can be calculated, then by the counted eyelet flow of formula (26a), band entry format (26b) can calculate pit shaft Pressure distribution；Said process is repeated, until solving result meets the iteration termination condition set in advance.

Further, in step C, when building perforating parameter Optimized model, if not considering water, gas coning problem, with Straight well production capacity is object function, using hole position as bound variable, makes production capacity maximum；If water, gas coning problem are considered, with straight Well capacity is object function, is become a mandarin uniform for constraints, made while water, gas coning is suppressed with hole position and section Production capacity reaches maximum；

Wherein, the straight well production capacity is the influx summation of all entrance eyelets in perforated interval：

Along pit shaft direction, if coordinate meets restrictive condition：

0≤x₁≤…≤x_i≤…≤x_N≤L (28)

With J-1 nodes X_jPerforated 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 Interval is

[X_j, X_j+1], j=0,1 ..., J-1, X₀=0, X_J=L (29)

The each upper coordinate of I eyelet on that segment of segmentation is represented by：

x_I×j+i=X_j+(X_j+1-X_j) i/I, i=0,1 ..., I, j=0,1 ..., J-1 (30)

When considering water, gas coning problem, it is equal to have to meet inbound traffics in the segmentation of each perforation, i.e.,

Further, in step C, the structure perforating parameter Optimized model comprises the following steps：

C1. the Optimized model of infinite fluid diversion well is built：

If C11. not considering water, the influence of gas coning, the object function of production capacity optimization is

I.e. using the summation of the inbound traffics of each preforation tunnel as total production capacity of perforation straight well, include about in object function Shu Bianliang, i.e. eyelet location parameter；Due to infinite fluid diversion well do not consider pressure at wellbore pressure loss, therefore each eyelet be with End pressure p_d；Simultaneously for perforation straight well section, along the direction of well depth, the position coordinates of each perforated interval node has size pass System, i.e. X_j+1≥X_j, conditions above is to constitute the optimization constraints, can obtain infinite fluid diversion well and not consider water, gas coning influence When Optimized model：

If C22. considering, water, the influence of gas coning, it is necessary to make the inbound traffics on each perforation unit as equal as possible, that is, exist On the basis of model (32), additional constraint condition (31) can obtain optimization mould of the infinite fluid diversion well when considering water, the influence of gas coning Type：

C2. the Optimized model of limited fluid diversion well is built：

C21. the wellbore pressure of limited fluid diversion well changes with well depth, i.e. p_i=p_wi, do not considering water, gas coning problem When, its Optimized model is：

C22. when considering water, gas coning problem, its Optimized model is：

Further, in step D, perforating parameter Optimized model is solved, specifically included：

D1. initial value is givenp_dWith allowable error ε=10^-3；

D2. the inclination angle at each point is calculated

I represents the numbering of perforation waypoint, s in formula_kRepresent inclined angle alpha_kAnd α_k-1Between measurement length, Δ s_iExpression is inclined The material calculation at oblique angle；

D3. Reynolds number is calculated according to local flow

D4. the turbulent skn friction factor is calculated：

D5. perforated hole wellbore pressure and perforation injection stream flow are calculated using iterative formula (26a) and (26b)；

D6. the Optimized model of structure is solved, obtains straight well perforation Optimal Distribution.

Further, in step D6, the method that the Optimized model of described pair of structure is solved is：Using the secondary rule of sequence Draw and calculated, g is used respectively_j(X)≤0, h_i(X)=0, (i, j=1,2 ..., J）Represent inequality constraints condition and equality constraint Condition；Construct Lagrangian：

λ in formula_i, λ_jFor Lagrange multiplier；It is equivalent to for nonlinear Optimized model on direction of search d a series of Quadratic programming subproblem, in kth time iteration, iteration point X_kThe subproblem of satisfaction is：

Iteration is

X_k+1=X_k+γ_kd_k

Wherein step factor γ_kLinear search is carried out by quadratic interpolattion to obtain, matrix B^kUsing the BFGS amendments after improvement Formula is calculated

Iteration point in formula

s^k=X^k+1-X^k

With

z_k=θ y_k+(1-θ)B_ks_k, θ ∈ [0,1]

Wherein

With

Optimized model (33) is solved using the algorithm, infinitely leading when not considering water, gas coning influence is obtained Flow the optimal perforation tunnel distribution of well：

Optimized model (34) is solved using the algorithm, the infinite fluid diversion when considering water, gas coning influence is obtained The optimal perforation tunnel distribution of well：

Optimized model (35) is solved using the algorithm, limited leading when not considering water, gas coning influence is obtained Flow the optimal perforation tunnel distribution of well：

Optimized model (36) is solved using the algorithm, the limited fluid diversion when considering water, gas coning influence is obtained The optimal perforation tunnel distribution of well.

The beneficial effects of the invention are as follows：Make accurate prediction to perforating parameter, be conducive to optimization straight well design, to improve oil gas Well capacity ratio.

Brief description of the drawings

Fig. 1 is HTHP oil gas straight well single-phase flow perforation completion parameter optimization method flow chart of the present invention；

Fig. 2 is perforation pit shaft subdivision structure chart；

Fig. 3 is perforation unit cross section structure figure；

Fig. 4 (a), 4 (b) are respectively perforated hole pressure drop schematic diagram, perforation unit pressure drop schematic diagram；

Fig. 5 (a), 5 (b) are respectively the optimal cloth hole and comparison of production figure of infinite fluid diversion well；

Fig. 6 (a), 6 (b) are limited the optimal cloth hole and comparison of production figure of water conservancy diversion well respectively；

Fig. 7 (a), 7 (b) are respectively Optimized model I optimal cloth hole and comparison of production figure；

Fig. 8 (a), 8 (b) are respectively Optimized model II optimal cloth hole and comparison of production figure.

