CN106285568A - A kind of branch horizontal well recovery method based on Green's function - Google Patents

Abstract

The invention discloses a kind of branch horizontal well recovery method based on Green's function, specifically implement according to following steps: first calculate the theoretical value of the shale gas yield of branch horizontal well, secondly carry out the operation of branch horizontal well day actual production according to theoretical value and draw the curve chart of branch horizontal well day actual production and time, when trip point occurs in curve chart, it is adjusted till curve chart occurs without trip point, when accumulative aquifer yield and critical aquifer yield are equal, branch horizontal well is scrapped.A kind of branch horizontal well recovery method based on Green's function, it is adjusted after transition point produces, shale gas is conducive to carry the output water in horizontal wellbore in time, reduce air-water mixture and return the harm in shaft bottom, reduce the gathering in shaft bottom of the output water, thus reducing maintenance cost, efficiency is high, saves maintenance cost.

Description

A kind of branch horizontal well recovery method based on Green's function

Technical field

The invention belongs to shale gas mining operations technical field, relate to the exploitation of a kind of branch horizontal well based on Green's function Method.

Background technology

In shale gas is developed, drilling through Multilateral Wells on the basis of horizontal well can increase target zone length, increase draining face Long-pending, improve oil and gas production, therefore, after shale gas cost of winning in 2010 reduces, China's branch horizontal well drilling technology is sent out Exhibition rapidly, and enters the scale application stage.At present, branch horizontal well technology is the exploitation relatively effective hands of shale gas reservoir Section.In the exploitation of shale gas well, in order to obtain the cumulative production of maximum, usually, a kind of method is to control gas well horizontal well The pressure in shaft bottom is constant, and another kind of method is that the well head flow of control gas well is constant.

But, existing shale gas branch horizontal well recovery method is usually present weak point: keep bottom pressure constant And As time goes on, gas well yield is gradually lowered, the economic benefit of gas well exploitation also decreases；If being to maintain well head Flow constant and As time goes on, strata pressure difference causes output formation water at the bottom of Horizontal Well, formation water blocking shale gas Gas channel, reduce gas well the exploitation life-span.Both recovery methods all do not account for shale gas well at reservoir branches angle Degree, i.e. the Green's function of shale gas well, this is one of the physical property of shale gas well.Green's function is along dispersal direction, at page The rock gas well Multilateral Wells difference Branch Angle a kind of method to shale gas Multilateral Wells volume analysis.Therefore prior art needs one badly Plant and consider shale gas Green's function to improve the branch horizontal well recovery method of shale gas recovery ratio.

Summary of the invention

It is an object of the invention to provide a kind of branch horizontal well recovery method based on Green's function, solve existing shale Edema caused by disorder of QI props up along with the prolongation of recovery time present in horizontal wells, and at the bottom of Horizontal Well, the air-flow of formation water blocking shale gas leads to Road, the problem reducing the exploitation life-span of gas well.

The technical solution adopted in the present invention is, a kind of branch horizontal well recovery method based on Green's function, specifically presses Implement according to following steps:

Step 1: determine rock core absolute permeability k of target reservoir₀Viscosity, mu with shale gas_g；

Step 2: set up the air water two phase fluid flow formula under the influence of Green's function:

$\left\{\begin{array}{c}{q}_w=-\frac{k_0{k}_{rw}}{{\mathrm{\μ}}_w}\frac{dp}{dx}\\ q_g=-\frac{1}{G_l(r_D,t_D)}\frac{k_0{k}_{rg}}{{\mathrm{\μ}}_g}\frac{dp}{dx}\end{array}\right.---\left(1\right)$

Wherein,

In formula, k_rwRepresent aqueous phase relative permeability；μ_wRepresent aqueous viscosity；Represent the barometric gradient of reservoir；q_wTable Show the theoretical water yield per day of branch horizontal well；q_gRepresent the daily output tolerance of branch horizontal well；k_rgRepresent shale gas relative permeability； P represents the pressure of optional position, reservoir；For dimensionless radius；For non dimensional time；For Zero dimension horizontal well length；For zero dimension horizontal well branch length；r_wRepresent horizontal well radius；R represents that reservoir is appointed Meaning point is to the distance at the bottom of Horizontal Well；φ represents the porosity of rock core；C represents the coefficient of compressibility of rock core；r_wnRepresent Multilateral Wells half Footpath；T represents the production time；L represents Horizontal Well segment length；L_nRepresent Multilateral Wells well segment length；l₁Represent that reservoir is along horizontal well Axial direction random length；G_l(r_D,t_D) represent Green's function；θ represents Multilateral Wells and horizontal well angle angle；

