CN105422071A - Method for evaluating rationality of low-permeability non-homogeneous gas reservoir fracturing horizontal well fracture parameters - Google Patents

Abstract

The invention discloses a method for evaluating the rationality of low-permeability non-homogeneous gas reservoir fracturing horizontal well fracture parameters. The method comprises the steps that the parameters of the reservoir physical property, the fluid property, fracturing horizontal well fractures, a horizontal shaft and the propping agent property are collected; the permeability distribution condition of a non-homogeneous gas reservoir is divided into relatively homogeneous permeable zones in the length direction of the horizontal shaft, and the permeable zones contain artificial fractures; a fracturing fracture physical model of the permeable zones containing the artificial fractures and a mathematical model for fracture parameter evaluating are built; the high-speed non-darcy-flow effective permeability in the factures is corrected; a fracture yield model taking high-speed non-darcy flow of the fractures into account is solved, and an evaluating chart of the non-homogeneous gas reservoir fracturing horizontal well fracture parameters is built; the rationality of the low-permeability non-homogeneous gas reservoir fracturing horizontal well fracture parameters is evaluated. According to the method, the low-permeability gas reservoir heterogeneity characteristics and the comprehensive influence that the high-speed non-darcy-flow exists in the fracturing horizontal well fractures can be taken into account, and therefore the fracture parameters of all sections of a low-permeability non-homogeneous gas reservoir fracturing horizontal well are quickly and efficiently evaluated.

Description

Evaluate the rational method of low-permeable heterogeneous gas reservoir fracture parameters of fractured horizontal wells

Technical field

The application belongs to oil-gas field development field, specifically, relates to a kind of rational method of evaluation low-permeable heterogeneous gas reservoir fracture parameters of fractured horizontal wells.

Background technology

Low permeability gas reservoir outstanding behaviours is the feature of reservoir permeability flat transverse non-homogeneity, by significantly improving output to low permeability gas reservoir staged fracturing of horizontal well, now shows again high speed Non-Darcy's flow feature in crack.When to low permeability gas reservoir pressure break horizontal well fracture evaluation, the impact of the factor such as high speed Non-Darcy's flow in permeability non-homogeneity and crack must be considered.Current fracture parameters of fractured horizontal wells evaluation method mainly contains electrical simulation experiment method, parsing-semi-analytic method and method for numerical simulation etc.

It is average that electrical analogue method and parsing-semi-analytic method will get permeability mainly through reservoir permeability weighted average method, is namely homogeneous depending on reservoir, considers reservoir flat transverse aeolotropic characteristics; Method for numerical simulation can consider the Lateral heterogeneity of reservoir, but can not consider high speed Non-Darcy's flow feature in crack, and when using the method, need a large amount of reservoir data, computational speed is also slow.Therefore for horizontal low-permeable heterogeneous gas reservoir, consider high speed Non-Darcy's flow impact in crack simultaneously, be badly in need of a kind of fracture parameters evaluation method rapidly and efficiently.

Summary of the invention

In view of this, technical problems to be solved in this application are combined influences that prior art does not consider high speed Non-Darcy's flow in low permeability gas reservoir aeolotropic characteristics and pressure break horizontal well crack.

In order to solve the problems of the technologies described above, this application discloses a kind of rational method of evaluation low-permeable heterogeneous gas reservoir fracture parameters of fractured horizontal wells, comprising the following steps:

1) basic parameter of reservoir properties, fluid properties, pressure break horizontal well crack, horizontal wellbore, proppant character is collected respectively;

2) heterogeneous body gas reservoir is divided into the vadose zone of at least two homogeneous along horizontal wellbore length direction seepage flow rate distribution situation, described vadose zone contains man-made fracture;

3) Mathematical Modeling of the fracturing fracture physical model containing man-made fracture permeable belt and fracture parameters evaluation is set up;

4) described step 3 is revised) effective permeability of high speed non-Darcy flow in crack;

5) set up the crack yield model considering crack high speed Non-Darcy's flow, set up the evaluation plate of heterogeneous body gas reservoir fracture parameters of fractured horizontal wells;

6) reasonability of low-permeable heterogeneous gas reservoir fracture parameters of fractured horizontal wells is evaluated.

Further, described step 1) in, the basic parameter of described reservoir properties, fluid properties, pressure break horizontal well crack, horizontal wellbore, proppant character comprises: gas reservoir thickness, width, each permeable belt permeability, length; Gas viscosity, deviation factors, relative density; Each section of fracture length, width and height; Output and horizontal well wellbore pressure when reservoir temperature, average pressure, quasi-stable state; Initial support permeability.

Further, described step 2) by the method that heterogeneous body gas reservoir is divided into the permeable belt of at least two relative homogeneous along horizontal wellbore length direction seepage flow rate distribution situation be: according to the difference of reservoir permeability on horizontal wellbore length direction, reservoir division equal for permeability is become same permeable belt, and what permeability was lower is considered as the interlayer hindering gas flowing.

Further, step 3) described in foundation contain man-made fracture permeable belt fracturing fracture physical model (following step a) and the method for Mathematical Modeling (following step b-d) evaluated of fracture parameters comprise the following steps:

A, heterogeneous body gas reservoir pressure break horizontal well regarded as much similar homogeneity permeation band composition, each vadose zone all about horizontal wellbore and crack symmetrically relation, with in the 1st vadose zone 1/4th for research object, crack is divided into n _windividual segment;

B, based on matrix flow equation, calculate the flow differential pressure between any two points in crack, utilize Direct Boundary Element Method, due to n _wsegment point source affects, and gas reservoir and the i-th segment point source quasi-stable state pressure drop are:

${\mathrm{\Δp}}_{o,i}={\stackrel{\‾}{p}}^2-{p^2}_{o,i}=\frac{\mathrm{\α}\mathrm{\μ}ZT}{k_{m1}h}\underset{k=1}{\overset{n_w}{\Σ}}{q}_{k}a\[x_{oD,i},y_{oD,i},x_{wD,k},y_{wD,k},y_{eD}\]=\frac{{\mathrm{\α}}_1\mathrm{\μ}ZT}{k_{m1}h}\underset{k=1}{\overset{n_w}{\Σ}}{q}_{j}a\[o_i,w_k\]---\left(1\right)$

Gas reservoir and the pressure drop of jth segment point source quasi-stable state are:

${\mathrm{\Δp}}_{o,j}={\stackrel{\‾}{p}}^2-{p^2}_{o,j}=\frac{\mathrm{\α}\mathrm{\μ}ZT}{k_{m1}h}\underset{k=1}{\overset{n_w}{\Σ}}{q}_{k}a\[x_{oD,j},y_{oD,j},x_{wD,k},y_{wD,k},y_{eD}\]=\frac{{\mathrm{\α}}_1\mathrm{\μ}ZT}{k_{m1}h}\underset{k=1}{\overset{n_w}{\Σ}}{q}_{k}a\[o_j,w_k\]---\left(2\right)$

The quasi-stable state pressure drop of i-th section and jth section is subtracted each other, and works as i=1, during j=2, to obtain in crack the 1st section and the 2nd section of flow pressure drop is:

${{\mathrm{\Δp}}^2}_{R,2\→1}=\frac{\mathrm{\α}\mathrm{\μ}ZT}{k_{m1}h}\underset{k=1}{\overset{n_w}{\Σ}}\[q_1(a\[o_1,w_1\]-a\[o_2,w_1\])+...+q_{n_w}(a\[o_1,w_{n_w}\]-a\[o_2,w_{n_w}\])\]---\left(3\right)$

In formula: Δ p _o,i, Δ p _o,jbe respectively the quasi-stable state pressure drop of gas reservoir and the i-th segment and jth segment, Δ p _{r, 2 → 1}for based on the 2nd segment of matrix flow and the flow pressure drop of the 1st segment, unit is MPa; α=774.6 are constant; μ is gas viscosity, and unit is mPas; Z is deviation factor for gas, dimensionless; T is reservoir temperature, and unit is K; k _m1be the 1st permeable belt matrix permeability, unit is mD; H is gas reservoir thickness, and unit is m; n _wit is the hop count of half long crack decile; α [o _i, w _j] for jth section is to the influence function of i-th section, w is point of observation, o is source point;

C, to flow based in crack, calculate the flow differential pressure of adjacent segment in crack, for high speed Non-Darcy's flow in crack, non-for high speed darcy is treated to Darcy Flow, obtains flowing in crack partial differential equation according to Darcy's law:

$q=-\frac{k_{fe}{A}_f}{\mathrm{\μ}}\frac{\∂p}{\∂x}---\left(4\right)$

By flow between the 1st section and the 2nd section of crack be the 2nd section to n-th _wthe total flow of section, then based on flow in fracture, the 1st section and the 2nd section of flow pressure drop are:

${{\mathrm{\Δp}}^2}_{f,1\→2}=\frac{2\mathrm{\α}\mathrm{\μ}ZT}{k_{fe}{\mathrm{hw}}_f}\[q_2(x_{o2}-x_{o1})+...+q_{nw}(x_{o2}-x_{o1})\]---\left(5\right)$