Embodiment

The present invention is directed to propose a kind of HTHP oil gas straight well single-phase flow perforation completion parameter optimization method, joins to perforation Number makees accurate prediction, to improve Oil ＆ Gas Productivity ratio.As shown in figure 1, HTHP oil gas straight well single-phase flow perforation completion parameter Optimization method, comprises the following steps：

A, structure Wellbore Flow Pressure Drop Model；

B, structure petrol-gas permeation fluid and Wellbore Flow coupling model；

C, structure perforating parameter Optimized model；

D, perforating parameter Optimized model solved.

It is specifically described below for each step：

Build Wellbore Flow Pressure Drop Model：

If the uniform perforated interval in straight well pit shaft, which is split into N number of isometric perforation unit, each unit, only includes one Individual preforation tunnel, its cross-section structure is as shown in Figure 3.In Fig. 3, Δ x is the length of pit shaft unit, p₁, U₁, A₁Respectively on unit End pressure, speed and cross-sectional area, p₂, U₂, A₂End pressure, speed and cross-sectional area control volume in the axial direction respectively under unit The law of conservation of momentum is applied in member, i.e. the summation of external force suffered by control volume elements CV is equal to the fluid by controlling volume elements surface C S Momentum and the fluid momentum increment rate sum in control volume elements, thus equation of momentum form is：

ρ is fluid density in formula, and A is the area in any section of pit shaft.

For stable state pit shaft stream

In general, axial flow velocity is all uneven along wellbore section, is to discuss convenient here, by along section Two-dimensional flow problem is considered as One-Dimensional flows problem.The mean flow rate for taking section is U, and using mass-conservation equation, formula (7) is deployable For

The above formula equal sign left side is the power sum that control volume surface is in downward direction acted on along pit shaft axis

Mass flow in formula

Section 1 represents the net pressure acted in control volume elements on the right of formula (9) equation；Section 2 represents to act on well casing The shear stress of wall, the power can cause friction pressure drop

τ_ω(π D Δs x)=Δ p_wallA(12)

The right Section 3 represents Action of Gravity Field, and gravitational pressure drop is

Δp_g=ρ g Δ x cos θ (13)

Convolution (9)-(13) can be obtained

Section 1 represents net momentum (i.e. fluid accelerates pressure drop) on the right of equation, is due to that more fluids are entered by perforation Pipeline causes caused by axial flow velocity change.The pressure drop is due to acceleration effect Δ p_accProduce, can be described as

The overall presure drop of perforation downhole well fluid includes friction pressure drop Δ p_wall, accelerate pressure drop Δ p_accWith gravitational pressure drop Δ p_g

Δp_w=Δ p_wall+Δp_acc+Δp_g (16)

The pressure drop as caused by wall friction depends on perforation mean flow rate U in perforation unit₂, Darcy-Weisbach can be used Equation is calculated：

For the ease of calculating wellbore pressure, along the direction of perforation depth, the pressure representative at perforation unit i is p_wi, Then according to formula (16), can obtain preforation tunnel for pit shaft shaft position calculation of pressure relational expression

P in formula_dFor position x₁The downstream at place is with end pressure, Δ p_{Wall, i}, Δ p_{Acc, i}, Δ p_{G, i}Wall friction pressure is represented respectively Drop, accelerate pressure drop and gravitational pressure drop in the pressure drop of the corresponding pit shaft axial positions of perforation i.

For calculating formula (18), the discrete form of the formula is provided first.Consider perforation unit i, the discrete scheme of formula (17) For

Mean flow rate U in formula_iAvailable expressionCalculated.Integrated flow at this is

Accelerate pressure drop be as more fluids by perforation into pipeline cause axial flow velocity change caused by, depend on Fluid density and mean flow rate.

Gravitational pressure drop is that the gravity for having fluid is produced, and is represented by

Δp_{G, i}=ρ g cos α_i|x_i+1-x_i| (22)

α in formula_iRepresent perforation unit i inclination angle.

Bring formula (19), (21) and (22) into formula (18), both can obtain the Pressure Drop Model of Wellbore Flow.

Above formula is the recurrence Relation of downhole well fluid calculation of pressure, and given pit shaft flow can both calculate the pressure of pit shaft Power.

Petrol-gas permeation fluid and Wellbore Flow coupling model are built：By the petrol-gas permeation fluid of straight well and the stream of straight well wellbore fluids The dynamic entirety for being considered as an interaction, while pressure and discharge relation between comprehensive oil reservoir and pit shaft, pressure is with flow on side Continuity at boundary, sets up the coupling model of oil-gas reservoir and pit shaft.

Using the vector representation form above provided, by formula (23), the pressure drop correlations of downhole well fluid be represented by as Under vector form：

Notice that straight well pit shaft and reservoir are in same system, therefore, at same position, the pressure drop of downhole well fluid Equal to the pressure drop of reservoir fluid, the downhole well fluid flow at this is equal to the integrated flow that downstream perforation is flowed into.So as to, oil reservoir and Pit shaft meets coupling condition, by formula (6) and formula (24), obtains coupling model

For there is a pit shaft of N number of perforation, coupling model is include that 2N equation of 2N unknown function constitute suitable fixed Mathematical problem, generally, the coupling model be it is nonlinear, therefore, need to be with numerical method to model solution.In order to solve The coupled problem, uses following Iteration below

Given initial valuep_d, i.e. the initial pressure on stratum.According to the iterative algorithm of coupling model, by Iteration (26a), brings pressure data into, can both calculate the flow at each eyelet and come.Again by the counted eyelet flow of form (26a), bring into Form (26b), can calculate the pressure distribution of pit shaft.Said process is repeated, until solving result meets the iteration set in advance Termination condition.

