CN105160056A - High-temperature high-pressure oil-gas vertical well two-phase flow perforation completion parameter and capacity optimization method - Google Patents

Abstract

The invention belongs to the technical field of oil and gas reservoir development engineering management, and particularly discloses a high-temperature high-pressure oil-gas vertical well two-phase flow perforation completion parameter and capacity optimization method, which relates to construction of a high-temperature high-pressure oil-gas vertical well two-phase flow model, a reservoir filtration steady-state model and a wellbore two-phase flow model, liquid holdup analysis, two-phase flow capacity optimization, algorithm flow design and the like. The method comprises the following steps: A, constructing the reservoir filtration steady-state model; B, constructing the wellbore two-phase flow model; C, analyzing and calculating liquid holdup of a fluid; D, constructing a two-phase flow capacity optimization model; and E, solving the two-phase flow capacity optimization model. According to the method, optimal perforation distribution is accurately predicted and parameters are optimized, so that the design level of an oil-gas mining device can be greatly improved and oil-gas reservoir development is facilitated.

Description

High Temperature High Pressure oil gas straight well two-phase flow perforation completion parameter and production capacity optimization method

Technical field

The invention belongs to development of oil and gas reservoir administrative skill field, be specially a kind of High Temperature High Pressure oil gas straight well two-phase flow perforation completion parameter and production capacity optimization method, it relates to the structure of High Temperature High Pressure oil gas straight well Two-phase flow's separation, flow through oil reservoir steady-state model, pit shaft Two-phase flow's separation, liquid holdup is analyzed, the optimization of two-phase flow production capacity and algorithm flow design etc.

Background technology

Because liquids and gases have the feature of flowing, both are generally referred to as fluid.So-called two-phase flow or polyphasic flow, refer to the flowing that simultaneously there are two or more different phase materials, the mixed flow of the mixed flow of the mixed flow of such as gas and liquid, gas and solid, liquid and solid and oil gas water mixed flow.Polyphasic flow can be divided into two-phase flow and three-phase flow according to the number participating in each phase of flowing, wherein especially the most common with two-phase flow.In petroleum engineering, the key problem of oil gas well mining is exactly the research to fluid flowing law in pipeline.Oil/gas Well when entering the middle and later periods of exploitation, fluid mainly diphasic flow in most of Oil/gas Well pipeline, but also may flow for oil gas water three phase.

To the research of two-phase flow in pipeline, the various energy equation of main employing, analyze by experiment, obtain the semi-theoretical model of corresponding semiempirical, conventional model mainly contains shunting model, uniform flow model, drift-flux model etc.Shunting model wherein and uniform flow model formulation fairly simple, but do not reach production accuracy requirement in engineer applied, uniform flow model is only applicable to part flow pattern, and shunting model is applicable to flow in horizontal pipe and can not be used for straight well pipe stream.Comparatively speaking, drift-flux model considers the flow characteristics between two-phase flow, is easy to get its mathematical model, is the conventional disposal route of current two-phase flow problem.

Biphase gas and liquid flow mainly discusses gas and the flowing law of liquid two-phase medium under common flox condition, and in Oil-Gas Well Engineering, diphasic flow phenomenon often occurs.Two-phase medium is different from single-phase medium, there is phase interface, and in process fluid flow, two-phase medium, except the acting force between two-phase, also also exists acting force between medium and pipeline wall.Under continuous flow condition, the acting force between two-phase interface is in equilibrium state, but there is the exchange of energy; And in gas liquid two-phase flow, the flowing velocity of each phase is different, and this sliding phenomenon is called slippage.

Summary of the invention

Technical matters to be solved by this invention is: propose a kind of High Temperature High Pressure oil gas straight well two-phase flow perforation completion parameter and production capacity optimization method, make accurately predicting to perforating parameter, to improve Oil & Gas Productivity ratio.

The technical solution adopted for the present invention to solve the technical problems is: High Temperature High Pressure oil gas straight well two-phase flow perforation completion parameter and production capacity optimization method, comprise the following steps:

A, structure petrol-gas permeation fluid steady-state model;

B, structure pit shaft two phase flow model;

C, analytical calculation fluid liquid holdup;

D, structure two-phase flow production capacity Optimized model;

E, two-phase flow production capacity Optimized model to be solved.

Concrete, in steps A, the method for described structure petrol-gas permeation fluid steady-state model comprises:

Suppose perforation interval be long for lperf, radius be the cylinder of rperf, the perforated interval in whole straight well pit shaft comprises N number of perf, from bottom, the position of the i-th perforation be xi (i=1,2 ..., N); Flow q is entered by i-th perf _imithe pressure p produced _iican be described as

$p_{ii}=-\frac{\mathrm{\μ}}{4\mathrm{\π}k}\frac{q_{\mathrm{Im},i}}{r_{peq}}---\left(1\right)$

Q in formula (1) _imfor the mixed traffic in unit perf;

q _Im＝q _IL+q _IG(2)

Q in formula (2) _iGand q _iLgas respectively in representation unit perf, liquid become a mandarin flow:

q _IG＝A _IV _ISL(3)

q _IL＝A _IV _ISG(4)

Wherein, A _irepresent the cross-sectional area of eyelet, V _iSLand V _iSGbe respectively superficial liquid velocity and the superficial gas velocity of perf inner fluid; Based on perforation and fracture area infringement epidermis s thereof _ppoint sink radius r of equal value _peqcan be described as:

$r_{peq}={\{-\frac{2}{l_{perf}}\[ln\left(\frac{r_{perf}}{l_{perf}}\right)-s_p\]\}}^{-1}---\left(5\right)$

If the spacing between perforation is fully large, then the point sink flow q at perf j place _{im, j}can produce pressure at eyelet i place, eyelet j can be described as the steady state pressure that eyelet j produces:

$p_{ij}=\frac{\mathrm{\μ}}{4\mathrm{\π}k}\frac{q_{\mathrm{Im},j}}{|x_i-x_j|}---\left(6\right)$

The pressure that what the general pressure at eyelet i place was eyelet i self become a mandarin produces and other perforations become a mandarin the pressure sum produced

$p_i=p_{ii}+\underset{j\≠i}{\mathrm{\Σ}}{p}_{ij}---\left(7\right)$

Bring formula (1) and formula (6) into formula (7), can obtain:

$p_i=-\frac{\mathrm{\μ}}{4\mathrm{\π}k}\frac{q_{\mathrm{Im},i}}{r_{peq}}+\underset{j\≠i}{\Σ}\frac{\mathrm{\μ}}{4\mathrm{\π}k}\frac{q_{\mathrm{Im},j}}{|x_i-x_j|}---\left(8\right)$

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

The pressure at N number of eyelet place and flow are expressed as N dimensional vector, can obtain:

p＝(p ₁，p ₂，…，p _N) ^T，q＝(q _Im，1，q _Im，2，…，q _Im，N) ^T(9)

Formula (9) is expressed as matrix form:

p＝Aq(10)

Coefficient matrices A is determined by perforating parameter and cloth hole site in formula (10), given perforation pressure distribution and perforation tunnel distribution, if the coefficient matrices A in formula (10) is reversible, then to become a mandarin flow by asking N × N rank inverse matrix to calculate perforation:

q＝A ^-1p(11)。

Concrete, the method building pit shaft two phase flow model described in step B comprises:

If downhole well fluid is gas-liquid two-phase fluid, the total pressure drop of the long perforated interval of Δ x can be obtained:

Δp _w＝Δp _f+Δp _g+Δp _aW+Δp _aE(12)

Equal sign right-hand member Section 1 Δ p in formula (12) _frepresent the pressure drop caused by wall friction:

${\mathrm{\Δp}}_f=-\frac{{\mathrm{\τ}}_{w}S}{A}\mathrm{\Δ}x---\left(13\right)$

Wall friction shear stress τ _wbe defined as:

${\mathrm{\τ}}_w=\frac{1}{2}{f}_{tp}{\mathrm{\ρ}}_{tp}{V}_{tp}^2---\left(14\right)$

Wherein f _tprepresent two-phase flow Fanning friction factor, V _tprepresent the true average velocity of the two-phase flow fluid in pit shaft; The total mass flow rate M of two-phase flow _tpbe defined as in the unit interval gross mass of the gas-liquid mixed stream flowing through arbitrary xsect, according to mass balance, can obtain

M _tp＝AV _tpρ _tp(15)

Or be expressed as M _tp=M _l+ M _g=AV _sLρ _l+ AV _sGρ _g(16)