In formula: Δ p _{f, 2 → 1}for based on the 2nd segment of flow in fracture and the flow pressure drop of the 1st segment, unit is MPa; k _fefor considering effective permeability after high speed Non-Darcy's flow in crack, unit is mD; x _o1, x _o2be respectively and the 2nd position at the 1st, unit is m;

D, calculate correlation between crack flow and fracture parameters

Formula (3) and formula (5) are the flow differential pressure of the 1st section and the 2nd section, two formulas subtract each other obtain each section between flow and fracture parameters close be:

$\begin{array}{c}{q}_1(a\[o_1,w_1\]-a\[o_2,w_1\])+...+q_{n_w}(a\[o_1,w_{n_w}\]-a\[o_2,w_{n_w}\])\\ -\frac{2k}{k_{fe}{w}_f}\[q_2(x_{o2}-x_{o1})+...+q_{n_w}(x_{o2}-x_{o1})\]=0\end{array}---\left(6\right)$

By each section of flow, position, fracture half-length, fracture condudtiviy, proppant scale zero dimension

$q_{Di}=\frac{q_i{B}_g\mathrm{\μ}T}{2{\mathrm{\πk}}_{m1}h(p_{ave}^2-p_{wf}^2)}---\left(7\right)$

$x_{Doi}=\frac{x_{oi}}{x_e/2}---\left(8\right)$

$I_x=\frac{x_f}{x_e/2}---\left(9\right)$

$C_{fDe}=\frac{k_{fe}{w}_f}{{\mathrm{kx}}_f}---\left(10\right)$

$N_{pe}=\frac{2k_{fe}{v}_p}{{\mathrm{kv}}_r}=I_x^2{C}_{fD}\frac{x_e}{y_e}---\left(11\right)$

Obtain the zero dimension relation of each section of crack between flow and fracture parameters:

$\begin{array}{c}{q}_{D1}(a\[o_1,w_1\]-a\[o_2,w_1\])+...+q_{{\mathrm{Dn}}_w}(a\[o_1,w_{n_w}\]-a\[o_2,w_{n_w}\])\\ -\frac{4\mathrm{\π}k}{C_{fD}{I}_x}\[q_{D2}(x_{Do2}-x_{Do1})+...+q_{{\mathrm{Dn}}_w}(x_{Do2}-x_{Do1})\]=0\end{array}---\left(12\right)$

In formula, B _gfor gas volume factor, zero dimension; q _dibe i-th section of crack nondimensional mass flow, zero dimension; p _aveand p _wfbe respectively gas reservoir average pressure and horizontal wellbore pressure, unit is MPa; x _dibe i-th section of zero dimension position; x _e, y _ebe respectively permeable belt width and length, unit is m; x _f, w _fbe respectively fracture half-length, crack width, unit is m; k _fefor considering effective permeability during high speed Non-Darcy's flow in crack, unit is mD; I _xfor crack penetration ratio; C _fDe, N _pebe respectively in crack and consider the high speed effective flow conductivity of Non-Darcy's flow zero dimension and effective proppant index; v _p, v _rbe respectively proppant supporting crack volume and permeable belt volume, unit is m ³;

With should i=2, j=3, i=3, j=4 ..., i=n _w-1, j=n _wtime, all the other n can be obtained _w-2 adjacent slits section relational expressions, obtain n _w-1 each section of crack flow and fracture parameters zero dimension relational expression, last expression formula be the 1st section to horizontal wellbore pressure drop, n _windividual system of linear equations, solves n _wsection crack nondimensional mass flow (q _d1, q _d2... .q _dnw) and fracture parameters relation;

$\left[\begin{array}{cccc}{a}_{11}& a_{12}& ...& a_{11}\\ a_{21}& a_{22}& ...& a_{11}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ a_{nw1}& a_{nw2}& ...& a_{11}\end{array}\right]\·\left[\begin{array}{c}{q}_{D1}\\ q_{D2}\\ .\\ .\\ .\\ q_{Dnw}\end{array}\right]=\left[\begin{array}{c}1\\ 0\\ .\\ .\\ .\\ 0\end{array}\right]---\left(13\right)$

Wherein:

a _1j/(j＝1,…,n _w)＝a[o ₁,w _j]

a _i1/(i＝2,…,n _w)＝a[o ₁,w ₁]-a[o _i,w ₁](14)

$a_{ij}/(i,j=1,...,n_w)=a\[o_1,w_j\]-a\[o_i,w_j\]-\frac{4\mathrm{\π}}{C_{fD}{I}_x}(x_{Do\left(\min \right(i,j\left)\right)}-x_{Do1})$

Every crack dimensionless production be all slits section nondimensional mass flow and 4 times, whole piece crack dimensionless production expression formula:

$J_D=4\underset{j=1}{\overset{n_w}{\Σ}}{q}_{Di}---\left(15\right)$

In formula: J _dfor whole piece crack dimensionless production index.

Further, described step 4) utilize alternative manner, by effective permeability in Reynolds number correction crack, high speed Non-Darcy's flow is treated to Darcy Flow, comprises the following steps:

E, suppose that initial Reynolds number is N _re1be zero, according to crack effective permeability and Reynolds number relation, obtain incipient crack effective permeability:

$k_{fe1}=\frac{k_f}{1+N_{\mathrm{Re}1}}---\left(16\right)$

In formula: k _f, k _fe1be respectively supporting crack original permeability and initial effective permeability, unit is mD; N _re1for supposing initial Reynolds number, value is zero;

F, according to proppant exponential expression (formula 11), substitute into incipient crack effective permeability, obtain initially effectively proppant index:

$N_{pe1}=\frac{2k_{fe1}{v}_p}{k_{m1}{\mathrm{hx}}_e{y}_e}=I_x^2\·C_{fDe1}\·\frac{x_e}{y_e}---\left(17\right)$

G, at initial effectively proppant index N _pe1under, according to step 3) the crack nondimensional mass flow set up and fracture parameters relation, obtain and contrast different dimensionless fracture conductivity C _fDe1corresponding crack total nondimensional mass flow index J _d, and then obtain optimum zero dimension effective fracture flow conductivity C _fDe1opt;

H, according to optimum zero dimension effective fracture flow conductivity C _fDe1opt, calculate initial optimum fracture half-length and width:

$x_{f1opt}=\sqrt{\frac{k_{fe1}{v}_p}{2C_{fDe1opt}{k}_{m1}h}}---\left(18\right)$

$w_{f1opt}=\sqrt{\frac{C_{fDe1opt}{k}_{m1}{v}_p}{2k_{fe1}h}}---\left(19\right)$

In formula: x _f1opt, w _f1optbe respectively initial optimum fracture half-length and crack width, unit is m;

I, nondimensional mass flow is converted into crack actual production, by the relational expression of output and crack width, obtains pit shaft place gas flow rate:

$q_g=\frac{(p_{ave}^2-p_{wf}^2)k_{m1}h}{1.291\×{10}^{-3}\mathrm{\μ}ZT}{J}_D---\left(20\right)$

$v=\frac{q_g}{2A_{f1opt}(24\×3600)}=\frac{q_g}{172800{\mathrm{hw}}_{f1opt}}---\left(21\right)$

In formula: q _gfor crack total output, unit is m ³/ d; V is crack and pit shaft intersection gas flow rate, and unit is m/s; A _f1optfor crack under initial optimum crack width and pit shaft phase cross surface area, unit is m ²;

J, according to Reynolds number definition, calculate new effective Reynolds number N _re2:

$N_{\mathrm{Re}2}=\frac{{\mathrm{\βk}}_{fe1}{\mathrm{\ρ}}_{g}v}{{\mathrm{\μ}}_g}---\left(22\right)$

Wherein:

${\mathrm{\ρ}}_g=1.22\frac{{\mathrm{\γ}}_g}{B_g}---\left(23\right)$

$B_g=3.458\×{10}^{-4}\frac{ZT}{p_{wf}}---\left(24\right)$

$\mathrm{\β}=1\×{10}^8\frac{n}{k_{fe1}^m}---\left(25\right)$

In formula: β is porous media characteristic parameter; ρ _gfor gas density, unit is kg/m ³; γ _gfor gas relative density, zero dimension; M, n are that constant is relevant with proppant particle diameter;

K, contrast hypothesis Reynolds number N _re1with new Reynolds number N _re2if, two, differ regulation very among a small circle in (| R _e1-R _e2|≤ξ), then obtaining design flaw size is required flaw size, if not in prescribed limit, is then got by Reynolds number in formula (16) and is newly worth N _re2, iteration again, until Reynolds number is in prescribed limit.

