CN103590824B - Capacity calculation method for compact gas reservoir horizontal well after multi-section fracturing modification - Google Patents

Abstract

The invention discloses a capacity calculation method of a compact gas reservoir horizontal well after multi-section fracturing modification, which comprises the following steps: establishing a physical model; obtaining a dimensionless pressure P caused by any one of the n cracks_DA dimensionless crack flow q from the crack_D(α) a relation between; obtaining the pressure disturbance P generated by any one of the n fractures at the contact part with the well bore according to the flowing relation of the gas in the fractures and the boundary coupling relation between the fractures and the stratum_wfnQ of the flow of the crack under standard conditions_scnThe relational expression of (1); obtaining the pressure disturbance P generated by any one of the n fractures at the contact part with the well bore according to the flowing relation of the gas in the well bore and the boundary coupling relation between the fractures and the well bore_wfiPressure disturbance P generated at the contact of the fracture adjacent to the fracture and the well bore_wfi-1And the flow rate Q between the two fractures in the wellbore_sciThe relational expression of (1); and obtaining the productivity of the horizontal well by using a numerical iteration method.

Description

The Productivity of the tight gas reservoir horizontal well after multistage fracturing reform

Technical field

The present invention relates to a kind of Productivity, particularly relate to a kind of Productivity of the tight gas reservoir horizontal well after multistage fracturing reform.The present invention relates to a kind of AOF calculation system, particularly relate to a kind of AOF calculation system of the tight gas reservoir horizontal well after multistage fracturing reform.

Background technology

Tight gas reservoir (TightGas) refers to that permeability is less than the sandstone formation natural gas pool of 0.1 millidarcy (mD).Tight gas reservoir, as a kind of important natural gas resource, becomes the main growth factor of gas production gradually.In prior art, horizontal well is often adopted to exploit tight gas reservoir.Horizontal well refers to that hole angle reaches or close to 90 ° and well bore creeps into the well of certain length along horizontal direction.Horizontal well, after multistage fracturing reform, forms the transverse crack (hereinafter referred to as " crack ") that many forms are different.Crack is along the direction crack initiation perpendicular to pit shaft.Crack considerably increases the contact area on gas well and stratum, improves the seepage flow condition of shaft bottom surrounding formation simultaneously, adds oil reservoir drainage area.The gas of tight gas reservoir flows into crack from formation pore, in crack, flow to pit shaft, and then flows to well head along pit shaft.

In order to carry out production prediction to the tight gas reservoir horizontal well after multistage fracturing reform, the research that those skilled in the art deepen continuously.In the limited fluid diversion research of crack, fractured model develops into multiple cracking again to volume fracturing from monolete, and method for solving analytically method develops into semi-analytical solution and arrives numerical method again, and simulation precision improves constantly.Fractured horizontal well's productivity evaluation aspect, Fan Zifei utilizes the flow performance of horizontal wellbore to establish the Coupled with Flow model of reservoir and pit shaft, and Li Xiaoping application volumetric balance principle have modified coupling model.But the Model of Horizontal Well that they propose is the mode completion with bore hole, slotted liner or cutting seam sieve tube.Compared to other completion mode, after staged fracturing, the crack of tight gas reservoir horizontal well flow area compared with pit shaft is much bigger, so need to take into full account the impact of man-made fracture flowing on gas well deliverability.

Summary of the invention

Goal of the invention of the present invention is, provide a kind of Productivity of the tight gas reservoir horizontal well after multistage fracturing reform, the method can improve the accuracy of the tight gas reservoir HORIZONTAL WELL PRODUCTION FORECASTING after multistage fracturing reform.

The invention discloses a kind of Productivity of the tight gas reservoir horizontal well after multistage fracturing reform, it is characterized in that: it comprises the following steps

Steps A), set up physical model, described physical model has to give a definition: A1) stratum homogeneous uniform thickness, the face of overlooking on stratum is rectangle, and this rectangle has four and closes and the border of equipressure, and the wide of described rectangle is x _e, this value is carried out well test analysis by formation and is obtained, and the length of described rectangle is y _e, this value is carried out well test analysis by formation and is obtained; A2) have n crack, all n cracks run through stratum completely, wherein n=1,2,3 ..., the 1st crack is positioned at the butt of this horizontal well pit shaft, and the i-th crack is arranged to the toe-end of this horizontal well pit shaft gradually, wherein i=1,2,3 ..., n;

Described physical model is defined as follows characteristic:

$P_D=\frac{78.55\mathrm{kh}({P_i}^2-P^2)}{\mathrm{\μZT}{Q}_{\mathrm{sc}}},q_D=\frac{2x_f{q}_{\mathrm{sc}}}{Q_{\mathrm{sc}}},j_D=\frac{j}{x_f}(j=x,y),C_{\mathrm{fD}}=\frac{k_f{w}_f}{{\mathrm{kx}}_f}$

In formula:

P _drepresent dimensionless pressure; P _irepresent original formation pressure; P represents strata pressure; T represents formation temperature; K represents in-place permeability; H represents formation thickness; μ represents gas viscosity; Z represents Gaseous Z-factor, and it is obtained by laboratory experiment; Q _sccrack flow under representative mark condition; q _drepresent dimensionless crack flow; q _scfor Biao Kuangxia unit fracture length flow; j _dfor non-dimensional length; x _ffor fracture half-length; C _fDfor dimensionless fracture condudtiviy; k _ffor fracture permeabgility; w _ffor crack width;

Step B), physically based deformation model, according to gas percolation law in the earth formation, obtains arbitrary in the n crack dimensionless pressure P caused _dwith this crack dimensionless crack flow q _d(α) relational expression between,

$\begin{array}{c}{P}_D(x_D,y_D;x_{\mathrm{wD}},y_{\mathrm{wD}})\\ =2\underset{x_{\mathrm{wD}}-1}{\overset{x_{\mathrm{wD}}+1}{\∫}}\left\{\underset{m=1}{\overset{\∞}{\mathrm{\Σ}}}\frac{q_D\left(\mathrm{\α}\right)}{\mathrm{m\π}}\sin \frac{\mathrm{m\π}{x}_D}{x_{\mathrm{eD}}}\sin \frac{\mathrm{m\π\α}}{x_{\mathrm{eD}}}\frac{\cosh \frac{\mathrm{m\π}(y_{\mathrm{eD}}-|y_D-y_{\mathrm{wD}}\left|\right)}{x_{\mathrm{eD}}}-\cosh \frac{\mathrm{m\π}(y_{\mathrm{eD}}-|y_D+y_{\mathrm{wD}}\left|\right)}{x_{\mathrm{eD}}}}{\sinh \frac{\mathrm{m\π}{y}_{\mathrm{eD}}}{x_{\mathrm{eD}}}}\right\}\mathrm{d\α}\end{array}$

In formula: x _w, y _wfor fissured central coordinate, it is obtained by the definition of physical model;

Step C), physically based deformation model, according to the flowing relation of gas in crack and the border coupled relation between crack and stratum, obtains in n crack arbitrary at the pressure disturbance P produced with pit shaft contact position _wfnwith the Q of this crack flow under mark condition _scnrelational expression,

