CN117494601A - Fracture-cavity type reservoir acid fracturing effect evaluation method based on embedded discrete fracture - Google Patents
Fracture-cavity type reservoir acid fracturing effect evaluation method based on embedded discrete fracture Download PDFInfo
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Abstract
The invention discloses a fracture-cavity type reservoir acid fracturing effect evaluation method based on embedded discrete fracture, which belongs to the field of oil and gas field development and comprises the following steps: constructing a gridded stratum model; establishing a crack expansion model considering a karst cave system; acquiring seepage parameters at a certain moment in the acid fracturing construction process and judging whether cracks are expanded or not; judging whether the crack extends to the karst cave unit, if so, ending the acid fracturing, otherwise, updating the total number of the crack units, and iteratively calculating to judge the extension condition; establishing a gas well production model, taking a seepage parameter at the end of acid pressure as an initial parameter of the gas well production model, and acquiring pressure and liquid phase saturation parameters of the whole production process; the cumulative yield was obtained and the acid fracturing effect was evaluated based thereon. According to the invention, complex flow rules in various storage and seepage spaces are coupled through the model, and interaction of crack extension and etching is considered, so that more accurate acid fracturing effect of the fracture-cavity type reservoir can be realized.
Description
Technical Field
The invention belongs to the field of oil and gas field development, and particularly relates to a fracture-cavity type reservoir acid fracturing effect evaluation method based on embedded discrete fractures.
Background
Compared with the conventional reservoir, the fracture-cavity reservoir has the characteristics of multiple storage and seepage spaces, complex flow rules in acid fracturing and production processes, remarkable interaction between acid fracturing fracture extension and etching, difficult dynamic evaluation simulation of post-fracturing production and the like. Especially when the crack extends to meet the hole, the pump is often required to be stopped immediately after the acid liquid is lost and cannot be controlled. At this time, the distribution of the acid fracturing fracture conductivity along the fracture length direction can significantly influence the post-fracturing production effect. However, the current acid fracturing process numerical simulation method cannot be coupled with complex flow rules in various storage and seepage spaces, and cannot consider interaction of crack extension and etching, so that accurate evaluation of fracture-cavity type reservoir acid fracturing effect is difficult to realize.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a fracture-cavity type reservoir acid fracturing effect evaluation method based on embedded discrete fracture, which is characterized in that the influence of karst cavity on acid fracturing fracture extension and acid fluid loss and etching is considered in an Embedded Discrete Fracture Model (EDFM), an embedded discrete fracture cavity productivity model is established, the cumulative yield of a reservoir under a certain production time period is simulated, the cumulative yield-increasing multiple ratio is calculated, and the acid fracturing effect evaluation is carried out.
A fracture-cavity type reservoir acid fracturing effect evaluation method based on embedded discrete fracture comprises the following steps:
s1, determining the position of a large karst cave through a drilling method and a seismic wave method, acquiring target terrain parameters, constructing a reservoir geological model, and setting an initial crack unit, an initial matrix grid and a karst cave grid; the reservoir geological model adopts an embedded discrete fracture model;
s2, establishing a crack expansion model considering a karst cave system; the crack extension model comprises a crack width calculation model, a channeling flow calculation model among cracks, karst cave and reservoir matrixes, a discrete fracture cavity model acid liquor convection diffusion model and a reservoir matrix crack seepage model, wherein the models are specifically as follows:
(1) Crack width calculation model in acid fracturing process
W(x,t)＝Mδ md (x,t)+w(x,t)+w s (x,t)
Wherein:
w (x, t) is the width of the acid etching crack at the x position and m at the time t in the acid fracturing process;
m is a constant;
