CN103590824A - Productivity calculation method for tight gas horizontal wells modified by multi-stage fracturing - Google Patents

Abstract

The invention discloses a productivity calculation method for tight gas horizontal wells modified by multi-stage fracturing. The productivity calculation method includes the steps of building a physical model, acquiring the relation between the dimensionless pressure PD generated by any one of n fractures and the dimensionless fracture flow qD(alpha) of the fracture, acquiring the relation between the pressure disturbance Pwfn generated at the contact position of any one of the fracture with a well shaft and the fracture flow Qscn on standard conditions according to the flowing relation of gas in the fractures and the boundary coupling relation between the fractures and the stratum, acquiring the relation among the pressure disturbance Pwfi generated at the contact position of any one of the fractures with the well shaft, the pressure disturbance Pwfi-1 generated at the contact position of the adjacent fracture with the well shaft, and the flow Qsci of the two fractures in the well shaft according to the flowing relation of the gas in the well shaft and the boundary coupling relation between the fractures and the well shaft, and finally calculating the productivity of the horizontal wells by means of numeric iteration.

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, related in particular to a kind of Productivity of the tight gas reservoir horizontal well after multistage fracturing reform.The present invention relates to a kind of production capacity computing system, related in particular to the horizontal well capacity computing system of a kind of tight gas reservoir after multistage fracturing reform.

Background technology

Tight gas reservoir (Tight Gas) 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, has become the main growth point of gas production gradually.In prior art, often adopt horizontal well to exploit tight gas reservoir.Horizontal well refers to that hole angle reaches or approaches 90 ° and well bore and along horizontal direction, creeps into the well of certain length.Horizontal well, after multistage fracturing reform, forms many transverse cracks (hereinafter to be referred as " crack ") that form is different.Crack is along the direction crack initiation perpendicular to pit shaft.Crack has increased the contact area on gas well and stratum greatly, has improved the shaft bottom seepage flow condition of reservoir around simultaneously, has increased oil reservoir drainage area.The gas of tight gas reservoir flows in ， crack, crack and flows to pit shaft from formation pore, and then flows to well head along pit shaft.

For the tight gas reservoir horizontal well to after multistage fracturing reform carries out production prediction, those skilled in the art have carried out the research deepening continuously.Aspect the limited water conservancy diversion research in crack, fractured model develops into multiple cracking again to volume fracturing from monolete, and method for solving develops into half analytic solutions again to numerical method from analytic method, and simulation precision improves constantly.Fractured horizontal well's productivity evaluation aspect, Fan Zifei utilizes the flow performance of horizontal wellbore to set up the Coupled with Flow model of reservoir and pit shaft, the correction of Li Xiaoping application volumetric balance principle 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, to compare flow area much bigger for the crack of tight gas reservoir horizontal well and pit shaft, so need to take into full account the impact that man-made fracture flows on gas well deliverability.

Summary of the invention

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

The Productivity that the invention discloses a kind of 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, and the face of overlooking on stratum is rectangle, and this rectangle has four closures and isobaric border, and the wide of described rectangle is x _e, this value obtains by well test analysis is carried out in stratum, and the length of described rectangle is y _e, this value obtains by well test analysis is carried out in stratum; A2) have n crack, all n cracks run through stratum completely, n=1 wherein, 2,3 ..., the 1st crack is positioned at the butt of this horizontal well pit shaft, and i crack is arranged to the toe-end of this horizontal well pit shaft gradually, i=1 wherein, 2,3 ..., n;

Described physical model is defined as follows characteristic:

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

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 obtains by laboratory experiment; Q _sccrack flow under representative mark condition; q _drepresent dimensionless crack flow; q _scwei Biaokuangxia unit's fracture length flow; j _dfor dimensionless length; x _ffor fracture half-length; C _fDfor dimensionless fracture condudtiviy; k _ffor fracture permeabgility; w _ffor crack width;

Step B), based on physical model, the percolation law according to gas in stratum, obtains arbitrary in the n crack dimensionless pressure P causing _dwith this crack dimensionless crack flow q _d(α) relational expression between,

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

In formula: x _w, y _wfor crack centre coordinate, its definition by physical model obtains;

Step C), based on physical model, the border coupled relation between the flowing relation according to gas in crack and crack and stratum, obtains in n crack arbitrary at the pressure disturbance P producing with pit shaft contact position _wfnq with this crack flow under mark condition _scnrelational expression,

