CN104847314A - High-temperature high-pressure oil and gas vertical-well single-phase flow perforation well completion parameter optimization method - Google Patents

Abstract

The invention belongs to the technical field of oil and gas reservoir development engineering management, and particularly relates to a high-temperature high-pressure oil and gas vertical-well single-phase flow perforation well completion parameter optimization method, in particular to construction of a high-temperature high-pressure oil and gas vertical-well single-phase flow model and an oil reservoir seepage flow and wellbore flow coupling model and algorithm process design and the like. With the method, perforation parameters are accurately predicated so as to increase productivity ratio of oil gas wells. The method includes the steps of A, constructing a wellbore flow pressure dropping model; B, constructing the oil reservoir seepage flow and wellbore flow coupling model; C, constructing a perforation parameter optimization model; D, calculating the perforation parameter optimization model. The method is applicable to development of oil and gas reservoir.

Description

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

Technical field

The present invention relates to and belong to development of oil and gas reservoir administrative skill field, be specially a kind of HTHP oil gas straight well single-phase flow perforation completion parameter optimization method, be related specifically to HTHP oil gas straight well single-phase flow model, the structure of flow through oil reservoir and Wellbore Flow coupling model and algorithm flow design etc.

Background technology

Perforation is one of main at present completion method, be with special perforating gun by sleeve pipe and cement sheath partial penetrating, make to set up passage between pit shaft and stratum, reach the object that oil gas flows into pit shaft.Perforating gun is the assembly of equipment for perforating oil gas well and auxiliary equipment thereof.Most widely used is at present jet perforating rifle, perforating process has been come by the cumulative principle of perforating bullet, perforating bullet is detonated rear generation HTHP metal jet squeezing bushing, cement sheath and stratum, when jet pressure exceedes the yield strength of formation rock, duct will be formed in stratum.

Perforation completion is the most popular a kind of Well completion method in domestic and international oil field, and this completion mode is very large on the impact of oil well production effect, and done a large amount of research work to it both at home and abroad, main purpose studies perforating parameter exactly to improve productivity ratio.Usually, the performance of Oil/gas Well is by its geometric influence.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 in inflow pit shaft and the fluid on vertical cross-section.Change of fluid in Oil/gas Well mainly affects by overall presure drop, and therefore, the overall presure drop better understood in straight well contributes to optimizing straight well design.

Perforating parameter relates to hole depth, phase place, Kong Mi, aperture etc., the selection of these parameters has material impact to raising straight well production capacity, simultaneously, in order to suppress water, gas coning, delay water, gas break through, need to improve the inflow profile along straight well pit shaft, make the inflow profile distribution in well depth direction as far as possible evenly.Therefore, the choose reasonable of perforating parameter is to raising production capacity, and improvement becomes a mandarin significant.

Oil-gas reservoir single-phase flow perforation steady-state model: consider half unbounded oil-gas reservoir, be considered as by eyelet cylindrical, fluid enters pit shaft by eyelet from stratum, and becoming a mandarin of perforation all can have an impact to the pressure at other eyelet places, utilize the characteristic of stratum filtration, the pressure drop correlations at each eyelet place can be set up.Fluid in pit shaft is subject to the factor impacts such as gravity, frictional force and fluid acceleration, utilizes conservation of mass physical principle to set up wellbore fluids flow model.Before Modling model, be first described below basic assumption:

(1) oil reservoir is uniform and isotropic.Be constant at reservoir permeability, not with change in location, also do not measure Orientation differences with reservoir.

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

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

Being regarded as by perforated interval long is l _perf, radius is r _perfcylinder.Perforated interval in whole straight well pit shaft comprises N number of preforation tunnel, and structure as shown in Figure 2.

Suppose that formation damage is ignored, from bottom, the position of the i-th perforation is x _i(i=1,2 ..., N) and work as ratio time very little, according to the average pressure of even line source, enter flow q by i-th preforation tunnel _ithe pressure p produced _iican be described as

$p_{ii}=-\frac{\mathrm{\μ}}{2\mathrm{\π}k}\frac{Q_i}{l_{perf}}\ln \frac{r_{perf}}{l_{perf}}---\left(1\right)$

If the spacing between perforation is fully large, then the point sink intensity Q at perforation j place _jfollowing formula can be had to state perforation i place pressure influence

$p_{ij}=\frac{\mathrm{\μ}}{4\mathrm{\π}k}\frac{Q_j}{|x_i-x_j|}---\left(2\right)$

Inlet pressure and other perforation inlet pressure sums of the i-th perforation self is in the gross pressure of perforation i generation

$p_i=p_{ii}+\underset{j\≠i}{\Σ}{p}_{ij}---\left(3\right)$

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

$p_i=-\frac{\mathrm{\μ}}{2\mathrm{\π}k}\frac{Q_i}{l_{perf}}\ln \frac{r_{perf}}{l_{{}_{perf}}}+\underset{j\≠i}{\Σ}\frac{\mathrm{\μ}}{4\mathrm{\π}k}\frac{Q_j}{|x_i-x_j|}---\left(4\right)$

The position of perforation j is x=x _j, x ₁represent first perforating site from bottom perforated interval.Perforating site x _ifor known variables, the pressure of non-linear dependence in each perforation place and inbound traffics.

Adopt vector representation: $\stackrel{\→}{P}={(p_1,p_2,...,p_N)}^T,\stackrel{\→}{Q}={(Q_1,Q_2,...,Q_N)}^T,$ Formula (4) can be expressed as:

$\stackrel{\→}{P}=A\stackrel{\→}{Q}---\left(5\right)$

Wherein coefficient matrices A depends on perforation size and perforation distribution.

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

$\stackrel{\→}{Q}=A^{-1}\stackrel{\→}{P}---\left(6\right)$

Summary of the invention

Technical problem to be solved by this invention is: propose a kind of HTHP oil gas straight well single-phase flow perforation completion parameter optimization method, make accurately predicting, to improve Oil & Gas Productivity ratio to perforating parameter.

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, perforation optimization model to be solved.