δ md (x, t) is a karst cave communication judgment function, delta is obtained if the x position at time t belongs to the karst cave unit md (x, t) =1, otherwise δ md (x,t)＝0；
w (x, t) is the width of the reservoir fracture at the x position at time t, m;
w s (x, t) is the width of a crack at the x position at the time of acid fracturing construction t due to acid rock reaction, and m;
(2) Calculation model for channeling flow rate between fracture, karst cave and reservoir matrix
The entire acid fracturing and production phase is set and fluid can only flow into and out of the wellbore through the fracture. Taking the mining stage as an example, matrix fluid can flow into a karst cave or a fracture, the karst cave fluid can enter a shaft after passing through the fracture, and the acid fracturing process is opposite. In this embodiment, the channeling flow among the three is calculated by using the following model:
wherein:
Q mf (x,t)、Q fd (x,t)、Q md (x, t) is the flow of the matrix and the crack, the crack and the karst cave and the cross flow between the matrix and the karst cave at the position x at the moment t, m 3 /s；
T mf (x,t)、T fd (x,t)、T md (x, t) are the flow coefficients of the matrix and the crack, the crack and the karst cave, and the matrix and the karst cave at the position x at the moment t, m 3 /(s·MPa)；
P f (x,t)、P m (x,t)、P d (x, t) are respectively the pressures of the fluid in the crack, the matrix and the karst cave at the position x at the moment t in the acid fracturing process and MPa;
A mf 、A md the contact areas of the matrix unit and the crack unit, the contact area of the matrix unit and the karst cave unit are respectively m 2 ；
k mf 、k fd 、k m d is the average permeability, mD, of the matrix unit and the crack unit, the crack unit and the karst cave unit, and the matrix unit and the karst cave unit respectively;
L fd the intersection length of the crack unit and the karst cave unit is m;
the characteristic distance from the crack to the matrix grid where the crack is located is m;
k is an overcurrent correction coefficient, is dimensionless, and is 0.9 in the embodiment;
v l the acid liquid filtration speed is m/s;
S mwg for matrix grid cell area, m 2 ；
Mu is the viscosity of the acid liquor and MPa.s;
(3) Discrete fracture-cavity model acid liquor convection diffusion model
Wherein:
d is the crack opening;
c f ,c d respectively, the acid liquor concentration in cracks and karst cave, mol/m 3 ；
φ f Crack porosity,%;
D f ,D d respectively the effective diffusion coefficient of the acid liquor in the cracks, m 2 /s；
(4) Reservoir matrix fracture seepage model
Wherein:
k m is reservoir matrix permeability, mD;
μ w mPa.s as the viscosity of the liquid phase in the reservoir matrix;
μ g mPa.s for the gas phase viscosity in the reservoir matrix;
P mw 、P mg the pressure of liquid phase and gas phase in the reservoir matrix are respectively MPa;
k x ,k y the permeability of the acid etched cracks in the x and y directions and mD are respectively shown;
k rmg ，k rmw the relative permeability of the gas phase and the liquid phase of the reservoir matrix is dimensionless;
mu is the viscosity of the acid liquor in the reservoir matrix and is dimensionless;
b is the volume coefficient of acid liquor in the reservoir matrix, and is dimensionless;
S g ,S w the saturation of gas phase and liquid phase in the reservoir matrix is dimensionless;
B g ,B w the volume coefficients of the gas phase and the liquid phase in the reservoir matrix are dimensionless;
φ f ,φ m porosity of the acid etched fracture and reservoir matrix unit,%;
V f ,V b the volumes of the acid etched cracks and the reservoir matrix units, m 3 ；
δ mf (x, t) is the fracture communication constant, delta if there are fracture cells in the matrix grid at x-position at time t mf(x,t) =1, otherwise δ mf (x,t)＝0；
S3, carrying out numerical simulation by combining the crack expansion model in the S2 according to different acid fracturing schemes on the basis of the reservoir grid, and obtaining seepage parameters at a certain moment in the acid fracturing construction process; the fracture pressure of the well shaft position is modified to be equal to the pumping pressure during simulation, the concentration of the acid liquid in the initial fracture is equal to the concentration of the acid liquid in the pumping liquid, and the obtained seepage parameters comprise the width of a fracture unit, the fracture width of the tip of the acid corrosion fracture, the pressure in the acid corrosion fracture, the porosity of a matrix grid, the saturation of the liquid phase in a reservoir matrix and the like.