$\begin{array}{c}\frac{78.55\mathrm{kh}(P_i^2-P_{\mathrm{wfn}}^2)}{{\mathrm{\&mu;ZTQ}}_{\mathrm{scn}}}=\frac{1}{C_{\mathrm{fD}}}\frac{h}{x_f}[\ln \frac{h}{{2r}_w}-\frac{\mathrm{\&pi;}}{2}]+f\left(C_{\mathrm{fD}}\right)\\ +2\left\{\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{x_e^2}{m^3{\mathrm{\&pi;}}^2{x}_{\mathrm{<figure-callout\; id="2"\; label="f"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">f</figure-callout>}}^2}{\sin }^2\frac{{\mathrm{m\&pi;x}}_f}{x_e}{\sin }^2\frac{{\mathrm{m\&pi;x}}_w}{x_e}\frac{\cosh \frac{{\mathrm{m\&pi;y}}_e}{x_e}-\cosh \frac{\mathrm{m\&pi;}(y_e-{2y}_w)}{x_e}}{\sinh \frac{{\mathrm{m\&pi;y}}_e}{x_e}}\right\}\end{array},$

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

Step D), based on physical model, the border coupled relation between the flowing relation according to gas in pit shaft and crack and pit shaft, obtains in n crack arbitrary at the pressure disturbance P producing with pit shaft contact position _wfi, the crack adjacent with this crack be at the pressure disturbance P producing with pit shaft contact position _wfi-1and the flow Q of this two crack between in pit shaft _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 n crack _scn, measure the 1st crack at the pressure disturbance P with the generation of pit shaft contact position _wf, utilize Numerical Iteration Method to obtain this horizontal well capacity.

Preferably, at step C) in, the flowing relation of gas in crack will be considered difference between seepage effect, infinite fluid diversion crack and the limited water conservancy diversion crack in crack and the radially conflux effect of pit shaft.

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

E1) according to practical condition, estimate the maximum value Q of n crack flow _{scn (max)}with minimum value Q _{scn (min)}, get the arithmetic average Q of maximum value and minimum value _{scn (mid)}=0.5 * [Q _{scn (max)}+ Q _{scn (min)}];

E2) according to step C) in formula calculate 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 formula calculate corresponding Q _{scn-1 (max)}, Q _{scn-1 (min)}, Q _{scn-1 (mid)};

E3) repeating step E2) obtain P _{wf0 (max)}, P _{wf0 (min)}, P _{wf0 (mid)};

E4) by P _{wf0 (mid)}with P _wfcarry out difference comparison, if P _{wf0 (mid)}with P _wfdifference meet required precision and judge calculated value P _{wf0 (mid)}correctly, if P _{wf0 (mid)}with P _wfdifference do not meet required precision, if (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) repeating step E1) to E4), until P _{wf0 (mid)}with P _wfdifference meet required precision.

Preferably, at step D) in, described friction factor f is calculated by following formula:

$f_i=[1.14-21g(\frac{e}{1000D}+\frac{21.25}{R_{\mathrm{ei}}^{0.9}}){]}^{-2},$

wherein, e is shaft in wall roughness.

Preferably, this horizontal well capacity is

wherein, j=1,2,3 ..., n.

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

Preferably, described Z obtains by laboratory experiment; Described γ _gby laboratory experiment, obtain, described d obtains by FRACTURING DESIGN data.

The invention also discloses a kind of production capacity computing system that adopts above-mentioned computational methods, it comprises

Modeling unit, it is for setting up physical model;

The first computing unit, it is for according to gas, the percolation law on stratum obtains arbitrary in the n crack dimensionless pressure P causing _dwith this crack dimensionless crack flow q _d(α) relational expression between;

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

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

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

The inventor introduces tight gas reservoir fractured horizontal well's productivity list fracturing section and evaluates thinking, take single fracturing section as unit, application quality conservation principle is by seepage flow, crack endometamorphism amount seepage flow and the coupling of pit shaft channel flow with vari able mass flow rate Liu Liangyanliudongfangxiangbianhua in reservoir, the changes in flow rate of the different fracturing sections of research level well, derive to set up the theoretical formula that is 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, thereby form the new method that a set of tight gas reservoir staged fracturing horizontal productivity is evaluated.The present invention is based on percolation hydraulic theory, the flowing law of learning gas in stratum, crack, three autonomous systems of pit shaft, by the principle of mass conservation, seepage flow, crack endometamorphism amount seepage flow and pit shaft channel flow with vari able mass flow rate Liu Liangyanliudongfangxiangbianhua in reservoir are coupled, and determine multistage fractured horizontal well's productivity by iterative algorithm.