Further, described step 5) utilize influence function, solve crack output, and set up fracture parameters evaluation plate, comprise the following steps:

a[o _i,w _j]＝a[x _D,y _D,x _wD,y _wD,y _eD]＝a ¹[max(x _D,x _wD),max(y _D,y _wD),min(x _D,x _wD),min(y _D,y _wD),y _eD]

(26)

$a^1\&lsqb;x_D,y_D,x_{wD},y_{wD},y_{eD}\&rsqb;=\left\{\begin{array}{cc}{a}^0\&lsqb;x_D,y_D,x_{wD},y_{wD},y_{eD}\&rsqb;& \begin{array}{cc}if& (y_{eD}<1)\end{array}\\ a^0\&lsqb;x_D,y_D,x_{wD},y_{wD},\frac{1}{y_{eD}}\&rsqb;& \end{array}\right.---\left(27\right)$

$a^0\&lsqb;x_D,y_D,x_{wD},y_{wD},y_{eD}\&rsqb;=2{\mathrm{\&pi;y}}_{eD}(\frac{1}{3}-\frac{y_D}{y_{eD}}+\frac{y_D^2+y_{wD}^2}{2y_{eD}^2})+S_T---\left(28\right)$

Wherein:

$S_T=2\underset{m=1}{\overset{\mathrm{\&infin;}}{\&Sigma;}}\frac{t_m}{m}cos\left({m\mathrm{}\mathrm{\&pi;x}}_D\right)cos\left({m\mathrm{}\mathrm{\&pi;x}}_{wD}\right)---\left(29\right)$

$t_m=\frac{\cosh \&lsqb;m\mathrm{\&pi;}(y_{eD}-|y_D-y_{wD}\left|\right)\&rsqb;+\cosh \left(m\mathrm{\&pi;}\right(y_{eD}-\left|y_D+y_{wD}\right|\left)\right)}{\sinh \left({\mathrm{m\&pi;y}}_{eD}\right)}---\left(30\right)$

By infinite series S _tuse following formula finite process:

S _T＝S ₁+S ₂+S ₃(31)

$S_1=2\underset{m=1}{\overset{N}{\&Sigma;}}\frac{t_m}{m}cos\left({m\mathrm{}\mathrm{\&pi;x}}_D\right)cos\left({m\mathrm{}\mathrm{\&pi;x}}_{wD}\right)---\left(32\right)$

$\begin{array}{c}{S}_2=-\frac{t_N}{2}\ln \{{\&lsqb;1-\cos \left(\mathrm{\&pi;}\right(x_D+x_{wD}\left)\right)\&rsqb;}^2+{\&lsqb;\sin \left(\mathrm{\&pi;}\right(x_D+x_{wD}\left)\right)\&rsqb;}^2\}\\ -\frac{t_N}{2}\ln \{{\&lsqb;1-\cos \left(\mathrm{\&pi;}\right(x_D-x_{wD}\left)\right)\&rsqb;}^2+{\&lsqb;\sin \left(\mathrm{\&pi;}\right(x_D-x_{wD}\left)\right)\&rsqb;}^2\}\end{array}---\left(33\right)$

$S_3=-2t_N\underset{m=1}{\overset{N}{\&Sigma;}}\frac{1}{m}cos\left({m\mathrm{}\mathrm{\&pi;x}}_D\right)cos\left({m\mathrm{}\mathrm{\&pi;x}}_{wD}\right)---\left(34\right)$

In formula: y _eDfor permeable belt aspect ratio, y _eD=y _e/ x _e

The Mathematical Modeling (formula 26-34) of crack output is solved, with aspect ratio y by influence function _eD=1 is example, obtains different effectively proppant index N _peunder, zero dimension crack output index evaluates plate with the fracture parameters of dimensionless fracture conductivity variation relation.

Further, described step 6) evaluate the reasonability of hypotonic heterogeneous body gas reservoir fracture parameters of fractured horizontal wells, comprise the following steps:

L, by geology, interpretation of logging data result, to obtain along permeable belt permeability k each on horizontal wellbore length direction _mi, permeable belt length y _eiwith width x _e;

M, determining each permeable belt aspect ratio (y _eD=y _ei/ x _e) in situation, change proppant scale, obtain optimum crack output with proppant scale variation relation plate, i.e. proppant Scale Evaluation plate; In plate, crack output increases proppant scale when occurring mild is optimal value, according to each permeable belt aspect ratio and permeability thereof, this Mathematical Modeling is utilized to obtain corresponding proppant Scale Evaluation plate, contrast optimum proppant scale value in actual support agent scale and plate, carry out proppant Scale Evaluation;

N, in step l) under the underlying parameter that obtains, according to the Mathematical Modeling of crack Production rate, by the correction of high speed Non-Darcy's flow permeability in crack, calculate the revised supporting crack effective permeability of each permeable belt and effective proppant index N _pe;

O, according to aspect ratio and effective proppant index, select reflection crack parameter evaluation plate, and then obtain optimum crack zero dimension flow conductivity C corresponding to optimum crack production capacity index (zero dimension production capacity index peak) _fDe;

P, the actual fracture length utilizing the matching of fracture extension simulation softward to obtain and width, then according to dimensionless fracture conductivity definition (formula 10), obtain actual fracture condudtiviy C _fD, under identical effective proppant index, then obtain actual crack production capacity index in conjunction with plate;

Q, contrast actual dimensionless fracture conductivity C _fDwith optimum dimensionless fracture conductivity C _fDeif, bigger than normal, then illustrate that crack width is excessive, length is too small, if less than normal, illustrates that crack width is too small, width is excessive.

Compared with prior art, the application can obtain and comprise following technique effect:

1) technical scheme of the application can consider the combined influence that there is high speed Non-Darcy's flow in low permeability gas reservoir aeolotropic characteristics and pressure break horizontal well crack, realizes rapidly and efficiently evaluating low-permeable heterogeneous gas reservoir pressure break horizontal well each section of fracture parameters and proppant scale reasonability.

Certainly, the arbitrary product implementing the application must not necessarily need to reach above-described all technique effects simultaneously.

Accompanying drawing explanation

Accompanying drawing described herein is used to provide further understanding of the present application, and form a application's part, the schematic description and description of the application, for explaining the application, does not form the improper restriction to the application.In the accompanying drawings:

Fig. 1 is the heterogeneous reservoir pressure break horizontal well schematic diagram of the embodiment of the present application;

Fig. 2 is 1/4th first permeable belt schematic diagrames of the embodiment of the present application;

Fig. 3 is that the fracture parameters of the embodiment of the present application evaluates plate (y _eD=1, N _pe<0.1);

Fig. 4 is that the fracture parameters of the embodiment of the present application evaluates plate (y _eD=1, N _pe>=0.1);

Fig. 5 is the proppant Scale Evaluation plate of the embodiment of the present application;

Fig. 6 is each permeable belt crack actual support agent scale of the embodiment of the present application and optimum proppant scale comparison diagram;

Fig. 7 is the effective flow conductivity comparison diagram of the actual dimensionless fracture conductivity in each permeable belt crack and optimum zero dimension crack of the embodiment of the present application.

Detailed description of the invention

Drawings and Examples will be coordinated below to describe the embodiment of the application in detail, by this to the application how application technology means solve technical problem and the implementation procedure reaching technology effect can fully understand and implement according to this.

The rational method of evaluation low-permeable heterogeneous gas reservoir fracture parameters of fractured horizontal wells of the application, comprises the following steps:

1) basic parameter of reservoir properties, fluid properties, pressure break horizontal well crack, horizontal wellbore, proppant character is collected respectively;

2) heterogeneous body gas reservoir is divided into the vadose zone of at least 2 relative homogeneous along horizontal wellbore length direction seepage flow rate distribution situation, described vadose zone contains man-made fracture;

3) Mathematical Modeling of each fracturing fracture physical model containing man-made fracture permeable belt and fracture parameters evaluation is set up;

4) described step 3 is revised) effective permeability of high speed non-Darcy flow in crack;

5) solve the crack yield model considering crack high speed Non-Darcy's flow, set up the evaluation plate of heterogeneous body gas reservoir fracture parameters of fractured horizontal wells;

6) reasonability of low-permeable heterogeneous gas reservoir fracture parameters of fractured horizontal wells is evaluated.

Described step 1) in, the basic parameter of described reservoir properties, fluid properties, pressure break horizontal well crack, horizontal wellbore, proppant character comprises: gas reservoir thickness, width, each permeable belt permeability, length; Gas viscosity, deviation factors, relative density; Each section of fracture length, width and height; Output and horizontal well wellbore pressure when reservoir temperature, average pressure, quasi-stable state; Initial support permeability.

As shown in Figure 1, step 2) method that heterogeneous body gas reservoir is divided into the permeable belt of at least 2 relative homogeneous along horizontal wellbore length direction is: according to the difference of reservoir permeability on horizontal wellbore length direction, reservoir division equal for permeability is become same permeable belt, and what permeability was relatively low is considered as the interlayer hindering gas flowing.In figure, 1 is closed boundary, and 2 is horizontal wellbore, and 3 is man-made fracture, and 4-6 is different permeable belt, and 7 is impermeable band.