S4, judging whether the crack is expanded at a certain moment according to the expansion of the acid etching crack, and if the crack is not expanded, determining the total number N of the crack units F Unchanged; if the expansion occurs, the total number of the crack units is +1, and whether the karst cave unit is entered is judged;
acid etch crack propagation criterion: if the stress intensity factor of the crack tip of the crack unit is larger than the fracture toughness of the rock crack, fracture occurs, otherwise, fracture does not occur, wherein the fracture toughness of the crack unit is calculated by adopting a type II fracture toughness calculation model if the next grid in the extending direction of the crack unit is a karst cave unit grid, and the fracture toughness of the crack unit is calculated by adopting a type I fracture toughness calculation model if the next grid in the extending direction of the crack unit is not the karst cave unit grid;
the calculation formula of the crack tip stress intensity factor is as follows:
in the method, in the process of the invention,
k 11,t when the acid fracturing process is carried out at the time t, the stress intensity factor of the tip of the crack is calculated;
y i,j the width of the matrix grid at position i, j;
Δx is the width of the tip of the artificial crack at the acid fracturing construction time t, m;
the fracture toughness of the reservoir matrix rock is calculated as follows:
i type K ΙCI1 ＝0.4868ρ r -0.1502exp(V n )+0.09531ln(DT)-0.5041
I type
Wherein:
K ICI1 、K ICI2 i, II fracture toughness, MPa.m, of matrix reservoir rock, respectively 1/2 ；
ρ r Dan Midu for matrix reservoir rock, kg/m 3 ；
V n Average shale content,%;
DT is the matrix reservoir average sonic time difference, μs/m;
and S5, judging whether the crack is expanded to the karst cave unit, if so, ending the acid fracturing, otherwise, updating the total number of the crack units according to the crack expansion condition of S4, taking the updated total number of the crack units and the seepage parameters of the step S3 as initial values, and repeating the steps S3-S5 to calculate the crack expansion condition at the next moment until the crack is expanded to the karst cave unit and ending the acid fracturing.
S6, establishing a gas well production model, and taking seepage parameters at the end of acid fracturing as initial parameters of the gas well production model to obtain pressure and liquid phase saturation parameters of the whole production process;
the gas well production model includes a seepage differential equation:
S fg +S fw ＝1,S mg +S mw ＝1
wherein:
k x ,k y the permeability of the acid etched cracks in the x and y directions and mD are respectively shown;
k rfg ,k rfw the relative permeability of the gas phase and the liquid phase of the acid etching cracks is dimensionless;
ρ g ,ρ w density of gas phase and liquid phase in acid etched crack, kg/m 3 ；
q fg ,q fw Respectively the source and sink items of gas phase and liquid phase in the acid etched cracks, m 3 /s；
μ g ,μ w The viscosity of the gas phase and the liquid phase in the reservoir matrix are dimensionless;
S fg ,S fw ,S mg ,S mw the saturation of gas phase and liquid phase in acid etched cracks and reservoir matrixes is dimensionless;
and S7, calculating the accumulated yield of the gas well according to seepage data of the acid pressure process in the step S5 and pressure and liquid phase saturation parameters of the whole production process obtained by the gas well production model in the step S6, and drawing an accumulated yield graph.
Wherein:
x i,j ,y i,j the length and the width of the grid unit at the coordinate position i and the coordinate position j are respectively m;
h is the cell matrix grid height,
q is the accumulated output from the production of the gas well to the time t, m 3 ；
m i ,n j The total number of grids in the x direction and the y direction of the grid of the structured reservoir respectively;
for the end of acid press construction (t=t end ) The total number of acid etched crack units is dimensionless;
for the end of acid press construction (t=t end ) When the total number of karst cave units is communicated, the method has no dimension
D, F are numbers of karst cave units and fracture units respectively, and are dimensionless;
L F the length of the acid etching crack is m;
k is a flow correction coefficient, dimensionless, and the embodiment is defined as 0.9;
t end d, the time of ending the acid pressing process;
φ m (i, j, t) is the porosity of the matrix grid at the i, j position at the time t of gas well production, dimensionless;
φ f (F, t) is the porosity of an acid etched fracture unit of the F section from the production of the gas well to the time t, and is dimensionless;
S mw (i, j, t) is the liquid phase saturation of the matrix grid at the i, j position from the production of the gas well to the time t, dimensionless;
S fw (F, t) is the liquid phase saturation of an acid etched crack unit of the F-th section from the production of the gas well to the time t, and is dimensionless;
S mw (D, t) is the time from the production of the gas well to the time tThe liquid phase saturation of the karst cave unit of the D section is dimensionless;
V b,D the volume of the karst cave unit in the D section, m 3 ；
k is an overcurrent coefficient, and the value of the invention is 0.9;
s8, calculating the accumulated yield-increasing ratio of the construction scheme according to the accumulated yield of the gas well, wherein the larger the accumulated yield-increasing ratio of the construction scheme is, the better the acid fracturing effect is.