Wherein M _land M _grepresent liquid phase stream and vapor phase stream flow respectively, ρ _land ρ _grepresent liquid phase stream and gas phase current density respectively; According to the equation of gas state

${\mathrm{\ρ}}_G=\frac{pM}{Z_{g}RT}---\left(17\right)$

Combined type (15) and (16), can obtain

$V_{tp}=\frac{{\mathrm{\ρ}}_L}{{\mathrm{\ρ}}_{tp}}{V}_{SL}+\frac{{\mathrm{\ρ}}_G}{{\mathrm{\ρ}}_{tp}}{V}_{SG}---\left(18\right)$

In homogeneous phase model, two-phase flow density p _tpbe defined as gas, liquid fluid density with liquid holdup H _lfor the weighted mean of weight,

ρ _tp＝ρ _LH _L+ρ _G(1-H _L)(19)

In gas liquid two-phase flow process, the flow section area A of liquid phase _laccount for the ratio of total area of passage A, be liquid holdup:

$H_L=\frac{A_L}{A}=\frac{A_L}{A_L+A_G}---\left(20\right)$

A in formula _grepresent the flow section area of gas phase;

Void fraction is defined as $H_G=\frac{A_G}{A}=1-A_L---\left(21\right)$

The Section 2 Δ p of formula (12) equal sign right-hand member _gpressure drop for fluid gravity causes:

Δp _g＝-gp _tpΔxcosα(22)

The Section 3 of formula (12) equal sign right-hand member is the acceleration pressure drop of flowing and causing that becomes a mandarin, and according to quality and momentum balance, accelerates pressure drop and can be described as:

$\left\{\begin{array}{c}{\mathrm{\Δp}}_{aW1}=-\frac{1}{A}{\mathrm{\ρ}}_{tp}\mathrm{\Δ}x(V_m{Q}_{Itp}+V_{tp}{Q}_{\mathrm{Im}})\\ {\mathrm{\Δp}}_{aW2}=-\frac{2}{A}{\mathrm{\ρ}}_{tp}{\mathrm{\ΔxV}}_{tp}{Q}_{Itp}\end{array}\right.---\left(23\right)$

V in formula _mrepresent two-phase mixtures fluid speed, Q _itptwo-phase integrated flux in representation unit pit shaft length and Q _immixing integrated flux in representation unit pit shaft;

$Q_{Itp}=\frac{{\mathrm{\ρ}}_L}{{\mathrm{\ρ}}_{tp}}{Q}_{IL}+\frac{{\mathrm{\ρ}}_G}{{\mathrm{\ρ}}_{tp}}{Q}_{IG}---\left(24\right)$

Q _Im＝Q _IL+Q _IG≠Q _Itp(25)

V _m＝V _SL+V _SG(26)

Wherein Q _iGand Q _iLbe respectively the liquid and gas accumulation inbound traffics in unit pit shaft; By analyses and prediction value and experimental data,

Δ p _aW1with Δ p _aW2weighted mean can obtain accelerating the optimum prediction of pressure drop

Δp _aW＝ωΔp _aW1+(1-ω)Δp _aW2(27)

Bring formula (23) into, can obtain

${\mathrm{\Δp}}_{aW}=-\frac{{\mathrm{\ρ}}_{tp}\mathrm{\Δ}z}{A}\[\mathrm{\ω}(V_m{Q}_{Itp}+U_{tp}{V}_{\mathrm{Im}})+2(1-\mathrm{\ω})V_{tp}{Q}_{Itp}\]---\left(28\right)$

Best weight coefficient is ω=0.8;

Last expression of formula (12) equal sign right-hand member becomes a mandarin the acceleration pressure drop that fluid expansion causes, and can be multiplied to obtain by total pressure drop with expansion coefficient:

${\mathrm{\Δp}}_{aE}=\frac{{\mathrm{\β}}_{aE}}{1-{\mathrm{\β}}_{aE}}\[{\mathrm{\Δp}}_f+{\mathrm{\Δp}}_g+{\mathrm{\Δp}}_{aW}\]---\left(29\right)$

β in formula _aEfor expansion coefficient, available following formula is estimated

${\mathrm{\β}}_{aE}=\frac{{\mathrm{\ρ}}_{tp}{V}_m{V}_{SG}}{p}---\left(30\right)$

Along perforation straight well, in the pressure p at i-th eyelet place _w,imeet following formula:

$\left\{\begin{array}{c}{p}_{w,1}=p_d\\ p_{w,i+1}=p_{w,i}+{\mathrm{\Δp}}_{f,i}+{\mathrm{\Δp}}_{g,i}+{\mathrm{\Δp}}_{aW,i}+{\mathrm{\Δp}}_{aE,i}\end{array}\right.---\left(31\right)$

Wherein p _dfor bottom, downstream starting position x ₁the pressure at place;

About discrete type (31), the discrete scheme of frictional pressure drop is

${\mathrm{\Δp}}_{f,i}=-\frac{{\mathrm{Sf}}_{tp}{\mathrm{\ρ}}_{tp}{V}_{tp}^2}{2A}|x_{i+1}-x_i|---\left(32\right)$

The discrete scheme accelerating pressure drop is

${\mathrm{\Δp}}_{aW,i}=-\frac{{\mathrm{\ρ}}_{tp}}{A}\[\mathrm{\ω}(V_{m,i}{Q}_{Itp,i}+U_{tp,i}{V}_{\mathrm{Im},i})+2(1-\mathrm{\ω})V_{tp,i}Q{Itp,i}_{}\]|x_{i+1}-x_i|---\left(33\right)$

For biphase gas and liquid flow, the gas phase in unit pit shaft, liquid phase accumulation inbound traffics are

$Q_{IG,i}=\underset{j=1}{\overset{i-1}{\Σ}}{q}_{IG,j}---\left(34\right)$

$Q_{IL,i}=\underset{j=1}{\overset{i-1}{\Σ}}{q}_{IL,j}---\left(35\right)$

The discrete scheme of heavy position pressure drop is

Δp _g＝-gρ _tp|x _i+1-x _i|cosα(36)

Wherein α _iit is the pitch angle of the i-th perforation;

The discrete scheme of formula (29) is

${\mathrm{\Δp}}_{aE,i}=\frac{{\mathrm{\β}}_{aE}}{1-{\mathrm{\β}}_{aE}}\[{\mathrm{\Δp}}_{f,i}+{\mathrm{\Δp}}_{g,i}+{\mathrm{\Δp}}_{aW,i}\]---\left(37\right)$

Association type (30)-(36), wellbore fluids pressure drop can be expressed as matrix form

p＝F[q](38)。

Concrete, the method for the fluid of analytical calculation described in step C liquid holdup comprises:

For the speed VG of gas phase, the experimental constitutive relation containing two-phase mixtures fluid speed Vm is adopted to describe:

V _G＝C ₀V _m+V _d(39)

C in formula ₀and V _dfor drift parameter, C ₀represent distributed constant in pipeline section, V _drepresent the average velocity relative to liquid phase, the ascending velocity of bubble:

$V_d=\frac{(1-C_0{H}_G)C_0{V}_c{K}_u}{C_0{H}_G\sqrt{{\mathrm{\ρ}}_G/{\mathrm{\ρ}}_L}+1-C_0{H}_G}---\left(40\right)$

V in formula (40) _crepresentation feature speed, characterizes bubble ascending velocity in a liquid

$V_c={\[\frac{{\mathrm{g\σ}}_{GL}({\mathrm{\ρ}}_L-{\mathrm{\ρ}}_G)}{{\mathrm{\ρ}}_L^2}\]}^{\frac{1}{4}}---\left(41\right)$

Wherein σ _gLfor showing tension force, parameter K between gas phase and liquid phase _ufor Kutateladze number:

$K_u={\[\frac{C_{ku}}{\sqrt{N_B}}(\sqrt{1+\frac{N_B}{C_{ku}^2{C}_w}}-1)\]}^{\frac{1}{2}}---\left(42\right)$

C in formula (42) _wfor friction factor, C _kufor constant, and N _bfor Bondnumber number

$N_B=\frac{g({\mathrm{\ρ}}_L-{\mathrm{\ρ}}_G)D^2}{{\mathrm{\σ}}_{GL}}---\left(43\right)$

According to formula (39), void fraction H _gwith liquid holdup H _lbe expressed as

$\left\{\begin{array}{c}{H}_G=\frac{V_{SG}}{C_0{V}_m+V_d}\\ H_L=1-H_G\end{array}\right.---\left(44\right).$

Concrete, the method building two-phase flow production capacity Optimized model described in step D comprises:

Petrol-gas permeation fluid and wellbore pressure loss coupling model is set up according to formula (8) and formula (31):

$\left\{\begin{array}{c}q=A^{-1}p\\ p=F\[q\]\end{array}\right.---\left(45\right)$

One is included to the straight well of N number of eyelet, above-mentioned coupling model is that the suitable of 2N equation formation including 2N unknown function determines mathematical problem, adopts following iterative formula to solve:

$\{\begin{array}{c}{q}^{n+1}=A^{-1}{p}^n\\ p^{n+1}=F\[q^{n+1}\]\end{array}---\left(46\right)$

Given initial value p _d, according to the iterative algorithm of coupling model, calculate each flow at eyelet place and the pressure distribution of pit shaft; Work as p _iand q _iincrement is less than given departure, above-mentioned iterative formula convergence;

When building production capacity Optimized model, using total production as objective function, maximize the aggregated capacity of gas well

$q=\underset{i=1}{\overset{N}{\Σ}}{q}_i---\left(47\right)$

The variable of optimization problem is perforating site, satisfies condition:

0≤x ₁≤…≤x _i≤…≤x _N≤H _p(48)

Adopt 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＝H _p(49)

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(50)

As the eyelet number I>1 in each segmentation, then segmentation calculates and just can reduce workload, and decision variable is reduced to J-1 by N number of;

According to the relational expression that becomes a mandarin (45) of optimization strategy (47) and perforation straight well, the objective function obtaining the optimization of perforation straight well production capacity is

$f\left(X\right)=-\underset{i=1}{\overset{N}{\Σ}}{\[A^{-1}\left(X\right)p\]}_i---\left(51\right)$

If consider water, gas coning problem, then require that inbound traffics are as far as possible equal in each perforation segmentation, to slow down the time burst of water, gas coning

$\underset{i=Ik+1}{\overset{I(k+1)}{\mathrm{\Σ}}}{q}_{\mathrm{Im},i}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{q}_{\mathrm{Im},i}(X_{k+1}-X_k)/H_p,k=0,1,...,J-1---\left(52\right)$

Due to q _imalso be unknown, formula (52) is for comprising the system of equations of J-1 equation and J-1 unknown quantity;

Consider infinite fluid diversion well, i.e. p _i=p _d, obtain the straight well capacity Optimized model of infinite fluid diversion perforation:

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

$s.t.\left\{\begin{array}{cc}{p}_i-p_d=0& (i=1,2,...,N)\\ X_1\≥0& \\ X_{j+1}-X_j\≥0& (j=1,2,...,J-1)\\ H_p-X_J\≥0& \end{array}\right.---\left(53\right)$

Consider limited fluid diversion well, the pressure drop of straight well pit shaft can not be ignored, i.e. p _i=p _wi, obtain the straight well capacity Optimized model of limited fluid diversion perforation:

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

$s.t.\left\{\begin{array}{cc}{p}_i-p_{wi}=0& (i=1,2,...,N)\\ X_1\≥0& \\ X_{j+1}-X_j\≥0& (j=1,2,...,J-1)\\ H_p-X_J\≥0& \end{array}\right.---\left(54\right).$

Concrete, in step e, described the method that two-phase flow production capacity Optimized model solves to be comprised:

1) given initial value p _dwith permissible error ε=10 ^-3;

2) pitch angle 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 pitch angle;

3) the Reynolds number Retp of two-phase fluid is calculated:

${\mathrm{Re}}_{tp}=\frac{{\mathrm{\ρ}}_{tp}{\mathrm{DV}}_{tp}}{{\mathrm{\μ}}_{tp}}$

μ in formula _tp=μ _lh _l+ μ _g(1-H _l), wall thunder Lip river coefficients R _wcalculate with following formula

${\mathrm{Re}}_w=\frac{{\mathrm{\ρ}}_{Im}{\mathrm{DV}}_{\mathrm{Im}}}{{\mathrm{\μ}}_{\mathrm{Im}}}=\frac{q_{\mathrm{Im}}{\mathrm{\ρ}}_{\mathrm{Im}}}{{\mathrm{\π\μ}}_{\mathrm{Im}}}$

Wherein μ _im=μ _lf _iL+ μ _g(1-F _iL), ρ _im=ρ _lf _iL+ ρ _g(1-F _iL) and and F _iG=1 – C _iL;

4) two-phase pit shaft stream Fanning friction factor is calculated, for Axial Laminar:

$f_{tp}=f_0\[1+0.04304R_w^{0.6142}\]$

For axial turbulence:

$f_{tp}=\frac{16}{{\mathrm{Re}}_{tp}}\[1-0.0153R_w^{0.3978}\]$

Wherein without wall flow Fanning friction factor f ₀available Colebrook-White equation is estimated:

$f_0=0.25{\[log(\frac{\mathrm{\κ}}{3.7D}+\frac{1.255}{\sqrt{f_0}{\mathrm{Re}}_{tp}})\]}^{-2}$

5) using iterative formula (46) calculates the pressure of even cloth hole straight well and perforation and to become a mandarin distribution;

6) solving model (53) calculates the best perforation distribution of infinite fluid diversion well;

7) solving model (54) calculates the best perforation distribution of limited fluid diversion well.

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 High Temperature High Pressure oil gas straight well two-phase flow perforation completion parameter of the present invention and production capacity optimization method process flow diagram;

Fig. 2 is perf arrangement architecture figure;

Fig. 3 is pit shaft unit section figure;

Fig. 4 is pressure drop distribution figure;

Fig. 5 (a), 5 (b) are respectively the apparent velocity distribution plan changed with well depth for infinite fluid diversion well, limited fluid diversion well;

Fig. 6 (a), 6 (b) are respectively the current capacity contrast figure changed with well depth for infinite fluid diversion well, limited fluid diversion well;

Fig. 7 (a), 7 (b) are respectively the wellbore fluids flow velocity comparison diagram changed with well depth for infinite fluid diversion well, limited fluid diversion well;

Fig. 8 is the liquid holdup distribution plan with well depth change;

Fig. 9 (a), 9 (b) are respectively the shot density comparison diagram changed with well depth for infinite fluid diversion well, limited fluid diversion well.

Embodiment

The present invention is intended to propose a kind of High Temperature High Pressure oil gas straight well two-phase flow perforation completion parameter and production capacity optimization method, makes accurately predicting, to improve Oil & Gas Productivity ratio to perforating parameter.

As shown in Figure 1, the method comprises: 1. build petrol-gas permeation fluid steady-state model; 2. build pit shaft two phase flow model; 3. analytical calculation fluid liquid holdup; 4. build two-phase flow production capacity Optimized model; 5. pair two-phase flow production capacity Optimized model solves.

Below the embodiment of each step is illustrated:

Pressure drop in pit shaft be gas well design important parameter, for gas well parameter optimal design, stable yields volume increase and well testing be designed with significance.The pressure drop relationships of biphase gas and liquid flow in perforation straight well is below discussed.If be two-phase flow body in system, the fluid in pit shaft is one dimension constant temperature, stable-state flow, and oil reservoir homogeneous, does not have mass exchange between gas-liquid two-phase fluid.

(1) flow through oil reservoir steady-state model is set up:

Being regarded as by perforation interval long is l _perf, radius is r _perfcylinder.Perforated interval in whole straight well pit shaft comprises N number of perf, and the arrangement architecture of perforated well as shown in Figure 2.If formation damage is ignored, from bottom, the position of the i-th perforation is x _i(i=1,2 ..., N).For easy analysis, biphase gas and liquid flow is considered as pseudo-single-phase flow, works as ratio time very little, according to the mean pressure of even line source, enter flow q by i-th perf _imithe pressure p produced _iican be described as

$p_{ii}=-\frac{\mathrm{\μ}}{4\mathrm{\π}k}\frac{q_{\mathrm{Im},i}}{r_{peq}}---\left(1\right)$

Q in formula _imfor the mixed traffic in unit perf

q _Im＝q _IL+q _IG(2)

Q in formula _iGand q _iLgas-liquid respectively in representation unit perf becomes a mandarin flow, can be expressed as

q _IG＝A _IV _ISL(3)

q _IL＝A _IV _ISG(4)

Wherein, A _irepresent the cross-sectional area of eyelet, V _iSLand V _iSGbe respectively superficial liquid velocity and the superficial gas velocity of perf inner fluid.Because not considering pit shaft damage factor, based on perforation and fracture area infringement epidermis s thereof _ppoint sink radius r of equal value _peqcan be described as