Step 3: calculate theoretical value q of branch horizontal well shale gas yield₀；

Step 4: according to the q in step 3₀Carry out branch horizontal well day actual production q_sOperation, even if q_s=q₀, simultaneously The record production time, and draw the curve chart A of branch horizontal well day actual production and time, and it is real to draw branch horizontal well day The curve chart B of border aquifer yield and time；

Step 5: when trip point occurs in the curve chart A of described step 4, adjusts branch levels well yield q_s, it is designated as q₁；

Step 6: according to the q in step 5₁Carry out day actual production q of branch horizontal well_sOperation, even if q_s=q₁, with The Shi Jilu production time, and draw the curve chart A of branch horizontal well day actual production and time, and draw branch horizontal well day The curve chart B of actual aquifer yield and time；

Step 7: when trip point occurs in the curve chart A of described step 6, adjusts day actual production q of branch horizontal well_s, It is designated as q₂；

Step 8: repeat step 6 and step 7 until the curve chart A of branch levels well production and time occurs without trip point is Only, now the day actual production of branch horizontal well will no longer be adjusted；

Step 9: branch horizontal well day actual aquifer yield and the curve chart B of time on to water yield per day summation added up Aquifer yield Q_{Water is total}, when accumulative aquifer yield and critical aquifer yield are equal, branch horizontal well is scrapped.

The feature of the present invention also resides in:

Step 3 is fallen into a trap and is calculated theoretical value q of branch horizontal well shale gas yield₀Method particularly includes:

Step 3.1: according to steady percolation theory, utilizes pseudofunction method to be integrated drawing shale gas yield to formula (1) Formula is:

$q_0=\frac{{\mathrm{\πk}}_0{l}_0{Z}_{sc}{T}_{sc}{\mathrm{\ρ}}_{gsc}}{p_{sc}{\mathrm{T\μ}}_{g}Z}\underset{n=1}{\overset{m}{\Σ}}\frac{{p_e}^2-{p_{wn}}^2}{G_l(r_D,t_D)ln\frac{R\left(t\right)}{r_{wn}}}---\left(2\right)$

In formula, l₀Represent gas-bearing formation horizontal length；Z_scRepresent Gas Compression Factor under standard state；T_scRepresent under standard state Temperature；ρ_gscRepresent gas density under standard state；p_scRepresent standard state downforce；T represents formation temperature；Z represents gas pressure The contracting factor；p_eRepresent original formation pressure；p_wnRepresent horizontal well Multilateral Wells bottom pressure, under the influence of R (t) represents horizontal well branch Moving boundary；r_wnRepresent Multilateral Wells wellbore radius.

Step 5 adjusts branch levels well yield q_sMethod particularly includes:

Step 5.1: drilling well and perforation data according to branch horizontal well determine branch number m and each contiguous branch well perforation position Spacing l put, and it is as follows to set up Tuning function based on Green's function:

$f\left(t\right)=\left\{\begin{array}{cc}(m-INT(t{\left(\frac{l}{2\mathrm{\&beta;}v}\right)}^{-1}\left)\right)& INT\left(t{\left(\frac{l}{2\mathrm{\&beta;}v}\right)}^{-1}\right)<m\\ 1& INT\left(t{\left(\frac{l}{2\mathrm{\&beta;}v}\right)}^{-1}\right)\&GreaterEqual;m\end{array}\right.---\left(3\right)$

Wherein,

In formula, β represents shale formation pressure propagation coefficient；V represents that spread speed drops in strata pressure；F (t) represents adjustment letter Number；T represents recovery time；INT () represents bracket function；P represents strata pressure；

Step 5.2: according to Tuning function branch levels well yield q of step 5.1_sIt is adjusted,

$q_1=\frac{{\mathrm{\&pi;k}}_0{l}_0{Z}_{sc}{T}_{sc}{\mathrm{\&rho;}}_{gsc}}{p_{sc}{\mathrm{T\&mu;}}_{g}Z}\underset{n=1}{\overset{f\left(t\right)}{\&Sigma;}}\frac{{p_e}^2-{p_{wn}}^2}{G_l(r_D,t_D)ln\frac{R\left(t\right)}{r_{wn}}}---\left(4\right)$

In formula, q₁Represent that gas well mouth adjusts the daily output.