Step 3) described in foundation contain man-made fracture permeable belt fracturing fracture physical model (following step a) and the method for Mathematical Modeling (following step b-d) evaluated of fracture parameters comprise the following steps:

A, as shown in Figure 2, regards much similar homogeneity permeation band composition as by heterogeneous body gas reservoir pressure break horizontal well, each vadose zone all about horizontal wellbore and crack symmetrically relation, with in the 1st vadose zone 1/4th for research object, crack is divided into n _windividual segment;

B, based on matrix flow equation, calculate the flow differential pressure between any two points in crack, utilize Direct Boundary Element Method, due to n _wsegment point source affects, and gas reservoir and the i-th segment point source quasi-stable state pressure drop are:

${\mathrm{\&Delta;p}}_{o,i}={\stackrel{\&OverBar;}{p}}^2-{p^2}_{o,i}=\frac{\mathrm{\&alpha;}\mathrm{\&mu;}ZT}{k_{m1}h}\underset{k=1}{\overset{n_w}{\&Sigma;}}{q}_{k}a\&lsqb;x_{oD,i},y_{oD,i},x_{wD,k},y_{wD,k},y_{eD}\&rsqb;=\frac{{\mathrm{\&alpha;}}_1\mathrm{\&mu;}ZT}{k_{m1}h}\underset{k=1}{\overset{n_w}{\&Sigma;}}{q}_{j}a\&lsqb;o_i,w_k\&rsqb;---\left(1\right)$

Gas reservoir and the pressure drop of jth segment point source quasi-stable state are:

${\mathrm{\&Delta;p}}_{o,j}={\stackrel{\&OverBar;}{p}}^2-{p^2}_{o,j}=\frac{\mathrm{\&alpha;}\mathrm{\&mu;}ZT}{k_{m1}h}\underset{k=1}{\overset{n_w}{\&Sigma;}}{q}_{k}a\&lsqb;x_{oD,j},y_{oD,j},x_{wD,k},y_{wD,k},y_{eD}\&rsqb;=\frac{{\mathrm{\&alpha;}}_1\mathrm{\&mu;}ZT}{k_{m1}h}\underset{k=1}{\overset{n_w}{\&Sigma;}}{q}_{k}a\&lsqb;o_j,w_k\&rsqb;---\left(2\right)$

The quasi-stable state pressure drop of i-th section and jth section is subtracted each other, and works as i=1, during j=2, to obtain in crack the 1st section and the 2nd section of flow pressure drop is:

${{\mathrm{\&Delta;p}}^2}_{R,2\&RightArrow;1}=\frac{\mathrm{\&alpha;}\mathrm{\&mu;}ZT}{k_{m1}h}\underset{k=1}{\overset{n_w}{\&Sigma;}}\&lsqb;q_1(a\&lsqb;o_1,w_1\&rsqb;-a\&lsqb;o_2,w_1\&rsqb;)+...+q_{n_w}(a\&lsqb;o_1,w_{n_w}\&rsqb;-a\&lsqb;o_2,w_{n_w}\&rsqb;)\&rsqb;---\left(3\right)$

In formula: Δ p _o,i, Δ p _o,jbe respectively the quasi-stable state pressure drop of gas reservoir and the i-th segment and jth segment, Δ p _{r, 2 → 1}for based on the 2nd segment of matrix flow and the flow pressure drop of the 1st segment, unit is MPa; α=774.6 are constant; μ is gas viscosity, and unit is mPas; Z is deviation factor for gas, dimensionless; T is reservoir temperature, and unit is K; k _m1be the 1st permeable belt matrix permeability, unit is mD; H is gas reservoir thickness, and unit is m; n _wit is the hop count of half long crack decile; α [o _i, w _j] for jth section is to the influence function of i-th section, w refers to point of observation, and o refers to source point;

C, to flow based in crack, calculate the flow differential pressure of adjacent segment in crack, for high speed Non-Darcy's flow in crack, non-for high speed darcy is treated to Darcy Flow, obtains flowing in crack partial differential equation according to Darcy's law:

$q=-\frac{k_{fe}{A}_f}{\mathrm{\&mu;}}\frac{\&part;p}{\&part;x}---\left(4\right)$

By flow between the 1st section and the 2nd section of crack be the 2nd section to n-th _wthe total flow of section, then based on flow in fracture, the 1st section and the 2nd section of flow pressure drop are:

${{\mathrm{\&Delta;p}}^2}_{f,1\&RightArrow;2}=\frac{2\mathrm{\&alpha;}\mathrm{\&mu;}ZT}{k_{fe}{\mathrm{hw}}_f}\&lsqb;q_2(x_{o2}-x_{o1})+...+q_{nw}(x_{o2}-x_{o1})\&rsqb;---\left(5\right)$

In formula: Δ p _{f, 2 → 1}for based on the 2nd segment of flow in fracture and the flow pressure drop of the 1st segment, unit is MPa; k _fefor considering effective permeability after high speed Non-Darcy's flow in crack, unit is mD; x _o1, x _o2be respectively and the 2nd position at the 1st, unit is m;

D, calculate correlation between crack flow and fracture parameters

Formula (3) and formula (5) are the flow differential pressure of the 1st section and the 2nd section, two formulas subtract each other obtain each section between flow and fracture parameters close be:

$\begin{array}{c}{q}_1(a\&lsqb;o_1,w_1\&rsqb;-a\&lsqb;o_2,w_1\&rsqb;)+...+q_{n_w}(a\&lsqb;o_1,w_{n_w}\&rsqb;-a\&lsqb;o_2,w_{n_w}\&rsqb;)\\ -\frac{2k}{k_{fe}{w}_f}\&lsqb;q_2(x_{o2}-x_{o1})+...+q_{n_w}(x_{o2}-x_{o1})\&rsqb;=0\end{array}---\left(6\right)$

By each section of flow, position, fracture half-length, fracture condudtiviy, proppant scale zero dimension

$q_{Di}=\frac{q_i{B}_g\mathrm{\&mu;}T}{2{\mathrm{\&pi;k}}_{m1}h(p_{ave}^2-p_{wf}^2)}---\left(7\right)$

$x_{Doi}=\frac{x_{oi}}{x_e/2}---\left(8\right)$

$I_x=\frac{x_f}{x_e/2}---\left(9\right)$

$C_{fDe}=\frac{k_{fe}{w}_f}{{\mathrm{kx}}_f}---\left(10\right)$

$N_{pe}=\frac{2k_{fe}{v}_p}{{\mathrm{kv}}_r}=I_x^2{C}_{fD}\frac{x_e}{y_e}---\left(11\right)$

Obtain the zero dimension relation of each section of crack between flow and fracture parameters:

$\begin{array}{c}{q}_{D1}(a\&lsqb;o_1,w_1\&rsqb;-a\&lsqb;o_2,w_1\&rsqb;)+...+q_{{\mathrm{Dn}}_w}(a\&lsqb;o_1,w_{n_w}\&rsqb;-a\&lsqb;o_2,w_{n_w}\&rsqb;)\\ -\frac{4\mathrm{\&pi;}k}{C_{fD}{I}_x}\&lsqb;q_{D2}(x_{Do2}-x_{Do1})+...+q_{{\mathrm{Dn}}_w}(x_{Do2}-x_{Do1})\&rsqb;=0\end{array}---\left(12\right)$

In formula, B _gfor gas volume factor, zero dimension; q _dibe i-th section of crack nondimensional mass flow, zero dimension; p _aveand p _wfbe respectively gas reservoir average pressure and horizontal wellbore pressure, unit is MPa; x _dibe i-th section of zero dimension position; Xe, ye are respectively permeable belt width and length, and unit is m; x _f, w _fbe respectively fracture half-length, crack width, unit is m; k _fefor considering effective permeability during high speed Non-Darcy's flow in crack, unit is mD; I _xfor crack penetration ratio; C _fDe, N _pebe respectively in crack and consider the high speed effective flow conductivity of Non-Darcy's flow zero dimension and effective proppant index; v _p, v _rbe respectively proppant supporting crack volume and permeable belt volume, unit is m ³;

With should i=2, j=3, i=3, j=4 ..., i=n _w-1, j=n _wtime, all the other n can be obtained _w-2 adjacent slits section relational expressions, obtain n _w-1 each section of crack flow and fracture parameters zero dimension relational expression, last expression formula be the 1st section to horizontal wellbore pressure drop, n _windividual system of linear equations, solves n _wsection crack nondimensional mass flow (q _d1, q _d2... .q _dnw) and fracture parameters relation;

$\left[\begin{array}{cccc}{a}_{11}& a_{12}& ...& a_{11}\\ a_{21}& a_{22}& ...& a_{11}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ a_{nw1}& a_{nw2}& ...& a_{11}\end{array}\right]\&CenterDot;\left[\begin{array}{c}{q}_{D1}\\ q_{D2}\\ .\\ .\\ .\\ q_{Dnw}\end{array}\right]=\left[\begin{array}{c}1\\ 0\\ .\\ .\\ .\\ 0\end{array}\right]---\left(13\right)$

Wherein:

a _1j/(j＝1,…,n _w)＝a[o ₁,w _j]

a _i1/(i＝2,…,n _w)＝a[o ₁,w ₁]-a[o _i,w ₁](14)

$a_{ij}/(i,j=1,...,n_w)=a\&lsqb;o_1,w_j\&rsqb;-a\&lsqb;o_i,w_j\&rsqb;-\frac{4\mathrm{\&pi;}}{C_{fD}{I}_x}(x_{Do\left(\min \right(i,j\left)\right)}-x_{Do1})$

Every crack dimensionless production be all slits section nondimensional mass flow and 4 times, whole piece crack dimensionless production expression formula:

$J_D=4\underset{j=1}{\overset{n_w}{\&Sigma;}}{q}_{Di}---\left(15\right)$

In formula: J _dfor whole piece crack dimensionless production index.