The beneficial effects are that:
the invention provides a specific evaluation method for acid fracturing effect of a carbonate fracture-cavity reservoir. And a karst cave system is introduced into the embedded discrete fracture-cave model, so that the production condition of an acid fracturing fracture extension hole during the specific acid fracturing transformation of a reservoir can be represented. The complex flow rules in various storage and seepage spaces are coupled through the model, and meanwhile, interaction of crack extension and etching is considered, so that more accurate acid fracturing effect of the fracture-cavity type reservoir can be realized.
Drawings
FIG. 1 is a graph comparing simulated cumulative production for an x-well with different acid fracturing schemes and without acid fracturing modification;
FIG. 2 is a graph showing the comparison of simulated production and actual as-constructed cumulative production for an x-well using acid fracturing scheme one.
Detailed Description
The invention is further described below with reference to the drawings and examples to facilitate an understanding of the invention by those skilled in the art. It should be understood that the invention is not limited to the precise embodiments, and that various changes may be effected therein by one of ordinary skill in the art without departing from the spirit or scope of the invention as defined and determined by the appended claims.
Example 1
A fracture-cavity type reservoir acid fracturing effect evaluation method based on embedded discrete fracture comprises the following steps:
s1, determining the position of a large karst cave through a drilling method and a seismic wave method, acquiring target terrain parameters, constructing a reservoir geological model, and setting an initial crack unit, an initial matrix grid and a karst cave grid; the reservoir geological model adopts an embedded discrete fracture model;
in the embodiment, the embedded discrete fracture model is used for simplifying the fracture-cavity type reservoir solving area grid division. The reservoir matrix is an orthogonal structured grid, and the fracture is a line segment unit grid. The one-dimensional cracks do not have a substantial height, the embedded cracks exist in the form of "line-manifold" and the matrix remains continuous on both sides of the crack. The true physical volumes of the fractures are redefined in separate fracture grids forming a dual dielectric structure. The karst cave grids are duplicate grids of the matrix grids and are in one-to-one correspondence with the matrix grids. The karst cave unit grids are mutually independent, and no substance exchange occurs.
Construction in x-y coordinate system from geological exploration data (m i ×n i ) Reservoir structured grid, reservoir Length L x Reservoir width L y Wherein x is i,j Representing the length of each grid, y i,j The subscript i, j represents the location of the cell grid in the reservoir grid.
The method comprises the steps of establishing a fracture grid on the basis of a reservoir grid, adding initial artificial fractures according to geological data, dividing the initial artificial fractures into a plurality of fracture units by the reservoir grid, wherein the artificial fracture units are numbered as F=1, 2 and 3, and the length of each fracture unit is L F The total number of the crack units is N F The extension direction of the artificial crack is the tip direction of the artificial crack, and the derivative length is 1 unit grid.
And adding a duplicate grid of the matrix grid on the basis of the embedded discrete fracture model. And modifying parameters in the karst cave grid according to the geological exploration data. Because the karst cave grids and the matrix grids are in one-to-one correspondence, the sizes of the karst cave grids are equal to those of the matrix grids, positions of the karst cave exist, the permeability of the modified karst cave grids is equal to M times that of the matrix grids, and M is a very natural constant. Its corresponding matrix grid is defined as karst cave unit. The position without karst cave modifies the karst cave grid to an empty grid. The karst cave grid and the crack grid are regarded as fluid circulation channels when the matrix grid is communicated, and the influence of the porosity of the karst cave is compensated by adding a flow correction coefficient k when the flow is calculated. When the crack extends into the karst cave unit, the crack is regarded as the crack-cave communication. The inventionThe clear M value is 1000, and the k value is 0.9, and the technician can determine the value according to the needs. Karst cave unit number d=1, 2,3 D 。
S2, establishing a crack expansion model considering a karst cave system; the crack extension model comprises a crack width calculation model, a crack internal pressure calculation model, a channeling flow calculation model among cracks, karst cave and reservoir matrixes, and an acid liquid convection diffusion model of a discrete fracture cave model
(1) Crack width calculation model in acid fracturing process
W(x,t)＝Mδ md (x,t)+w(x,t)+w s (x,t) (1)
Wherein:
w (x, t) is the width of the acid etching crack at the x position and m at the time t in the acid fracturing process;
t is the construction time of acid fracturing, s;
m is a dimensionless maximum constant, which is set by people, and the embodiment is set to be 1000;