$r_{peq}={\{-\frac{2}{l_{perf}}\[ln\left(\frac{r_{perf}}{l_{perf}}\right)-s_p\]\}}^{-1}---\left(5\right)$

If the spacing between perforation is fully large, then the point sink flow q at perf j place _{im, j}can produce pressure at eyelet i place, eyelet j can be described as the steady state pressure that eyelet j produces:

$p_{ij}=\frac{\mathrm{\μ}}{4\mathrm{\π}k}\frac{q_{\mathrm{Im},j}}{|x_i-x_j|}---\left(6\right)$

The pressure that what the general pressure at eyelet i place was eyelet i self become a mandarin produces and other perforations become a mandarin the pressure sum produced

$p_i=p_{ii}+\underset{j\≠i}{\mathrm{\Σ}}{p}_{ij}---\left(7\right)$

Bring formula (1) and formula (6) into formula (7), can obtain

$p_i=-\frac{\mathrm{\μ}}{4\mathrm{\π}k}\frac{q_{\mathrm{Im},i}}{r_{peq}}+\underset{j\≠i}{\Σ}\frac{\mathrm{\μ}}{4\mathrm{\π}k}\frac{q_{\mathrm{Im},i}}{|x_i-x_j|}---\left(8\right)$

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

The pressure at N number of eyelet place and flow are expressed as N dimensional vector

p＝(p ₁，p ₂，…，p _N) ^T，q＝(q _Im，1，q _Im，2，…，q _Im，N) ^T(9)

Then the matrix representation forms of formula (9) is

p＝Aq(10)

In formula, coefficient matrices A is determined by perforating parameter and cloth hole site, given perforation pressure distribution and perforation tunnel distribution, if the coefficient matrices A in formula (10) is reversible, then to become a mandarin flow by asking N × N rank inverse matrix to calculate perforation

q＝A ^-1p(11)

(2) pit shaft Two-phase flow's separation is set up:

For setting up the flow model of downhole well fluid, if downhole well fluid is gas-liquid two-phase fluid, the perforated interval choosing Δ x long is analyzed, and its cross-section structure as shown in Figure 3.The total pressure drop of perforated interval comprises following four parts: heavy position pressure drop Δ p _g, frictional pressure drop Δ p _fand the acceleration pressure drop Δ p that pit shaft becomes a mandarin and fluid expansion causes _aWwith Δ p _aE.

Δp _w＝Δp _f+Δp _g+Δp _aW+Δp _aE(12)

In the ordinary course of things, accelerate pressure drop very little compared with frictional pressure drop, heavy position pressure drop, often eyelet is ignored.Only when high heat load, accelerate pressure drop and just can increase to the degree comparable with frictional pressure drop.

Equal sign right-hand member Section 1 Δ p in formula (12) _frepresenting the pressure drop caused by wall friction, is of paramount importance in two-phase pressure drop

An ingredient, reflects between two-phase and interaction effect between two-phase mixtures fluid and borehole wall wall.In homogeneous flow movable model, two-phase flow is regarded as a kind of single-phase flow, and its physical parameter is amounted to by the corresponding parameter of gas-liquid two-phase and obtains.According to quality and momentum balance, can obtain:

${\mathrm{\Δp}}_f=-\frac{{\mathrm{\τ}}_{w}S}{A}\mathrm{\Δ}x---\left(13\right)$

Wall fricting shearing stress τ in formula _wbe defined as

${\mathrm{\τ}}_w=\frac{1}{2}{f}_{tp}{\mathrm{\ρ}}_{tp}{V}_{tp}^2---\left(14\right)$

Wherein f _tprepresent peaceful (Fanning) friction factor of two-phase flow model, V _tprepresent the true average velocity of the two-phase flow fluid in pit shaft.

The total mass flow rate M of two-phase flow _tpbe defined as in the unit interval gross mass of the gas-liquid mixed stream flowing through arbitrary xsect, can obtain according to mass balance:

M _tp＝AV _tpρ _tp(15)

Also can be expressed as

M _tp＝M _L+M _G＝AV _SLρ _L+AV _SGρ _G(16)

Wherein M _land M _grepresent liquid phase stream and gas phase current mass flow respectively, ρ _land ρ _grepresent liquid phase stream and gas phase current density respectively.According to the equation of gas state

${\mathrm{\ρ}}_G=\frac{pM}{Z_{g}RT}---\left(17\right)$

Combined type (15) and (16), can obtain

$V_{tp}=\frac{{\mathrm{\ρ}}_L}{{\mathrm{\ρ}}_{tp}}{V}_{SL}+\frac{{\mathrm{\ρ}}_G}{{\mathrm{\ρ}}_{tp}}{V}_{SG}---\left(18\right)$

In homogeneous phase model, two-phase flow density p _tpbe defined as gas, liquid fluid density with liquid holdup H _lfor the weighted mean of weight

ρ _tp＝ρ _LH _L+ρ _G(1-H _L)(19)

In gas liquid two-phase flow process, the flow section area A of liquid phase _laccount for the ratio of total area of passage A, be liquid holdup, be also called true liquid holdup or liquid holdup

$H_L=\frac{A_L}{A}=\frac{A_L}{A_L+A_G}---\left(20\right)$

A in formula _grepresent the flow section area of gas phase, because density of liquid phase changes with well depth, therefore liquid holdup is not

Be a constant, also change with well depth.Same, void fraction is defined as:

$H_G=\frac{A_G}{A}=1-A_L---\left(21\right)$

The Section 2 Δ p of formula (12) equal sign right-hand member _gfor the pressure drop that fluid gravity causes.

Δp _g＝-gp _tpΔxcosα(22)

For perpendicular hole, heavy position pressure drop accounts for sizable proportion in total pressure drop, and the actual density of two-phase fluid is larger than the average density of fluid phase-splitting stream very large, differing greatly of result of calculation.

The acceleration pressure drop of two-phase flow is made up of two parts usually; The acceleration pressure drop caused and the acceleration pressure drop caused along well depth change (such as heat, cool, changed the expansion or contraction that cause by pressure) by two-phase flow density is changed along well depth by circulation area A.The Section 3 of formula (12) equal sign right-hand member is the acceleration pressure drop of flowing and causing that becomes a mandarin, and according to quality and momentum balance, accelerates pressure drop and can be described as following two formulas.

$\left\{\begin{array}{c}{\mathrm{\Δp}}_{aW1}=-\frac{1}{A}{\mathrm{\ρ}}_{tp}\mathrm{\Δ}x(V_m{Q}_{Itp}+V_{tp}{Q}_{\mathrm{Im}})\\ {\mathrm{\Δp}}_{aW2}=-\frac{2}{A}{\mathrm{\ρ}}_{tp}{\mathrm{\ΔxV}}_{tp}{Q}_{Itp}\end{array}\right.---\left(23\right)$

V in formula _mrepresent two-phase mixtures fluid speed, Q _itptwo-phase integrated flux in representation unit pit shaft length and Q _immixing integrated flux in representation unit pit shaft

$Q_{Itp}=\frac{{\mathrm{\ρ}}_L}{{\mathrm{\ρ}}_{tp}}{Q}_{IL}+\frac{{\mathrm{\ρ}}_G}{{\mathrm{\ρ}}_{tp}}{Q}_{IG}---\left(24\right)$

Q _Im＝Q _IL+Q _IG≠Q _Itp(25)

V _m＝V _SL+V _SG(26)

Wherein Q _iGand Q _iLbe respectively the liquid and gas accumulation inbound traffics in unit pit shaft.By analyses and prediction value and experimental data, Δ p _aW1with Δ p _aW2weighted mean can obtain accelerating the optimum prediction of pressure drop

Δp _aW＝ωΔp _aW1+(1-ω)Δp _aW2(27)

Bring formula (23) into, can obtain

${\mathrm{\Δp}}_{aW}=-\frac{{\mathrm{\ρ}}_{tp}\mathrm{\Δ}z}{A}\[\mathrm{\ω}(V_m{Q}_{Itp}+U_{tp}{V}_{\mathrm{Im}})+2(1-\mathrm{\ω})V_{tp}{Q}_{Itp}\]---\left(28\right)$

Best weight coefficient is ω=0.8.