Accumulative aquifer yield Q in step 9_{Water is total}Computational methods be:

In formula, q_{Daily output water}Represent shale gas well day actual aquifer yield；

In step 9, critical aquifer yield is determined by prospect pit and the well test data of target reservoir formation.

Rock core absolute permeability k in step 1₀Measured by automatic measuring instrument for permeability of rock core.

The viscosity, mu of shale gas in step 1_gObtained by curve-fitting method.

The invention has the beneficial effects as follows:

1, a kind of branch horizontal well recovery method based on Green's function, according to the spy of branch horizontal well shale gas exploitation Point, establish consider shale gas Green's function air water two phase fluid flow formula, can fully exploit reservoir shale gas thus Improve the recovery ratio of shale gas；

2, establish Tuning function based on Green's function, can reasonably adjust gas well yield, it is to avoid blindly Adjust, reduce the destruction to gas-bearing formation；

3, the formula according to Tuning function classification based on Green's function adjustment gas well mouth flow is established, by selecting Reasonably classification adjusts the well head flow of shale gas, can reduce stratum producing pressure differential, thus slow down formation water water breakthrough, extends and divides Prop up the production life of well of horizontal well；

When 4, transition point occurring according to recovery method based on Green's function on production curve chart, select suitably to adjust On opportunity, the drop of pressure speed in the region that pressure drop funnel feeds through to can be delayed, extend stripping gas and separate out time and amount of precipitation, from And increase cumulative production on the whole；Being adjusted after transition point produces, beneficially shale gas carries in horizontal wellbore in time Output water, reduces air-water mixture and returns the harm in shaft bottom, reduce the gathering in shaft bottom of the output water, thus reduce maintenance expense With, efficiency is high, saves maintenance cost.

Detailed description of the invention

A kind of branch horizontal well recovery method based on Green's function of the present invention, specifically includes following steps:

Step 1: determine rock core absolute permeability k of target reservoir₀Viscosity, mu with shale gas_g, wherein rock core Absolute permeation Rate k₀The viscosity, mu of shale gas is measured by automatic measuring instrument for permeability of rock core_gObtained by curve-fitting method；

Step 2: set up the air water two phase fluid flow formula under the influence of Green's function:

$\left\{\begin{array}{c}{q}_w=-\frac{k_0{k}_{rw}}{{\mathrm{\&mu;}}_w}\frac{dp}{dx}\\ q_g=-\frac{1}{G_l(r_D,t_D)}\frac{k_0{k}_{rg}}{{\mathrm{\&mu;}}_g}\frac{dp}{dx}\end{array}\right.---\left(1\right)$

Wherein,

In formula, k_rwRepresent aqueous phase relative permeability；μ_wRepresent aqueous viscosity；Represent the barometric gradient of reservoir；q_wTable Show the theoretical water yield per day of branch horizontal well；q_gRepresent the daily output tolerance of branch horizontal well；k_rgRepresent shale gas relative permeability； P represents the pressure of optional position, reservoir；For dimensionless radius；For non dimensional time；For Zero dimension horizontal well length；For zero dimension horizontal well branch length；r_wRepresent horizontal well radius；R represents that reservoir is appointed Meaning point is to the distance at the bottom of Horizontal Well；φ represents the porosity of rock core；C represents the coefficient of compressibility of rock core；r_wnRepresent Multilateral Wells half Footpath；T represents the production time；L represents Horizontal Well segment length；Ln represents Multilateral Wells well segment length；l₁Represent that reservoir is along level Well axial direction random length；G_l(r_D,t_D) represent Green's function；θ represents Multilateral Wells and horizontal well angle angle；

Step 3: calculate theoretical value q of branch horizontal well shale gas yield₀, method particularly includes:

According to steady percolation theory, pseudofunction method is utilized to be integrated formula (1) showing that shale gas production formula is:

$q_0=\frac{{\mathrm{\&pi;k}}_0{l}_0{Z}_{sc}{T}_{sc}{\mathrm{\&rho;}}_{gsc}}{p_{sc}{\mathrm{T\&mu;}}_{g}Z}\underset{n=1}{\overset{m}{\&Sigma;}}\frac{{p_e}^2-{p_{wn}}^2}{G_l(r_D,t_D)ln\frac{R\left(t\right)}{r_{wn}}}---\left(2\right)$

In formula, l₀Represent gas-bearing formation horizontal length；Z_scRepresent Gas Compression Factor under standard state；T_scRepresent under standard state Temperature；ρ_gscRepresent gas density under standard state；p_scRepresent standard state downforce；T represents formation temperature；Z represents gas pressure The contracting factor；p_eRepresent original formation pressure；p_wnRepresent horizontal well Multilateral Wells bottom pressure；Under the influence of R (t) represents horizontal well branch Moving boundary；r_wnRepresent Multilateral Wells wellbore radius；

Step 4: according to the q in step 3₀Carry out branch horizontal well day actual production q_sOperation, even if q_s=q₀, and remember The record production time, and draw the curve chart A of branch horizontal well day actual production and time, and it is actual to draw branch horizontal well day The curve chart B of aquifer yield and time；

Step 5: when trip point occurs in the curve chart A of described step 4, adjusts branch levels well yield q_s, it is designated as q₁；

Adjust branch levels well yield q_sMethod particularly includes:

Step 5.1: drilling well and perforation data according to branch horizontal well determine branch number m and each contiguous branch well perforation position Spacing l put, and it is as follows to set up Tuning function based on Green's function:

$f\left(t\right)=\left\{\begin{array}{cc}(m-INT(t{\left(\frac{l}{2\mathrm{\&beta;}v}\right)}^{-1}\left)\right)& INT\left(t{\left(\frac{l}{2\mathrm{\&beta;}v}\right)}^{-1}\right)<m\\ 1& INT\left(t{\left(\frac{l}{2\mathrm{\&beta;}v}\right)}^{-1}\right)\&GreaterEqual;m\end{array}\right.---\left(3\right)$

Wherein,

In formula, β represents shale formation pressure propagation coefficient；V represents that spread speed drops in strata pressure；F (t) represents adjustment letter Number；T represents recovery time；INT () represents bracket function；P represents strata pressure；

Step 5.2: according to Tuning function branch levels well yield q of step 5.1_sIt is adjusted,

$q_1=\frac{{\mathrm{\&pi;k}}_0{l}_0{Z}_{sc}{T}_{sc}{\mathrm{\&rho;}}_{gsc}}{p_{sc}{\mathrm{T\&mu;}}_{g}Z}\underset{n=1}{\overset{f\left(t\right)}{\&Sigma;}}\frac{{p_e}^2-{p_{wn}}^2}{G_l(r_D,t_D)ln\frac{R\left(t\right)}{r_{wn}}}---\left(4\right)$

In formula, q₁Represent that gas well mouth adjusts the daily output；

Step 6: according to the q in step 5₁Carry out day actual production q of branch horizontal well_sOperation, even if q_s=q₁, and The record production time, and draw the curve chart A of branch horizontal well day actual production and time, and it is real to draw branch horizontal well day The curve chart B of border aquifer yield and time；

Step 7: when trip point occurs in the curve chart A of described step 6, adjusts branch levels well yield q_s, it is designated as q₂；

Step 8: repeat step 6 and step 7 until the curve chart A of branch levels well production and time occurs without trip point is Only, now the day actual production of branch horizontal well will no longer be adjusted；

Step 9: branch horizontal well day actual aquifer yield and the curve chart B of time on to water yield per day summation added up Aquifer yield Q_{Water is total}, described accumulative aquifer yield Q_{Water is total}Computational methods be:

In formula, q_{Daily output water}Represent shale gas well day actual aquifer yield；

When accumulative aquifer yield and critical aquifer yield are equal, branch horizontal well is scrapped.