Further, in steps A, described structure Wellbore Flow Pressure Drop Model specifically comprises:

If the even perforated interval in straight well pit shaft is split into N number of isometric perforation unit, only comprises a preforation tunnel in each unit, represent the length of pit shaft unit with Δ x, p ₁, U ₁, A ₁end pressure, speed and cross-sectional area on representative unit respectively, p ₂, U ₂, A ₂end pressure, speed and cross-sectional area under representative unit respectively;

Control in the axial direction to apply the law of conservation of momentum in volume elements, the summation of the external force namely controlled suffered by volume elements CV equals fluid momentum by controlling volume elements surface C S and the fluid momentum increment rate sum controlled in volume elements, can obtain the equation of momentum:

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

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

For stable state pit shaft stream

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

Two-dimensional flow problem along cross section is considered as One-Dimensional flows problem, and the mean flow rate getting cross section is U, utilizes mass-conservation equation, formula (7) is expanded into:

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

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

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

Mass flow in formula

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

On the right of formula (9) equal sign, Section 1 represents the net pressure acting on and control in volume elements; Section 2 represents the shear stress acting on well casing wall:

τ _ω(πDΔx)＝Δp _wallA (12)

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

Δp _g＝ρgΔx cosθ (13)

Convolution (9)-(13) can obtain

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

On the right of formula (14) equal sign, Section 1 represents clean momentum, due to more fluid by perforation enter pipeline cause axial flow velocity change and cause, this 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 comprises friction pressure drop Δ p _wall, accelerate pressure drop Δ p _accwith gravitational pressure drop Δ p _g

Δp _w＝Δp _wall+Δp _acc+Δp _g(16)

The pressure drop caused by wall friction in perforation unit depends on perforation mean flow rate U ₂, available Darcy-Weisbach equation calculates:

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

Along the direction of perforation depth, be p in the pressure representative at perforation unit i place _wi, then according to formula (16), the calculation of pressure relational expression of pit shaft shaft position corresponding to preforation tunnel can be obtained

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

P in formula _dfor position x ₁the downstream heel end pressure at place, Δ p _{wall, i}, Δ p _{acc, i}, Δ p _{g, i}represent the pressure drop in the corresponding pit shaft axial positions of perforation i of wall friction pressure drop, acceleration pressure drop and gravitational pressure drop respectively;

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 expression calculate, the integrated flow at this place is

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

Accelerate pressure drop by more fluid by perforation enter pipeline cause axial flow velocity change and cause, depend 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 has the gravity of fluid to produce, and can be expressed as

Δp _g，i＝ρg cosα _i|x _i+1-x _i| (22)

α in formula _irepresent the angle of slope of perforation unit i;

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

Further, in step B, the flowing of the petrol-gas permeation fluid of straight well and straight well wellbore fluids is considered as an interactional entirety, pressure simultaneously comprehensively between oil reservoir and pit shaft and discharge relation, pressure versus flow is in the continuity of boundary, set up the coupling model of oil-gas reservoir and pit shaft, concrete grammar comprises:

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

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

Coupling model is obtained based on the vector expression of petrol-gas permeation fluid model and the vector expression of Wellbore Flow Pressure Drop Model:

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

Further, in step B, the coupling model also comprised obtaining solves, and method is as follows:

For the pit shaft having N number of perforation, coupling model is that the suitable of 2N equation formation including 2N unknown function determines mathematical problem, for this nonlinear coupling model, adopts following iterative formula to solve:

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

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

Given initial value p _d, according to the iterative algorithm of coupling model, by iterative formula (26a), bring pressure data into, the flow at each eyelet place can be calculated, then by eyelet flow that formula (26a) is calculated, band entry format (26b), can calculate the pressure distribution of pit shaft; Repeat said process, until solving result meets the iteration termination condition set in advance.

Further, in step C, build perforating parameter Optimized model time, if do not consider water, gas coning problem, then with straight well production capacity for object function, be bound variable with hole position, make production capacity maximum; If consider water, gas coning problem, then with straight well production capacity for object function, become a mandarin evenly for constraints with hole position and section, while suppression water, gas coning, make production capacity reach maximum;

Wherein, described straight well production capacity is all influx summations entering eyelet in perforated interval:

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

Along pit shaft direction, if coordinate meets restrictive condition:

0≤x ₁≤…≤x _i≤…≤x _N≤L (28)

By J-1 nodes X _j(j=1,2 ..., J-1) and perforated interval is divided into J section, every section comprises I perforation unit (N=I × J), and the Kong Mi namely in each segmentation limit interval is constant, but the Kong Mi of every segmentation 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，X ₀＝0，X _J＝L (29)

In each segmentation, I eyelet coordinate on that segment can be expressed as:

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, each perforation segmentation must meet inbound traffics equal, namely

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

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

C1. the Optimized model of infinite fluid diversion well builds:

If C11. do not consider the impact of water, 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)$

Namely using the summation of the inbound traffics of each preforation tunnel as total production capacity of perforation straight well, bound variable is included in object function, i.e. the location parameter of eyelet; Because infinite fluid diversion well does not consider wellbore pressure loss, therefore the pressure at each eyelet place is heel end pressure p _d; Meanwhile, 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, namely above condition forms this optimization constraints, can obtain the Optimized model of infinite fluid diversion well not considering water, when gas coning affects:

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

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

If C22. consider the impact of water, gas coning, need to make the inbound traffics on each perforation unit equal as far as possible, namely, on model (32) basis, additional constraint condition (31), can obtain the Optimized model of infinite fluid diversion well when considering water, the affecting 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}$

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

C2. the Optimized model of limited fluid diversion well builds:

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}$

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

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}$

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

Further, in step D, perforation optimization model is solved, specifically comprises:

D1. given initial value p _dwith allowable error ε=10 ^-3;

D2. the angle of slope at each point place is calculated

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

In formula, i represents the numbering of perforation waypoint, s _krepresent inclined angle alpha _kand α _k-1between measurement length, Δ s _irepresent the material calculation at angle of slope;

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. iterative formula (26a) and (26b) is adopted to calculate perforated hole wellbore pressure and perforation injection stream flow;

D6. the Optimized model built is solved, obtain straight well perforation Optimal Distribution.

Further, in step D6, the described method that solves of Optimized model to building is: adopt SQP to calculate, use g respectively _j(X)≤0, h _i(X)=0, (i, j=1,2 ..., J) and represent inequality constraints condition and equality constraint; Structure Lagrangian:

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

λ in formula _i, λ _jfor Lagrange multiplier; A series of quadratic programming subproblem is equivalent on direction of search d for nonlinear Optimized model, in kth time iteration, iteration point X _kthe subproblem met is:

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

$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_i\left(X^k\right)\≤0& (j=1,2,...,J)\end{array}\right.$

Iteration is

X _k+1＝X _k+γ _kd _k

Wherein step factor γ _kcarry out linear search by quadratic interpolattion to obtain, matrix B ^kthe BFGS correction formula after improving is adopted to 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＝θy _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

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

Adopt this algorithm to solve Optimized model (33), obtain not considering water, the optimum perforation tunnel distribution of the infinite fluid diversion well of gas coning when affecting:

Adopt this algorithm to solve Optimized model (34), obtain the optimum perforation tunnel distribution of the infinite fluid diversion well when consideration water, gas coning affect:

Adopt this algorithm to solve Optimized model (35), obtain not considering water, the optimum perforation tunnel distribution of the limited fluid diversion well of gas coning when affecting:

Adopt this algorithm to solve Optimized model (36), obtain the optimum perforation tunnel distribution of the limited fluid diversion well when consideration water, gas coning affect.