Perforating parameter Optimized model is built：Optimization straight well perforation tunnel distribution is related to several factors, the flow that become a mandarin as perforated, Hole depth, Kong Mi, aperture, mine shaft depth, perforating site, phase angle etc..If it is considered that all correlative factors optimize analysis, It is difficult to the optimisation strategy to perforation hole straight well parameter.In view of the influence of above-mentioned factor, the optimisation strategy of many can be proposed. Compare depth and total perforation number that effective, direct scheme is exactly given perforated interval, carrying out variable density along straight well section penetrates Hole, by changing the position of every section of perforation, that is, changes the Kong Mi of every section of perforated interval and is cutd open with reaching to improve straight well production capacity and become a mandarin The uniform purpose of face influx.

Flow through oil reservoir and wellbore fluids Coupled with Flow model based on the perforation straight well above set up, along well depth direction, hole Directly there is correlation in position, pressure drop and the eyelet flow that becomes a mandarin of eye so that, the pressure drop along well depth of the position of preforation tunnel and Eyelet, which becomes a mandarin, to be had an impact.Therefore, it is main using total production capacity as object function below, and above-mentioned factor is as bound variable, so that, Propose following two basic Optimized models：(1) using straight well production capacity as object function, using hole position as bound variable, production is made Can be maximum；(2) using straight well production capacity as object function, become a mandarin with hole position and section uniform for constraints, Optimal Parameters, Suppress to make production capacity reach maximum while water, gas coning.

Optimized model I：Generate well aggregated capacity maximum

Given downstream heel end pressure p_d(to limited fluid diversion well, heel end pressure p_dNeed to specify), wherein total production capacity is perforation All entrance eyelets in well section.

If considering water, gas coning problem, the inbound traffics of an eyelet are controlled, improve inflow profile, so as to suppress water, gas Coning, delays water, gas break through.Therefore, along well depth direction, it is desirable to which eyelet inflow profile is uniform as far as possible, so that, obtain To following Optimized model.

Optimized model II：Maximum generation well total output (27), gives downstream heel end pressure p_dAnd unit perforation is become a mandarin to the greatest extent May be uniform.

Above-mentioned optimization problem is using perforating site as bound variable, along pit shaft direction, if coordinate meets limitation bar Part：

0≤x₁≤…≤x_i≤…≤x_N≤L (28)

Preforation tunnel number N is generally than larger, in actual generating process, in order to reduce amount of calculation, general using segmentation The method of numerical computations reduces optimized variable number to reach.With J-1 nodes X_j(j=1,2 ..., J-1) perforated interval is divided Into J sections, every section of Kong Mi included in I perforation unit (N=I × J), i.e., each segmentation limit interval is constant, but is often segmented Kong Mi it is not necessarily identical.The N number of piecewise interval of straight well section is

[X_j, X_j+1], j=0,1 ..., J-1, X₀=0, X_J=L (29)

The each upper coordinate of I eyelet on that segment of segmentation is represented by

x_I×j+i=X_j+(X_j+1-X_j) i/I, i=0,1 ..., I, j=0,1 ..., J-1 (30)

If the eyelet number I=1 in each segmentation, there is X_j=x_j, it is now that all perforations are optimized, decision-making becomes Amount has N number of.If the eyelet number I ＞ 1 in each segmentation, perforation segmentation is calculated with regard to that can reduce Optimization Work amount, decision variable There is N number of J-1 of being reduced to.

If not considering water, gas coning problem, Optimized model I radially optimizes to perforation distribution, solves optimal perforation distribution, with To the maximum production capacity of perforation straight well.Because the minimum pressure drop of straight well downstream heel end is than larger, water, gas coning are likely to occur in directly mostly Well heel end, if considering water, gas coning problem, Optimized model I is optimized to perforation distribution, optimal perforation distribution is solved, to obtain Minimum producing pressure differential, alleviates water, the gas coning of downstream heel end.

Optimized model II mainly considers to slow down water, gas coning, by optimization problem, obtains uniform inflow profile, is formed Along the uniform profit of straight well or oil gas two-phase interface, to slow down the time burst of water, gas coning.Therefore, in the segmentation of each perforation Have to meet inbound traffics equal, i.e.,

Due to Q_jIt is also unknown, formula (31) is the equation group comprising J-1 equation and J-1 unknown quantitys.

(1) Optimized model of infinite fluid diversion well is built：

If straight well pressure drop is ignored relative to downstream with end pressure, wellbore pressure is considered as constant, i.e. p_i=p_d, claim Straight well is infinite fluid diversion well.The perforation distribution of limited long perforating well can be estimated with formula (6).

For Optimized model I, water, the influence of gas coning are not considered, and the object function of production capacity optimization is

I.e. using the summation of the inbound traffics of each preforation tunnel as total production capacity of perforation straight well, include about in object function Shu Bianliang, i.e. eyelet location parameter.Due to infinite fluid diversion well do not consider pressure at wellbore pressure loss, therefore each eyelet be with End pressure p_d.Simultaneously for perforation straight well section, along the direction of well depth, the position coordinates of each perforated interval node has size pass System, i.e. X_j+1≥X_j, conditions above is to constitute the optimization constraints, so that, Optimized model can be described as

For optimization problem II, in order to suppress water, gas coning, slow down water, gas break through to make each perforation unit On inbound traffics it is as equal as possible, i.e., on the basis of model (10), additional constraint condition (31) obtains corresponding production capacity optimization mould Type is

Production capacity Optimized model (33)-(34) established above are nonlinear optimal problem, and the position of perforated interval is about Include J-1 bound variable in Shu Bianliang, each model, optimization problem can be carried out with the method for numerical computations.By asking Solve optimization problem, the hole position distribution situation of perforated interval when both can obtain optimal production capacity.Infinite fluid diversion well is not related to pressure drop Influence, therefore, gives pit shaft with end pressure, can both obtain optimal hole position by Optimized model and perforation becomes a mandarin flow, Influence available for analysis flow to optimal Kong Mi, to improve straight well production capacity.