Obviously, described embodiment is only some embodiments of the present application rather than whole embodiments.Based on this Embodiment in application, the every other reality that those of ordinary skill in the art are obtained under not making creative work premise Execute example, all should belong to the scope of the application protection.Cause owing to total gas production of shale gas well comprises the decline of gas-bearing formation pressure Yield and yield two parts of causing of shale gas stripping gas, therefore the well head yield by adjusting shale gas can reach to delay Formation water output and prolongation gas well life-span are to increase stripping gas yield, thus are finally reached the mesh increasing shale gas well total output 's.

A kind of branch horizontal well recovery method based on Green's function, according to the feature of branch horizontal well shale gas exploitation, Establish the air water two phase fluid flow formula considering shale gas Green's function, can fully exploit the shale gas of reservoir thus improve The recovery ratio of shale gas；Establish Tuning function based on Green's function, can reasonably adjust gas well yield, it is to avoid be blind Purpose adjusts, and reduces the destruction to gas-bearing formation；Establish and adjust gas well mouth according to Tuning function classification based on Green's function The formula of flow, by selecting rational classification to adjust the well head flow of shale gas, can reduce stratum producing pressure differential, thus subtract Slow formation water water breakthrough, extends the production life of well of branch horizontal well；Curve chart is being produced according to recovery method based on Green's function On time transition point occurs, select suitably to adjust opportunity, the drop of pressure speed in the region that pressure drop funnel feeds through to can be delayed, Extend stripping gas and separate out time and amount of precipitation, thus increase cumulative production on the whole；It is adjusted, favorably after transition point produces Carry the output water in horizontal wellbore in time in shale gas, reduce air-water mixture and return the harm in shaft bottom, reduce output water and exist The gathering in shaft bottom, thus reduce maintenance cost, efficiency is high, saves maintenance cost.

Claims (7)

1. a branch horizontal well recovery method based on Green's function, it is characterised in that specifically include following steps:

Step 1: determine rock core absolute permeability k of target reservoir₀Viscosity, mu with shale gas_g；

Step 2: set up the air water two phase fluid flow formula under the influence of Green's function:

$\left\{\begin{array}{c}{q}_w=-\frac{k_0{k}_{rw}}{{\mathrm{\&mu;}}_w}\frac{dp}{dx}\\ q_g=-\frac{1}{G_l(r_D,t_D)}\frac{k_0{k}_{rg}}{{\mathrm{\&mu;}}_g}\frac{dp}{dx}\end{array}\right.---\left(1\right)$

Wherein,

In formula, k_rwRepresent aqueous phase relative permeability；μ_wRepresent aqueous viscosity；Represent the barometric gradient of reservoir；q_wRepresent and divide Prop up the theoretical water yield per day of horizontal well；q_gRepresent the daily output tolerance of branch horizontal well；k_rgRepresent shale gas relative permeability；P table Show the pressure of optional position, reservoir；For dimensionless radius；For non dimensional time；For nothing Dimension horizontal well length；For zero dimension horizontal well branch length；r_wRepresent horizontal well radius；R represents that reservoir is any Point is to the distance at the bottom of Horizontal Well；φ represents the porosity of rock core；C represents the coefficient of compressibility of rock core；r_wnRepresent Multilateral Wells radius； T represents the production time；L represents Horizontal Well segment length；Ln represents Multilateral Wells well segment length；l₁Represent that reservoir is along horizontal borehole axis To direction random length；G_l(r_D,t_D) represent Green's function；θ represents Multilateral Wells and horizontal well angle angle；

Step 3: calculate theoretical value q of branch horizontal well shale gas yield₀；

Step 4: according to the q in step 3₀Carry out branch horizontal well day actual production q_sOperation, even if q_s=q₀, record life simultaneously The product time, and draw the curve chart A of branch horizontal well day actual production and time, and draw branch horizontal well day actual product water Amount and the curve chart B of time；

Step 5: when trip point occurs in the curve chart A of described step 4, adjusts branch levels well yield q_s, it is designated as q₁；

Step 6: according to the q in step 5₁Carry out day actual production q of branch horizontal well_sOperation, even if q_s=q₁, record simultaneously Production time, and draw the curve chart A of branch horizontal well day actual production and time, and draw branch horizontal well day actual product The curve chart B of the water yield and time；

Step 7: when trip point occurs in the curve chart A of described step 6, adjusts day actual production q of branch horizontal well_s, it is designated as q₂；

Step 8: till repetition step 6 and the step 7 curve chart A until branch levels well production and time occur without trip point, Now the day actual production of branch horizontal well will no longer be adjusted；

Step 9: branch horizontal well day actual aquifer yield and the curve chart B of time on obtain water yield per day summation accumulative producing water Amount Q_{Water is total}, when accumulative aquifer yield and critical aquifer yield are equal, branch horizontal well is scrapped.