$\begin{array}{c}\frac{78.55\mathrm{kh}({P_i}^2-P_{\mathrm{wfn}}^2)}{\mathrm{\μZT}{Q}_{\mathrm{scn}}}=\frac{1}{C_{\mathrm{fD}}}\frac{h}{x_f}[\ln \frac{h}{2r_w}-\frac{\mathrm{\π}}{2}]+f\left(C_{\mathrm{fD}}\right)\\ +2\left\{\underset{m=1}{\overset{\∞}{\mathrm{\Σ}}}\frac{x_e^2}{m^3{\mathrm{\π}}^2{x}_f^2}{\sin }^2\frac{\mathrm{m\π}{x}_f}{x_e}{\sin }^2\frac{\mathrm{m\π}{x}_w}{x_e}\frac{\cosh \frac{\mathrm{m\π}{y}_e}{x_e}-\cosh \frac{\mathrm{m\π}(y_e-2y_w)}{x_e}}{\sinh \frac{\mathrm{m\π}{y}_e}{x_e}}\right\}\end{array},$

In formula: P _wfnfor arbitrary in n crack is in the pressure disturbance produced with pit shaft contact position; r _wfor horizontal wellbore radius;

Step D), physically based deformation model, according to gas flowing relation in the wellbore and the border coupled relation between crack and pit shaft, obtains in n crack arbitrary at the pressure disturbance P produced with pit shaft contact position _wfi, adjacent with this crack crack is at the pressure disturbance P produced with pit shaft contact position _wfi-1and this two crack in pit shaft between flow Q _scirelational expression,

$P_{\mathrm{wfi}}^2-P_{\mathrm{wfi}-1}^2=9\×{10}^{-12}\frac{\mathrm{ZT}{\mathrm{\γ}}_g}{r_w^5}{f}_i{d}_i{\left(\underset{j=i}{\overset{n}{\mathrm{\Σ}}}{Q}_{\mathrm{scj}}\right)}^2$

Wherein, P _wf0=P _wf;

In formula: Z is Gaseous Z-factor; γ _gfor gas relative density; F is the coefficient of friction resistance; D is fracture interval;

Step e), estimate the flow Q of the n-th crack _scn, measure and obtain the 1st crack at the pressure disturbance P produced with pit shaft contact position _wf, utilize Numerical Iteration Method to obtain this horizontal well capacity.

Preferably, in step C) in, the flowing relation of gas in crack will consider the radial conflux effect of the seepage effect in crack, the difference between infinite fluid diversion crack and limited fluid diversion crack and pit shaft.

Preferably, in step e) in, further comprising the steps of:

E1) the maximum value Q of the n-th crack flow is estimated according to practical condition _{scn (max)}with minimum value Q _{scn (min)}, get the arithmetic average Q of maxima and minima _{scn (mid)}=0.5 × [Q _{scn (max)}+ Q _{scn (min)}];

E2) according to step C) in formulae discovery obtain corresponding P _{wfn (max)}, P _{wfn (min)}and P _{wfn (mid)}, according to step D) in formula obtain corresponding P _{wfn-1 (max)}, P _{wfn-1 (min)}and P _{wfn-1 (mid)}, according to step C) in formulae discovery obtain corresponding Q _{scn-1 (max)}, Q _{scn-1 (min)}, Q _{scn-1 (mid)};

E3) step e 2 is repeated) obtain P _{wf0 (max)}, P _{wf0 (min)}, P _{wf0 (mid)};

E4) by P _{wf0 (mid)}with P _wfcarry out difference comparsion, if P _{wf0 (mid)}with P _wfdifference meet required precision and then judge calculated value P _{wf0 (mid)}correctly, if P _{wf0 (mid)}with P _wfdifference do not meet required precision, if then (P _{wf0 (max)}-P _wf) × (P _{wf0 (min)}-P _wf) <0, so Q _{scn (min)}=Q _{scn (mid)}, otherwise Q _{scn (max)}=Q _{scn (mid)};

E5) step e 1 is repeated) to E4), until P _{wf0 (mid)}with P _wfdifference meet required precision.

Preferably, in step D) in, described coefficient of friction resistance f is obtained by following formulae discovery:

$f_i={[1.14-2\lg (\frac{e}{1000D}+\frac{21.25}{R_{\mathrm{ei}}^{0.9}})]}^{-2},$

wherein, e is shaft in wall roughness.

Preferably, this horizontal well capacity is wherein, j=1,2,3 ..., n.

Preferably, described P _iby obtaining unquarried stratum measurement, described P obtains by carrying out measurement to the stratum after exploitation, described T obtains by carrying out measurement to the temperature on the stratum after exploitation, described k is obtained by laboratory experiment or well test analysis, described h is obtained by well log interpretation, described μ is obtained by laboratory experiment, and described Z is obtained by laboratory experiment, described x _fobtained by well test analysis, described k _fobtained by well test analysis, described w _fobtained by well test analysis.

Preferably, described Z is obtained by laboratory experiment; Described γ _gobtained by laboratory experiment, described d is obtained by FRACTURING DESIGN data.

The invention also discloses a kind of AOF calculation system adopting above-mentioned computational methods, it comprises

Modeling unit, it is for setting up physical model;

First computing unit, it is for obtaining arbitrary in the n crack dimensionless pressure P caused according to gas percolation law in the earth formation _dwith this crack dimensionless crack flow q _d(α) relational expression between;

Second computing unit, it is for obtaining in n crack arbitrary at the pressure disturbance P produced with pit shaft contact position according to the flowing relation of gas in crack and the border coupled relation between crack and stratum _wfnwith the Q of this crack flow under mark condition _scnrelational expression;

3rd computing unit, it is for obtaining in n crack arbitrary at the pressure disturbance P produced with pit shaft contact position according to the flowing relation of gas in crack and the border coupled relation between crack and stratum _wfi, adjacent with this crack crack is at the pressure disturbance P produced with pit shaft contact position _wfi-1and this two crack in pit shaft between flow Q _scirelational expression;

4th computing unit, it is for receiving the flow Q of estimation n-th crack _scn, it obtains the 1st crack at the pressure disturbance P produced with pit shaft contact position for receiving by measuring _wf, it obtains this horizontal well capacity for adopting Numerical Iteration Method.

The present inventor introduces tight gas reservoir fractured horizontal well's productivity list fracturing section and evaluates thinking, with single fracturing section for unit, application quality conservation principle is by seepage flow, crack endometamorphism amount seepage flow and pit shaft channel flow with variable mass flow rate coupling in reservoir, the changes in flow rate of the different fracturing section of research level well, to derive the theoretical formula set up and be suitable for evaluating production capacity after tight gas reservoir fractured horizontal well, provide corresponding iterative algorithm and carry out analysis interpretation in conjunction with example, thus forming the new method of a set of tight gas reservoir staged fracturing horizontal productivity evaluation.The present invention is based on percolation hydraulic theory, the flowing law of learning gas in stratum, crack, pit shaft three autonomous systems, by the principle of mass conservation by seepage flow, crack endometamorphism amount seepage flow and pit shaft channel flow with variable mass flow rate coupling in reservoir, and by iterative algorithm determination multistage fractured horizontal well's productivity.

Accompanying drawing explanation

Figure 1A shows the physical model of horizontal well.

Figure 1B shows the gas flow schematic diagram in Figure 1A in single hop crack.