Described step 4) utilize alternative manner, by effective permeability in Reynolds number correction crack, high speed Non-Darcy's flow is treated to Darcy Flow, comprises the following steps:

E, suppose that initial Reynolds number is N _re1be zero, according to crack effective permeability and Reynolds number relation, obtain incipient crack effective permeability:

$k_{fe1}=\frac{k_f}{1+N_{\mathrm{Re}1}}---\left(16\right)$

In formula: k _f, k _fe1be respectively supporting crack original permeability and initial effective permeability, unit is mD; N _re1for supposing initial Reynolds number, value is zero;

F, according to proppant exponential expression (formula 11), substitute into incipient crack effective permeability, obtain initially effectively proppant index:

$N_{pe1}=\frac{2k_{fe1}{v}_p}{k_{m1}{\mathrm{hx}}_e{y}_e}=I_x^2\&CenterDot;C_{fDe1}\&CenterDot;\frac{x_e}{y_e}---\left(17\right)$

G, at initial effectively proppant index N _pe1under, according to step 3) the crack nondimensional mass flow set up and fracture parameters relation, obtain and contrast different dimensionless fracture conductivity C _fDe1corresponding crack total nondimensional mass flow index J _d, and then obtain optimum zero dimension effective fracture flow conductivity C _fDe1opt;

H, according to optimum zero dimension effective fracture flow conductivity C _fDe1opt, calculate initial optimum fracture half-length and width:

$x_{f1opt}=\sqrt{\frac{k_{fe1}{v}_p}{2C_{fDe1opt}{k}_{m1}h}}---\left(18\right)$

$w_{f1opt}=\sqrt{\frac{C_{fDe1opt}{k}_{m1}{v}_p}{2k_{fe1}h}}---\left(19\right)$

In formula: x _f1opt, w _f1optbe respectively initial optimum fracture half-length and crack width, unit is m;

I, nondimensional mass flow is converted into crack actual production, by the relational expression of output and crack width, obtains pit shaft place gas flow rate:

$q_g=\frac{(p_{ave}^2-p_{wf}^2)k_{m1}h}{1.291\&times;{10}^{-3}\mathrm{\&mu;}ZT}{J}_D---\left(20\right)$

$v=\frac{q_g}{2A_{f1opt}(24\&times;3600)}=\frac{q_g}{172800{\mathrm{hw}}_{f1opt}}---\left(21\right)$

In formula: q _gfor crack total output, unit is m ³/ d; V is crack and pit shaft intersection gas flow rate, and unit is m/s; A _f1optfor crack under initial optimum crack width and pit shaft phase cross surface area, unit is m ²;

J, according to Reynolds number definition, calculate new effective Reynolds number N _re2:

$N_{\mathrm{Re}2}=\frac{{\mathrm{\&beta;k}}_{fe1}{\mathrm{\&rho;}}_{g}v}{{\mathrm{\&mu;}}_g}---\left(22\right)$

Wherein:

${\mathrm{\&rho;}}_g=1.22\frac{{\mathrm{\&gamma;}}_g}{B_g}---\left(23\right)$

$B_g=3.458\&times;{10}^{-4}\frac{ZT}{p_{wf}}---\left(24\right)$

$\mathrm{\&beta;}=1\&times;{10}^8\frac{n}{k_{fe1}^m}---\left(25\right)$

In formula: β is porous media characteristic parameter; ρ _gfor gas density, unit is kg/m ³; γ _gfor gas relative density, zero dimension; M, n are constant, relevant with proppant particle diameter, and its value is as shown in table 1.

The value of m, n under the different proppant particle diameter of table 1

Proppant particle diameter	m	n	Proppant particle diameter	m	n
						8/12	1.24	17423	20/40	1.54	110470
12/20	1.34	27539	40/60	1.60	69405

K, contrast hypothesis Reynolds number N _re1with new Reynolds number N _re2if, two, differ regulation very among a small circle in (| R _e1-R _e2|≤ξ), then obtaining design flaw size is required flaw size, if not in prescribed limit, is then got by Reynolds number in formula (16) and is newly worth N _re2, iteration again, until Reynolds number is in prescribed limit.

Described step 5) utilize influence function, solve crack output, and set up fracture parameters evaluation plate, comprise the following steps:

a[o _i,w _j]＝a[x _D,y _D,x _wD,y _wD,y _eD]＝a ¹[max(x _D,x _wD),max(y _D,y _wD),min(x _D,x _wD),min(y _D,y _wD),y _eD]

(26)

$a^1\&lsqb;x_D,y_D,x_{wD},y_{wD},y_{eD}\&rsqb;=\left\{\begin{array}{cc}{a}^0\&lsqb;x_D,y_D,x_{wD},y_{wD},y_{eD}\&rsqb;& \begin{array}{cc}if& (y_{eD}<1)\end{array}\\ a^0\&lsqb;x_D,y_D,x_{wD},y_{wD},\frac{1}{y_{eD}}\&rsqb;& \end{array}\right.---\left(27\right)$

$a^0\&lsqb;x_D,y_D,x_{wD},y_{wD},y_{eD}\&rsqb;=2{\mathrm{\&pi;y}}_{eD}(\frac{1}{3}-\frac{y_D}{y_{eD}}+\frac{y_D^2+y_{wD}^2}{2y_{eD}^2})+S_T---\left(28\right)$

Wherein:

$S_T=2\underset{m=1}{\overset{\mathrm{\&infin;}}{\&Sigma;}}\frac{t_m}{m}cos\left({m\mathrm{}\mathrm{\&pi;x}}_D\right)cos\left({m\mathrm{}\mathrm{\&pi;x}}_{wD}\right)---\left(29\right)$

$t_m=\frac{\cosh \&lsqb;m\mathrm{\&pi;}(y_{eD}-|y_D-y_{wD}\left|\right)\&rsqb;+\cosh \left(m\mathrm{\&pi;}\right(y_{eD}-\left|y_D+y_{wD}\right|\left)\right)}{\sinh \left({\mathrm{m\&pi;y}}_{eD}\right)}---\left(30\right)$

By infinite series S _tuse following formula finite process:

S _T＝S ₁+S ₂+S ₃(31)

$S_1=2\underset{m=1}{\overset{N}{\&Sigma;}}\frac{t_m}{m}cos\left({m\mathrm{}\mathrm{\&pi;x}}_D\right)cos\left({m\mathrm{}\mathrm{\&pi;x}}_{wD}\right)---\left(32\right)$

$\begin{array}{c}{S}_2=-\frac{t_N}{2}\ln \{{\&lsqb;1-\cos \left(\mathrm{\&pi;}\right(x_D+x_{wD}\left)\right)\&rsqb;}^2+{\&lsqb;\sin \left(\mathrm{\&pi;}\right(x_D+x_{wD}\left)\right)\&rsqb;}^2\}\\ -\frac{t_N}{2}\ln \{{\&lsqb;1-\cos \left(\mathrm{\&pi;}\right(x_D-x_{wD}\left)\right)\&rsqb;}^2+{\&lsqb;\sin \left(\mathrm{\&pi;}\right(x_D-x_{wD}\left)\right)\&rsqb;}^2\}\end{array}---\left(33\right)$

$S_3=-2t_N\underset{m=1}{\overset{N}{\&Sigma;}}\frac{1}{m}cos\left({m\mathrm{}\mathrm{\&pi;x}}_D\right)cos\left({m\mathrm{}\mathrm{\&pi;x}}_{wD}\right)---\left(34\right)$

In formula: y _eDfor permeable belt aspect ratio, y _eD=y _e/ x _e

The Mathematical Modeling (formula 26-34) of crack output is solved, with aspect ratio y by influence function _eD=1 is example, obtains different effectively proppant index N _peunder, zero dimension crack output index evaluates plate with the fracture parameters of dimensionless fracture conductivity variation relation, as shown in Figure 3 and Figure 4.

Described step 6) evaluate the reasonability of hypotonic heterogeneous body gas reservoir fracture parameters of fractured horizontal wells, comprise the following steps:

L, by geology, interpretation of logging data result, to obtain along permeable belt permeability k each on horizontal wellbore length direction _mi, permeable belt length y _eiwith width x _e;

M, as shown in Figure 5, determining each permeable belt aspect ratio (y _eD=y _ei/ x _e) in situation, change proppant scale, obtain optimum crack output with proppant scale variation relation plate, i.e. proppant Scale Evaluation plate; In plate, crack output increases proppant scale when occurring mild is optimal value, according to each permeable belt aspect ratio and permeability thereof, this Mathematical Modeling is utilized to obtain corresponding proppant Scale Evaluation plate, contrast optimum proppant scale value in actual support agent scale and plate, carry out proppant Scale Evaluation;

N, in step l) under the underlying parameter that obtains, according to the Mathematical Modeling of crack Production rate, by the correction of high speed Non-Darcy's flow permeability in crack, calculate the revised supporting crack effective permeability of each permeable belt and effective proppant index N _pe;

O, according to aspect ratio and effective proppant index, select reflection crack parameter evaluation plate, and then obtain optimum crack zero dimension flow conductivity C corresponding to optimum crack production capacity index (zero dimension production capacity index peak) _fDe;

P, the actual fracture length utilizing the matching of fracture extension simulation softward to obtain and width, then according to dimensionless fracture conductivity definition (formula 10), obtain actual fracture condudtiviy C _fD, under identical effective proppant index, then obtain actual crack production capacity index in conjunction with plate;

Q, contrast actual dimensionless fracture conductivity C _fDwith optimum dimensionless fracture conductivity C _fDeif, bigger than normal, then illustrate that crack width is excessive, length is too small, if less than normal, illustrates that crack width is too small, width is excessive.