A kind of branch horizontal well recovery method based on Green's function the most according to claim 1, it is characterised in that described Rock core absolute permeability k in step 1₀Measured by automatic measuring instrument for permeability of rock core.

A kind of branch horizontal well recovery method based on Green's function the most according to claim 1, it is characterised in that described The viscosity, mu of shale gas in step 1_gObtained by curve-fitting method.

A kind of branch horizontal well recovery method based on Green's function the most according to claim 1, it is characterised in that described Step 3 is fallen into a trap and is calculated theoretical value q of branch horizontal well shale gas yield₀Method particularly includes:

According to steady percolation theory, pseudofunction method is utilized to be integrated formula (1) showing that shale gas production formula is:

$q_0=\frac{{\mathrm{\&pi;k}}_0{l}_0{Z}_{sc}{T}_{sc}{\mathrm{\&rho;}}_{gsc}}{p_{sc}{\mathrm{T\&mu;}}_{g}Z}\underset{n=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{{p_e}^2-{p_{wn}}^2}{G_l(r_D,t_D)ln\frac{R\left(t\right)}{r_{wn}}}---\left(2\right)$

In formula, l₀Represent gas-bearing formation horizontal length；Z_scRepresent Gas Compression Factor under standard state；T_scRepresent temperature under standard state Degree；ρ_gscRepresent gas density under standard state；p_scRepresent standard state downforce；T represents formation temperature；Z represents gas compression The factor；p_eRepresent original formation pressure；p_wnRepresent horizontal well Multilateral Wells bottom pressure；It is dynamic that R (t) represents under the influence of horizontal well branch Border；r_wnRepresent Multilateral Wells wellbore radius.

A kind of branch horizontal well recovery method based on Green's function the most according to claim 1, it is characterised in that described Step 5 adjusts branch levels well yield q_sMethod particularly includes:

Step 5.1: determine branch number m and each contiguous branch well perforating site according to the drilling well of branch horizontal well and perforation data Spacing l, and it is as follows to set up Tuning function based on Green's function:

$f\left(t\right)=\left\{\begin{array}{cc}(m-IN(Tt{\left(\frac{l}{2\mathrm{\&beta;}v}\right)}^{-1}\left)\right)& IN\left(Tt{\left(\frac{l}{2\mathrm{\&beta;}v}\right)}^{-1}\right)<m\\ 1& IN\left(Tt{\left(\frac{l}{2\mathrm{\&beta;}v}\right)}^{-1}\right)\&GreaterEqual;m\end{array}\right.---\left(3\right)$

Wherein,

Step 5.2: according to Tuning function branch levels well yield q of step 5.1_sIt is adjusted,

$q_1=\frac{{\mathrm{\&pi;k}}_0{l}_0{Z}_{sc}{T}_{sc}{\mathrm{\&rho;}}_{gsc}}{p_{sc}{\mathrm{T\&mu;}}_{g}Z}\underset{n=1}{\overset{f\left(t\right)}{\mathrm{\&Sigma;}}}\frac{{p_e}^2-{p_{wn}}^2}{G_l(r_D,t_D)ln\frac{R\left(t\right)}{r_{wn}}}---\left(4\right)$

In formula, q₁Represent that gas well mouth adjusts the daily output.

A kind of branch horizontal well recovery method based on Green's function the most according to claim 1, it is characterised in that described Accumulative aquifer yield Q in step 9_{Water is total}Computational methods be:

In formula, q_{Daily output water}Represent shale gas well day actual aquifer yield.

A kind of branch horizontal well recovery method based on Green's function the most according to claim 1, it is characterised in that described In step 9, critical aquifer yield is determined by prospect pit and the well test data of target reservoir formation.