Fig. 2 shows the schematic diagram of gas seepage flow in crack.

Fig. 3 shows flow conductivity C under Different Effects parameter _fDwith bottom pressure P _wDvariation relation.

Fig. 4 shows limited fluid diversion crack bottom pressure and flow conductivity variation relation.

Fig. 5 shows the pit shaft conflux effect in crack.

Fig. 6 shows flow in horizontal pipe sectional drawing in horizontal wellbore.

Fig. 7 shows horizontal well yield and bottom pressure variation relation figure.

Fig. 8 under showing different flowing bottomhole pressure (FBHP) each crack along the pressure distribution of horizontal wellbore.

Fig. 9 shows the well track of this well.

Detailed description of the invention

Below in conjunction with accompanying drawing, preferred embodiment of the present invention is described in detail, can be easier to make advantages and features of the invention be those skilled in the art will recognize that thus make more explicit defining to protection scope of the present invention.

First embodiment of Productivity in the present invention, the Productivity of the tight gas reservoir horizontal well after multistage fracturing reform, it comprises the following steps: set up physical model.Physically based deformation model, according to gas percolation law in the earth formation, obtains arbitrary in the n crack dimensionless pressure P caused _dwith this crack dimensionless crack flow q _d(α) relational expression between.Physically based deformation model, according to the flowing relation of gas in crack and the border coupled relation between crack and stratum, obtains in n crack arbitrary at the pressure disturbance P produced with pit shaft contact position _wfnwith the Q of this crack flow under mark condition _scnrelational expression.Physically based deformation model, according to gas flowing relation in the wellbore and the border coupled relation between crack and pit shaft, obtains in n crack arbitrary at the pressure disturbance P produced with pit shaft contact position _wfi, adjacent with this crack crack is at the pressure disturbance P produced with pit shaft contact position _wfi-1and this two crack in pit shaft between flow Q _scirelational expression.Estimate the flow Q of the n-th crack _scn, measure and obtain the 1st crack at the pressure disturbance P produced with pit shaft contact position _wf, utilize Numerical Iteration Method to obtain this horizontal well capacity.

Concrete, in steps A) in, set up physical model, described physical model has to give a definition: A1) stratum homogeneous uniform thickness.The face of overlooking on stratum is rectangle.This rectangle has four and closes and the border of equipressure.The wide of described rectangle is x _e, this value is carried out well test analysis by formation and is obtained, and the length of described rectangle is y _e, this value is carried out well test analysis by formation and is obtained.A2) have n crack, all n cracks run through stratum completely, wherein n=1,2,3 ..., the 1st crack is positioned at the butt of this horizontal well, and the i-th crack is arranged to the toe-end of this horizontal well gradually, wherein i=1,2,3 ..., n.

Described physical model is defined as follows characteristic:

$P_D=\frac{78.55\mathrm{kh}({P_i}^2-P^2)}{\mathrm{\&mu;ZT}{Q}_{\mathrm{sc}}},q_D=\frac{2x_f{q}_{\mathrm{sc}}}{Q_{\mathrm{sc}}},j_D=\frac{j}{x_f}(j=x,y),C_{\mathrm{fD}}=\frac{k_f{w}_f}{{\mathrm{kx}}_f}$

In above-mentioned formula: P _dfor dimensionless pressure.P _ifor original formation pressure, it is by obtaining unquarried stratum measurement, and unit is MPa (MPa).P is strata pressure, and it obtains by carrying out measurement to the stratum after exploitation, and unit is MPa (MPa).T is formation temperature, and it obtains by carrying out measurement to the temperature on the stratum after exploitation, and unit is Kelvin (K); K is in-place permeability, and it is obtained by laboratory experiment or well test analysis, and its unit is darcy (D).H is formation thickness, and it is obtained by well log interpretation, and its unit is rice (m). μ is gas viscosity, and it is obtained by laboratory experiment, and its unit is milli handkerchief second (mPas).Z is Gaseous Z-factor, and it is obtained by laboratory experiment.Q _scfor crack flow under mark condition, its unit is 10 ⁴* cubic meter/day (10 ⁴m ³/ d) .q _dfor dimensionless crack flow.Q _scfor Biao Kuangxia unit fracture length flow, its unit is 10 ⁴* cubic meter/day/rice (10 ⁴m ³/ d/m).J _dfor non-dimensional length.X _ffor fracture half-length, it is obtained by well test analysis, and its unit is rice (m).C _fDfor dimensionless fracture condudtiviy.K _ffor fracture permeabgility, it is obtained by well test analysis, and its unit is darcy (D).W _ffor crack width, it is obtained by well test analysis, and its unit is rice (m).X, y are the coordinate of j in physical model.

Well test analysis is exactly based on percolation hydraulic theory, by the research to oil well test information, determines the method for the various physical parameters, production capacity etc. reflecting testing well and formation characteristics.

The relation applied between well log interpretation determination well logging information and geological information, adopts and on sound lines well logging information is processed into geological information.

Figure 1A shows the physical model of horizontal well.As shown in Figure 1A, the pit shaft of horizontal well extends along horizontal direction.Crack is longitudinally perpendicular to horizontal well pit shaft.Figure 1B shows the gas flow schematic diagram in Figure 1A in wall scroll crack.In fig. ib, gas from stratum along hyperbola form streamline flow to crack.After gas flow into crack from stratum, move to horizontal wellbore by seepage effect.Because stratum is run through completely in crack, can think that the flowing in crack is one-dimensional linear flowing, and this flowing is a kind of mass variable flow along fracture length change.Be far longer than the flow channel size in stratum and crack due to pit shaft internal diameter, the gas flowing therefore in pit shaft calculates by phasmajector stream.

In this physical model, the gas in stratum follows Darcy's law (Darcy ' sLaw), is the Darcy flowing of variable mass in crack, is the pipe stream of variable mass in horizontal wellbore.Three kinds of types of flow are disturbed mutually, by the border coupling of intersecting.

In step B) in, physically based deformation model, according to gas percolation law in the earth formation, obtains arbitrary in the n crack dimensionless pressure P caused _dwith this crack dimensionless crack flow q _d(α) relational expression between.

As shown in Figure 1B, in the stratum of crack periphery, the streamline form of gas is similar to hyperbola.In the region that stratum is beyond hyperbola streamline, the streamline form of gas radially, shows as pseudoradial flow feature.

Formula (1) is obtained according to Laplace transform formula:

$\frac{{\&PartialD;}^2{P}_D}{{\&PartialD;x}_D^2}+\frac{{\&PartialD;}^2{P}_D}{{\&PartialD;y}_D^2}+q_D\left(x_D\right)\mathrm{\&delta;}(y_D-y_{\mathrm{wD}})=0---\left(1\right)$

The four edges circle equipressure on the stratum defined in physically based deformation model obtains formula (2) and (3):

P _D(x _D,0)＝P _D(x _D,x _eD)(2)

P _D(0,y _D)＝P _D(y _eD,y _D)(3)

In formula: x _w, y _wfor fissured central coordinate, it is obtained by the definition of physical model, and its unit is rice (m).δ is Di Like function.