Embodiment:

The rational method of the present embodiment applicating evaluating extra-low permeability heterogeneous body gas reservoir fracture parameters of fractured horizontal wells, specific as follows:

This extra-low permeability heterogeneous body gas reservoir is casing gas reservoir, wide x _efor 300m, thickness h is 22.5m.Comprising the permeable belt that 9 permeabilities are different with length, for there is interlayer, permeable belt being separated between each permeable belt.When reaching quasi-stable state production, formation temperature T _gfor 359K, mean reservoir pressure p _efor 12.37MPa, wellbore pressure p _wffor 11MPa; Formation gas relative density γ _gbe 0.665, viscosity, mu _gfor 0.27mPas, deviation factors Z is 0.91; During fracturing reform, use 20/40 order original permeability k _f1for the haydite of 170000mD, in the middle of each permeable belt, all press off a man-made fracture about pit shaft symmetry.Each permeable belt position, length, permeability, crack location, pressure break use proppant scale as shown in table 2.

The each permeable belt basic parameter of table 2

For permeable belt 1, detailed process and the result of proppant Scale Evaluation is described.

A, permeable belt 1 aspect ratio are 0.33 (y _eD1=y _e1/ x _e), permeability k _m1for 0.38mD.Utilize step 3) the middle fracture parameters evaluation Mathematical Modeling set up, at initial Reynolds number N _re1be under zero condition, integrating step 5) Mathematical Modeling method for solving, calculate the quasi-stable state initial optimum crack production capacity under different proppant scale, as shown in table 3.

Crack initial optimum crack production capacity under different proppant scale in table 3 permeable belt 1

B, utilize step 4) alternative manner, revise Reynolds number in crack, to solve under different proppant scale effective permeability in crack, then integrating step 3) Mathematical Modeling and step 5) Mathematical Modeling method for solving, obtain optimum crack production capacity final after revising, as shown in table 4.

Crack final optimal crack production capacity under different proppant scale in table 4 permeable belt 1

In d, consideration crack after high speed Non-Darcy's flow, final optimal crack production capacity under different proppant scale in contrast table 3, known is 35m at proppant consumption ³time, optimum crack production capacity increases and slows down, and therefore the optimum proppant scale of permeable belt 1 should be 35m ³left and right, and actual support agent scale is 48m ³.

According to identical method, for the permeable belt of different permeability and length, utilize this method to be supported agent Scale Evaluation plate (Fig. 5), obtain optimum proppant scale needed for each permeable belt, contrast actual support agent scale and optimum proppant scale, as shown in Figure 6.

As shown in Figure 6: in permeable belt 2,3 and 8, crack actual support agent scale is 55-65m ³, be slightly less than optimum proppant scale, it is 55-70m ³, illustrate that its proppant scale design is comparatively reasonable; In permeable belt 5,6 and 7, crack actual support agent scale is 40m ³left and right, is greater than optimum proppant scale 30m ³left and right, illustrates that its proppant scale is bigger than normal; In permeable belt 1 and 9, crack actual support agent scale is 50m ³left and right, is greater than optimum proppant scale 40m ³left and right, illustrates that its proppant scale design is bigger than normal.And crack actual support agent scale is 60m in permeable belt 4 ³left and right, much larger than optimum proppant scale 35m ³, illustrate that its proppant consumption is excessive.

The matching of fracture extension simulation softward is utilized to obtain each section of crack actual parameter as shown in table 5:

Table 5 extra-low permeability heterogeneous body gas reservoir each section of results of fracture simulation parameter

Permeable belt is numbered	Support the long x of seam f(m)	Propped fracture width w f(mm)	Dimensionless fracture conductivity C fD
				1	95	2.46	9.1
2	135	2.78	2.5
				3	120	2.78	2.9
4	130	2.69	2.6
				5	84	2.18	15.0
6	80	2.08	17.0
				7	75	2.22	19.5
8	115	2.54	2.7
				9	104	2.40	2.8

According to this method, utilize each permeable belt underlying parameter and actual support agent scale, obtain each permeable belt effective proppant index N _pe, then evaluate plate in conjunction with fracture parameters, obtain the optimum effective flow conductivity C in zero dimension crack of each permeable belt _fDeopt, the effective flow conductivity of the actual dimensionless fracture conductivity that comparative simulation obtains and optimum zero dimension crack, as shown in Figure 7.

As shown in Figure 7: in permeable belt 1, results of fracture simulation obtains actual dimensionless fracture conductivity is about 9, much larger than the effective flow conductivity about 4 in optimum zero dimension crack, in permeable belt 5,6 and 7, results of fracture simulation obtains actual dimensionless fracture conductivity is about 17, much larger than the effective flow conductivity about 8 in optimum zero dimension crack, illustrate that its crack width is bigger than normal, length is less than normal; In permeable belt 2,3,4,8 and 9, the actual dimensionless fracture conductivity in crack is about 2.5, and be slightly less than the effective flow conductivity about 3.5 in optimum zero dimension crack, illustrate that its crack width is slightly biased little, fracture length is greatly slightly biased.

The technical scheme of the application can consider the combined influence that there is high speed Non-Darcy's flow in low permeability gas reservoir aeolotropic characteristics and pressure break horizontal well crack, realizes rapidly and efficiently evaluating low-permeable heterogeneous gas reservoir pressure break horizontal well each section of fracture parameters and proppant scale reasonability.

Also it should be noted that, term " comprises ", " comprising " or its any other variant are intended to contain comprising of nonexcludability, thus make to comprise the commodity of a series of key element or system not only comprises those key elements, but also comprise other key elements clearly do not listed, or also comprise by this commodity or the intrinsic key element of system.When not more restrictions, the key element limited by statement " comprising ... ", and be not precluded within the commodity or system comprising described key element and also there is other identical element.

Above-mentioned explanation illustrate and describes some preferred embodiments of the application, but as previously mentioned, be to be understood that the application is not limited to the form disclosed by this paper, should not regard the eliminating to other embodiments as, and can be used for other combinations various, amendment and environment, and can in application contemplated scope described herein, changed by the technology of above-mentioned instruction or association area or knowledge.And the change that those skilled in the art carry out and change do not depart from the spirit and scope of the application, then all should in the protection domain of the application's claims.

Claims (7)

1. evaluate the rational method of low-permeable heterogeneous gas reservoir fracture parameters of fractured horizontal wells, it is characterized in that, comprise the following steps:

1) parameter of reservoir properties, fluid properties, pressure break horizontal well crack, horizontal wellbore, proppant character is collected respectively;

2) heterogeneous body gas reservoir is divided into the vadose zone of at least two homogeneous along horizontal wellbore length direction seepage flow rate distribution situation, described vadose zone contains man-made fracture;

3) Mathematical Modeling of the fracturing fracture physical model containing man-made fracture permeable belt and fracture parameters evaluation is set up;

4) revise described step 3) in the effective permeability of high speed non-Darcy flow in crack;

5) set up the crack yield model of crack high speed Non-Darcy's flow, set up the evaluation plate of heterogeneous body gas reservoir fracture parameters of fractured horizontal wells;

6) reasonability of low-permeable heterogeneous gas reservoir fracture parameters of fractured horizontal wells is evaluated.

2. the method for claim 1, it is characterized in that, described step 1) in, the parameter of described reservoir properties, fluid properties, pressure break horizontal well crack, horizontal wellbore, proppant character comprises: gas reservoir thickness, width, each permeable belt permeability, length; Gas viscosity, deviation factors, relative density; Each section of fracture length, width and height; Output and horizontal well wellbore pressure when reservoir temperature, average pressure, quasi-stable state; Initial support permeability.

3. method as claimed in claim 2, it is characterized in that, described step 2) by the method that heterogeneous body gas reservoir is divided into the permeable belt of at least two homogeneous along horizontal wellbore length direction seepage flow rate distribution situation be: according to the difference of reservoir permeability on horizontal wellbore length direction, reservoir division equal for permeability is become same permeable belt, and what permeability was low is considered as the interlayer hindering gas flowing.