Accompanying drawing explanation

Figure 1A has shown the physical model of horizontal well.

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

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

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

Fig. 4 has shown limited water conservancy diversion crack bottom pressure and flow conductivity variation relation.

Fig. 5 has shown the pit shaft conflux effect in crack.

Fig. 6 has shown flow in horizontal pipe sectional drawing in horizontal wellbore.

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

Fig. 8 has shown under different flowing bottomhole pressure (FBHP)s that each crack is along the pressure distribution of horizontal wellbore.

Fig. 9 has shown the well track of this well.

The specific embodiment

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

The 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.Based on physical model, the percolation law according to gas in stratum, obtains arbitrary in the n crack dimensionless pressure P causing _dwith this crack dimensionless crack flow q _d(α) relational expression between.Based on physical model, the border coupled relation between the flowing relation according to gas in crack and crack and stratum, obtains in n crack arbitrary at the pressure disturbance P producing with pit shaft contact position _wfnq with this crack flow under mark condition _scnrelational expression.Based on physical model, the border coupled relation between the flowing relation according to gas in pit shaft and crack and pit shaft, obtains in n crack arbitrary at the pressure disturbance P producing with pit shaft contact position _wfi, the crack adjacent with this crack be at the pressure disturbance P producing with pit shaft contact position _wfi-1 and the flow Q of this two crack between in pit shaft _scirelational expression.Estimate the flow Q of n crack _scn, measure the 1st crack at the pressure disturbance P with the generation of 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 closures and isobaric border.The wide of described rectangle is x _e, this value obtains by well test analysis is carried out in stratum, and the length of described rectangle is y _e, this value obtains by well test analysis is carried out in stratum.A2) have n crack, all n cracks run through stratum completely, n=1 wherein, 2,3 ..., the 1st crack is positioned at the butt of this horizontal well, and i crack is arranged to the toe-end of this horizontal well gradually, i=1 wherein, 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 above-mentioned formula: P _dfor dimensionless pressure.P _ifor original formation pressure, it is by unquarried stratum measurement is obtained, and unit is MPa (MPa).P is strata pressure, and it measures by the stratum to after exploitation, and unit is MPa (MPa).T is formation temperature, and its temperature by the stratum to after exploitation measures, and unit is Kelvin (K); K is in-place permeability, and it obtains ，Qi unit by laboratory experiment or well test analysis is darcy (D).H is formation thickness, and it obtains ，Qi unit for rice (m) by well log interpretation. μ is gas viscosity, and it obtains ，Qi unit for milli handkerchief second (mPas) by laboratory experiment.Z is Gaseous Z-factor, and it obtains by laboratory experiment.Q _scfor crack flow ，Qi unit under mark condition is 10 ⁴* cubic meter/days (10 ⁴m ³/ d) .q _dfor dimensionless crack flow.Q _scfracture length flow ，Qi unit of Wei Biaokuangxia unit is 10 ⁴* cubic meter/day/rice (10 ⁴m ³/ d/m).J _dfor dimensionless length.X _ffor fracture half-length, it obtains ，Qi unit for rice (m) by well test analysis.C _fDfor dimensionless fracture condudtiviy.K _ffor fracture permeabgility, it obtains ，Qi unit by well test analysis is darcy (D).W _ffor crack width, it obtains ，Qi unit for rice (m) by well test analysis.

Well test analysis be take percolation hydraulic theory exactly as basis, by the research to oil well test information, and the method for the various physical parameters of definite reflection testing well and formation characteristics, production capacity etc.

Well log interpretation is determined the relation of applying between well logging information and geological information, adopts on sound lines well logging information is processed into geological information.

Figure 1A has shown 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 has shown the gas flow schematic diagram in wall scroll crack in Figure 1A.In Figure 1B, gas from stratum along hyperbola form streamline flow to crack.Gas, from stratum flow into crack, moves to horizontal wellbore by seepage effect.Because stratum is run through in crack completely, can think flowing for one-dimensional linear flows in crack, and this flowing is that a kind of variable mass changing along fracture length flows.Because pit shaft internal diameter is far longer than the flow channel size in stratum and crack, so the gas flow in pit shaft is calculated by phasmajector stream.