To each variable in formula (1) along x _dand y _dfourier (Fourier) limited integral sine is done in direction, is designated as respectively:

${\hat{P}}_D={\&Integral;}_0^{x_{\mathrm{eD}}}{P}_D\sin \left({\mathrm{\&beta;}}_m{x}_D\right){\mathrm{dx}}_D---\left(4\right)$

${\stackrel{\&OverBar;}{P}}_D={\&Integral;}_0^{y_{\mathrm{eD}}}{P}_D\sin \left({\mathrm{\&gamma;}}_n{y}_D\right){\mathrm{dy}}_D---\left(5\right)$

${\tilde{q}}_D={\&Integral;}_0^{x_{\mathrm{eD}}}{q}_D\left(x_D\right)\sin \left({\mathrm{\&gamma;}}_n{x}_D\right){\mathrm{dx}}_D---\left(6\right)$

Utilize formula (2) (3) to process formula (1) simultaneously, the relational expression of pressure under dual Fourier (Fourier) integral transformation and crack flow can be obtained:

$-{\mathrm{\&pi;}}^2(\frac{m^2}{x_{\mathrm{eD}}^2}+\frac{n^2}{y_{\mathrm{eD}}^2}){\widehat{\stackrel{\&OverBar;}{P}}}_D+{\tilde{q}}_D\sin {\mathrm{\&gamma;}}_n{y}_{\mathrm{wD}}=0---\left(7\right)$

Utilize reconstructed formula to carry out twice inverting and can obtain pressure function:

$P_D=\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{\sin \left({\mathrm{\&gamma;}}_n{y}_D\right)}{N\left({\mathrm{\&beta;}}_n\right)}\left(\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{\sin \left({\mathrm{\&beta;}}_m{x}_D\right)}{N\left({\mathrm{\&beta;}}_m\right)}{\widehat{\stackrel{\&OverBar;}{P}}}_D\right)---\left(8\right)$

Wherein characteristic value:

β _m＝mπ/x _eD；γ _n＝nπ/y _eD(9)

Norm inverse meets:

$N\left({\mathrm{\&beta;}}_m\right)={\&Integral;}_0^{x_{\mathrm{eD}}}{\sin }^2\left({\mathrm{\&beta;}}_m{x}_D\right){\mathrm{dx}}_D=\frac{x_{\mathrm{eD}}}{2};N\left({\mathrm{\&gamma;}}_n\right)={\&Integral;}_0^{y_{\mathrm{eD}}}{\sin }^2\left({\mathrm{\&gamma;}}_n{y}_D\right){\mathrm{dy}}_D=\frac{y_{\mathrm{eD}}}{2}---\left(10\right)$

Formula (7), formula (9) and formula (10) substitution formula (8) can be obtained pressure formula is:

$P_D=\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{2{\tilde{q}}_D}{x_{\mathrm{eD}}{y}_{\mathrm{eD}}}\sin \frac{\mathrm{m\&pi;}{x}_D}{x_{\mathrm{eD}}}\left[\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{\cos \mathrm{n\&pi;}(y_D-y_{\mathrm{wD}})/y_{\mathrm{eD}}-\cos \mathrm{n\&pi;}(y_D+y_{\mathrm{wD}})/y_{\mathrm{eD}}}{{\mathrm{\&pi;}}^2(m^2/x_{\mathrm{eD}}^2+n^2/y_{\mathrm{eD}}^2)}\right]---\left(11\right)$

Only have and just have flow distribution along crack, so formula (6) can be rewritten as the integral relation about fracture length:

${\tilde{q}}_D={\&Integral;}_{x_{\mathrm{wD}}-1}^{x_{\mathrm{wD}}+1}{q}_D\left(\mathrm{\&alpha;}\right)\sin \left(\frac{\mathrm{m\&pi;\&alpha;}}{x_{\mathrm{eD}}}\right)\mathrm{d\&alpha;}---\left(12\right)$

Note transformation relation simultaneously:

$\underset{k=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{\cos \mathrm{k\&pi;x}}{k^2+a^2}=\frac{\mathrm{\&pi;}}{2a}\frac{\cosh \left[\mathrm{a\&pi;}(1-x)\right]}{\sinh \left(\mathrm{a\&pi;}\right)}-\frac{1}{2a^2};[0\&le;x\&le;2\mathrm{\&pi;}]---\left(13\right)$

Utilize formula (12), formula (13) to rewrite formula (11), obtain arbitrary in the n crack dimensionless pressure P caused _dwith this crack dimensionless crack flow q _d(α) relational expression between:

$\begin{array}{c}{P}_D(x_D,y_D;x_{\mathrm{wD}},y_{\mathrm{wD}})\\ =2\underset{x_{\mathrm{wD}}-1}{\overset{x_{\mathrm{wD}}+1}{\&Integral;}}\left\{\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{q_D\left(\mathrm{\&alpha;}\right)}{\mathrm{m\&pi;}}\sin \frac{\mathrm{m\&pi;}{x}_D}{x_{\mathrm{eD}}}\sin \frac{\mathrm{m\&pi;\&alpha;}}{x_{\mathrm{eD}}}\frac{\cosh \frac{\mathrm{m\&pi;}(y_{\mathrm{eD}}-|y_D-y_{\mathrm{wD}}\left|\right)}{x_{\mathrm{eD}}}-\cosh \frac{\mathrm{m\&pi;}(y_{\mathrm{eD}}-|y_D+y_{\mathrm{wD}}\left|\right)}{x_{\mathrm{eD}}}}{\sinh \frac{\mathrm{m\&pi;}{y}_{\mathrm{eD}}}{x_{\mathrm{eD}}}}\right\}\mathrm{d\&alpha;}\end{array}---\left(14\right)$

In formula: x _w, y _wfor fissured central coordinate, it is obtained by the definition of physical model, and its unit is rice (m).

In step C) in, physically based deformation model, according to the flowing relation of gas in crack and the border coupled relation between crack and stratum, obtains in n crack arbitrary at the pressure disturbance P produced with pit shaft contact position _wfnwith the Q of this crack flow under mark condition _scnrelational expression:

$\begin{array}{c}\frac{78.55\mathrm{kh}({P_i}^2-P_{\mathrm{wfn}}^2)}{\mathrm{\&mu;ZT}{Q}_{\mathrm{scn}}}=\frac{1}{C_{\mathrm{fD}}}\frac{h}{x_f}[\ln \frac{h}{2r_w}-\frac{\mathrm{\&pi;}}{2}]+f\left(C_{\mathrm{fD}}\right)\\ +2\left\{\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{x_e^2}{m^3{\mathrm{\&pi;}}^2{x}_f^2}{\sin }^2\frac{\mathrm{m\&pi;}{x}_f}{x_e}{\sin }^2\frac{\mathrm{m\&pi;}{x}_w}{x_e}\frac{\cosh \frac{\mathrm{m\&pi;}{y}_e}{x_e}-\cosh \frac{\mathrm{m\&pi;}(y_e-2y_w)}{x_e}}{\sinh \frac{\mathrm{m\&pi;}{y}_e}{x_e}}\right\}\end{array},$

In formula: P _wfnfor arbitrary in n crack is in the pressure disturbance produced with pit shaft contact position, its unit is MPa (MPa).R _wfor the radius of pit shaft, it is obtained by technical manual, and its unit is rice (m).