Last expression of formula (12) equal sign right-hand member becomes a mandarin the acceleration pressure drop that fluid expansion causes, and usually can be multiplied with expansion coefficient by total pressure drop obtains

${\mathrm{\Δp}}_{aE}=\frac{{\mathrm{\β}}_{aE}}{1-{\mathrm{\β}}_{aE}}\[{\mathrm{\Δp}}_f+{\mathrm{\Δp}}_g+{\mathrm{\Δp}}_{aW}\]---\left(29\right)$

β in formula _aEfor expansion coefficient, available following formula is estimated

${\mathrm{\β}}_{aE}=\frac{{\mathrm{\ρ}}_{tp}{V}_m{V}_{SG}}{p}---\left(30\right)$

Along perforation straight well, in the pressure p at i-th eyelet place _w,imeet following formula

$\left\{\begin{array}{c}{p}_{w,1}=p_d\\ p_{w,i+1}=p_{w,i}+{\mathrm{\Δp}}_{f,i}+{\mathrm{\Δp}}_{g,i}+{\mathrm{\Δp}}_{aW,i}+{\mathrm{\Δp}}_{aE,i}\end{array}\right.---\left(31\right)$

Wherein p _dfor bottom, downstream starting position x ₁the pressure at place.

About discrete type (31), the discrete scheme of frictional pressure drop is

${\mathrm{\Δp}}_{f,i}=-\frac{{\mathrm{Sf}}_{tp}{\mathrm{\ρ}}_{tp}{V}_{tp}^2}{2A}|x_{i+1}-x_i|---\left(32\right)$

The discrete scheme accelerating pressure drop is

${\mathrm{\Δp}}_{aW,i}=-\frac{{\mathrm{\ρ}}_{tp}}{A}\[\mathrm{\ω}(V_{m,i}{Q}_{Itp,i}+U_{tp,i}{V}_{\mathrm{Im},i})+2(1-\mathrm{\ω})V_{tp,i}Q{Itp,i}_{}\]|x_{i+1}-x_i|---\left(33\right)$

For biphase gas and liquid flow, the gas phase in unit pit shaft, liquid phase accumulation inbound traffics are

$Q_{IG,i}=\underset{j=1}{\overset{i-1}{\Σ}}{q}_{IG,j}---\left(34\right)$

$Q_{IL,i}=\underset{j=1}{\overset{i-1}{\Σ}}{q}_{IL,j}---\left(35\right)$

The discrete scheme of heavy position pressure drop is

Δp _g＝-gρ _tp|x _i+1-x _i|cosα(36)

Wherein α _iit is the pitch angle of the i-th perforation.

The discrete scheme of formula (29) is

${\mathrm{\Δp}}_{aE,i}=\frac{{\mathrm{\β}}_{aE}}{1-{\mathrm{\β}}_{aE}}\[{\mathrm{\Δp}}_{f,i}+{\mathrm{\Δp}}_{g,i}+{\mathrm{\Δp}}_{aW,i}\]---\left(37\right)$

Association type (30)-(36), wellbore fluids pressure drop can be expressed as matrix form

p＝F[q](38)

(3) liquid holdup analysis:

For two-phase flow, in pipeline, the quantity of monophasic fluid is not often in its ratio in total flow.At the biphase gas and liquid flow that upwards flows, the speed that gas phase flows than liquid phase is fast.Therefore, occur trapping phenomena, the original position volume of liquid phase will be greater than the volume of liquid phase inflow, and namely relative to gas phase, liquid phase is in the duct by " interception ".

In order to calculate the slippage in homogeneous model between liquids and gases phase, drift model flux is used for describing the Multiphase Flow in pit shaft.Drift model flux is that Zuber and Findlay proposed first in nineteen sixty-five.Its basic thought is that gas-liquid two-phase fluid-mixing is considered as monophasic fluid, and the drift between gas, liquid fluid is exactly due to velocity distribution heterogeneous between gas phase and liquid phase.The speed V of gas phase _g, available containing two-phase mixtures fluid speed V _mexperimental constitutive relation describe:

V _G＝C ₀V _m+V _d(39)

C in formula ₀and V _dfor drift parameter, C ₀represent distributed constant in pipeline section, when flow velocity increases, the more and more even and C of velocity profile ₀be tending towards unified.V _drepresent the average velocity relative to liquid phase, the ascending velocity of bubble, can be described as

$V_d=\frac{(1-C_0{H}_G)C_0{V}_c{K}_u}{C_0{H}_G\sqrt{{\mathrm{\ρ}}_G/{\mathrm{\ρ}}_L}+1-C_0{H}_G}---\left(40\right)$

V in formula _crepresentation feature speed, characterizes bubble ascending velocity in a liquid

$V_c={\[\frac{{\mathrm{g\σ}}_{GL}({\mathrm{\ρ}}_L-{\mathrm{\ρ}}_G)}{{\mathrm{\ρ}}_L^2}\]}^{\frac{1}{4}}---\left(41\right)$

Wherein σ _gLfor showing tension force, parameter K between gas phase and liquid phase _ufor Kutateladze number, following formula is had to represent

$K_u={\[\frac{C_{ku}}{\sqrt{N_B}}(\sqrt{1+\frac{N_B}{C_{ku}^2{C}_w}}-1)\]}^{\frac{1}{2}}---\left(42\right)$

C in formula _wfor friction factor, C _kufor constant, and N _bfor Bondnumber number

$N_B=\frac{g({\mathrm{\ρ}}_L-{\mathrm{\ρ}}_G)D^2}{{\mathrm{\σ}}_{GL}}---\left(43\right)$

According to formula (39), original position void fraction H _gwith liquid holdup H _lbe expressed as

$\left\{\begin{array}{c}{H}_G=\frac{V_{SG}}{C_0{V}_m+V_d}\\ H_L=1-H_G\end{array}\right.---\left(44\right)$

The structure of two-phase flow production capacity Optimized model: notice that straight well pit shaft and reservoir are included in identical pressure system, therefore, at same position 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 (8) and formula (31), obtain coupling model

$\left\{\begin{array}{c}q=A^{-1}p\\ p=F\[q\]\end{array}\right.---\left(45\right)$

One is included to the straight well of N number of eyelet, coupling model is that the suitable of 2N equation formation including 2N unknown function determines mathematical problem.Solve coupled problem, adopt following iterative formula:

$\{\begin{array}{c}{q}^{n+1}=A^{-1}{p}^n\\ p^{n+1}=F\[q^{n+1}\]\end{array}---\left(46\right)$

Given initial value p _d, pressure and the perforation flow of downhole well fluid can be gone out with step by step calculation with this Iteration.Work as p _iand q _iincrement is less than given departure, above-mentioned Iteration convergence.The optimization of perforation distribution relates to many factors, and such as become a mandarin flow, eyelet radius, pit shaft length, eyelet etc.Above factor herein using total production as objective function is as constraint condition.

Maximize the aggregated capacity of gas well

$q=\underset{i=1}{\overset{N}{\Σ}}{q}_i---\left(47\right)$

The variable of optimization problem is perforating site, satisfies condition:

0≤x ₁≤…≤x _i≤…≤x _N≤H _p(48)

In the generative process of reality, in order to reduce calculated amount, the general method of segmentally numerical calculation that adopts reduces optimized variable number to reach.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＝H _p(49)

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(50)

As the eyelet number I>1 in each segmentation, then segmentation calculates and just can reduce workload, and decision variable is reduced to J-1 by N number of.

According to the relational expression that becomes a mandarin (45) of optimization strategy (47) and perforation straight well, the objective function obtaining the optimization of perforation straight well production capacity is:

$f\left(X\right)=-\underset{i=1}{\overset{N}{\Σ}}{\[A^{-1}\left(X\right)p\]}_i---\left(51\right)$

If consider water, gas coning problem, then require that inbound traffics are as far as possible equal in each perforation segmentation, to slow down the time burst of water, gas coning

$\underset{i=Ik+1}{\overset{I(k+1)}{\mathrm{\Σ}}}{q}_{\mathrm{Im},i}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{q}_{\mathrm{Im},i}(X_{k+1}-X_k)/H_p,k=0,1,...,J-1---\left(52\right)$

Due to q _imalso be unknown, formula (52) is for comprising the system of equations of j-1 equation and j-1 unknown quantity.Consider infinite fluid diversion well, i.e. p _i=p _d, obtain perforating parameter optimization problem:

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

$s.t.\left\{\begin{array}{cc}{p}_i-p_d=0& (i=1,2,...,N)\\ X_1\≥0& \\ X_{j+1}-X_j\≥0& (j=1,2,...,J-1)\\ H_p-X_J\≥0& \end{array}\right.---\left(53\right)$

The straight well capacity Optimized model (53) of the infinite fluid diversion perforation more than set up is with the position of perforated interval for bound variable, and include j-1 bound variable in model, this optimization problem is nonlinear optimal problem, selects numerical optimisation algorithms to solve.Solving model, both can obtain the hole position distribution situation of perforation interval during optimum production capacity.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.