(2) Optimized model of limited fluid diversion well is built：

If the pressure drop of straight well pit shaft can not be ignored, wellbore pressure loss is calculated in each perforation unit, now, along well depth Direction, the pressure of pit shaft no longer keeps constant, but changes with well depth, i.e. pi=p_wi, now, straight well is limited fluid diversion Well.

For Optimized model I, water, gas coning problem are not considered, and affix obtains production capacity to the constraints of wellbore pressure Optimized model is

For Optimized model II, it is contemplated that water, the influence of gas coning, it is necessary to make perforation unit meet uniform inflow section, Additional constraint condition (31), therefore obtain the production capacity Optimized model of the uniform inflow section of limited fluid diversion well and be

Production capacity Optimized model (35)-(36) established above are nonlinear optimal problem, and the position of perforated interval is about Include J-1 bound variable in Shu Bianliang, each model, with production capacity Optimized model (33)-(34) equally, it is necessary to use numerical value meter The method of calculation is solved.Limited fluid diversion well considers pressure drop considerations in pit shaft, with reference to the flow through oil reservoir and pit shaft above set up Coupled with Flow model, pressure and perforation when obtaining optimal hole position become a mandarin flow, available for analysis pressure and flow Influence to optimal Kong Mi, and improve straight well production capacity, improve inflow profile, flow-after-flow test.

Solve perforating parameter Optimized model：In order to simplify calculating, perforation straight well is divided into some sections, every section from bottom dome Length depend on perforation fluid flow, borehole wall thickness, aperture, inside and outside pipeline fluid density and pipeline geometric properties.The mould Type is calculated first since a position specified：The bottom of pipeline.Based on discussed above, the specific algorithm step that model is calculated It is as follows：

Step 1：Given initial valuep_dWith allowable error ε=10^-3。

Step 2：Calculate the inclination angle at each point

I represents the numbering of perforation waypoint, s in formula_kRepresent inclined angle alpha_kAnd α_k-1Between measurement length, Δ s_iExpression is inclined The material calculation at oblique angle.

Step 3：Reynolds number is calculated according to local flow

Step 4：The turbulent skn friction factor uses Miller methods

Step 5：Successively perforated hole wellbore pressure and perforation injection stream flow are calculated using iterative formula (26a) and (26b). For infinite fluid diversion well, well cylinder pressure is constant, therefore, can directly utilize (26a) to calculate perforated hole wellbore pressure.

Step 6：Calculation optimization problem (33) obtains the optimal perforation tunnel distribution of infinite fluid diversion well without water, gas coning. Because (33) are a nonlinear programming problems, calculated using SQP (SQP).In order to simplify calculating, respectively Use g_j(X)≤0, h_i(X)=0, (i, j=1,2 ..., J）Represent inequality constraints condition and equality constraint.Construct glug bright Day function

λ in formula_i, λ_jFor Lagrange multiplier.Because nonlinear problem (33) is equivalent to a series of two on direction of search d Secondary planning subproblem, in kth time iteration, iteration point X_kThe subproblem of satisfaction can be described as

Iteration is

X_k+1=X_k+γ_kd_k

Wherein step factor γ_kLinear search is carried out by quadratic interpolattion to obtain, matrix B^kUsing the BFGS amendments after improvement Formula is calculated

Iteration point in formula

s^k=X^k+1-X^k

With

z_k=θ y_k+(1-θ)B_ks_k, θ ∈ [0,1]

Wherein θ can be obtained by following formula

With

Straight well perforation Optimal Distribution can be calculated to obtain according to above-mentioned algorithm.

Step 7：It is optimal that the limited fluid diversion well without water, gas coning is obtained by step 1- step 6 calculation optimization models (34) Perforation tunnel distribution.

Step 8：Water is obtained by step 1- step 6 calculation optimization models (35), the infinite fluid diversion well of gas coning optimal is penetrated Hole perforation distribution.

Step 9：Water is obtained by step 1- step 6 calculation optimization models (33), the limited fluid diversion well of gas coning optimal is penetrated Hole perforation distribution.

Embodiment：

By taking the YB-X gas well at HTHP of western part of China as an example, using the production capacity Optimized model of above-mentioned foundation, perforation is analyzed The optimal perforation distribution of well and parameter optimization.As described in above-mentioned model analysis and solution procedure, modeling process be from The bottom of perforated interval starts, and the continuous well section being divided into by pit shaft is in turn calculated until the top of perforated interval.Will Perforated interval is split into some perforation units since bottom.In order to simplify calculating, perforated interval is divided into many perforations and is segmented, The perforation unit that each perforation fragmented packets contain is not necessarily identical, is calculated according still further to above-mentioned calculation procedure.