Fig. 2 shows the schematic diagram of gas seepage flow in crack.As shown in Figure 2, after gas flow into crack from stratum, move to horizontal wellbore by seepage effect.Because stratum is run through completely in crack, can think that the flowing in crack is one-dimensional linear flowing, and this flowing is a kind of mass variable flow along fracture length change.

Because crevice volume is less, elasticity is less, can ignore the flexible impact in crack, and the dimensionless percolation equationk of fluid in crack is reduced to form stable, obtains formula (15) and formula (16).

$\frac{d^2{P}_{\mathrm{fD}}}{{\mathrm{dx}}_D^2}+\frac{2}{C_{\mathrm{fD}}}{q}_D\left(x_D\right)=0,[-1\&le;x_D\&le;1]---\left(15\right)$

$\frac{{\mathrm{dP}}_{\mathrm{fD}}\left(x_{\mathrm{wD}}\right)}{{\mathrm{dx}}_D}=-\frac{\mathrm{\&pi;}}{C_{\mathrm{fD}}}---\left(16\right)$

Wherein, P in formula _fDfor the pressure disturbance caused by guide functions.

To formula (15) about x _d carry out twice integration, can have:

$P_{\mathrm{wD}}-P_{\mathrm{fD}}\left(x_D\right)=\frac{\mathrm{\&pi;}}{C_{\mathrm{fD}}}\left[\right|x_D-x_{\mathrm{wD}}|-{\&Integral;}_{x_{\mathrm{wD}}}^{x_D}\mathrm{dv}{\&Integral;}_{x_{\mathrm{wD}}}^v{q}_D\left(u\right)\mathrm{du}]---\left(17\right)$

Because pressure is the function about position, therefore, identical with the pressure of the intersection on stratum in crack.The coupling condition on crack and stratum is:

P _fD(x _D)＝P _D(x _D,y _wD；x _wD,y _wD)，[-1≤x _D≤1](18)

Formula (14) is substituted into formula (18), form Fredholm type integral equation, this equation cannot Analytical Solution, adopts numerical solution here: crack is divided into n part, the flow of equal segments, pressure uniform, will form n+1 rank variable is like this each section of flow q _dj(j=1,2,3 ...., n) and bottom pressure P _wDsystem of linear equations, formula (19):

$\begin{array}{c}{P}_{\mathrm{wD}}+2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{q}_{\mathrm{Di}}\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\mathrm{}\left\{\begin{array}{c}\frac{x_{\mathrm{eD}}}{m^2{\mathrm{\&pi;}}^2}\sin \mathrm{m\&pi;}\frac{x_{\mathrm{wD}}+(j-0.5)\mathrm{\&Delta;x}}{x_{\mathrm{eD}}}[\cos \mathrm{m\&pi;}\frac{x_{\mathrm{wD}}+\mathrm{i\&Delta;}{x}_D}{x_{\mathrm{eD}}}-\cos \mathrm{m\&pi;}\frac{x_{\mathrm{wD}}+(i-1)\mathrm{\&Delta;}{x}_D}{x_{\mathrm{eD}}}]\\ \&times;\frac{\cosh [\mathrm{m\&pi;}{y}_{\mathrm{eD}}/x_{\mathrm{eD}}]-\cosh [\mathrm{m\&pi;}(y_{\mathrm{eD}}-|2y_{\mathrm{wD}}\left|\right)/x_{\mathrm{eD}}]}{\sinh (\mathrm{m\&pi;}{y}_{\mathrm{eD}}/x_{\mathrm{eD}})}\end{array}\right\}\\ =\frac{\mathrm{\&pi;}}{C_{\mathrm{fD}}}\{(x_{\mathrm{wD}}+(j-0.5)\mathrm{\&Delta;x})(1-\underset{i=1}{\overset{j-1}{\mathrm{\&Sigma;}}}{q}_{\mathrm{Di}}{\mathrm{\&Delta;x}}_D-\frac{{\mathrm{\&Delta;x}}_D}{2}{q}_{\mathrm{Dj}})+\underset{i=1}{\overset{j-1}{\mathrm{\&Sigma;}}}{q}_{\mathrm{Di}}{\mathrm{\&Delta;x}}_D[x_{\mathrm{wD}}+(i-0.5){\mathrm{\&Delta;x}}_D]+q_{\mathrm{Dj}}{\mathrm{\&Delta;x}}_D\frac{x_{\mathrm{wD}}+(j-0.75){\mathrm{\&Delta;x}}_D}{2}\}\end{array}---\left(19\right)$

Traffic constraints equation

$\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{q}_{\mathrm{Di}}=1---\left(20\right)$

Newton iteration method is utilized to solve system of linear equations (19), and flow conductivity C under calculating Different Effects parameter _fDwith bottom pressure P _wDvariation relation.The result obtained as shown in Figure 3, learns limited fluid diversion crack bottom pressure P according to Fig. 3 _wDwith C _fDincrease and reduce.Work as C _fDp time >300 (being set as 300) _wDlevel off to constant, be the bottom pressure P that infinite fluid diversion crack is corresponding _infwD.And this variation tendency only and C _fDrelevant, not by the impact of other parameters.Fig. 4 shows limited fluid diversion crack bottom pressure and flow conductivity variation relation.As shown in Figure 4, the difference functions f (C between infinite fluid diversion crack and limited fluid diversion crack can be obtained by data regression _fD):

$f\left(C_{\mathrm{fD}}\right)=\frac{1.65-0.328\ln C_{\mathrm{fD}}+0.116{\left(\ln C_{\mathrm{fD}}\right)}^2}{1.0+0.18\ln C_{\mathrm{fD}}+0.064{\left(\ln C_{\mathrm{fD}}\right)}^2+0.005{\left(\ln C_{\mathrm{fD}}\right)}^3}---\left(21\right)$

Formula (21) is also the influence function of crack limited fluid diversion ability, and wherein the bottom pressure in infinite fluid diversion crack is:

$P_{\mathrm{infwD}}=2\left\{\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{x_{\mathrm{eD}}}{n^2\mathrm{\&pi;}}\sin \mathrm{n\&pi;}\frac{x_D}{x_{\mathrm{eD}}}\sin \mathrm{n\&pi;}\frac{1}{x_{\mathrm{eD}}}\sin \mathrm{n\&pi;}\frac{x_{\mathrm{wD}}}{x_{\mathrm{eD}}}\frac{\cosh \frac{\mathrm{n\&pi;}{y}_{\mathrm{eD}}}{x_{\mathrm{eD}}}-\cosh \frac{\mathrm{n\&pi;}(y_{\mathrm{eD}}-2y_{\mathrm{wD}})}{x_{\mathrm{eD}}}}{\sinh \frac{\mathrm{n\&pi;}{y}_{\mathrm{eD}}}{x_{\mathrm{eD}}}}\right\}---\left(22\right)$

Fig. 5 shows the pit shaft conflux effect in crack.As shown in Figure 5, can Radial Flow be formed at the nearly near wellbore in crack simultaneously, additional Pressure Drop can be produced compared with vertically fractured well, i.e. the radial conflux effect of pit shaft.Introduce skin factor herein to take in.