In this physical model, the gas in stratum is followed Darcy's law (Darcy ' s Law), is that the Darcy of variable mass flows in crack, be that the pipe of variable mass flows in horizontal wellbore.The mutual interference of three kinds of type of flow phases, is coupled by crossing border.

At step B) in, based on physical model, the percolation law according to gas in stratum, obtains arbitrary in the n crack dimensionless pressure P causing _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.On stratum, be hyperbola streamline region in addition, the streamline form of gas radially, shows as pseudoradial flow feature.

According to Laplace transform formula, obtain formula (1):

$\frac{{\&PartialD;}^2{P}_D}{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="x\; D"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">x</figure-callout>}}_D^{}}+\frac{{\&PartialD;}^2{P}_D}{{\&PartialD;\mathrm{<figure-callout\; id="2"\; label="y\; D"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">y</figure-callout>}}_D^{}}+q_D\left(x_D\right)\mathrm{\&delta;}(y_D-y_{\mathrm{wD}})=0---\left(1\right)$

The four edges circle equipressure on the stratum based on defining in physical 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 crack centre coordinate, its definition by physical model obtains ，Qi unit for rice (m).δ is Di Like function.

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

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

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

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

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

${-\mathrm{\&pi;}}^2(\frac{m^2}{x_{\mathrm{<figure-callout\; id="2"\; label="eD"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">eD</figure-callout>}}^2}+\frac{n^2}{y_{\mathrm{eD}}^2}){\stackrel{\widehat{\&OverBar;}}{P}}_D+{\tilde{q}}_D\sin {\mathrm{\&gamma;}}_n{y}_{\mathrm{wD}}=0---\left(7\right)$

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

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

Characteristic value wherein:

β _m=mπ/x _eD；γ _n=nπ/y _eD （9）

Norm is reciprocal to be met:

$N\left({\mathrm{\&beta;}}_m\right)={\&Integral;}_0^{x_{\mathrm{eD}}}{\sin }^2\left({\mathrm{\&beta;}}_m{x}_D\right){\mathrm{dx}}_D=\frac{x_{\mathrm{<figure-callout\; id="2"\; label="eD"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">eD</figure-callout>}}}{2};N\left({\mathrm{\&gamma;}}_n\right)={\&Integral;}_0^{y_{\mathrm{eD}}}{\sin }^2\left({\mathrm{\&gamma;}}_n{y}_D\right){\mathrm{dy}}_D=\frac{y_{\mathrm{eD}}}{2}---\left(10\right)$

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

$P_D=\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{2{\tilde{q}}_D}{x_{\mathrm{eD}}{y}_{\mathrm{eD}}}\sin \frac{{\mathrm{m\&pi;x}}_D}{x_{\mathrm{eD}}}\left[\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{\cos \mathrm{n\&pi;}(y_D-y_{\mathrm{wD}})/y_{\mathrm{eD}}-\cos \mathrm{n\&pi;}(y_D+y_{\mathrm{wD}})/y_{\mathrm{eD}}}{{\mathrm{\&pi;}}^2({\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">m</figure-callout>}}^2/{\mathrm{<figure-callout\; id="2"\; label="x\; eD"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">x</figure-callout>}}_{\mathrm{eD}}^{}+{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">n</figure-callout>}}^2/y_{\mathrm{eD}}^2)}\right]---\left(11\right)$

Only have and along crack, just have flow distribution, 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:

$\underset{k=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{\cos \mathrm{k\&pi;x}}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+a^2}=\frac{\mathrm{\&pi;}}{2a}\frac{\cosh \left[\mathrm{a\&pi;}(1-x)\right]}{\sinh \left(\mathrm{a\&pi;}\right)}-\frac{1}{{2a}^2};[0\&le;x\&le;2\mathrm{\&pi;}]---\left(13\right)$

Utilize formula (12), formula (13) rewriting formula (11), obtain arbitrary in the n crack dimensionless pressure P causing _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 crack centre coordinate, its definition by physical model obtains ，Qi unit for rice (m).