Model parameter and measurement data：On oil pipe data, sleeve pipe data and well depth measurement, hole deviation in real case simulation The data such as angle, azimuth and well vertical depth are shown in Table 1- tables 3.In addition, in addition it is also necessary to supplement partial data, including：Straight well Perforation scope be 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

Numerical Analysis：Obtained a series of numerical result to the simulation of perforated hole, including pressure drop, eyelet flow with And the optimal perforation distribution of perforated interval, to estimate the variation tendency of perforation straight well overall presure drop, 500m infinite fluid diversion is considered first Equally distributed 500 eyelets on perforated interval, optimizing application model is simulated, change in pressure drop trend such as Fig. 4 (a), 4 (b) It is shown, as a result show that the overall presure drop of uniform perforated hole includes 81.28% gravitational pressure drop, 15.25% wall friction pressure drop and 3.47% fluid accelerates pressure drop, and it is the important component of straight well overall presure drop to illustrate gravitational pressure drop.Utilize production capacity coupled mode Type, calculates infinite fluid diversion well capacity for 33617m³/ d, limited fluid diversion well capacity is 31427m³/d。

Consider that a 500m includes the infinite fluid diversion perforated interval of 500 eyelets, flow optimal case and uniform inflow perforation The optimal shot density and production capacity result of scheme are shown in that Fig. 5 (a), 5 (b) are shown, are compared in figure with uniform perforated hole.It is different In the case of the distribution of optimization perforation be shown in Table 5.Optimal perforating scheme shows that the bottom of perforated interval and the eyelet at top divide Cloth comparatively dense is to be optimal production capacity, and the perforation distribution of uniform inflow is on the contrary.The production capacity of flow optimal case is 34460m³The production capacity of the more uniform perforations of/d adds 2.51%；The production capacity 34231m of uniform inflow perforating scheme³/ d is more uniform to be penetrated The production capacity increase by 1.83% in hole, shows that influence of the constraint of uniform inflow to production capacity is little；

Fig. 6 (a), 6 (b) show the uniform inflow production capacity optimum results of 500m limited fluid diversion straight wells, optimization perforation distribution It is shown in Table 5.Found out by eyelet, close twice of the close almost top-portion apertures in the hole of bottom.Optimal case shows that perforation is in the big well that becomes a mandarin It is more intensive that section is distributed, compared to uniform perforation, optimization perforation production capacity 32258m³/ d volume increase 2.64%.If in view of steam Coning influences, and the production capacity of uniform inflow is 32056m³/ d, than uniform perforation production capacity increase by 2%.

Table 5

Optimized model I result of calculation such as Fig. 7 (a) and 7 (b) are shown.Because the bottom and top of perforated interval have larger Supply scope, it is also larger through the inbound traffics at this from oil reservoirs.The medium position of perforated interval has the less extent of supply, therefore It is relatively low through the inbound traffics at this from oil reservoirs.Change of production change is smaller, and tends to more in the high position distribution of pressure Perforation.Therefore, in order to reach Optimized model I optimal production capacity, eyelet is distributed more dense in perforated interval bottom.Due in the wellbore Without pressure drop, the flow and shot density of infinite fluid diversion well are symmetrical.The influence for the drop that is stressed, limited fluid diversion well capacity from Perforated interval bottom tapers off trend to top, meanwhile, shot density is successively decreased also along perforated interval.About apart from bottom 4H/5's Position, shot density reaches its minimum value, and gradually increases at top.

Fig. 7 (a) and Fig. 7 (b) show, to reach the yield of maximum, and Gao Kongmi perforation point is needed at maximum pressure drop Cloth.If overcoming aqueous vapor to bore well problem, perforation becomes a mandarin should evenly.Under the conditions of uniform inflow, shot density becomes a mandarin in height Position at should reduce, similar, shot density should increase at the position become a mandarin.

For Optimized model II solution, shown in its result such as Fig. 8 (a), 8 (b)；Under the conditions of uniform inflow, infinitely lead Flow well close larger in the hole of medium position, due to pressure drop influence, limited fluid diversion well has higher bottom pressure drop than infinite fluid diversion well Bigger inbound traffics.

Claims (2)

1. HTHP oil gas straight well single-phase flow perforation completion parameter optimization method, it is characterised in that comprise the following steps：

A, structure Wellbore Flow Pressure Drop Model；

B, structure petrol-gas permeation fluid and Wellbore Flow coupling model；

C, structure perforating parameter Optimized model；

D, perforating parameter Optimized model solved；

In step A, the structure Wellbore Flow Pressure Drop Model is specifically included：

Only penetrated if the uniform perforated interval in straight well pit shaft is split into N number of isometric perforation unit, each unit comprising one Hole eyelet, the length of pit shaft unit, p are represented with Δ x₁, U₁, A₁End pressure, speed and cross-sectional area, p on difference representative unit₂, U₂, A₂End pressure, speed and cross-sectional area under difference representative unit；

The law of conservation of momentum is applied in control volume elements in the axial direction, that is, controls the summation of the external force suffered by volume elements CV to be equal to by control Voxel Surface CS processed fluid momentum and the fluid momentum increment rate sum in control volume elements, can obtain the equation of momentum：

$\Σ\stackrel{\→}{F}=\frac{\∂}{\∂t}\∫\∫{\∫}_{CV}\mathrm{\ρ}\stackrel{\→}{u}dV+\∫{\∫}_{CS}\mathrm{\ρ}\stackrel{\→}{u}(\stackrel{\→}{u}\·\stackrel{\→}{n})dA---\left(7\right)$

ρ is fluid density in formula, and A is the area in any section of pit shaft；

For stable state pit shaft stream

$\frac{\∂}{\∂t}\∫\∫{\∫}_{CV}\mathrm{\ρ}\stackrel{\→}{u}dV=0---\left(8\right)$

One-Dimensional flows problem will be considered as along the two-dimensional flow problem in section, the mean flow rate for taking section is U, utilizes the conservation of mass Equation, formula (7) is expanded into：