$\mathrm{skin}=\frac{\mathrm{kh}}{k_f{w}_f}[\ln \frac{h}{2r_w}-\frac{\mathrm{\&pi;}}{2}]---\left(23\right)$

So, consider the bottom pressure P in the limited fluid diversion crack of pit shaft conflux effect _finwDcan obtain:

P _finwD＝P _infwD+f(C _fD)+skin(24)

Bottom pressure after having dimension to launch is:

$\begin{array}{c}\frac{78.55\mathrm{kh}({P_i}^2-P_{\mathrm{wfn}}^2)}{\mathrm{\&mu;ZT}{Q}_{\mathrm{scn}}}=\frac{1}{C_{\mathrm{fD}}}\frac{h}{x_f}[\ln \frac{h}{2r_w}-\frac{\mathrm{\&pi;}}{2}]+f\left(C_{\mathrm{fD}}\right)\\ +2\left\{\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{x_e^2}{m^3{\mathrm{\&pi;}}^2{x}_f^2}{\sin }^2\frac{\mathrm{m\&pi;}{x}_f}{x_e}{\sin }^2\frac{\mathrm{m\&pi;}{x}_w}{x_e}\frac{\cosh \frac{\mathrm{m\&pi;}{y}_e}{x_e}-\cosh \frac{\mathrm{m\&pi;}(y_e-2y_w)}{x_e}}{\sinh \frac{\mathrm{m\&pi;}{y}_e}{x_e}}\right\}\end{array}---\left(25\right)$

In formula: P _wfnfor arbitrary in n crack is in the pressure disturbance produced with pit shaft contact position, MPa.

Formula (25) obtains in n crack arbitrary at the pressure disturbance P produced with pit shaft contact position _wfnwith the Q of this crack flow under mark condition _scnrelational expression.

In step D) in, physically based deformation model, according to gas flowing relation in the wellbore and the border coupled relation between crack and pit shaft, obtains in n crack arbitrary at the pressure disturbance P produced with pit shaft contact position _wfi, adjacent with this crack crack is at the pressure disturbance P produced with pit shaft contact position _wfi-1and this two crack in pit shaft between flow Q _scirelational expression.

Fig. 6 shows flow in horizontal pipe sectional drawing in horizontal wellbore.As shown in Figure 6, be far longer than the flow channel size in stratum and crack due to pit shaft internal diameter, the gas flowing therefore in pit shaft calculates by phasmajector stream.Flow in horizontal wellbore is change, therefore, adopts segmentation to calculate herein.Ignore because flow velocity increases the kinetic energy pressure drop caused, according to (Li Shilun, Deng. gas engineering [M]. Beijing: petroleum industry publishing house, 2008.LiSL, etal.NaturalGasEngineering [M] .Beijing:PetroleumIndustryPress, 2008.) content in, gross pressure gradient is:

$\frac{\mathrm{dP}}{\mathrm{dy}}=f\frac{{\mathrm{\&rho;v}}^2}{2r_w}---\left(26\right)$

Adopt mean parameter method variables separation integration, obtain in n crack arbitrary at the pressure disturbance P produced with pit shaft contact position _wfi, adjacent with this crack crack is at the pressure disturbance P produced with pit shaft contact position _wfi-1and this two crack in pit shaft between flow Q _scirelational expression:

$P_{\mathrm{wfi}}^2-P_{\mathrm{wfi}-1}^2=9\&times;{10}^{-12}\frac{\mathrm{ZT}{\mathrm{\&gamma;}}_g}{r_w^5}{f}_i{d}_i{\left(\underset{j=i}{\overset{n}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{scj}}\right)}^2,$ (wherein, P _wf0=P _wf) (27)

Wherein, e is shaft in wall roughness, and it is obtained by technical manual, and its unit is millimeter (mm).Z is Gaseous Z-factor, and it is obtained by laboratory experiment.γ _gfor gas relative density, it is obtained by laboratory experiment.F is the coefficient of friction resistance.D is fracture interval, and it is obtained by FRACTURING DESIGN data, and its unit is rice (m).The explicit formula that coefficient of friction resistance f is proposed by Jain calculates, and the Reynolds number in formula all considers turbulent condition, is calculated by (27).

$f_i={[1.14-2\lg (\frac{e}{1000D}+\frac{21.25}{R_{\mathrm{ei}}^{0.9}})]}^{-2}---\left(28\right)$

$R_{\mathrm{ei}}=\frac{177.1{\mathrm{\&gamma;}}_g\underset{j=i}{\overset{n}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{scj}}}{2{\mathrm{\&mu;}}_g{r}_w}---\left(29\right)$

In step e) in, estimate the flow Q of the n-th crack _scn, measure and obtain the 1st crack at the pressure disturbance P produced with pit shaft contact position _wf, utilize Numerical Iteration Method to obtain this horizontal well capacity.

E1) the maximum value Q of the n-th crack flow is estimated according to practical condition _{scn (max)}with minimum value Q _{scn (min)}, get the arithmetic average Q of maxima and minima _{scn (mid)}=0.5 × [Q _{scn (max)}+ Q _{scn (min)}];

E2) according to step C) in formulae discovery obtain corresponding P _{wfn (max)}, P _{wfn (min)}and P _{wfn (mid)}, according to step D) in formula obtain corresponding P _{wfn (max)}, P _{wfn (min)}and P _{wfn (mid)}, according to step C) in formulae discovery obtain corresponding Q _{scn-1 (max)}, Q _{scn-1 (min)}, Q _{scn-1 (mid)};

E3) step e 2 is repeated) obtain P _{wf0 (max)}, P _{wf0 (min)}, P _{wf0 (mid)};

E4) by P _{wf0 (mid)}with P _wfcarry out difference comparsion, if P _{wf0 (mid)}with P _wfdifference meet required precision and then judge calculated value P _{wf0 (mid)}correctly, if P _{wf0 (mid)}with P _wfdifference do not meet required precision, if then (P _{wf0 (max)}-P _wf) × (P _{wf0 (min)}-P _wf) <0, so Q _{scn (min)}=Q _{scn (mid)}, otherwise Q _{scn (max)}=Q _{scn (mid)};

E5) step e 1 is repeated) to E4), until P _{wf0 (mid)}with P _wfdifference meet required precision.

In above-mentioned steps, P _{wf0 (mid)}meet required precision and refer to P _{wf0 (mid)}with actual P _wfidentical or and P _wfdifference in allowed limits.P _{wf0 (mid)}do not meet required precision and refer to P _{wf0 (mid)}with P _wfdifference beyond allow scope.

Work as P _{wf0 (mid)}when meeting required precision, this horizontal well capacity can be obtained.

This horizontal well capacity is wherein, j=1,2,3 ..., n.

Work as P _{wf0 (mid)}when meeting required precision, also obtain the production capacity index such as the flow along horizontal wellbore falloff curve, each crack and flow under different fracture parameters and bottom pressure condition.

Compared with conventional art, the Productivity of the tight gas reservoir horizontal well after multistage fracturing reform that the present invention proposes, consider the Coupled Flow production capacity theoretic prediction methods of stratum-crack-pit shaft overall process, substantially increase the degree of accuracy of tight gas reservoir multistage fractured horizontal well's productivity prediction theoretically.

In another embodiment of the present invention, to revive, Sulige gas field well carries out computational analysis.According to geologic information display, the control area of this well is about 1600m × 600m (x _e* y _e), the Productivity Formulae utilizing the real data of table 1 and table 2 gas well and derive herein, calculated level well capacity.