At step C) in, based on physical model, the border coupled relation between the flowing relation according to gas in crack and crack and stratum, obtains in n crack arbitrary at the pressure disturbance P producing with pit shaft contact position _wfnq with this crack flow under mark condition _scnrelational expression:

$\begin{array}{c}\frac{78.55\mathrm{kh}(P_i^2-P_{\mathrm{wfn}}^2)}{{\mathrm{\&mu;ZTQ}}_{\mathrm{scn}}}=\frac{1}{C_{\mathrm{fD}}}\frac{h}{x_f}[\ln \frac{h}{{2r}_w}-\frac{\mathrm{\&pi;}}{2}]+f\left(C_{\mathrm{fD}}\right)\\ +2\left\{\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{x_e^2}{m^3{\mathrm{\&pi;}}^2{\mathrm{<figure-callout\; id="2"\; label="x\; f"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">x</figure-callout>}}_f^{}}{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\frac{{\mathrm{m\&pi;x}}_f}{{\mathrm{<figure-callout\; id="2"\; label="x\; e\; sin"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">x</figure-callout>}}_e}{\sin }^{}{}^2\frac{{\mathrm{m\&pi;x}}_w}{x_e}\frac{\cosh \frac{{\mathrm{m\&pi;y}}_e}{x_e}-\cosh \frac{\mathrm{m\&pi;}(y_e-{2y}_w)}{x_e}}{\sinh \frac{{\mathrm{m\&pi;y}}_e}{x_e}}\right\}\end{array},$

In formula: P _wfnfor arbitrary in n crack in the pressure disturbance ，Qi unit producing with pit shaft contact position, be MPa (MPa).R _wfor the radius of pit shaft, it obtains ，Qi unit for rice (m) by technical manual.

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

Because crevice volume is less, elasticity is less, can ignore the flexible impact in crack, and the dimensionless seepage flow equation simplification by fluid in crack is form stable, obtains formula (15) and formula (16).

$\frac{d^2{P}_{\mathrm{<figure-callout\; id="2"\; label="fD\; dx\; D"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">fD</figure-callout>}}}{{\mathrm{dx}}_D^{}}+\frac{2}{C_{\mathrm{fD}}}{q}_D\left(x_D\right)=0,[-1\&le;x_D\&le;1]---\left(15\right)$

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

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

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

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

$\begin{array}{c}{P}_{\mathrm{wD}}+2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{q}_{\mathrm{Di}}\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\left\{\begin{array}{c}\frac{{\mathrm{<figure-callout\; id="2"\; label="x\; eD\; m"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">x</figure-callout>}}_{\mathrm{eD}}}{m^{}}\sin \mathrm{m\&pi;}\frac{x_{\mathrm{wD}}+(j-0.5)\mathrm{\&Delta;x}}{x_{\mathrm{eD}}}[\cos \mathrm{m\&pi;}\frac{x_{\mathrm{wD}}+\mathrm{i\&Delta;}{x}_D}{x_{\mathrm{eD}}}-\cos \mathrm{m\&pi;}\frac{x_{\mathrm{wD}}+(i-1)\mathrm{\&Delta;}{x}_D}{x_{\mathrm{eD}}}\\ \&times;\frac{\cosh [\mathrm{m\&pi;}{y}_{\mathrm{eD}}/x_{\mathrm{eD}}]-\cosh [\mathrm{m\&pi;}(y_{\mathrm{eD}}-|2y_{\mathrm{wD}}\left|\right)/x_{\mathrm{eD}}]}{\sinh (\mathrm{m\&pi;}{y}_{\mathrm{eD}}/x_{\mathrm{eD}})}\end{array}\right\}\\ =\frac{\mathrm{\&pi;}}{C_{\mathrm{fD}}}\{(x_{\mathrm{wD}}+(j-0.5)\mathrm{\&Delta;x})(1-\underset{i=1}{\overset{j-1}{\mathrm{\&Sigma;}}}{q}_{\mathrm{Di}}{\mathrm{\&Delta;x}}_D-\frac{{\mathrm{\&Delta;x}}_D}{2}{q}_{\mathrm{Dj}})+\underset{i=1}{\overset{j-1}{\mathrm{\&Sigma;}}}{q}_{\mathrm{Di}}\mathrm{\&Delta;}{x}_D[x_{\mathrm{wD}}+(i-0.5)\mathrm{\&Delta;}{x}_D]+q_{\mathrm{Dj}}\mathrm{\&Delta;}{x}_D\frac{x_{\mathrm{wD}}+(j-0.75)\mathrm{\&Delta;}{x}_D}{2}\}\end{array}---\left(19\right)$