δ md (x, t) is a karst cave communication judgment function, delta is obtained if the x position at time t belongs to the karst cave unit md (x, t) =1, otherwise δ md (x,t)＝0；
w (x, t) is the width of the reservoir fracture at the x position at time t, m;
w s (x, t) is the width of a crack at the x position at the time of acid fracturing construction t due to acid rock reaction, and m;
e is Young's modulus of the reservoir rock sample and MPa;
mu is the viscosity of the acid liquor and MPa.s;
v is poisson ratio of reservoir rock sample, dimensionless;
v l the acid liquid filtration speed is m/s;
h is the height of the acid etching crack, m;
beta is the acid rock dissolving capacity, kg/mol;
ρ r dan Midu for matrix reservoir rock, kg/m 3 ；
φ m Porosity of reservoir matrix,%;
η is the mass fraction of the acid liquid in the fluid loss acid liquid which participates in etching the crack wall surface, and is dimensionless;
C f the concentration of acid liquid in the crack, mol/m 3 ；
k c Is mass transfer coefficient, m/s;
(2) Calculation model for seam internal pressure in acid fracturing process
Wherein:
P f (x, t) is the fluid pressure in the crack at the x position at the time t in the acid fracturing process and MPa;
σ n is the horizontal minimum principal stress, MPa;
c (x, t) is a judging function, if the position x at the moment t belongs to the karst cave unit, c (x, t) =0.5, otherwise c (x, t) =1;
(3) Calculation model for channeling flow rate between fracture, karst cave and reservoir matrix
The entire acid fracturing and production phase is set and fluid can only flow into and out of the wellbore through the fracture. Taking the mining stage as an example, matrix fluid can flow into a karst cave or a fracture, the karst cave fluid can enter a shaft after passing through the fracture, and the acid fracturing process is opposite. In this embodiment, the channeling flow among the three is calculated by using the following model:
wherein:
Q mf (x,t)、Q fd (x,t)、Q md (x, t) is the flow of the matrix and the crack, the crack and the karst cave and the cross flow between the matrix and the karst cave at the position x at the moment t, m 3 /s；
T mf (x,t)、T fd (x,t)、T md (x, t) are the flow coefficients of the matrix and the crack, the crack and the karst cave, and the matrix and the karst cave at the position x at the moment t, m 3 /(s•MPa)；
P f (x,t)、P m (x,t)、P d (x, t) are respectively the pressures of the fluid in the crack, the matrix and the karst cave at the position x at the moment t in the acid fracturing process and MPa;
A mf 、A md the contact areas of the matrix unit and the crack unit, the contact area of the matrix unit and the karst cave unit are respectively m 2 ；
k mf 、k fd 、k md The average permeability, mD, of the matrix unit and the crack unit, the crack unit and the karst cave unit, and the matrix unit and the karst cave unit respectively;
L fd the intersection length of the crack unit and the karst cave unit is m;
the characteristic distance from the crack to the matrix grid where the crack is located is m;
k is an overcurrent correction coefficient, is dimensionless, and is 0.9 in the embodiment;
v l the acid liquid filtration speed is m/s;
S mwg for matrix grid cell area, m 2 ；
(4) Discrete fracture-cavity model acid liquor convection diffusion model
Wherein:
d is the crack opening;
c f ,c d respectively, the acid liquor concentration in cracks and karst cave, mol/m 3 ；
φ f Crack porosity,%;
D f ,D d respectively the effective diffusion coefficient of the acid liquor in the cracks, m 2 /s；
(5) Reservoir matrix fracture seepage model
Wherein:
k m is reservoir matrix permeability, mD;
μ w mPa.s as the viscosity of the liquid phase in the reservoir matrix;
μ g mPa.s for the gas phase viscosity in the reservoir matrix;
P mw 、P mg the pressure of liquid phase and gas phase in the reservoir matrix are respectively MPa;
k x ,k y the permeability of the acid etched cracks in the x and y directions and mD are respectively shown;
k rmg ，k rmw the relative permeability of the gas phase and the liquid phase of the reservoir matrix is dimensionless;
mu is the viscosity of the acid liquor in the reservoir matrix and is dimensionless;
b is the volume coefficient of acid liquor in the reservoir matrix, and is dimensionless;
S g ,S w the saturation of gas phase and liquid phase in the reservoir matrix is dimensionless;
B g ,B w the volume coefficients of the gas phase and the liquid phase in the reservoir matrix are dimensionless;
φ f ,φ m porosity of the acid etched fracture and reservoir matrix unit,%;
V f ,V b the volumes of the acid etched cracks and the reservoir matrix units, m 3 ；
δ mf (x, t) is the fracture communication constant, delta if there are fracture cells in the matrix grid at x-position at time t mf(x,t) =1, otherwise
δ mf (x,t)＝0；
(6) Rock porosity and permeability calculation model
In the acid-rock reaction process of acid liquor and rock, the rock porosity and permeability change, and the calculation model is as follows:
wherein:
c s the concentration of acid liquor at the pore wall surface, mol/m 3 ；
k s The reaction rate is constant and dimensionless;
a v to the specific surface area of reservoir matrix rock, m 2 /m 3 ；
a v0 For the initial rock specific surface area of the reservoir matrix, m 2 /m 3 ；
k mo Initial permeability, md, for reservoir matrix;
φ mo initial porosity for reservoir matrix,%;
gamma is a parameter related to the pore structure, and is dimensionless.