Table 1 is revived the basic parameter of Sulige gas field well

Table 2 is revived the multistage fracture parameters of Sulige gas field well after artificial fracturing

As bottom pressure P _wfduring=0.1MPa, consider that pit shaft frictional resistance each crack flow is respectively Q _sc1=22.08 × 10 ⁴m ³/ d, Q _sc2=16.85 × 10 ⁴m ³/, Q _sc3=2.18 × 10 ⁴m ³/ d, gas well capacity is Q _aOFbe 41.12 × 10 ⁴m ³/ d scene utilizes pressure buildup test data and this well capacity of Topaze well test analysis software evaluation to be 40.72 × 10 ⁴m ³/ d, relative error is 0.98%, demonstrates the correctness of model and algorithm.

Calculate the gas well flow Q under different bottom pressure (0.1MPa, 1MPa, 5MPa, 10MPa, 20MPa) _scand draw Fig. 7, each crack flow (table 3) and distribute along wellbore pressure and draw Fig. 8.Fig. 7 shows flow and the bottom pressure variation relation figure of horizontal well.Fig. 8 under showing different flowing bottomhole pressure (FBHP) each crack along the pressure distribution of horizontal wellbore.As shown in Figure 7, pit shaft frictional resistance is to gas well flow Q _scimpact increase with the reduction of flowing bottomhole pressure (FBHP), work as P _wfduring >25MPa, the impact of pit shaft frictional resistance can be ignored.As shown in Figure 8, each crack is homogeneous along the pressure distribution of pit shaft, and difference is less.Table 3 reflects when considering frictional resistance, and crack constantly increases to heel end flow from the toe-end of pit shaft.

Fig. 9 shows the well track of this well.From the well track figure of this well of Fig. 9, the reservoir near toe-end does not almost implement sand fracturing, and one section of invalid reservoir met by pit shaft toe-end brill, and therefore pit shaft toe-end part does not almost have traffic contributions.

Each crack flow distribution under the different flowing bottomhole pressure (FBHP) of table 3

The invention also discloses a kind of AOF calculation system adopting above-mentioned computational methods, it comprises modeling unit, the first computing unit, the second computing unit, the 3rd computing unit and the 4th computing unit.

Modeling unit is used for setting up physical model.This physical model has to give a definition: A1) stratum homogeneous uniform thickness.The face of overlooking on stratum is rectangle.This rectangle has four and closes and the border of equipressure.The wide of described rectangle is x _e, the length of described rectangle is y _e.A2) have n crack, all n cracks run through stratum completely, wherein n=1,2,3 ..., the 1st crack is positioned at the butt of this horizontal well, and the i-th crack is arranged to the toe-end of this horizontal well gradually, wherein i=1,2,3 ..., n.

First computing unit, it is for obtaining arbitrary in the n crack dimensionless pressure P caused according to gas percolation law in the earth formation _dwith this crack dimensionless crack flow q _d(α) relational expression between, concrete formula can see formula (14).

Second computing unit, it is for obtaining in n crack arbitrary at the pressure disturbance P produced with pit shaft contact position according to the flowing relation of gas in crack and the border coupled relation between crack and stratum _wfnwith the Q of this crack flow under mark condition _scnrelational expression, concrete formula can see formula (25).

3rd computing unit, it is for obtaining in n crack arbitrary at the pressure disturbance P produced with pit shaft contact position according to the flowing relation of gas in crack and the border coupled relation between crack and stratum _wfi, adjacent with this crack crack is at the pressure disturbance P produced with pit shaft contact position _wfi-1and this two crack in pit shaft between flow Q _scirelational expression, concrete formula can see formula (27).

4th computing unit, it is for receiving the flow Q of estimation n-th crack _scn, it obtains the 1st crack at the pressure disturbance P produced with pit shaft contact position for receiving by measuring _wf, it obtains this horizontal well capacity for adopting Numerical Iteration Method, and concrete steps are as step e) as shown in.

Each embodiment in this manual all adopts the mode of going forward one by one to describe, and what each embodiment stressed is the difference with other embodiments, between each embodiment identical similar part mutually see.

Above-described embodiment, only for technical conceive of the present invention and feature are described, its object is to person skilled in the art can be understood content of the present invention and implement according to this, can not limit the scope of the invention with this.All equivalences done according to Spirit Essence of the present invention change or modify, and all should be encompassed within protection scope of the present invention.

Claims (8)

1. a Productivity for the tight gas reservoir horizontal well after multistage fracturing reform, is characterized in that: it comprises the following steps

Steps A), set up physical model, described physical model has to give a definition: A1) stratum homogeneous uniform thickness, the face of overlooking on stratum is rectangle, and this rectangle has four and closes and the border of equipressure, and the wide of described rectangle is x _e, this value is carried out well test analysis by formation and is obtained, and the length of described rectangle is y _e, this value is carried out well test analysis by formation and is obtained; A2) have n crack, all n cracks run through stratum completely, wherein n=1,2,3 ..., the 1st crack is positioned at the butt of this horizontal well pit shaft, and the i-th crack is arranged to the toe-end of this horizontal well pit shaft gradually, wherein i=1,2,3 ..., n;

Described physical model is defined as follows characteristic:

$P_D=\frac{78.55\mathrm{kh}(P_i^2-P^2)}{\mathrm{\&mu;}{\mathrm{ZTQ}}_{\mathrm{sc}}},q_D=\frac{2x_f{q}_{\mathrm{sc}}}{Q_{\mathrm{sc}}},j_D=\frac{j}{x_f}(j=x,y),C_{\mathrm{fD}}=\frac{k_f{w}_f}{{\mathrm{kx}}_f}$

In formula:

P _drepresent dimensionless pressure; P _irepresent original formation pressure; P represents strata pressure; T represents formation temperature; K represents in-place permeability; H represents formation thickness; μ represents gas viscosity; Z represents Gaseous Z-factor, and it is obtained by laboratory experiment; Q _sccrack flow under representative mark condition; q _drepresent dimensionless crack flow; q _scfor Biao Kuangxia unit fracture length flow; j _dfor non-dimensional length; x _ffor fracture half-length; C _fDfor dimensionless fracture condudtiviy; k _ffor fracture permeabgility; w _ffor crack width; X, y are the coordinate of j in physical model;

Step B), physically based deformation model, according to gas percolation law in the earth formation, obtains arbitrary in the n crack dimensionless pressure P caused _dwith this crack dimensionless crack flow q _d(α) relational expression between, P _d(x _d, y _d; x _wD, y _wD)

$=2\underset{x_{\mathrm{wD}-1}}{\overset{x_{\mathrm{wD}}+1}{\&Integral;}}\left\{\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{q_D\left(\mathrm{\&alpha;}\right)}{\mathrm{m\&pi;}}\sin \frac{\mathrm{m\&pi;}{x}_D}{x_{\mathrm{eD}}}\sin \frac{\mathrm{m\&pi;\&alpha;}}{x_{\mathrm{eD}}}\frac{\cosh \frac{\mathrm{m\&pi;}(y_{\mathrm{eD}}-|y_{D-}{y}_{\mathrm{wD}}\left|\right)}{x_{\mathrm{eD}}}-\cosh \frac{\mathrm{m\&pi;}(y_{\mathrm{eD}}-|y_D+y_{\mathrm{wD}}\left|\right)}{x_{\mathrm{eD}}}}{\sinh \frac{\mathrm{m\&pi;}{y}_{\mathrm{eD}}}{x_{\mathrm{eD}}}}\right\}\mathrm{d\&alpha;}$