4. method as claimed in claim 3, is characterized in that, step 3) described in the foundation method that contains the fracturing fracture physical model of man-made fracture permeable belt and the Mathematical Modeling of fracture parameters evaluation comprise the following steps:

A, heterogeneous body gas reservoir pressure break horizontal well regarded as much similar homogeneity permeation band composition, each vadose zone all about horizontal wellbore and crack symmetrically relation, with in the 1st vadose zone 1/4th for research object, crack is divided into n _windividual segment;

B, based on matrix flow equation, calculate the flow differential pressure between any two points in crack, utilize Direct Boundary Element Method, due to n _wsegment point source affects, and gas reservoir and the i-th segment point source quasi-stable state pressure drop are:

${\mathrm{\&Delta;p}}_{o,i}={\stackrel{\&OverBar;}{p}}^2-{p^2}_{o,i}=\frac{\mathrm{\&alpha;}\mathrm{\&mu;}ZT}{k_{m1}h}\underset{k=1}{\overset{n_w}{\&Sigma;}}{q}_{k}a\&lsqb;x_{oD,i},y_{oD,i},x_{wD,k},y_{wD,k},y_{eD}\&rsqb;=\frac{{\mathrm{\&alpha;}}_1\mathrm{\&mu;}ZT}{k_{m1}h}\underset{k=1}{\overset{n_w}{\&Sigma;}}{q}_{j}a\&lsqb;o_i,w_k\&rsqb;---\left(1\right)$

Gas reservoir and the pressure drop of jth segment point source quasi-stable state are:

${\mathrm{\&Delta;p}}_{o,j}={\stackrel{\&OverBar;}{p}}^2-{p^2}_{o,j}=\frac{\mathrm{\&alpha;}\mathrm{\&mu;}ZT}{k_{m1}h}\underset{k=1}{\overset{n_w}{\&Sigma;}}{q}_{k}a\&lsqb;x_{oD,j},y_{oD,j},x_{wD,k},y_{wD,k},y_{eD}\&rsqb;=\frac{{\mathrm{\&alpha;}}_1\mathrm{\&mu;}ZT}{k_{m1}h}\underset{k=1}{\overset{n_w}{\&Sigma;}}{q}_{k}a\&lsqb;o_j,w_k\&rsqb;---\left(2\right)$

The quasi-stable state pressure drop of i-th section and jth section is subtracted each other, and works as i=1, during j=2, to obtain in crack the 1st section and the 2nd section of flow pressure drop is:

${{\mathrm{\&Delta;p}}^2}_{R,2\&RightArrow;1}=\frac{\mathrm{\&alpha;}\mathrm{\&mu;}ZT}{k_{m1}h}\underset{k=1}{\overset{n_w}{\&Sigma;}}\&lsqb;q_1(a\&lsqb;o_1,w_1\&rsqb;-a\&lsqb;o_2,w_1\&rsqb;)+...+q_{n_w}(a\&lsqb;o_1,w_{n_w}\&rsqb;-a\&lsqb;o_2,w_{n_w}\&rsqb;)\&rsqb;---\left(3\right)$

In formula: Δ p _o,i, Δ p _o,jbe respectively the quasi-stable state pressure drop of gas reservoir and the i-th segment and jth segment, Δ p _{r, 2 → 1}for based on the 2nd segment of matrix flow and the flow pressure drop of the 1st segment, unit is MPa; α=774.6; μ is gas viscosity, and unit is mPa.s; Z is deviation factor for gas; T is reservoir temperature, and unit is K; k _m1be the 1st permeable belt matrix permeability, unit is mD; H is gas reservoir thickness, and unit is m; n _wit is the hop count of half long crack decile; α [o _i, w _j] for jth section is to the influence function of i-th section, w is point of observation, o is source point;

C, to flow based in crack, calculate the flow differential pressure of adjacent segment in crack, for high speed Non-Darcy's flow in crack, non-for high speed darcy is treated to Darcy Flow, obtains flowing in crack partial differential equation according to Darcy's law:

$q=-\frac{k_{fe}{A}_f}{\mathrm{\&mu;}}\frac{\&part;p}{\&part;x}---\left(4\right)$

By flow between the 1st section and the 2nd section of crack be the 2nd section to n-th _wthe total flow of section, then based on flow in fracture, the 1st section and the 2nd section of flow pressure drop are:

${{\mathrm{\&Delta;p}}^2}_{f,1\&RightArrow;2}=\frac{2\mathrm{\&alpha;}\mathrm{\&mu;}ZT}{k_{fe}{\mathrm{hw}}_f}\&lsqb;q_2(x_{o2}-x_{o1})+...+q_{nw}(x_{o2}-x_{o1})\&rsqb;---\left(5\right)$

In formula: Δ p _{f, 2 → 1}for based on the 2nd segment of flow in fracture and the flow pressure drop of the 1st segment, unit is MPa; k _fefor considering effective permeability after high speed Non-Darcy's flow in crack, unit is mD; x _o1, x _o2be respectively and the 2nd position at the 1st, unit is m;

D, calculate correlation between crack flow and fracture parameters

Formula (3) and formula (5) are subtracted each other, obtaining each section of pass between flow and fracture parameters is:

$\begin{array}{c}{q}_1(a\&lsqb;o_1,w_1\&rsqb;-a\&lsqb;o_2,w_1\&rsqb;)+...+q_{n_w}(a\&lsqb;o_1,w_{n_w}\&rsqb;-a\&lsqb;o_2,w_{n_w}\&rsqb;)\\ -\frac{2k}{k_{fe}{w}_f}\&lsqb;q_2(x_{o2}-x_{o1})+...+q_{n_w}(x_{o2}-x_{o1})\&rsqb;=0\end{array}---\left(6\right)$

By each section of flow, position, fracture half-length, fracture condudtiviy, proppant scale zero dimension

$q_{Di}=\frac{q_i{B}_g\mathrm{\&mu;}T}{2{\mathrm{\&pi;k}}_{m1}h(p_{ave}^2-p_{wf}^2)}---\left(7\right)$

$x_{Doi}=\frac{x_{oi}}{x_e/2}---\left(8\right)$

$I_x=\frac{x_f}{x_e/2}---\left(9\right)$

$C_{fDe}=\frac{k_{fe}{w}_f}{{\mathrm{kx}}_f}---\left(10\right)$

$N_{pe}=\frac{2k_{fe}{v}_p}{{\mathrm{kv}}_r}=I_x^2{C}_{fD}\frac{x_e}{y_e}---\left(11\right)$

Obtain the zero dimension relation of each section of crack between flow and fracture parameters:

$\begin{array}{c}{q}_{D1}(a\&lsqb;o_1,w_1\&rsqb;-a\&lsqb;o_2,w_1\&rsqb;)+...+q_{{\mathrm{Dn}}_w}(a\&lsqb;o_1,w_{n_w}\&rsqb;-a\&lsqb;o_2,w_{n_w}\&rsqb;)\\ -\frac{4\mathrm{\&pi;}k}{C_{fD}{I}_x}\&lsqb;q_{D2}(x_{Do2}-x_{Do1})+...+q_{{\mathrm{Dn}}_w}(x_{Do2}-x_{Do1})\&rsqb;=0\end{array}---\left(12\right)$

In formula, B _gfor gas volume factor; q _dibe i-th section of crack nondimensional mass flow; p _aveand p _wfbe respectively gas reservoir average pressure and horizontal wellbore pressure, unit is MPa; x _dibe i-th section of zero dimension position; x _e, y _ebe respectively permeable belt width and length, unit is m; x _f, w _fbe respectively fracture half-length, crack width, unit is m; k _fefor considering effective permeability during high speed Non-Darcy's flow in crack, unit is mD; I _xfor crack penetration ratio; C _fDe, N _pebe respectively in crack and consider the high speed effective flow conductivity of Non-Darcy's flow zero dimension and effective proppant index; v _p, v _rbe respectively proppant supporting crack volume and permeable belt volume, unit is m ³;

With should i=2, j=3, i=3, j=4 ..., i=n _w-1, j=n _wtime, all the other n can be obtained _w-2 adjacent slits section relational expressions, obtain n _w-1 each section of crack flow and fracture parameters zero dimension relational expression, last expression formula be the 1st section to horizontal wellbore pressure drop, n _windividual system of linear equations, solves n _wsection crack nondimensional mass flow and fracture parameters relation;

$\left[\begin{array}{cccc}{a}_{11}& a_{12}& ...& a_{11}\\ a_{21}& a_{22}& ...& a_{11}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ a_{nw1}& a_{nw2}& ...& a_{11}\end{array}\right]\&CenterDot;\left[\begin{array}{c}{q}_{D1}\\ q_{D2}\\ .\\ .\\ .\\ q_{Dnw}\end{array}\right]=\left[\begin{array}{c}1\\ 0\\ .\\ .\\ .\\ 0\end{array}\right]---\left(13\right)$

Wherein:

a _1j/(j＝1,…,n _w)＝a[o ₁,w _j]

a _i1/(i＝2,…,n _w)＝a[o ₁,w ₁]-a[o _i,w ₁](14)

$a_{ij}/(i,j=1,...,n_w)=a\&lsqb;o_1,w_j\&rsqb;-a\&lsqb;o_i,w_j\&rsqb;-\frac{4\mathrm{\&pi;}}{C_{fD}{I}_x}(x_{Do\left(min\right(i,j\left)\right)}-x_{Do1})$

Every crack dimensionless production be all slits section nondimensional mass flow and 4 times, whole piece crack dimensionless production expression formula:

$J_D=4\underset{j=1}{\overset{n_w}{\&Sigma;}}{q}_{Di}---\left(15\right)$

In formula: J _dfor whole piece crack dimensionless production index.