(7) Crack extension boundary
P f(F＝1),t ＝P jd,t (17)
Wherein:
Q Zr injection displacement for acid pressure construction, m 3 /min；
G is the bulk modulus of the reservoir rock sample and MPa;
X F＝1 rectangular coordinates of the 1 st acid etching crack unit are dimensionless;
L Fi the length of the ith crack unit, m;
N F,t the total number of acid etching crack units at the time t of the acid fracturing construction time is dimensionless;
P f(F＝1),t the fluid pressure in the first section of acid etching crack unit body at t time in the acid fracturing process is MPa;
P jd,t the bottom hole pressure is the pressure of the acid pressure construction well, and the pressure is MPa;
(8) Reservoir matrix seepage boundary conditions:
wherein:
p mw is the liquid phase pressure of the reservoir matrix and MPa;
L x ,L y reservoir length, width, m, respectively;
(9) Reservoir seepage initiation conditions
P mg (i,j,t)| t＝0 ＝P e (19)
Wherein:
P mg (i, j, t) is the gas phase pressure of the matrix grid with the position i, j at the moment t, and MPa;
P e the pressure is the original stratum pressure of the reservoir, and the pressure is MPa;
(10) The boundary conditions and initial conditions of the in-seam acid migration reaction model are as follows:
wherein:
C f (0, t) is the acid liquor concentration in the initial fracture unit at the time t of acid fracturing construction, and mol/m 3 ；
C f (L f T) is the acid liquor concentration at the tip of the crack and mol/m under the acid pressure construction t moment 3 ；
C m,t 、C s,t 、C f,t The concentration of acid liquid in matrix grids, pore wall surfaces and acid fracturing cracks at the initial time of acid fracturing construction are mol/m respectively 3 ；
L f The coordinates corresponding to the tip of the crack unit at the time of acid fracturing construction t are dimensionless;
C 0,t pumping acid liquor concentration, mol/m for construction at time t of acid pressure construction 3 ；
S3, carrying out numerical simulation by combining the crack expansion model in the S2 according to different acid fracturing schemes on the basis of the reservoir grid, and obtaining seepage parameters at a certain moment in the acid fracturing construction process; the fracture pressure of the well shaft position is modified to be equal to the pumping pressure during simulation, the concentration of the acid liquid in the initial fracture is equal to the concentration of the acid liquid in the pumping liquid, and the obtained seepage parameters comprise the width of a fracture unit, the fracture width of the tip of the acid corrosion fracture, the pressure in the acid corrosion fracture, the porosity of a matrix grid, the saturation of the liquid phase in a reservoir matrix and the like.