Traffic constraints equation

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

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

$P_{\mathrm{infwD}}=2\left\{\underset{n=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{{\mathrm{<figure-callout\; id="2"\; label="x\; eD\; n"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">x</figure-callout>}}_{\mathrm{eD}}}{n^{}}\sin \mathrm{n\&pi;}\frac{x_D}{x_{\mathrm{eD}}}\sin \mathrm{n\&pi;}\frac{1}{x_{\mathrm{eD}}}\sin \mathrm{n\&pi;}\frac{x_{\mathrm{wD}}}{x_{\mathrm{eD}}}\frac{\cosh \frac{{\mathrm{n\&pi;y}}_{\mathrm{eD}}}{x_{\mathrm{eD}}}-\cosh \frac{\mathrm{n\&pi;}(y_{\mathrm{eD}}-{2y}_{\mathrm{wD}})}{x_{\mathrm{eD}}}}{\sinh \frac{{\mathrm{n\&pi;y}}_{\mathrm{eD}}}{x_{\mathrm{eD}}}}\right\}---\left(22\right)$

Fig. 5 has shown the pit shaft conflux effect in crack.As shown in Figure 5, near the nearly pit shaft in crack, can form Radial Flow simultaneously, compare with vertically fractured well and can produce additional Pressure Drop, the i.e. radially conflux effect of pit shaft.Introducing skin factor herein takes in.

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

So, considered the bottom pressure P in the limited water conservancy diversion crack of pit shaft conflux effect _finwDcan obtain:

P _finwD=P _infwD+f(C _fD)+skin （24）

Have the bottom pressure after dimension is launched to be:

$\begin{array}{c}\frac{78.55\mathrm{kh}(P_i^2-P_{\mathrm{wfn}}^2)}{{\mathrm{\&mu;ZTQ}}_{\mathrm{scn}}}=\frac{1}{C_{\mathrm{fD}}}\frac{h}{x_f}[\ln \frac{h}{{2r}_w}-\frac{\mathrm{\&pi;}}{2}]+f\left(C_{\mathrm{fD}}\right)\\ +2\left\{\underset{m=1}{\overset{\&infin;}{\mathrm{\&Sigma;}}}\frac{x_e^2}{m^3{\mathrm{\&pi;}}^2{\mathrm{<figure-callout\; id="2"\; label="x\; f"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">x</figure-callout>}}_f^{}}{\mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">sin</figure-callout>}}^2\frac{{\mathrm{m\&pi;x}}_f}{{\mathrm{<figure-callout\; id="2"\; label="x\; e\; sin"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">x</figure-callout>}}_e}{\sin }^{}{}^2\frac{{\mathrm{m\&pi;x}}_w}{x_e}\frac{\cosh \frac{{\mathrm{m\&pi;y}}_e}{x_e}-\cosh \frac{\mathrm{m\&pi;}(y_e-{2y}_w)}{x_e}}{\sinh \frac{{\mathrm{m\&pi;y}}_e}{x_e}}\right\}\end{array}---\left(25\right)$

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

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

At step D) in, based on physical model, the border coupled relation between the flowing relation according to gas in pit shaft and crack and pit shaft, obtains in n crack arbitrary at the pressure disturbance P producing with pit shaft contact position _wfi, the crack adjacent with this crack be at the pressure disturbance P producing with pit shaft contact position _wfi-1and the flow Q of this two crack between in pit shaft _scirelational expression.

Fig. 6 has shown flow in horizontal pipe sectional drawing in horizontal wellbore.As shown in Figure 6, because pit shaft internal diameter is far longer than the flow channel size in stratum and crack, so the gas flow in pit shaft is calculated by phasmajector stream.Flow in horizontal wellbore changes, and therefore, adopts segmentation to calculate herein.Ignore because flow velocity increases the kinetic energy pressure drop causing, according to (Li Shilun, Deng. gas engineering [M]. Beijing: petroleum industry publishing house, 2008.Li S L, et al.Natural Gas Engineering[M] .Beijing:Petroleum Industry Press, 2008.) content in, gross pressure gradient is:

$\frac{\mathrm{dP}}{\mathrm{dy}}=f\frac{{\mathrm{\&rho;<figure-callout\; id="2"\; label="v"\; filenames="HDA0000398988010000041.png"\; state="\{\{state\}\}">v</figure-callout>}}^2}{{2r}_w}---\left(26\right)$