Consider limited fluid diversion well, the pressure drop of straight well pit shaft can not be ignored, i.e. p _i=p _wI, perforating parameter optimization problem is:

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

$s.t.\left\{\begin{array}{cc}{p}_i-p_{wi}=0& (i=1,2,...,N)\\ X_1\≥0& \\ X_{j+1}-X_j\≥0& (j=1,2,...,J-1)\\ H_p-X_J\≥0& \end{array}\right.---\left(54\right)$

Limited fluid diversion perforation straight well production capacity Optimized model (54) more than set up with the position of perforated interval for bound variable, j-1 bound variable is included in each model, model is nonlinear optimal problem, the same with production capacity Optimized model (53), select numerical optimisation algorithms to solve this optimization problem.Limited fluid diversion well considers pressure drop considerations in pit shaft, solves pressure when obtaining best hole position and perforation and to become a mandarin flow, can be used for analyzing pressure and flow to the impact of best Kong Mi, and improves straight well production capacity, improves inflow profile, flow-after-flow test.

Algorithm flow designs: based on above-mentioned discussion, and the specific algorithm step that model calculates is as follows:

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

Step 2: the pitch angle calculating each point place

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

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 pitch angle.

Step 3: the Reynolds number Retp calculating two-phase fluid:

${\mathrm{Re}}_{tp}=\frac{{\mathrm{\ρ}}_{tp}{\mathrm{DV}}_{tp}}{{\mathrm{\μ}}_{tp}}$

μ in formula _tp=μ _lh _l+ μ _g(1-H _l), wall thunder Lip river coefficients R _wcalculate with following formula:

${\mathrm{Re}}_w=\frac{{\mathrm{\ρ}}_{Im}{\mathrm{DV}}_{\mathrm{Im}}}{{\mathrm{\μ}}_{\mathrm{Im}}}=\frac{q_{\mathrm{Im}}{\mathrm{\ρ}}_{\mathrm{Im}}}{{\mathrm{\π\μ}}_{\mathrm{Im}}}$

Wherein μ Im=μ LFIL+ μ G (1-FIL), ρ Im=ρ LFIL+ ρ G (1-FIL) and and FIG=1 – CIL.

Step 4: calculate two-phase pit shaft stream Fanning friction factor, for Axial Laminar

$f_{tp}=f_0\[1+0.04304R_w^{0.6142}\]$

For axial turbulence:

$f_{tp}=\frac{16}{{\mathrm{Re}}_{tp}}\[1-0.0153R_w^{0.3978}\]$

Wherein without wall flow Fanning friction factor f ₀available Colebrook-White equation is estimated:

$f_0=0.25{\[log(\frac{\mathrm{\κ}}{3.7D}+\frac{1.255}{\sqrt{f_0}{\mathrm{Re}}_{tp}})\]}^{-2}$

Step 5: using iterative formula (46) calculates the pressure of even cloth hole straight well and perforation and to become a mandarin distribution.

Step 6: separate the best perforation distribution that Parametric optimization problem (53) calculates infinite fluid diversion well.

Step 7: separate the best perforation distribution that Parametric optimization problem (54) calculates limited fluid diversion well.

For the YB-X gas well at HTHP of western part of China, utilize the above Optimized model set up, analyze optimum perforation distribution and the parameter optimization of perforated well.As described in above-mentioned model analysis and solution procedure, perforated interval is split into from bottom some perforation unit.In order to simplify calculating, perforation 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 measurement data: in real case simulation about data such as oil pipe data, sleeve pipe data and well depth measurement, hole drift angle, position angle 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 well correlation parameter is in table 4.

Table 1

Table 2

Table 3

Table 4

Analog computation is analyzed: carry out numerical simulation to high-temperature high-pressure perforation well, obtain a series of numerical result, comprise pressure drop, each phase flow rate, the optimum perforation distribution of speed and perforation interval.In simulation, even shot density is taken as 5 holes/rice, and as shown in Figure 3, the become a mandarin superficial velocity of flow of perforation is shown in Fig. 4 in the pressure drop of simulation.Perforation well capacity optimum solution and uniform inflow optimization solution as shown in Fig. 5 (a), 5 (b), and compare with even cloth hole analog result.Analog result shows, and for even cloth hole, infinite fluid diversion well capacity is 34450m ³/ d and limited fluid diversion well capacity are 30070m ³/ d.

Fig. 6 (a) shows, the high density eyelet of infinite fluid diversion well is distributed in bottom and the tip position of perforated interval more.Optimum production capacity is 34661m ³/ d, increases by 3.19% than even cloth hole well capacity.And uniform inflow is little to the raising effect of production capacity, its production capacity 34431m ³/ d, reduces by 5.52% than even cloth hole well capacity.Limited fluid diversion well capacity optimize and uniform inflow optimum results as shown in Fig. 6 (b), result show perforation height become a mandarin well section distribution comparatively dense.Optimum production capacity is 30151m ³/ d, more even perforated well volume increase 2.69%.Uniform inflow constraint correlation pore size distribution be adverse effect, and namely more sparse at the height well Duan Bukong that becomes a mandarin, as far as possible even to ensure becoming a mandarin of pit shaft, its optimum production capacity is 29973m ³/ d, than the even perforated well underproduction 3.23%.Fig. 7 (a), 7 (b) show the flowing velocity of two-phase wellbore fluids, and the increase become a mandarin along with eyelet and accumulation perforation, the flow velocity of wellbore fluids increases with the well depth of straight well.Fig. 8 shows that the liquid holdup of two-phase flow changes with perforation depth, and its scope is between 0.6823 and 0.7114.

As shown in Figure 9, because oil reservoir improves larger supply scope, higher inbound traffics are arranged at the bottom of perforated interval and top, and the supply scope in the middle part of perforated interval is little, thus inbound traffics are less in optimum perforation distribution.For infinite fluid diversion well, the fluid in pit shaft has the impact of pressure drop, and its perforation becomes a mandarin and is symmetric, shot density also distribution symmetrically.Under the constraint of uniform inflow, the well section that the shot density of limited fluid diversion well becomes a mandarin at height reduces gradually, increases in the low well section become a mandarin; And infinitely become a mandarin at two ends and the low perforation cloth hole of well section of water conservancy diversion well is closeer.Due to the factor of pressure drop, limited fluid diversion well has higher bottom pressure drop and height to become a mandarin flow than infinite fluid diversion well tools.

Claims (6)

1. High Temperature High Pressure oil gas straight well two-phase flow perforation completion parameter and production capacity optimization method, is characterized in that, comprise the following steps:

A, structure petrol-gas permeation fluid steady-state model;

B, structure pit shaft two phase flow model;

C, analytical calculation fluid liquid holdup;

D, structure two-phase flow production capacity Optimized model;

E, two-phase flow production capacity Optimized model to be solved.

2. High Temperature High Pressure oil gas straight well two-phase flow perforation completion parameter as claimed in claim 1 and production capacity optimization method, it is characterized in that, in steps A, the method for described structure petrol-gas permeation fluid steady-state model comprises:

Suppose perforation interval be long for lperf, radius be the cylinder of rperf, the perforated interval in whole straight well pit shaft comprises N number of perf, from bottom, the position of the i-th perforation be xi (i=1,2 ..., N); Flow q is entered by i-th perf _imithe pressure p produced _iican be described as

$p_{ii}=-\frac{\mathrm{\μ}}{4\mathrm{\π}k}\frac{q_{\mathrm{Im},i}}{r_{peq}}---\left(1\right)$

Q in formula (1) _imfor the mixed traffic in unit perf;

q _Im＝q _IL+q _IG(2)

Q in formula (2) _iGand q _iLgas respectively in representation unit perf, liquid become a mandarin flow:

q _IG＝A _IV _ISL(3)

q _IL＝A _IV _ISG(4)

Wherein, A _irepresent the cross-sectional area of eyelet, V _iSLand V _iSGbe respectively superficial liquid velocity and the superficial gas velocity of perf inner fluid; Based on perforation and fracture area infringement epidermis s thereof _ppoint sink radius r of equal value _peqcan be described as:

$r_{peq}={\left\{-\frac{2}{l_{perf}}\[\ln \left(\frac{r_{perf}}{l_{perf}}\right)-s_p\]\right\}}^{-1}---\left(5\right)$

If the spacing between perforation is fully large, then the point sink flow q at perf j place _{im, j}can produce pressure at eyelet i place, eyelet j can be described as the steady state pressure that eyelet j produces:

$p_{ij}=\frac{\mathrm{\μ}}{4\mathrm{\π}k}\frac{q_{\mathrm{Im},j}}{\left|x_i-x_j\right|}---\left(6\right)$

The pressure that what the general pressure at eyelet i place was eyelet i self become a mandarin produces and other perforations become a mandarin the pressure sum produced

$p_i=p_{ii}+\underset{j\≠i}{\Σ}{p}_{ij}---\left(7\right)$

Bring formula (1) and formula (6) into formula (7), can obtain:

$p_i=-\frac{\mathrm{\μ}}{4\mathrm{\π}k}\frac{q_{\mathrm{Im},i}}{r_{peq}}+\underset{j\≠i}{\Σ}\frac{\mathrm{\μ}}{4\mathrm{\π}k}\frac{q_{\mathrm{Im},j}}{\left|x_i-x_j\right|}---\left(8\right)$

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

The pressure at N number of eyelet place and flow are expressed as N dimensional vector, can obtain:

p＝(p ₁，p ₂，...，p _N) ^T，q＝(q _Im，1，q _Im，2，...，q _Im，N) ^T(9)

Formula (9) is expressed as matrix form:

p＝Aq(10)

Coefficient matrices A is determined by perforating parameter and cloth hole site in formula (10), given perforation pressure distribution and perforation tunnel distribution, if the coefficient matrices A in formula (10) is reversible, then to become a mandarin flow by asking N × N rank inverse matrix to calculate perforation:

q＝A ^-1p(11)。

3. High Temperature High Pressure oil gas straight well two-phase flow perforation completion parameter as claimed in claim 2 and production capacity optimization method, it is characterized in that, the method building pit shaft two phase flow model described in step B comprises:

If downhole well fluid is gas-liquid two-phase fluid, the total pressure drop of the long perforated interval of Δ x can be obtained:

Δp _w＝Δp _f+Δp _g+Δp _aW+Δp _aE(12)

Equal sign right-hand member Section 1 Δ p in formula (12) _frepresent the pressure drop caused by wall friction:

${\mathrm{\Δp}}_f=-\frac{{\mathrm{\τ}}_{w}S}{A}\mathrm{\Δ}x---\left(13\right)$

Wall friction shear stress τ _wbe defined as:

${\mathrm{\τ}}_w=\frac{1}{2}{f}_{tp}{\mathrm{\ρ}}_{tp}{V}_{tp}^2---\left(14\right)$

Wherein f _tprepresent two-phase flow Fanning friction factor, V _tprepresent the true average velocity of the two-phase flow fluid in pit shaft; The total mass flow rate M of two-phase flow _tpbe defined as in the unit interval gross mass of the gas-liquid mixed stream flowing through arbitrary xsect, according to mass balance, can obtain

M _tp＝AV _tpρ _tp(15)

Or be expressed as

M _tp＝M _L+M _G＝AV _SLρL+AV _SGρG(16)

Wherein M _land M _grepresent liquid phase stream and gas phase current mass flow respectively, ρ _land ρ _grepresent liquid phase stream and gas phase current density respectively; According to the equation of gas state

${\mathrm{\ρ}}_G=\frac{pM}{Z_{g}RT}---\left(17\right)$

Combined type (15) and (16), can obtain

$V_{tp}=\frac{{\mathrm{\ρ}}_L}{{\mathrm{\ρ}}_{tp}}{V}_{SL}+\frac{{\mathrm{\ρ}}_G}{{\mathrm{\ρ}}_{tp}}{V}_{SG}---\left(18\right)$

In homogeneous phase model, two-phase flow density p _tpbe defined as gas, liquid fluid density with liquid holdup H _lfor the weighted mean of weight,

ρ _tp＝ρ _LH _L+ρ _G(1-H _L)(19)

In gas liquid two-phase flow process, the flow section area A of liquid phase _laccount for the ratio of total area of passage A, be liquid holdup:

$H_L=\frac{A_L}{A}=\frac{A_L}{A_L+A_G}---\left(20\right)$

A in formula _grepresent the flow section area of gas phase;

$H_G=\frac{A_G}{A}=1-A_L---\left(21\right)$

The Section 2 Δ p of formula (12) equal sign right-hand member _gpressure drop for fluid gravity causes:

Δp _g＝-gρ _tpΔxcosα(22)

The Section 3 of formula (12) equal sign right-hand member is the acceleration pressure drop of flowing and causing that becomes a mandarin, and according to quality and momentum balance, accelerates pressure drop and can be described as:

$\left\{\begin{array}{c}{\mathrm{\Δp}}_{aW1}=-\frac{1}{A}{\mathrm{\ρ}}_{tp}\mathrm{\Δ}x(V_m{Q}_{Itp}+V_{tp}{Q}_{\mathrm{Im}})\\ {\mathrm{\Δp}}_{aW2}=-\frac{2}{A}{\mathrm{\ρ}}_{tp}{\mathrm{\ΔxV}}_{tp}{Q}_{Itp}\end{array}\right.---\left(23\right)$

V in formula _mrepresent two-phase mixtures fluid speed, Q _itptwo-phase integrated flux in representation unit pit shaft length and Q _immixing integrated flux in representation unit pit shaft;

$Q_{Itp}=\frac{{\mathrm{\ρ}}_L}{{\mathrm{\ρ}}_{tp}}{Q}_{IL}+\frac{{\mathrm{\ρ}}_G}{{\mathrm{\ρ}}_{tp}}{Q}_{IG}---\left(24\right)$

Q _Im＝Q _IL+Q _IG≠Q _Itp(25)

V _m＝V _SL+V _SG(26)

Wherein Q _iGand Q _iLbe respectively the liquid and gas accumulation inbound traffics in unit pit shaft; By analyses and prediction value and experimental data, Δ p _aW1with Δ p _aW2weighted mean can obtain accelerating the optimum prediction of pressure drop

Δp _aW＝ωΔp _aW1+(1-ω)Δp _aW2(27)

Bring formula (23) into, can obtain

${\mathrm{\Δp}}_{a}w=\frac{{\mathrm{\ρ}}_{tp}\mathrm{\Δ}z}{A}\[\mathrm{\ω}(V_m{Q}_{Itp}+U_{tp}{V}_{\mathrm{Im}})+2(1-\mathrm{\ω})V_{tp}{Q}_{Itp}\]---\left(28\right)$

Best weight coefficient is ω=0.8;

Last expression of formula (12) equal sign right-hand member becomes a mandarin the acceleration pressure drop that fluid expansion causes, and can be multiplied to obtain by total pressure drop with expansion coefficient

${\mathrm{\Δp}}_{aE}=\frac{{\mathrm{\β}}_{aE}}{1-{\mathrm{\β}}_{aE}}\[{\mathrm{\Δp}}_f+{\mathrm{\Δp}}_g+{\mathrm{\Δp}}_{aW}\]---\left(29\right)$

β in formula _aEfor expansion coefficient, available following formula is estimated

${\mathrm{\β}}_{aE}=\frac{{\mathrm{\ρ}}_{tp}{V}_m{V}_{SG}}{p}---\left(30\right)$

Along perforation straight well, in the pressure p at i-th eyelet place _{w, i}meet following formula:

$\left\{\begin{array}{c}{p}_{w,1}=p_d\\ p_{w,i+1}=p_{w,i}+{\mathrm{\Δp}}_{f,i}+{\mathrm{\Δp}}_{g,i}+{\mathrm{\Δp}}_{aW,i}+{\mathrm{\Δp}}_{aE,i}\end{array}\right.---\left(31\right)$

Wherein p _dfor bottom, downstream starting position x ₁the pressure at place;

About discrete type (31), the discrete scheme of frictional pressure drop is

${\mathrm{\Δp}}_{f,i}=-\frac{{\mathrm{Sf}}_{tp}{\mathrm{\ρ}}_{tp}{V}_{tp}^2}{2A}\left|x_{i+1}-x_i\right|---\left(32\right)$

The discrete scheme accelerating pressure drop is

${\mathrm{\Δp}}_{aW,i}=-\frac{{\mathrm{\ρ}}_{tp}}{A}\[\mathrm{\ω}(V_{m,i}{Q}_{Itp,i}+U_{tp,i}{V}_{\mathrm{Im},i})+2(1-\mathrm{\ω})V_{tp,i}{Q}_{Itp,i}\]\left|x_{i+1}-x_i\right|---\left(33\right)$

For biphase gas and liquid flow, the gas phase in unit pit shaft, liquid phase accumulation inbound traffics are