The invention has the beneficial effects as follows: accurately predicting is done to perforating parameter, be conducive to optimizing straight well design, to improve Oil & Gas Productivity ratio.

Accompanying drawing explanation

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 best cloth hole and the comparison of production figure of infinite fluid diversion well;

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

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

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

Detailed description of the invention

The present invention is intended to propose a kind of HTHP oil gas straight well single-phase flow perforation completion parameter optimization method, makes accurately predicting, to improve Oil & Gas Productivity ratio to perforating parameter.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, perforation optimization model to be solved.

Be specifically described for each step below:

Build Wellbore Flow Pressure Drop Model:

If the even perforated interval in straight well pit shaft is split into N number of isometric perforation unit, only comprise a preforation tunnel in each unit, its cross-section structure as shown in Figure 3.In Fig. 3, Δ x is the length of pit shaft unit, p ₁, U ₁, A ₁be respectively end pressure on unit, speed and cross-sectional area, p ₂, U ₂, A ₂under being respectively unit, end pressure, speed and cross-sectional area control to apply the law of conservation of momentum in volume elements in the axial direction, namely the summation controlling external force suffered by volume elements CV equals fluid momentum by controlling volume elements surface C S and the fluid momentum increment rate sum controlled in volume elements, and thus equation of momentum form is:

$\&Sigma;\stackrel{\&RightArrow;}{F}=\frac{\&part;}{\&part;t}\&Integral;\&Integral;{\&Integral;}_{CV}\mathrm{\&rho;}\stackrel{\&RightArrow;}{u}dV+\&Integral;{\&Integral;}_{CS}\mathrm{\&rho;}\stackrel{\&RightArrow;}{u}(\stackrel{\&RightArrow;}{u}\&CenterDot;\stackrel{\&RightArrow;}{n})dA---\left(7\right)$

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

For stable state pit shaft stream

$\frac{\&part;}{\&part;t}\&Integral;\&Integral;{\&Integral;}_{CV}\mathrm{\&rho;}\stackrel{\&RightArrow;}{u}dV=0---\left(8\right)$

In general, axial flow velocity is all uneven along wellbore section, convenient for discussing here, and the two-dimensional flow problem along cross section is considered as One-Dimensional flows problem.The mean flow rate getting cross section is U, utilizes mass-conservation equation, and formula (7) is deployable is

$\&Sigma;\stackrel{\&RightArrow;}{F}=(p_{w1}A-p_{w2}A)-{\mathrm{\&tau;}}_w\left(\mathrm{\&pi;}D\mathrm{\&Delta;}x\right)-\mathrm{\&rho;}gA\mathrm{\&Delta;}xcos\mathrm{\&theta;}---\left(9\right)$

Above formula equal sign left side item is the power sum acting on control volume surface along pit shaft axis in downward direction

$\mathrm{\&Sigma;}\stackrel{\&RightArrow;}{F}={\stackrel{\&CenterDot;}{m}}_2{U}_2-{\stackrel{\&CenterDot;}{m}}_1{U}_1---\left(10\right)$

Mass flow in formula

$\stackrel{\&CenterDot;}{m}=\mathrm{\&rho;}AU---\left(11\right)$

On the right of formula (9) equation, Section 1 represents the net pressure acting on and control in volume elements; Section 2 represents the shear stress acting on well casing wall, and this power can cause friction pressure drop

τ _ω(πDΔx)＝Δp _wallA(12)

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

Δp _g＝ρgΔx cosθ(13)

Convolution (9)-(13) can obtain

$p_{w2}-p_{w1}=\mathrm{\&rho;}(U_2^2-U_1^2)+{\mathrm{\&Delta;p}}_{wall}+{\mathrm{\&Delta;p}}_g---\left(14\right)$

On the right of equation, Section 1 represents clean momentum (i.e. fluid accelerate pressure drop), causes axial flow velocity to change because more fluid enters pipeline by perforation and causes.This pressure drop is due to acceleration effect Δ p _accproduce, can be described as

${\mathrm{\&Delta;p}}_{acc}=\mathrm{\&rho;}(U_2^2-U_1^2)---\left(15\right)$

The overall presure drop of perforation downhole well fluid comprises friction pressure drop Δ p _wall, accelerate pressure drop Δ p _accwith gravitational pressure drop Δ p _g

Δp _w＝Δp _wall+Δp _acc+Δp _g(16)

The pressure drop caused by wall friction in perforation unit depends on perforation mean flow rate U ₂, available Darcy-Weisbach equation calculates:

${\mathrm{\&Delta;p}}_{wall}=\frac{f\mathrm{\&rho;}}{2D}{\mathrm{\&Delta;xU}}_2^2---\left(17\right)$

For the ease of calculating wellbore pressure, along the direction of perforation depth, be p in the pressure representative at perforation unit i place _wi, then according to formula (16), can obtain preforation tunnel for the calculation of pressure relational expression of pit shaft shaft position

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

P in formula _dfor position x ₁the downstream heel end pressure at place, Δ p _{wall, i}, Δ p _{acc, i}, Δ p _{g, i}represent the pressure drop in the corresponding pit shaft axial positions of perforation i of wall friction pressure drop, acceleration pressure drop and gravitational pressure drop respectively.

In order to calculating formula (18), first provide the discrete form of this formula.Consider perforation unit i, the discrete scheme of formula (17) is

${\mathrm{\&Delta;p}}_{wall,i}=\frac{{\mathrm{\&rho;f}}_i}{2D}\frac{q_i^2}{A^2}|x_{i+1}-x_i|---\left(19\right)$

Mean flow rate U in formula _iavailable expression calculate.The integrated flow at this place is

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

Accelerate pressure drop by more fluid by perforation enter pipeline cause axial flow velocity change and cause, depend on fluid density and mean flow rate.

${\mathrm{\&Delta;p}}_{acc,i}=\mathrm{\&rho;}(U_{i+1}^2-U_i^2)---\left(21\right)$

Gravitational pressure drop has the gravity of fluid to produce, and can be expressed as

Δp _g，i＝ρg cosα _i|x _i+1-x _i| (22)

α in formula _irepresent the angle of slope of perforation unit i.