Adopt mean parameter method variables separation integration, obtain in n crack arbitrary at the pressure disturbance P producing with pit shaft contact position _wfi, the crack adjacent with this crack be at the pressure disturbance P producing with pit shaft contact position _wfi-1and the flow Q of this two crack between in pit shaft _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) (27)

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

$f_i=[1.14-21g(\frac{e}{1000D}+\frac{21.25}{R_{\mathrm{ei}}^{0.9}}){]}^{-2}---\left(28\right)$

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

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

E1) according to practical condition, estimate the maximum value Q of n crack flow _{scn (max)}with minimum value Q _{scn (min)}, get the arithmetic average Q of maximum value and minimum value _{scn (mid)}=0.5 * [Q _{scn (max)}+ Q _{scn (min)}];

E2) according to step C) in formula calculate 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 formula calculate corresponding Q _{scn-1 (max)}, Q _{scn-1 (min)}, Q _{scn-1 (mid)};

E3) repeating step E2) obtain P _{wf0 (max)}, P _{wf0 (min)}, P _{wf0 (mid)};

E4) by P _{wf0 (mid)}with P _wfcarry out difference comparison, if P _{wf0 (mid)}with P _wfdifference meet required precision and judge calculated value P _{wf0 (mid)}correctly, if P _{wf0 (mid)}with P _wfdifference do not meet required precision, if (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) repeating step E1) 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 exceeded the scope allowing.

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

This horizontal well capacity is

wherein, j=1,2,3 ..., n.

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

Compare 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 theoretical prediction method of stratum-crack-pit shaft overall process, greatly improved theoretically the degree of accuracy of tight gas reservoir multistage fractured horizontal well's productivity prediction.

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

The basic parameter of table 1 Soviet Union Sulige gas field well

The multistage fracture parameters of table 2 Soviet Union Sulige gas field well after artificial fracturing

As bottom pressure P _wfduring=0.1MPa, consider that each crack flow of pit shaft frictional resistance 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 ³it is 40.72 * 10 that/d scene utilizes pressure buildup test data and this well capacity of Topaze well test analysis software evaluation ⁴m ³/ d, relative error is 0.98%, has verified the correctness of model and algorithm.

Calculate the gas well flow Q under different bottom pressures (0.1MPa, 1MPa, 5MPa, 10MPa, 20MPa) _scand draw Fig. 7, each crack flow (table 3) and distribute and draw Fig. 8 along wellbore pressure.Fig. 7 has shown flow and the bottom pressure variation relation figure of horizontal well.Fig. 8 has shown under different flowing bottomhole pressure (FBHP)s that each crack is along the pressure distribution of horizontal wellbore.As shown in Figure 7, pit shaft frictional resistance is to gas well flow Q _scimpact with the reducing and increase 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 along the pressure distribution homogeneous of pit shaft, and difference is less.Table 3 has reflected that crack constantly increases to heel end flow from the toe-end of pit shaft when considering frictional resistance.

Fig. 9 has shown the well track of this well.From the well track figure of this well of Fig. 9, near the reservoir of toe-end, almost do not implement sand fracturing, and pit shaft toe-end bores and met one section of invalid reservoir, so pit shaft toe-end part almost do not have traffic contributions.

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

The invention also discloses a kind of production capacity computing system that adopts 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 closures and isobaric border.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, n=1 wherein, 2,3 ..., the 1st crack is positioned at the butt of this horizontal well, and i crack is arranged to the toe-end of this horizontal well gradually, i=1 wherein, 2,3 ..., n.

The first computing unit, it is for according to gas, the percolation law on stratum obtains arbitrary in the n crack dimensionless pressure P causing _dwith this crack dimensionless crack flow q _d(α) relational expression between, concrete formula can be referring to formula (14).

The second computing unit, it is for obtaining in n crack arbitrary at the pressure disturbance P producing with pit shaft contact position according to gas at the flowing relation in crack and the border coupled relation between crack and stratum _wfnq with this crack flow under mark condition _scnrelational expression, concrete formula can be referring to formula (25).

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

The 4th computing unit, it is for receiving the flow Q of estimation n crack _scn, it is for receiving by measuring the 1st crack at the pressure disturbance P with the generation of pit shaft contact position _wf, it is for adopting Numerical Iteration Method to obtain this horizontal well capacity, 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 each embodiment stresses is the difference with other embodiment, between each embodiment identical similar part mutually referring to.