$\Σ\stackrel{\→}{F}=(p_{w1}A-p_{w2}A)-{\mathrm{\τ}}_w\left(\mathrm{\π}D\mathrm{\Δ}x\right)-\mathrm{\ρ}gA\mathrm{\Δ}x\cos \mathrm{\θ}---\left(9\right)$

Formula (9) equal sign left side is the power sum that control volume surface is in downward direction acted on along pit shaft axis

$\Σ\stackrel{\→}{F}={\stackrel{\·}{m}}_2{U}_2-{\stackrel{\·}{m}}_1{U}_1---\left(10\right)$

Mass flow in formula

$\stackrel{\·}{m}=\mathrm{\ρ}AU---\left(11\right)$

Section 1 represents the net pressure acted in control volume elements on the right of formula (9) equal sign；Section 2 represents to act on well casing wall Shear stress：

π_w(π D Δs x)=Δ p_wallA (12)

The right Section 3 represents Action of Gravity Field, and gravitational pressure drop is

Δp_g=ρ g Δ x cos θ (13)

Convolution (9)-(13) can be obtained

$p_{w2}-p_{w1}=\mathrm{\ρ}(U_2^2-U_1^2)+{\mathrm{\Δp}}_{wall}+{\mathrm{\Δp}}_g---\left(14\right)$

Section 1 represents net momentum on the right of formula (14) equal sign, is due to that more fluids cause axial stream by perforation into pipeline Caused by speed changes, the pressure drop is due to acceleration effect Δ p_accProduce, can be described as：

${\mathrm{\Δp}}_{acc}=\mathrm{\ρ}(U_2^2-U_1^2)---\left(15\right)$

The overall presure drop of perforation downhole well fluid includes friction pressure drop Δ p_wall, accelerate pressure drop Δ p_accWith gravitational pressure drop Δ p_g

Δp_w=Δ p_wall+Δp_acc+Δp_g (16)

The pressure drop as caused by wall friction depends on perforation mean flow rate U in perforation unit₂, Darcy-Weisbach equations can be used Calculated：

${\mathrm{\Δp}}_{wall}=\frac{f\mathrm{\ρ}}{2D}{\mathrm{\ΔxU}}_2^2---\left(17\right)$

Along the direction of perforation depth, the pressure representative at perforation unit i is p_wi, then according to formula (16), perforation can be obtained The calculation of pressure relational expression of the corresponding pit shaft shaft position of eyelet

$\left\{\begin{array}{c}{p}_{w1}=p_d\\ p_{wi+1}=p_{wi}+{\mathrm{\Δp}}_{wall,i}+{\mathrm{\Δp}}_{acc,i}+{\mathrm{\Δp}}_{g,i}\end{array}\right.---\left(18\right)$

P in formula_dFor position x₁The downstream at place is with end pressure, Δ p_{Wall, i}, Δ p_{Acc, i}, Δ p_{G, i}Wall friction pressure drop is represented respectively, added The pressure drop in the corresponding pit shaft axial positions of perforation i with gravitational pressure drop drops in ram compression；

Consider perforation unit i, the discrete scheme of formula (17) is：

${\mathrm{\Δp}}_{wall,i}=\frac{{\mathrm{\ρf}}_i}{2D}\frac{q_i^2}{A^2}|x_{i+1}-x_i|---\left(19\right)$

Mean flow rate U in formula_iAvailable expressionCalculated, the integrated flow at this is

$q_i=\underset{j=1}{\overset{i-1}{\Σ}}{Q}_j---\left(20\right)$

Accelerate pressure drop be as more fluids by perforation into pipeline cause axial flow velocity change caused by, dependent on fluid Density and mean flow rate；

${\mathrm{\Δp}}_{acc,i}=\mathrm{\ρ}(U_{i+1}^2-U_i^2)---\left(21\right)$

Gravitational pressure drop is that the gravity for having fluid is produced, and is represented by

Δp_{G, i}=ρ g cos α_i|x_i+1-x_i| α in (22) formula_iRepresent perforation unit i inclination angle；

Bring formula (19), (21) and (22) into formula (18), both can obtain the Pressure Drop Model of Wellbore Flow：

$\left\{\begin{array}{c}{p}_{w1}=p_d\\ p_{wi+1}=p_{wi}|+\frac{{\mathrm{\ρf}}_i}{2D}\frac{q_i^2}{A^2}|x_{i+1}-x_i|+\mathrm{\ρ}(U_{i+1}^2-U_i^2)+\mathrm{\ρ}g{\mathrm{cos\α}}_i|x_{i+1}-x_i|\end{array}\right.---\left(23\right);$

In step B, the flowing of the petrol-gas permeation fluid of straight well and straight well wellbore fluids is considered as to the entirety of an interaction, simultaneously Pressure and discharge relation between comprehensive oil reservoir and pit shaft, pressure, in the continuity of boundary, set up oil-gas reservoir and pit shaft with flow Coupling model, specific method includes：

By formula (23), the vector form that the pressure drop correlations of downhole well fluid are expressed as：

${\stackrel{\→}{P}}_w=F\[\stackrel{\→}{Q}\]---\left(24\right)$

The vector expression of vector expression and Wellbore Flow Pressure Drop Model based on petrol-gas permeation fluid model obtains coupling model：

$\left\{\begin{array}{c}\stackrel{\→}{Q}=A^{-1}\stackrel{\→}{P}\\ \stackrel{\→}{P}=F\[\stackrel{\→}{Q}\]\end{array}\right.---\left(25\right);$

In step B, also solved including the coupling model to acquisition, method is as follows：

For there is the pit shaft of N number of perforation, coupling model is to include the suitable fixed number that 2N equation of 2N unknown function is constituted Problem, for the nonlinear coupling model, is solved using following iterative formula：