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 both can calculate the pressure of pit shaft.

Petrol-gas permeation fluid and Wellbore Flow coupling model build: the flowing of the petrol-gas permeation fluid of straight well and straight well wellbore fluids is considered as an interactional entirety, pressure simultaneously comprehensively between oil reservoir and pit shaft and discharge relation, pressure versus flow, in the continuity of boundary, sets up the coupling model of oil-gas reservoir and pit shaft.

The vector representation form that utilization provides above, by formula (23), the vector form that the pressure drop correlations of downhole well fluid can be expressed as:

${\stackrel{\&RightArrow;}{P}}_w=F\&lsqb;\stackrel{\&RightArrow;}{Q}\&rsqb;---\left(24\right)$

Notice that straight well pit shaft and reservoir are in same system, therefore, at same position place, the pressure drop of downhole well fluid equals the pressure drop of reservoir fluid, and the downhole well fluid flow at this place equals the integrated flow of downstream perforation inflow.Thus oil reservoir and pit shaft meet coupling condition, by formula (6) and formula (24), obtain coupling model

$\left\{\begin{array}{c}\stackrel{\&RightArrow;}{Q}=A^{-1}\stackrel{\&RightArrow;}{P}\\ \stackrel{\&RightArrow;}{P}=F\&lsqb;\stackrel{\&RightArrow;}{Q}\&rsqb;\end{array}\right.---\left(25\right)$

For the pit shaft having N number of perforation, coupling model is that the suitable of 2N equation formation including 2N unknown function determines mathematical problem, and generally, this coupling model is nonlinear, therefore, and need by numerical method to model solution.In order to solve this coupled problem, adopt following Iteration below

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

${\stackrel{\&RightArrow;}{P}}^{n+1}=F\&lsqb;{\stackrel{\&RightArrow;}{Q}}^{n+1}\&rsqb;---\left(26b\right)$

Given initial value p _d, i.e. the initial pressure on stratum.According to the iterative algorithm of coupling model, by Iteration (26a), bring pressure data into, the flow that both can calculate each eyelet place comes.Again by the eyelet flow that form (26a) is calculated, band entry format (26b), can calculate the pressure distribution of pit shaft.Repeat said process, until solving result meets the iteration termination condition set in advance.

Perforating parameter Optimized model builds: optimize straight well perforation tunnel distribution and relate to several factors, as the flow, hole depth, Kong Mi, aperture, mine shaft depth, perforating site, phase angle etc. of becoming a mandarin of boring a hole.If consider that all correlative factors are optimized analysis, be just difficult to the optimisation strategy of perforation hole straight well parameter.Consider the impact of above-mentioned factor, many optimisation strategy can be proposed.Total be exactly relatively effectively, directly the given perforated interval of scheme the degree of depth and perforation number, variable density perforation is carried out along straight well section, by changing the position of every section of perforation, the Kong Mi namely changing every section of perforated interval improves straight well production capacity and the uniform object of inflow profile influx to reach.

Based on flow through oil reservoir and the wellbore fluids Coupled with Flow model of the perforation straight well set up above, along well depth direction, directly there is correlation in the position of eyelet, pressure drop and the eyelet flow that becomes a mandarin, thus the position of preforation tunnel to have become a mandarin impact along the pressure drop of well depth and eyelet.Therefore, below main with total production capacity for object function, and above-mentioned factor is as bound variable, thus, following two basic Optimized models are proposed: (1) for object function, take hole position as bound variable with straight well production capacity, makes production capacity maximum; (2) with straight well production capacity for object function, become a mandarin evenly for constraints with hole position and section, Optimal Parameters, while suppressing water, gas coning, make production capacity reach maximum.

Optimized model I: generate well aggregated capacity maximum

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

Given downstream heel end pressure p _d(to limited fluid diversion well, heel end pressure p _dneed to specify), wherein total production capacity is all eyelets that enters in perforated interval.

If consider water, gas coning problem, then to control the inbound traffics of an eyelet, improve inflow profile, thus suppress water, gas coning, delay water, gas break through.Therefore, along well depth direction, require that eyelet inflow profile is even as much as possible, thus, obtain following Optimized model.

Optimized model II: maximum generation well total output (27), given downstream heel end pressure p _dand it is even as far as possible to make unit perforation become a mandarin.

Above-mentioned optimization problem is all using perforating site as bound variable, along pit shaft direction, if coordinate meets restrictive condition:

0≤x ₁≤…≤x _i≤…≤x _N≤L (28)

Preforation tunnel number N is usually larger, and in the generative process of reality, in order to reduce amount of calculation, the general method of segmentally numerical calculation that adopts reduces optimized variable number to arrive.By J-1 nodes X _j(j=1,2 ..., J-1) and perforated interval is divided into J section, every section comprises I perforation unit (N=I × J), and the Kong Mi namely in each segmentation limit interval is constant, but the Kong Mi of every segmentation 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，X ₀＝0，X _J＝L (29)

In each segmentation, I eyelet coordinate on that segment can be expressed as

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, then have X _j=x _j, be now be optimized all perforations, decision variable has N number of.If the eyelet number I > 1 in each segmentation, then perforation segmentation calculates and just can reduce Optimization Work amount, and decision variable has N number of J-1 that is reduced to individual.

If do not consider water, gas coning problem, Optimized model I correlation pore size distribution radial direction is optimized, and solves the distribution of best perforation, to obtain the maximum production capacity of perforation straight well.Because the minimum pressure drop of straight well downstream heel end is larger, water, gas coning may occur in straight well heel end mostly, if consider water, gas coning problem, the pore size distribution of Optimized model I correlation is optimized, solve the distribution of optimum perforation, to obtain minimum producing pressure differential, alleviate the water of downstream heel end, gas coning.

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, each perforation segmentation must meet inbound traffics equal, namely

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

Due to Q _jalso be unknown, formula (31) is for comprising the equation group of J-1 equation and J-1 unknown quantity.