$Q_{IG,i}=\underset{j=1}{\overset{i-1}{\Σ}}{q}_{IG,j}---\left(34\right)$

$Q_{IL,i}=\underset{j=1}{\overset{i-1}{\Σ}}{q}_{IL,j}---\left(35\right)$

The discrete scheme of heavy position pressure drop is

Δp _g＝-gρ _tp|x _i+1-x _i|cosα(36)

Wherein α _iit is the pitch angle of the i-th perforation;

The discrete scheme of formula (29) is

${\mathrm{\Δp}}_{aE,i}=\frac{{\mathrm{\β}}_{aE}}{1-{\mathrm{\β}}_{aE}}\[{\mathrm{\Δp}}_{f,i}+{\mathrm{\Δp}}_{g,i}+{\mathrm{\Δp}}_{aW,i}\]---\left(37\right)$

Association type (30)-(36), wellbore fluids pressure drop can be expressed as matrix form

p＝F[q](38)。

4. High Temperature High Pressure oil gas straight well two-phase flow perforation completion parameter as claimed in claim 3 and production capacity optimization method, it is characterized in that, the method for the fluid of analytical calculation described in step C liquid holdup comprises:

For the speed VG of gas phase, adopt containing two-phase mixtures fluid speed V _mexperimental constitutive relation describe:

V _G＝C ₀V _m+V _d(39)

C in formula ₀and V _dfor drift parameter, C ₀represent distributed constant in pipeline section, V _drepresent the average velocity relative to liquid phase, the ascending velocity of bubble:

$V_d=\frac{(1-C_0{H}_G)C_0{V}_c{K}_u}{C_0{H}_G\sqrt{{\mathrm{\ρ}}_G/{\mathrm{\ρ}}_L}+1-C_0{H}_G}---\left(40\right)$

V in formula (40) _crepresentation feature speed, characterizes bubble ascending velocity in a liquid

$V_c={\[\frac{{\mathrm{g\σ}}_{GL}({\mathrm{\ρ}}_L-{\mathrm{\ρ}}_G)}{{\mathrm{\ρ}}_L^2}\]}^{\frac{1}{4}}---\left(41\right)$

Wherein σ _gLfor showing tension force, parameter K between gas phase and liquid phase _ufor Kutateladze number:

$K_u={\[\frac{C_{ku}}{\sqrt{N_B}}(\sqrt{1+\frac{N_B}{C_{ku}^2{C}_w}}-1)\]}^{\frac{1}{2}}---\left(42\right)$

C in formula (42) _wfor friction factor, C _kufor constant, and N _bfor Bondnumber number

$N_B=\frac{g({\mathrm{\ρ}}_L-{\mathrm{\ρ}}_G)D^2}{{\mathrm{\σ}}_{GL}}---\left(43\right)$

According to formula (39), void fraction H _gwith liquid holdup H _lbe expressed as

$\left\{\begin{array}{c}{H}_G=\frac{V_{SG}}{C_0{V}_m+V_d}\\ H_L=1-H_G\end{array}\right.---\left(44\right).$

5. High Temperature High Pressure oil gas straight well two-phase flow perforation completion parameter as claimed in claim 4 and production capacity optimization method, it is characterized in that, the method building two-phase flow production capacity Optimized model described in step D comprises:

Petrol-gas permeation fluid and wellbore pressure loss coupling model is set up according to formula (8) and formula (31):

$\left\{\begin{array}{c}q=A^{-1}p\\ p=F\[q\]\end{array}\right.---\left(45\right)$

One is included to the straight well of N number of eyelet, above-mentioned coupling model is that the suitable of 2N equation formation including 2N unknown function determines mathematical problem, adopts following iterative formula to solve:

$\left\{\begin{array}{c}{q}^{n+1}=A^{-1}{p}^n\\ p^{n+1}=F\[q^{n+1}\]\end{array}\right.---\left(46\right)$

Given initial value according to the iterative algorithm of coupling model, calculate each flow at eyelet place and the pressure distribution of pit shaft; Work as p _iand q _iincrement is less than given departure, above-mentioned iterative formula convergence;

When building production capacity Optimized model, using total production as objective function, maximize the aggregated capacity of gas well

$q=\underset{i=1}{\overset{N}{\Σ}}{q}_i---\left(47\right)$

The variable of optimization problem is perforating site, satisfies condition:

0≤x ₁≤…≤x _i≤…≤x _N≤H _p(48)

Adopt 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＝H _p(49)

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(50)

As the eyelet number I>1 in each segmentation, then segmentation calculates and just can reduce workload, and decision variable is reduced to J-1 by N number of;

According to the relational expression that becomes a mandarin (45) of optimization strategy (47) and perforation straight well, the objective function obtaining the optimization of perforation straight well production capacity is

$f\left(X\right)=-\underset{i=1}{\overset{N}{\Σ}}{\[A^{-1}\left(X\right)p\]}_i---\left(51\right)$

If consider water, gas coning problem, then require that inbound traffics are as far as possible equal in each perforation segmentation, to slow down the time burst of water, gas coning

$\underset{i=Ik+1}{\overset{I(k+1)}{\Σ}}{q}_{Im,i}=\underset{i=1}{\overset{N}{\Σ}}{q}_{Im,i}(X_{k+1}-X_k)/H_p,k=0,1,\mathrm{...},J-1---\left(52\right)$

Due to q _imalso be unknown, formula (52) is for comprising the system of equations of J-1 equation and J-1 unknown quantity;

Consider infinite fluid diversion well, i.e. p _i=p _d, obtain the straight well capacity Optimized model of infinite fluid diversion perforation:

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

$s.t.\left\{\begin{array}{cc}{p}_i-p_d=0& (i=1,2,\mathrm{...},N)\\ X_1\≥0& \\ X_{j+1}-X_j\≥0& (j=1,2,\mathrm{...},J-1)\\ H_p-X_J\≥0& \end{array}\right.---\left(53\right)$

Consider limited fluid diversion well, the pressure drop of straight well pit shaft can not be ignored, i.e. p _i=p _wi, obtain the straight well capacity Optimized model of limited fluid diversion perforation:

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

$s.t.\left\{\begin{array}{cc}{p}_i-p_{wi}=0& (i=1,2,\mathrm{...},N)\\ X_1\≥0& \\ X_{j+1}-X_j\≥0& (j=1,2,\mathrm{...},J-1)\\ H_p-X_J\≥0& \end{array}\right.---\left(54\right).$

6. High Temperature High Pressure oil gas straight well two-phase flow perforation completion parameter as claimed in claim 5 and production capacity optimization method, is characterized in that, in step e, describedly to comprise the method that two-phase flow production capacity Optimized model solves:

1) given initial value with permissible error ε=10 ^-3;

2) pitch angle 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 pitch angle;

3) the Reynolds number Retp of two-phase fluid is calculated:

${\mathrm{Re}}_{tp}=\frac{{\mathrm{\ρ}}_{tp}{\mathrm{DV}}_{tp}}{{\mathrm{\μ}}_{tp}}$

μ in formula _tp=μ _lh _l+ μ _g(1-H _l), wall thunder Lip river coefficients R _wcalculate with following formula

${\mathrm{Re}}_w=\frac{{\mathrm{\ρ}}_{\mathrm{Im}}{\mathrm{DV}}_{\mathrm{Im}}}{{\mathrm{\μ}}_{\mathrm{Im}}}=\frac{q_{\mathrm{Im}}{\mathrm{\ρ}}_{\mathrm{Im}}}{{\mathrm{\π\μ}}_{\mathrm{Im}}}$

Wherein μ Im=μ LFIL+ μ G (1-FIL), ρ Im=ρ LFIL+ ρ G (1-FIL) and and FIG=1 – GIL;

4) two-phase pit shaft stream Fanning friction factor is calculated, for Axial Laminar:

$f_{tp}=f_0\[1+0.04304R_w^{0.6142}\]$

For axial turbulence:

$f_{tp}=\frac{16}{{\mathrm{Re}}_{tp}}\[1-0.0153R_w^{0.3978}\]$

Wherein without wall flow Fanning friction factor f ₀available Colebrook-White equation is estimated:

$f_0=0.25{\[log\left(\frac{\mathrm{\κ}}{3.7D}+\frac{1.255}{\sqrt{f_0}{\mathrm{Re}}_{tp}}\right)\]}^{-2}$

5) using iterative formula (46) calculates the pressure of even cloth hole straight well and perforation and to become a mandarin distribution;

6) solving model (53) calculates the best perforation distribution of infinite fluid diversion well;

7) solving model (54) calculates the best perforation distribution of limited fluid diversion well.