5. method as claimed in claim 4, is characterized in that, described step 4) utilize alternative manner, by effective permeability in Reynolds number correction crack, high speed Non-Darcy's flow is treated to Darcy Flow, comprises the following steps:

E, suppose that initial Reynolds number is N _re1be zero, according to crack effective permeability and Reynolds number relation, obtain incipient crack effective permeability:

$k_{fe1}=\frac{k_f}{1+N_{\mathrm{Re}1}}---\left(16\right)$

In formula: k _f, k _fe1be respectively supporting crack original permeability and initial effective permeability, unit is mD; N _re1for supposing initial Reynolds number, value is zero;

F, according to proppant exponential expression (formula 11), substitute into incipient crack effective permeability, obtain initially effectively proppant index:

$N_{pe1}=\frac{2k_{fe1}{v}_p}{k_{m1}{\mathrm{hx}}_e{y}_e}=I_x^2\&CenterDot;C_{fDe1}\&CenterDot;\frac{x_e}{y_e}---\left(17\right)$

G, at initial effectively proppant index N _pe1under, according to step 3) the crack nondimensional mass flow set up and fracture parameters relation, obtain and contrast different dimensionless fracture conductivity C _fDe1corresponding crack total nondimensional mass flow index J _d, and then obtain optimum zero dimension effective fracture flow conductivity C _fDe1opt;

H, according to optimum zero dimension effective fracture flow conductivity C _fDe1opt, calculate initial optimum fracture half-length and width:

$x_{f1opt}=\sqrt{\frac{k_{fe1}{v}_p}{2C_{fDe1opt}{k}_{m1}h}}---\left(18\right)$

$w_{f1opt}=\sqrt{\frac{C_{fDe1opt}{k}_{m1}{v}_p}{2k_{fe1}h}}---\left(19\right)$

In formula: x _f1opt, w _f1optbe respectively initial optimum fracture half-length and crack width, unit is m;

I, nondimensional mass flow is converted into crack actual production, by the relational expression of output and crack width, obtains pit shaft place gas flow rate:

$q_g=\frac{(p_{ave}^2-p_{wf}^2)k_{m1}h}{1.291\&times;{10}^{-3}\mathrm{\&mu;}ZT}{J}_D---\left(20\right)$

$v=\frac{q_g}{2A_{f1opt}(24\&times;3600)}=\frac{q_g}{172800{\mathrm{hw}}_{f1opt}}---\left(21\right)$

In formula: qg is crack total output, unit is m ³/ d; V is crack and pit shaft intersection gas flow rate, and unit is m/s; A _f1optfor crack under initial optimum crack width and pit shaft phase cross surface area, unit is m ²;

J, according to Reynolds number definition, calculate new effective Reynolds number N _re2:

$N_{\mathrm{Re}2}=\frac{{\mathrm{\&beta;k}}_{fe1}{\mathrm{\&rho;}}_{g}v}{{\mathrm{\&mu;}}_g}---\left(22\right)$

Wherein:

${\mathrm{\&rho;}}_g=1.22\frac{{\mathrm{\&gamma;}}_g}{B_g}---\left(23\right)$

$B_g=3.458\&times;{10}^{-4}\frac{ZT}{p_{wf}}---\left(24\right)$

$\mathrm{\&beta;}=1\&times;{10}^8\frac{n}{k_{fe1}^m}---\left(25\right)$

In formula: β is porous media characteristic parameter; ρ g is gas density, and unit is kg/m ³; γ g is gas relative density; M, n are the relevant constant of proppant particle diameter;

K, contrast hypothesis Reynolds number N _re1with new Reynolds number N _re2if, two, differ | R _e1-R _e2| within the scope of≤ξ, then obtaining design flaw size is required flaw size, if not in prescribed limit, is then got by Reynolds number in formula (16) and is newly worth N _re2, iteration again, until Reynolds number is in prescribed limit.

6. method as claimed in claim 5, is characterized in that, described step 5) utilize influence function, solve crack output, and set up fracture parameters evaluation plate, comprise the following steps:

a[o _i,w _j]＝a[x _D,y _D,x _wD,y _wD,y _eD]＝a ¹[max(x _D,x _wD),max(y _D,y _wD),min(x _D,x _wD),min(y _D,y _wD),y _eD]

(26)

$a^1\&lsqb;x_D,y_D,x_{wD},y_{wD},y_{eD}\&rsqb;=\left\{\begin{array}{cc}{a}^0\&lsqb;x_D,y_D,x_{wD},y_{wD},y_{eD}\&rsqb;& \begin{array}{cc}if& (y_{eD}<1)\end{array}\\ a^0\&lsqb;x_D,y_D,x_{wD},y_{wD},\frac{1}{y_{eD}}\&rsqb;& \end{array}\right.---\left(27\right)$

$a^0\&lsqb;x_D,y_D,x_{wD},y_{wD},y_{eD}\&rsqb;=2{\mathrm{\&pi;y}}_{eD}(\frac{1}{3}-\frac{y_D}{y_{eD}}+\frac{y_D^2+y_{wD}^2}{2y_{eD}^2})+S_T---\left(28\right)$

Wherein:

$S_T=2\underset{m=1}{\overset{\mathrm{\&infin;}}{\&Sigma;}}\frac{t_m}{m}cos\left({\mathrm{m\&pi;x}}_D\right)cos\left({\mathrm{m\&pi;x}}_{wD}\right)---\left(29\right)$

$t_m=\frac{\cosh \&lsqb;m\mathrm{\&pi;}(y_{eD}-|y_D-y_{wD}\left|\right)\&rsqb;+\cosh \left(m\mathrm{\&pi;}\right(y_{eD}-\left|y_D+y_{wD}\right|\left)\right)}{\sinh \left({\mathrm{m\&pi;y}}_{eD}\right)}---\left(30\right)$

By infinite series S _tuse following formula finite process:

S _T＝S ₁+S ₂+S ₃(31)

$S_1=2\underset{m=1}{\overset{N}{\&Sigma;}}\frac{t_m}{m}cos\left({\mathrm{m\&pi;x}}_D\right)cos\left({\mathrm{m\&pi;x}}_{wD}\right)---\left(32\right)$

$\begin{array}{c}{S}_2=-\frac{t_N}{2}\ln \{{\&lsqb;1-\cos \left(\mathrm{\&pi;}\right(x_D+x_{wD}\left)\right)\&rsqb;}^2+{\&lsqb;\sin \left(\mathrm{\&pi;}\right(x_D+x_{wD}\left)\right)\&rsqb;}^2\}\\ -\frac{t_N}{2}\ln \{{\&lsqb;1-\cos \left(\mathrm{\&pi;}\right(x_D-x_{wD}\left)\right)\&rsqb;}^2+{\&lsqb;\sin \left(\mathrm{\&pi;}\right(x_D-x_{wD}\left)\right)\&rsqb;}^2\}\end{array}---\left(33\right)$

$S_3=-2t_N\underset{m=1}{\overset{N}{\&Sigma;}}\frac{1}{m}cos\left({\mathrm{m\&pi;x}}_D\right)cos\left({\mathrm{m\&pi;x}}_{wD}\right)---\left(34\right)$

In formula: y _eDfor permeable belt aspect ratio, y _eD=y _e/ x _e

The Mathematical Modeling of crack output is solved, with aspect ratio y by influence function _eD=1 is example, obtains different effectively proppant index N _peunder, zero dimension crack output index evaluates plate with the fracture parameters of dimensionless fracture conductivity variation relation.

7. method as claimed in claim 6, is characterized in that, described step 6) evaluate the reasonability of hypotonic heterogeneous body gas reservoir fracture parameters of fractured horizontal wells, comprise the following steps:

L, by geology, interpretation of logging data result, to obtain along permeable belt permeability k each on horizontal wellbore length direction _mi, permeable belt length y _eiwith width x _e;

M, determining each permeable belt aspect ratio y _eD=y _ei/ x _ewhen, change proppant scale, obtain optimum crack output with proppant scale variation relation plate; In plate, crack output increases proppant scale when occurring mild is optimal value, according to each permeable belt aspect ratio and permeability thereof, this Mathematical Modeling is utilized to obtain corresponding proppant Scale Evaluation plate, contrast optimum proppant scale value in actual support agent scale and plate, carry out proppant Scale Evaluation;

N, in step l) under the underlying parameter that obtains, according to the Mathematical Modeling of crack Production rate, by the correction of high speed Non-Darcy's flow permeability in crack, calculate the revised supporting crack effective permeability of each permeable belt and effective proppant index N _pe;

O, according to aspect ratio and effective proppant index, select reflection crack parameter evaluation plate, and then obtain optimum crack production capacity index, corresponding optimum crack zero dimension flow conductivity C _fDe;

P, the actual fracture length utilizing the matching of fracture extension simulation softward to obtain and width, then according to dimensionless fracture conductivity definition (formula 10), obtain actual fracture condudtiviy C _fD, under identical effective proppant index, then obtain actual crack production capacity index in conjunction with plate;

Q, contrast actual dimensionless fracture conductivity C _fDwith optimum dimensionless fracture conductivity C _fDeif, bigger than normal, then illustrate that crack width is excessive, length is too small, if less than normal, illustrates that crack width is too small, width is excessive.