(1) Optimized model of infinite fluid diversion well builds:

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

For Optimized model I, do not consider the impact of water, gas coning, the object function of production capacity optimization is

$\min f\left(X\right)=-\underset{i=1}{\overset{N}{\&Sigma;}}{\&lsqb;A^{-1}\left(X\right)P\&rsqb;}_i---\left(32\right)$

Namely using the summation of the inbound traffics of each preforation tunnel as total production capacity of perforation straight well, bound variable is included in object function, i.e. the location parameter of eyelet.Because infinite fluid diversion well does not consider wellbore pressure loss, therefore the pressure at each eyelet place is heel end pressure p _d.Meanwhile, 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, namely above condition forms this optimization constraints, thus Optimized model can be described as

$\min f\left(X\right)=-\underset{i=1}{\overset{N}{\&Sigma;}}{\&lsqb;A^{-1}\left(X\right)P\&rsqb;}_i$

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

For optimization problem II, in order to suppress water, gas coning, slow down water, gas break through, the inbound traffics on each perforation unit will be made equal as far as possible, namely, on model (10) basis, additional constraint condition (31), obtaining corresponding production capacity Optimized model is

$\begin{array}{cc}\min & f\left(X\right)=-\underset{i=1}{\overset{N}{\&Sigma;}}{\&lsqb;A^{-1}\left(X\right)P\&rsqb;}_i\end{array}$

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

Production capacity Optimized model (33)-(34) more than set up are nonlinear optimal problem, and the position of perforated interval is bound variable, includes J-1 bound variable in each model, and optimization problem can be undertaken by the method for numerical computations.By solving-optimizing problem, the hole position distribution situation of perforated interval during optimum production capacity both can be obtained.Infinite fluid diversion well does not relate to the impact of pressure drop, and therefore, given pit shaft heel end pressure, both obtains best hole position and perforation by Optimized model and to become a mandarin flow, can be used for analyzing flow to the impact of best Kong Mi, to improve straight well production capacity.

(2) Optimized model of limited fluid diversion well builds:

If the pressure drop of straight well pit shaft can not be ignored, then will calculate wellbore pressure loss at each perforation unit, now, along the direction of well depth, the pressure of pit shaft no longer remains unchanged, but changes with well depth, i.e. pi=p _wi, now, straight well is limited fluid diversion well.

For Optimized model I, do not consider water, gas coning problem, affix is to the constraints of wellbore pressure, and obtaining production capacity Optimized model is

$\begin{array}{cc}\min & f\left(X\right)=-\underset{i=1}{\overset{N}{\&Sigma;}}{\&lsqb;A^{-1}\left(X\right)P\&rsqb;}_i\end{array}$

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

For Optimized model II, consider the impact of water, gas coning, need to make perforation unit meet uniform inflow section, additional constraint condition (31), the production capacity Optimized model therefore obtaining the uniform inflow section of limited fluid diversion well is

$\begin{array}{cc}\min & f\left(X\right)=-\underset{i=1}{\overset{N}{\&Sigma;}}{\&lsqb;A^{-1}\left(X\right)P\&rsqb;}_i\end{array}$

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

Production capacity Optimized model (35)-(36) more than set up are nonlinear optimal problem, the position of perforated interval is bound variable, J-1 bound variable is included in each model, the same with production capacity Optimized model (33)-(34), need to solve by the method for numerical computations.Limited fluid diversion well considers pressure drop considerations in pit shaft, in conjunction with the flow through oil reservoir set up above and Wellbore Flow coupling model, pressure when obtaining best hole position and perforation become a mandarin flow, can be used for analyzing pressure and flow to the impact of best 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 be divided into some sections from bottom dome, the length of every section depends on that perforation fluid flow, the borehole wall are thick, aperture, inside and outside pipeline fluid density with the geometric properties of pipeline.First this model calculates from a position of specifying: the bottom of pipeline.Based on above-mentioned discussion, the specific algorithm step that model calculates is as follows:

Step 1: given initial value p _dwith allowable error ε=10 ^-3.

Step 2: the angle of slope calculating each point place

${\mathrm{\&alpha;}}_i={\mathrm{\&alpha;}}_{i-1}+\frac{{\mathrm{\&alpha;}}_k-{\mathrm{\&alpha;}}_{k-1}}{{\mathrm{\&Delta;s}}_k}{\mathrm{\&Delta;s}}_i$

In formula, i represents the numbering of perforation waypoint, s _krepresent inclined angle alpha _kand α _k-1between measurement length, Δ s _irepresent the material calculation at angle of slope.

Step 3: calculate Reynolds number according to local flow

${\mathrm{Re}}_i=\frac{{\mathrm{\&rho;Dq}}_i}{2\mathrm{\&mu;}A}$

Step 4: the turbulent skn friction factor adopts Miller method

$f_i=0.25{\&lsqb;log(\frac{\mathrm{\&epsiv;}}{3.7D}+\frac{5.74}{{\mathrm{Re}}_i^{0.9}})\&rsqb;}^{-2}$

Step 5: using iterative formula (26a) and (26b) calculate perforated hole wellbore pressure and perforation injection stream flow successively.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 optimum perforation tunnel distribution of infinite fluid diversion well not having water, gas coning.Because (33) are nonlinear programming problems, SQP (SQP) is adopted to calculate.In order to simplify calculating, use g respectively _j(X)≤0, h _i(X)=0, (i, j=1,2 ..., J) and represent inequality constraints condition and equality constraint.Structure Lagrangian

$L(X,\mathrm{\&lambda;})=f\left(X\right)+\underset{i=1}{\overset{J}{\&Sigma;}}{\mathrm{\&lambda;}}_i{h}_i\left(X\right)+\underset{j=1}{\overset{J}{\&Sigma;}}{\mathrm{\&lambda;}}_{jg}\left(X\right)$

λ in formula _i, λ _jfor Lagrange multiplier.Because nonlinear problem (33) is equivalent to a series of quadratic programming subproblem on direction of search d, in kth time iteration, iteration point X _kthe subproblem met can be described as

$\begin{array}{cc}min& \frac{1}{2}{d}^T{H}_{k}d+{\&lsqb;\&dtri;f\left(X_k\right)\&rsqb;}^{T}d\end{array}$

$s.t.\left\{\begin{array}{cc}{\&lsqb;\&dtri;h_i\left(X_k\right)\&rsqb;}^{T}d+h_i\left(X_k\right)=0& (i=1,2,...,J)\\ {\&lsqb;\&dtri;g_j\left(X^k\right)\&rsqb;}^{T}d+g_i\left(X^k\right)\&le;0& (j=1,2,...,J)\end{array}\right.$

Iteration is

X _k+1＝X _k+γ _kd _k

Wherein step factor γ _kcarry out linear search by quadratic interpolattion to obtain, matrix B ^kthe BFGS correction formula after improving is adopted to 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＝θy _k+(1-θ)B _ks _k，θ∈[0，1]

Wherein θ can be obtained by following formula

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

With

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

Namely straight well perforation Optimal Distribution is can be regarded as to obtain according to above-mentioned algorithm.