${\stackrel{\→}{Q}}^{n+1}=A^{-1}{\stackrel{\→}{P}}^n---\left(26a\right)$

${\stackrel{\→}{P}}^{n+1}=F\[{\stackrel{\→}{Q}}^{n+1}\]---\left(26b\right)$

Given initial valuep_d, according to the iterative algorithm of coupling model, by iterative formula (26a), bring pressure data into, you can The flow at each eyelet is calculated, then by the counted eyelet flow of formula (26a), band entry format (26b) can calculate the pressure of pit shaft Distribution；Said process is repeated, until solving result meets the iteration termination condition set in advance；

In step C, when building perforating parameter Optimized model, if water, gas coning problem are not considered, using straight well production capacity as target Function, using hole position as bound variable, makes production capacity maximum；If water, gas coning problem are considered, using straight well production capacity as target letter Number, is become a mandarin uniform for constraints with hole position and section, production capacity is reached maximum while water, gas coning is suppressed；

Wherein, the straight well production capacity is the influx summation of all entrance eyelets in perforated interval：

$Q=\underset{i=1}{\overset{N}{\Σ}}{Q}_i---\left(27\right)$

Along pit shaft direction, if coordinate meets restrictive condition：

0≤x₁≤…≤x_i≤…≤x_N≤L (28)

With J-1 nodes X_jPerforated interval is divided into J sections by (j=1,2 ..., J-1), every section comprising 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 segment identifier of straight well section Between be

[X_j, X_j+1], j=0,1 ..., J-1, X₀=0, X_J=L (29)

The each upper coordinate of I eyelet on that segment of segmentation is represented by：

x_I×j+i=X_j+(X_j+1-X_j) i/I, i=0,1 ..., I, j=0,1 ..., J-1 (30)

When considering water, gas coning problem, it is equal to have to meet inbound traffics in the segmentation of each perforation, i.e.,

$\underset{i=I\×j+1}{\overset{I\×(j+1)}{\Σ}}{Q}_j=\underset{i=1}{\overset{N}{\Σ}}{Q}_j(X_{j+1}-X_j)/L,j=0,1,...,J-1---\left(31\right);$

In step C, the structure perforating parameter Optimized model comprises the following steps：

C1. the Optimized model of infinite fluid diversion well is built：

If C11. not considering water, the influence of gas coning, the object function of production capacity optimization is

$\min f\left(X\right)=-\underset{i=1}{\overset{N}{\Σ}}{\[A^{-1}\left(X\right)P\]}_i---\left(32\right)$

I.e. using the summation of the inbound traffics of each preforation tunnel as total production capacity of perforation straight well, become in object function comprising Constrained Amount, the i.e. location parameter of eyelet；It is with side pressure that the pressure at wellbore pressure loss, therefore each eyelet is not considered due to infinite fluid diversion well Power pd；Simultaneously for perforation straight well section, along the direction of well depth, the position coordinates of each perforated interval node has magnitude relationship, i.e., X_j+1≥X_j, conditions above be constitute the optimization constraints, can obtain infinite fluid diversion well do not consider water, gas coning influence when Optimized model：

$\min f\left(X\right)=-\underset{i=1}{\overset{N}{\Σ}}{\[A^{-1}\left(X\right)P\]}_i$

$\begin{array}{cc}s.t.& \left\{\begin{array}{cc}{p}_i-p_d=0& (i=1,2,...,N)\\ X_1\≥0& \\ X_{j+1}-X_j\≥0& (j=1,2,...,J-1)\\ L-X_J\≥0& \end{array}\right.\end{array}---\left(33\right)$

If C22. considering water, the influence of gas coning, it is necessary to make the inbound traffics on each perforation unit as equal as possible, i.e., in model (32) on the basis of, additional constraint condition (31) can obtain Optimized model of the infinite fluid diversion well when considering water, the influence of gas coning：

$\begin{array}{cc}\min & f\left(X\right)=-\underset{i=1}{\overset{N}{\Σ}}{\[A^{-1}\left(X\right)P\]}_i\end{array}$

$\begin{array}{cc}s.t.& \left\{\begin{array}{cc}{p}_i-p_d=0& (i=1,2,\mathrm{...},N)\\ \underset{i=Ik+1}{\overset{I(k+1)}{\Σ}}{Q}_i=\underset{i=1}{\overset{N}{\Σ}}{Q}_i(X_{k+1}-X_k)/L& (k=0,1,\mathrm{...},J-1)\\ X_1\≥0& \\ X_{j+1}-X_j\≥0& (j=1,2,\mathrm{...},J-1)\\ L-X_J\≥0& \end{array}\right.\end{array}---\left(34\right)$

C2. the Optimized model of limited fluid diversion well is built：

C21. the wellbore pressure of limited fluid diversion well changes with well depth, i.e. p_i=p_wi, when not considering water, gas coning problem, its Optimized model is：

$\begin{array}{cc}\min & f\left(X\right)=-\underset{i=1}{\overset{N}{\Σ}}{\[A^{-1}\left(X\right)P\]}_i\end{array}$

$\begin{array}{cc}s.t.& \left\{\begin{array}{cc}{p}_i-p_{wi}=0& (i=1,2,...,N)\\ X_1\≥0& \\ X_{j+1}-X_j\≥0& (j=1,2,...,J-1)\\ L-X_J\≥0& \end{array}\right.\end{array}---\left(35\right)$

C22. when considering water, gas coning problem, its Optimized model is：

$\begin{array}{cc}\min & f\left(X\right)=-\underset{i=1}{\overset{N}{\Σ}}{\[A^{-1}\left(X\right)P\]}_i\end{array}$