In formula: x _w, y _wfor fissured central coordinate, it is obtained by the definition of physical model;

Step C), physically based deformation model, according to the flowing relation of gas in crack and the border coupled relation between crack and stratum, obtains in n crack arbitrary at the pressure disturbance P produced with pit shaft contact position _wfnwith the Q of this crack flow under mark condition _scnrelational expression,

$\begin{array}{c}\frac{78.55\mathrm{kh}(P_i^2-P_{\mathrm{wfn}}^2)}{\mathrm{\&mu;}{\mathrm{ZTQ}}_{\mathrm{scn}}}=\frac{1}{C_{\mathrm{fD}}{x}_f}[\ln \frac{h}{2r_w}-\frac{\mathrm{\&pi;}}{2}]+f\left(C_{\mathrm{fD}}\right)\\ +2\left\{\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{x_e^2}{m^3{\mathrm{\&pi;}}^2{x}_f^2}{\sin }^2\frac{\mathrm{m\&pi;}{x}_f}{x_e}{\sin }^2\frac{\mathrm{m\&pi;}{x}_w}{x_e}\frac{\cosh \frac{\mathrm{m\&pi;}{y}_e}{x_e}-\cosh \frac{\mathrm{m\&pi;}(y_e-2y_w)}{x_e}}{\sinh \frac{\mathrm{m\&pi;}{y}_e}{x_e}}\right\}\end{array},$

In formula: P _wfnfor arbitrary in n crack is in the pressure disturbance produced with pit shaft contact position; r _wfor horizontal wellbore radius;

Step D), physically based deformation model, according to gas flowing relation in the wellbore and the border coupled relation between crack and pit shaft, obtains in n crack arbitrary at the pressure disturbance P produced with pit shaft contact position _wfi, adjacent with this crack crack is at the pressure disturbance P produced with pit shaft contact position _wfi-1and this two crack in pit shaft between flow Q _scirelational expression,

$P_{\mathrm{wfi}}^2-P_{\mathrm{wfi}-1}^2=9\&times;{10}^{-12}\frac{{\mathrm{ZT\&gamma;}}_g}{r_w^5}{f}_i{d}_i{\left(\underset{j=i}{\overset{n}{\mathrm{\&Sigma;}}}{Q}_{\mathrm{scj}}\right)}^2$

Wherein, P _wf0=P _wf;

In formula: Z is Gaseous Z-factor; γ _gfor gas relative density; F is the coefficient of friction resistance; D is fracture interval;

Step e), estimate the flow Q of the n-th crack _scn, measure and obtain the 1st crack at the pressure disturbance P produced with pit shaft contact position _wf, utilize Numerical Iteration Method to obtain this horizontal well capacity.

2. Productivity according to claim 1, it is characterized in that: in step C) in, the flowing relation of gas in crack will consider the radial conflux effect of the seepage effect in crack, the difference between infinite fluid diversion crack and limited fluid diversion crack and pit shaft.

3. Productivity according to claim 1, is characterized in that: in step e) in, further comprising the steps of:

E1) the maximum value Q of the n-th crack flow is estimated according to practical condition _{scn (max)}with minimum value Q _{scn (min)}, get the arithmetic average Q of maxima and minima _{scn (mid)}=0.5 × [Q _{scn (max)}+ Q _{scn (min)}];

E2) according to step C) in formulae discovery obtain corresponding P _{wfn (max)}, P _{wfn (min)}and P _{wfn (mid)}, according to step D) in formula obtain corresponding P _{wfn-1 (max)}, P _{wfn-1 (min)}and P _{wfn-1 (mid)}, according to step C) in formulae discovery obtain corresponding Q _{scn-1 (max)}, Q _{scn-1 (min)}, Q _{scn-1 (mid)};

E3) step e 2 is repeated) obtain P _{wf0 (max)}, P _{wf0 (min)}, P _{wf0 (mid)};

E4) by P _{wf0 (mid)}with P _wfcarry out difference comparsion, if P _{wf0 (mid)}with P _wfdifference meet required precision and then judge calculated value P _{wf0 (mid)}correctly, if P _{wf0 (mid)}with P _wfdifference do not meet required precision, if then (P _{wf0 (max)}-P _wf) × (P _{wf0 (min)}-P _wf) <0, so Q _{scn (min)}=Q _{scn (mid)}, otherwise Q _{scn (max)}=Q _{scn (mid)};

E5) step e 1 is repeated) to E4), until P _{wf0 (mid)}with P _wfdifference meet required precision.

4. Productivity according to claim 1, is characterized in that: in step D) in, described coefficient of friction resistance f is obtained by following formulae discovery:

$f_i={[1.14-2\lg (\frac{e}{1000D}+\frac{21.25}{R_{\mathrm{ei}}^{0.9}})]}^{-2},$

wherein, e is shaft in wall roughness.

5. Productivity according to claim 1, is characterized in that: this horizontal well capacity is wherein, j=1,2,3 ..., n.

6. Productivity according to claim 1, is characterized in that: described P _iby obtaining unquarried stratum measurement, described P obtains by carrying out measurement to the stratum after exploitation, described T obtains by carrying out measurement to the temperature on the stratum after exploitation, described k is obtained by laboratory experiment or well test analysis, described h is obtained by well log interpretation, described μ is obtained by laboratory experiment, and described Z is obtained by laboratory experiment, described x _fobtained by well test analysis, described k _fobtained by well test analysis, described w _fobtained by well test analysis.

7. Productivity according to claim 1, is characterized in that: described Z is obtained by laboratory experiment; Described γ _gobtained by laboratory experiment, described d is obtained by FRACTURING DESIGN data.

8. adopt the AOF calculation system as the computational methods of one of claim 1 to 7, it is characterized in that: it comprises

Modeling unit, it is for setting up physical model;

First computing unit, it is for obtaining arbitrary in the n crack dimensionless pressure P caused according to gas percolation law in the earth formation _dwith this crack dimensionless crack flow q _d(α) relational expression between;

Second computing unit, it is for obtaining in n crack arbitrary at the pressure disturbance P produced with pit shaft contact position according to the flowing relation of gas in crack and the border coupled relation between crack and stratum _wfnwith the Q of this crack flow under mark condition _scnrelational expression;

3rd computing unit, it is for obtaining in n crack arbitrary at the pressure disturbance P produced with pit shaft contact position according to the flowing relation of gas in crack and the border coupled relation between crack and stratum _wfi, adjacent with this crack crack is at the pressure disturbance P produced with pit shaft contact position _wfi-1and this two crack in pit shaft between flow Q _scirelational expression;

4th computing unit, it is for receiving the flow Q of estimation n-th crack _scn, it obtains the 1st crack at the pressure disturbance P produced with pit shaft contact position for receiving by measuring _wf, it obtains this horizontal well capacity for adopting Numerical Iteration Method.