Step 7: obtain the optimum perforation tunnel distribution of limited fluid diversion well not having water, gas coning by step 1-step 6 calculation optimization model (34).

Step 8: the optimum perforation tunnel distribution of infinite fluid diversion well obtaining water, gas coning by step 1-step 6 calculation optimization model (35).

Step 9: the optimum perforation tunnel distribution of limited fluid diversion well obtaining water, gas coning by step 1-step 6 calculation optimization model (33).

Embodiment:

For the YB-X gas well at HTHP of western part of China, utilize the production capacity Optimized model of above-mentioned foundation, analyze optimum perforation distribution and the parameter optimization of perforated hole.As described in above-mentioned model analysis and solution procedure, modeling process is from the bottom of perforated interval, and the continuous well section be divided into by pit shaft in turn carries out calculating until the top of perforated interval.Perforated interval is split into from bottom some perforation unit.In order to simplify calculating, perforated interval is divided into many perforation segmentations, the perforation unit that each perforation fragmented packets contains is not necessarily identical, then calculates according to above-mentioned calculation procedure.

Model parameter and survey data: in real case simulation about data such as oil pipe data, sleeve pipe data and well depth measurement, hole angle, azimuth and well vertical depths in Table 1-table 3.In addition, also need supplementary portion divided data, comprising: the perforation scope of straight well is 6600-7100m, and the pressure of downstream base portion is 39.8949MPa, and perforated hole relevant parameter is in table 4.

Table 1

Table 2

Table 3

Table 4

Numerical Analysis: a series of numerical result is obtained to the simulation of perforated hole, comprise pressure drop, the optimum perforation distribution of eyelet flow and perforated interval, for estimating the variation tendency of perforation straight well overall presure drop, first equally distributed 500 eyelets on the infinite fluid diversion perforated interval considering 500m, optimizing application model is simulated, change in pressure drop trend is as Fig. 4 (a), shown in 4 (b), result shows that the overall presure drop of even perforated hole comprises the gravitational pressure drop of 81.28%, the wall friction pressure drop of 15.25% and the fluid of 3.47% accelerate pressure drop, describe the important component part that gravitational pressure drop is straight well overall presure drop.Utilize production capacity coupling model, calculating infinite fluid diversion well capacity is 33617m ³/ d, limited fluid diversion well capacity is 31427m ³/ d.

Consider that a 500m comprises the infinite fluid diversion perforated interval of 500 eyelets, the best shot density of flow optimal case and uniform inflow perforating scheme and production capacity the results are shown in Figure shown in 5 (a), 5 (b), compare in figure with even perforated hole.The distribution of the Optimum Perforation under different situations is shown in Table 5.Best perforating scheme shows, the bottom of perforated interval and the perforation distribution comparatively dense at top are to reach optimum production capacity, and the perforation distribution of uniform inflow is on the contrary.The production capacity of flow optimal case is 34460m ³the production capacity of the more even perforation of/d adds 2.51%; The production capacity 34231m of uniform inflow perforating scheme ³the production capacity of the more even perforation of/d increases by 1.83%, shows that the impact of the constraint of uniform inflow on production capacity is little;

Fig. 6 (a), 6 (b) show the uniform inflow production capacity optimum results of 500m limited fluid diversion straight well, and Optimum Perforation distribution is in table 5.Found out by eyelet, the Kong Mi of bottom is almost the close twice of top-portion apertures.Optimal case shows, perforation at large the comparatively intensive of well section distribution that become a mandarin, compared to even perforation, Optimum Perforation production capacity 32258m ³/ d volume increase 2.64%.If consider, steam is bored into impact, and the production capacity of uniform inflow is 32056m ³/ d, increases by 2% than even perforation production capacity.

Table 5

The result of calculation of Optimized model I is as shown in Fig. 7 (a) He 7 (b).Because larger supply scope is arranged at the bottom of perforated interval and top, also larger through this inbound traffics from oil reservoirs.The medium position of perforated interval has the less extent of supply, therefore lower through this inbound traffics from oil reservoirs.Change of production change is less, and tends to distribute more perforation in the position that pressure is high.Therefore, in order to reach the best production capacity of Optimized model I, eyelet distributes more intensive bottom perforated interval.Due in the wellbore without pressure drop, flow and the shot density of infinite fluid diversion well are symmetrical.Be stressed the impact of falling, and limited fluid diversion well capacity is from the trend that tapers off to top bottom perforated interval, and meanwhile, shot density is also successively decreased along perforated interval.Greatly about the position of distance bottom 4H/5, shot density reaches its minimum value, and increases gradually at top.

Fig. 7 (a) and Fig. 7 (b) shows, for reaching maximum output, needs the perforation of Gao Kongmi to distribute in maximum pressure drop place.If overcome aqueous vapor cone well problem, perforation become a mandarin should evenly.Under uniform inflow condition, shot density should reduce in the position that height becomes a mandarin, similar, and shot density should increase in the position become a mandarin.

For solving of Optimized model II, its result is as shown in Fig. 8 (a), 8 (b); Under uniform inflow condition, infinite fluid diversion well is comparatively large at the Kong Mi of medium position, and due to pressure drop impact, limited fluid diversion well has higher bottom pressure drop and larger inbound traffics than infinite fluid diversion well.

Claims (8)

1. HTHP oil gas straight well single-phase flow perforation completion parameter optimization method, is characterized 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, perforation optimization model to be solved.

2. HTHP oil gas straight well single-phase flow perforation completion parameter optimization method as claimed in claim 1, it is characterized in that, in steps A, described structure Wellbore Flow Pressure Drop Model specifically comprises:

If the even perforated interval in straight well pit shaft is split into N number of isometric perforation unit, only comprises a preforation tunnel in each unit, represent the length of pit shaft unit with Δ x, p ₁, U ₁, A ₁end pressure, speed and cross-sectional area on representative unit respectively, p ₂, U ₂, A ₂end pressure, speed and cross-sectional area under representative unit respectively;

Control in the axial direction to apply the law of conservation of momentum in volume elements, the summation of the external force namely controlled suffered by volume elements CV equals fluid momentum by controlling volume elements surface C S and the fluid momentum increment rate sum controlled in volume elements, can obtain the equation of momentum:

$\mathrm{\&Sigma;}\stackrel{\&RightArrow;}{F}=\frac{\&part;}{\&part;t}\&Integral;\&Integral;{\&Integral;}_{CV}\mathrm{\&rho;}\stackrel{\&RightArrow;}{u}dV+\&Integral;{\&Integral;}_{CS}\mathrm{\&rho;}\stackrel{\&RightArrow;}{u}(\stackrel{\&RightArrow;}{u}\&CenterDot;\stackrel{\&RightArrow;}{n})dA---\left(7\right)$

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

For stable state pit shaft stream

$\frac{\&part;}{\&part;t}\&Integral;\&Integral;{\&Integral;}_{CV}\mathrm{\&rho;}\stackrel{\&RightArrow;}{u}dV=0---\left(8\right)$

Two-dimensional flow problem along cross section is considered as One-Dimensional flows problem, and the mean flow rate getting cross section is U, utilizes mass-conservation equation, formula (7) is expanded into:

$\mathrm{\&Sigma;}\stackrel{\&RightArrow;}{F}=(p_{w1}A-p_{w2}A)-{\mathrm{\&tau;}}_w\left(\mathrm{\&pi;}D\mathrm{\&Delta;}x\right)-\mathrm{\&rho;}gA\mathrm{\&Delta;}xcos\mathrm{\&theta;}---\left(9\right)$

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

$\mathrm{\&Sigma;}\stackrel{\&RightArrow;}{F}={\stackrel{\&CenterDot;}{m}}_2{U}_2-{\stackrel{\&CenterDot;}{m}}_1{U}_1---\left(10\right)$

Mass flow in formula

$\stackrel{\&CenterDot;}{m}=\mathrm{\&rho;}AU---\left(11\right)$

On the right of formula (9) equal sign, Section 1 represents the net pressure acting on and control in volume elements; Section 2 represents the shear stress acting on well casing wall:

τ _π(πDΔx)＝Δp _wallA (12)

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

Δp _g=ρgΔx cosθ (13)

Convolution (9)-(13) can obtain

$p_{w2}-p_{w1}=\mathrm{\&rho;}(U_2^2-U_1^2)+{\mathrm{\&Delta;p}}_{wall}+{\mathrm{\&Delta;p}}_g---\left(14\right)$

On the right of formula (14) equal sign, Section 1 represents clean momentum, due to more fluid by perforation enter pipeline cause axial flow velocity change and cause, this pressure drop is due to acceleration effect Δ p _accproduce, can be described as:

${\mathrm{\&Delta;p}}_{acc}=\mathrm{\&rho;}(U_2^2-U_1^2)---\left(15\right)$

The overall presure drop of perforation downhole well fluid comprises friction pressure drop Δ p _wall, accelerate pressure drop Δ p _accwith gravitational pressure drop Δ p _g

Δp _w＝Δp _wall+Δp _acc+Δp _g(16)

The pressure drop caused by wall friction in perforation unit depends on perforation mean flow rate U ₂, available Darcy-Weisbach equation calculates:

${\mathrm{\&Delta;p}}_{wall}=\frac{f\mathrm{\&rho;}}{2D}{\mathrm{\&Delta;xU}}_2^2---\left(17\right)$

Along the direction of perforation depth, be p in the pressure representative at perforation unit i place _wi, then according to formula (16), the calculation of pressure relational expression of pit shaft shaft position corresponding to preforation tunnel can be obtained

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

P in formula _dfor position x ₁the downstream heel end pressure at place, Δ p _{wall, i}, Δ p _{acc, i}, Δ p _{g, i}represent the pressure drop in the corresponding pit shaft axial positions of perforation i of wall friction pressure drop, acceleration pressure drop and gravitational pressure drop respectively;

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

${\mathrm{\&Delta;p}}_{wall,i}=\frac{{\mathrm{\&rho;f}}_i}{2D}\frac{q_i^2}{A^2}|x_{i+1}-x_i|---\left(19\right)$

Mean flow rate U in formula _iavailable expression calculate, the integrated flow at this place is

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

Accelerate pressure drop by more fluid by perforation enter pipeline cause axial flow velocity change and cause, depend on fluid density and mean flow rate;

${\mathrm{\&Delta;p}}_{acc,i}=\mathrm{\&rho;}(U_{i+1}^2-U_i^2)---\left(21\right)$

Gravitational pressure drop has the gravity of fluid to produce, and can be expressed as

Δp _g，i＝ρg cosα _i|x _i+1-x _i| (22)

α in formula _irepresent the angle of slope of perforation unit i;

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

$\{\begin{array}{c}{p}_{w1}=p_d\\ p_{wi+1}=p_{wi}|+\frac{{\mathrm{\&rho;f}}_i}{2D}\frac{q_i^2}{A^2}|x_{i+1}-x_i|+\mathrm{\&rho;}(U_{i+1}^2-U_i^2)+{\mathrm{\&rho;gcos\&alpha;}}_i|x_{i+1}-x_i|\end{array}---\left(23\right).$

3. HTHP oil gas straight well single-phase flow perforation completion parameter optimization method as claimed in claim 2, it is characterized in that, in step B, the flowing of the petrol-gas permeation fluid of straight well and straight well wellbore fluids is considered as an interactional entirety, pressure simultaneously comprehensively between oil reservoir and pit shaft and discharge relation, pressure versus flow is in the continuity of boundary, and set up the coupling model of oil-gas reservoir and pit shaft, concrete grammar comprises:

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

${\stackrel{\&RightArrow;}{P}}_w=F\&lsqb;\stackrel{\&RightArrow;}{Q}\&rsqb;---\left(24\right)$

Coupling model is obtained based on the vector expression of petrol-gas permeation fluid model and the vector expression of Wellbore Flow Pressure Drop Model:

$\left\{\begin{array}{c}\stackrel{\&RightArrow;}{Q}=A^{-1}\stackrel{\&RightArrow;}{P}\\ \stackrel{\&RightArrow;}{P}=F\&lsqb;\stackrel{\&RightArrow;}{Q}\&rsqb;\end{array}\right.---\left(25\right).$

4. HTHP oil gas straight well single-phase flow perforation completion parameter optimization method as claimed in claim 3, is characterized in that, in step B, the coupling model also comprised obtaining solves, and method is as follows:

For the pit shaft having N number of perforation, coupling model is that the suitable of 2N equation formation including 2N unknown function determines mathematical problem, for this nonlinear coupling model, adopts following iterative formula to solve:

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

${\stackrel{\&RightArrow;}{P}}^{n+1}=F\&lsqb;{\stackrel{\&RightArrow;}{Q}}^{n+1}\&rsqb;---\left(26b\right)$

Given initial value p _d, according to the iterative algorithm of coupling model, by iterative formula (26a), bring pressure data into, the flow at each eyelet place can be calculated, then by eyelet flow that formula (26a) is calculated, band entry format (26b), can calculate the pressure distribution of pit shaft; Repeat said process, until solving result meets the iteration termination condition set in advance.