$\begin{array}{cc}s.t.& \left\{\begin{array}{cc}{p}_i-p_{wi}=0& (i=1,2,\mathrm{...},N)\\ \underset{i=Ik+1}{\overset{I(k+1)}{\Σ}}{Q}_i=\underset{i=1}{\overset{N}{\Σ}}{Q}_i(X_{k+1}-X_k)/L& (k=0,1,\mathrm{...},J-1)\\ X_1\≥0& \\ X_{j+1}-X_j\≥0& (j=1,2,\mathrm{...},J-1)\\ L-X_J\≥0& \end{array}\right.\end{array}---\left(36\right);$

In step D, perforating parameter Optimized model is solved, specifically included：

D1. initial value is givenWith allowable error ε=10^-3；

D2. the inclination angle at each point is calculated

${\mathrm{\α}}_i={\mathrm{\α}}_{i-1}+\frac{{\mathrm{\α}}_k-{\mathrm{\α}}_{k-1}}{{\mathrm{\Δs}}_k}{\mathrm{\Δs}}_i$

I represents the numbering of perforation waypoint, s in formula_kRepresent inclined angle alpha_kAnd α_k-1Between measurement length, Δ s_iRepresent inclination angle Material calculation；

D3. Reynolds number is calculated according to local flow

${\mathrm{Re}}_i=\frac{{\mathrm{\ρDq}}_i}{2\mathrm{\μ}A};$

D4. the turbulent skn friction factor is calculated：

$f_i=0.25{\[log(\frac{\mathrm{\ϵ}}{3.7D}+\frac{5.74}{{\mathrm{Re}}_i^{0.9}})\]}^{-2};$

D5. perforated hole wellbore pressure and perforation injection stream flow are calculated using iterative formula (26a) and (26b)；

D6. the Optimized model of structure is solved, obtains straight well perforation Optimal Distribution.

2. HTHP oil gas straight well single-phase flow perforation completion parameter optimization method as claimed in claim 1, it is characterised in that In step D6, the method that the Optimized model of described pair of structure is solved is：Calculated, used respectively using SQP g_j(X)≤0, h_i(X)=0, (i, j=1,2 ..., J) represents inequality constraints condition and equality constraint；Construction Lagrange Function：

$L(X,\mathrm{\λ})=f\left(X\right)+\underset{i=1}{\overset{J}{\Σ}}{\mathrm{\λ}}_i{h}_i\left(X\right)+\underset{j=1}{\overset{J}{\Σ}}{\mathrm{\λ}}_{j}g\left(X\right)$

λ in formula_i, λ_jFor Lagrange multiplier；It is equivalent to for nonlinear Optimized model on direction of search d a series of secondary Subproblem is planned, in kth time iteration, iteration point X_kThe subproblem of satisfaction is：

$\begin{array}{cc}\min & \frac{1}{2}{d}^T{H}_{k}d+{\[\▿f\left(X_k\right)\]}^{T}d\end{array}$

$\begin{array}{cc}s.t.& \left\{\begin{array}{cc}{\[\▿h_i\left(X_k\right)\]}^{T}d+h_i\left(X_k\right)=0& (i=1,2,...,J)\\ {\[\▿g_j\left(X^k\right)\]}^{T}d+g_j\left(X^k\right)\≤0& (j=1,2,...,J)\end{array}\right.\end{array}$

Iteration is

X_k+1=X_k+γ_kd_k

Wherein step factor γ_kLinear search is carried out by quadratic interpolattion to obtain, matrix B^kUsing the BFGS correction formulas after improvement Calculate

$B_{k+1}=B_k-\frac{B_k{s}_k{s}_k^T{B}_k}{s_k^T{B}_k{s}_k}+\frac{z_k{z}_k^T}{z_k^T{y}_k}$

Iteration point in formula

s^k=X^k+1-X^k

With

z_k=θ y_k+(1-θ)B_ks_k, θ ∈ [0,1]

Wherein

$\mathrm{\&theta;}=\left\{\begin{array}{cc}1,& y_k^T{s}_k\&GreaterEqual;0.2s_k^T{B}_k{s}_k,\\ \frac{0.8s_k^T{B}_k{s}_k}{s_k^T{B}_k{s}_k-y_k^T{s}_k},& y_k^T{s}_k<0.2s_k^T{B}_k{s}_k.\end{array}\right.$

With

$\begin{array}{c}{y}^k=\&dtri;f\left(X^{k+1}\right)+\underset{i=1}{\overset{J}{\&Sigma;}}{\mathrm{\&lambda;}}_i\&dtri;h_i\left(X^{k+1}\right)+\underset{j=1}{\overset{J}{\&Sigma;}}{\mathrm{\&lambda;}}_j\&dtri;g_j\left(X^{k+1}\right)\\ -\&lsqb;\&dtri;f\left(X^k\right)+\underset{i=1}{\overset{J}{\&Sigma;}}{\mathrm{\&lambda;}}_i\&dtri;h_i\left(X^k\right)+\underset{j=1}{\overset{J}{\&Sigma;}}{\mathrm{\&lambda;}}_j\&dtri;g_j\left(X^k\right)\&rsqb;\end{array};$

Optimized model (33) is solved using the algorithm, the infinite fluid diversion well when not considering water, gas coning influence is obtained Optimal perforation tunnel distribution：

Optimized model (34) is solved using the algorithm, infinite fluid diversion well of the acquisition when considering water, gas coning influence Optimal perforation tunnel distribution：

Optimized model (35) is solved using the algorithm, the limited fluid diversion well when not considering water, gas coning influence is obtained Optimal perforation tunnel distribution：

Optimized model (36) is solved using the algorithm, limited fluid diversion well of the acquisition when considering water, gas coning influence Optimal perforation tunnel distribution.