Above-described embodiment is only explanation technical conceive of the present invention and feature, and its object is to allow person skilled in the art can understand content of the present invention and implement according to this, can not limit the scope of the invention with this.All equivalences that Spirit Essence is done according to the present invention change or modify, within all should being encompassed in 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, and the face of overlooking on stratum is rectangle, and this rectangle has four closures and isobaric border, and the wide of described rectangle is x _e, this value obtains by well test analysis is carried out in stratum, and the length of described rectangle is y _e, this value obtains by well test analysis is carried out in stratum; A2) have n crack, all n cracks run through stratum completely, n=1 wherein, 2,3 ..., the 1st crack is positioned at the butt of this horizontal well pit shaft, and i crack is arranged to the toe-end of this horizontal well pit shaft gradually, i=1 wherein, 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 obtains by laboratory experiment; Q _sccrack flow under representative mark condition; q _drepresent dimensionless crack flow; q _scwei Biaokuangxia unit's fracture length flow; j _dfor dimensionless length; x _ffor fracture half-length; C _fDfor dimensionless fracture condudtiviy; k _ffor fracture permeabgility; w _ffor crack width;

Step B), based on physical model, the percolation law according to gas in stratum, obtains arbitrary in the n crack dimensionless pressure P causing _dwith this crack dimensionless crack flow q _d(α) relational expression between,

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

In formula: x _w, y _wfor crack centre coordinate, its definition by physical model obtains;

Step C), based on physical model, the border coupled relation between the flowing relation according to gas in crack and crack and stratum, obtains in n crack arbitrary at the pressure disturbance P producing with pit shaft contact position _wfnq with this crack flow under mark condition _scnrelational expression,

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

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

Step D), based on physical model, the border coupled relation between the flowing relation according to gas in pit shaft and crack and pit shaft, obtains in n crack arbitrary at the pressure disturbance P producing with pit shaft contact position _wfi, the crack adjacent with this crack be at the pressure disturbance P producing with pit shaft contact position _wfi-1and the flow Q of this two crack between in pit shaft _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 n crack _scn, measure the 1st crack at the pressure disturbance P with the generation of 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: at step C) in, the flowing relation of gas in crack will be considered difference between seepage effect, infinite fluid diversion crack and the limited water conservancy diversion crack in crack and the radially conflux effect of pit shaft.

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

E1) according to practical condition, estimate the maximum value Q of n crack flow _{scn (max)}with minimum value Q _{scn (min)}, get the arithmetic average Q of maximum value and minimum value _{scn (mid)}=0.5 * [Q _{scn (max)}+ Q _{scn (min)}];

E2) according to step C) in formula calculate 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 formula calculate corresponding Q _{scn-1 (max)}, Q _{scn-1 (min)}, Q _{scn-1 (mid)};

E3) repeating step E2) obtain P _{wf0 (max)}, P _{wf0 (min)}, P _{wf0 (mid)};

E4) by P _{wf0 (mid)}with P _wfcarry out difference comparison, if P _{wf0 (mid)}with P _wfdifference meet required precision and judge calculated value P _{wf0 (mid)}correctly, if P _{wf0 (mid)}with P _wfdifference do not meet required precision, if (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) repeating step E1) to E4), until P _{wf0 (mid)}with P _wfdifference meet required precision.

4. Productivity according to claim 1, is characterized in that: at step D) in, described friction factor f is calculated by following formula:

$f_i={[1.14-21g(\frac{e}{1000D}+\frac{21.25}{R_{\mathrm{ei}}^{0.9}})]}^{-2},$

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 unquarried stratum measurement is obtained, described P measures by the stratum to after exploitation, described T measures by the temperature on the stratum to after exploitation, described k obtains by laboratory experiment or well test analysis, described h obtains by well log interpretation, described μ obtains by laboratory experiment, and described Z obtains by laboratory experiment, described x _fby well test analysis, obtain described k _fby well test analysis, obtain described w _fby well test analysis, obtain.

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

8. employing, as a production capacity computing system for the computational methods of one of claim 1 to 7, is characterized in that: it comprises

Modeling unit, it is for setting up physical model;

The first computing unit, it is for according to gas, the percolation law on stratum obtains arbitrary in the n crack dimensionless pressure P causing _dwith this crack dimensionless crack flow q _d(α) relational expression between;

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

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

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

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