5. HTHP oil gas straight well single-phase flow perforation completion parameter optimization method as claimed in claim 4, it is characterized in that, in step C, when building perforating parameter Optimized model, if do not consider water, gas coning problem, then with straight well production capacity for object function, be bound variable with hole position, make production capacity maximum; If consider water, gas coning problem, then with straight well production capacity for object function, become a mandarin evenly for constraints with hole position and section, while suppression water, gas coning, make production capacity reach maximum;

Wherein, described straight well production capacity is all influx summations entering eyelet in perforated interval:

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

Along pit shaft direction, if coordinate meets restrictive condition:

0≤x ₁≤…≤x _i≤…≤x _N≤L (28)

By J-1 nodes X _j(j=1,2 ..., J-1) and perforated interval is divided into J section, every section comprises I perforation unit (N=I × J), and the Kong Mi namely in each segmentation limit interval is constant, but the Kong Mi of every segmentation is not necessarily identical; The N number of piecewise interval of straight well section is

[X _j，X _j+1]，＝0，1，…，J-1，X ₀＝0，X _J＝L (29)

In each segmentation, I eyelet coordinate on that segment can be expressed as:

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, each perforation segmentation must meet inbound traffics equal, namely

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

6. HTHP oil gas straight well single-phase flow perforation completion parameter optimization method as claimed in claim 5, it is characterized in that, in step C, described structure perforating parameter Optimized model comprises the following steps:

C1. the Optimized model of infinite fluid diversion well builds:

If C11. do not consider the impact of water, gas coning, the object function of production capacity optimization is

$\min f\left(X\right)=-\underset{i=1}{\overset{N}{\&Sigma;}}{\&lsqb;A^{-1}\left(X\right)P\&rsqb;}_i---\left(32\right)$

Namely using the summation of the inbound traffics of each preforation tunnel as total production capacity of perforation straight well, bound variable is included in object function, i.e. the location parameter of eyelet; Because infinite fluid diversion well does not consider wellbore pressure loss, therefore the pressure at each eyelet place is heel end pressure p _d;

Meanwhile, 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, namely above condition forms this optimization constraints, can obtain the Optimized model of infinite fluid diversion well not considering water, when gas coning affects:

$\min f\left(X\right)=-\underset{i=1}{\overset{N}{\&Sigma;}}{\&lsqb;A^{-1}\left(X\right)P\&rsqb;}_i$

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

If C22. consider the impact of water, gas coning, need to make the inbound traffics on each perforation unit equal as far as possible, namely, on model (32) basis, additional constraint condition (31), can obtain the Optimized model of infinite fluid diversion well when considering water, the affecting of gas coning:

$\min f\left(X\right)=-\underset{i=1}{\overset{N}{\&Sigma;}}{\&lsqb;A^{-1}\left(X\right)P\&rsqb;}_i$

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

C2. the Optimized model of limited fluid diversion well builds:

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:

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

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

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

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

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

7. HTHP oil gas straight well single-phase flow perforation completion parameter optimization method as claimed in claim 6, is characterized in that, in step D, solve, specifically comprise perforation optimization model:

D1. given initial value p _dwith allowable error ε=10 ^-3;

D2. the angle of slope at each point place is calculated

${\mathrm{\&alpha;}}_i={\mathrm{\&alpha;}}_{i-1}+\frac{{\mathrm{\&alpha;}}_k-{\mathrm{\&alpha;}}_{k-1}}{{\mathrm{\&Delta;s}}_k}{\mathrm{\&Delta;s}}_i$

In formula, i represents the numbering of perforation waypoint, s _krepresent inclined angle alpha _kand α _k-1between measurement length, Δ s _irepresent the material calculation at angle of slope;

D3. Reynolds number is calculated according to local flow

${\mathrm{Re}}_i=\frac{{\mathrm{\&rho;Dq}}_i}{2\mathrm{\&mu;}A};$

D4. the turbulent skn friction factor is calculated:

$f_i=0.25{\&lsqb;\log (\frac{\mathrm{\&epsiv;}}{3.7D}+\frac{5.74}{{\mathrm{Re}}_i^{0.9}})\&rsqb;}^{-2};$

D5. iterative formula (26a) and (26b) is adopted to calculate perforated hole wellbore pressure and perforation injection stream flow;

D6. the Optimized model built is solved, obtain straight well perforation Optimal Distribution.

8. HTHP oil gas straight well single-phase flow perforation completion parameter optimization method as claimed in claim 7, is characterized in that, in step D6, describedly to the method that the Optimized model built solves is: adopt SQP to calculate, use g respectively _j(X)≤0, h _i(X)=0, (i, j=1,2 ..., J) and represent inequality constraints condition and equality constraint; Structure Lagrangian:

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

λ in formula _i, λ _jfor Lagrange multiplier; A series of quadratic programming subproblem is equivalent on direction of search d for nonlinear Optimized model, in kth time iteration, iteration point X _kthe subproblem met is:

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

$s.t.\left\{\begin{array}{cc}{\&lsqb;\&dtri;h_i\left(X_k\right)\&rsqb;}^{T}d+h_i\left(X_k\right)=0& (i=1.2,\mathrm{...},J)\\ {\&lsqb;\&dtri;g_j\left(X^k\right)\&rsqb;}^{T}d+g_j\left(X^k\right)\&le;0& (j=1,2,\mathrm{...},J)\end{array}\right.$

Iteration is

X _k+1＝X _k+γ _kd _k

Wherein step factor γ _kcarry out linear search by quadratic interpolattion to obtain, matrix B ^kthe BFGS correction formula after improving is adopted to calculate

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

Iteration point in formula

s ^k＝X ^k+1-X ^k

With

z _k＝θy _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

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

Adopt this algorithm to solve Optimized model (33), obtain not considering water, the optimum perforation tunnel distribution of the infinite fluid diversion well of gas coning when affecting:

Adopt this algorithm to solve Optimized model (34), obtain the optimum perforation tunnel distribution of the infinite fluid diversion well when consideration water, gas coning affect:

Adopt this algorithm to solve Optimized model (35), obtain not considering water, the optimum perforation tunnel distribution of the limited fluid diversion well of gas coning when affecting:

Adopt this algorithm to solve Optimized model (36), obtain the optimum perforation tunnel distribution of the limited fluid diversion well when consideration water, gas coning affect.