S4, judging the crack at a certain moment according to the acid etching crack extension standardIf the crack is expanded, if not, the total number of crack units N F Unchanged; if the expansion occurs, the total number of the crack units is +1;
acid etch crack propagation criterion: if the stress intensity factor of the crack tip of the crack unit is larger than the fracture toughness of the rock crack, fracture occurs, otherwise, fracture does not occur, wherein the fracture toughness of the crack unit is calculated by adopting a type II fracture toughness calculation model if the next grid in the extending direction of the crack unit is a karst cave unit grid, and the fracture toughness of the crack unit is calculated by adopting a type I fracture toughness calculation model if the next grid in the extending direction of the crack unit is not the karst cave unit grid;
the calculation formula of the crack tip stress intensity factor is as follows:
in the method, in the process of the invention,
k 11,t when the acid fracturing process is carried out at the time t, the stress intensity factor of the tip of the crack is calculated;
y i,j the width of the matrix grid at position i, j;
Δx is the width of the tip of the artificial crack at the acid fracturing construction time t, m;
the fracture toughness of the reservoir matrix rock is calculated as follows:
i type K ΙCI1 ＝0.4868ρ r -0.1502exp(V n )+0.09531ln(DT)-0.5041 (22)
Type II
Wherein:
K ICI1 、K ICI2 i, II fracture toughness, MPa.m, of matrix reservoir rock, respectively 1/2 ；
ρ r Dan Midu for matrix reservoir rock, kg/m 3 ；
V n Average shale content,%;
DT is the matrix reservoir average sonic time difference, μs/m;
and S5, updating the total number of the crack units according to all the crack expansion conditions obtained in the step S4, if cracks expanding to karst cave units exist, ending acid fracturing, otherwise, taking the updated total number of the crack units and the seepage parameters of the step S3 as initial values, and repeating the steps S3-S5 to calculate the crack expansion conditions at the next moment.
In this embodiment, the matrix grid number where the crack is located at the time t is set to be a, and the number b of the next grid unit in the crack extending direction is set. If the grid unit b is a fracture-cavity unit grid, judging whether the crack is expanded according to the acid etching crack expansion judging criterion of S4, if so, communicating the crack with the karst cavity unit, and ending acid fracturing; if the crack cannot be expanded, the next crack is selected for judgment. If the grid unit b is a matrix unit grid, judging whether the crack expands according to the acid etching crack expansion judging criterion of S4, if so, increasing the total number of the crack units by 1, then selecting the next crack for judging, if not, keeping the total number of the crack units unchanged, and then selecting the next crack for judging; after all the cracks are judged, if all the cracks are not expanded to the fracture hole unit grid, the updated total number of the crack units and the seepage parameters of the step S3 are used as initial values, and the steps S3-S5 are repeated to calculate the crack expansion condition at the next moment.
The acid fracturing process parameters comprise the total number of artificial fracture units, the width of the fracture units, the intra-fracture pressure in the fracture units, the porosity of the fracture units, the liquid phase saturation of each fracture grid, the porosity of each matrix grid and the liquid phase saturation of each matrix grid.
S6, establishing a gas well production model, and taking the pressure distribution of each phase of an acid etching crack unit, the saturation distribution of each phase of the acid etching crack unit, the pressure distribution of each phase of a matrix grid and the saturation distribution of each phase of the matrix grid at the end of acid pressure construction as initial parameters of the gas well production model to obtain pressure and liquid phase saturation parameters of the whole production process;
the gas well production model includes a seepage differential equation:
S fg +S fw ＝1,S mg +S mw ＝1 (26)
wherein:
k x ,k y the permeability of the acid etched cracks in the x and y directions and mD are respectively shown;
k rfg ,k rfw the relative permeability of the gas phase and the liquid phase of the acid etching cracks is dimensionless;
ρ g ,ρ w density of gas phase and liquid phase in acid etched crack, kg/m 3 ；
q fg ,q fw Respectively the source and sink items of gas phase and liquid phase in the acid etched cracks, m 3 /s；
μ g ,μ w The viscosity of the gas phase and the liquid phase in the reservoir matrix are dimensionless;
S fg ,S fw ,S mg ,S mw the saturation of gas phase and liquid phase in acid etched cracks and reservoir matrixes is dimensionless;
(2) Initial conditions
Initial saturation distribution:
wherein:
S fw (i, j, t) liquid phase saturation of the slit grid cells at the coordinate position i, j at time t in the production process;
S mw (i, j, t) liquid phase saturation of the matrix grid cells at the time t coordinate position i, j in the production process;
S mw (i, j, t 1) is the matrix web at the coordinate position i, j at time t1 during acid fracturingLiquid phase saturation of the lattice cells;
t end the construction time is the construction ending time of acid pressure;
outer boundary conditions: the pressure, temperature and saturation of the grids on the boundary are equal to those of the adjacent grids by adopting a closed boundary, namely:
P mv (i, j, t) is the liquid phase pressure of the matrix grid with the position i, j at the moment t, and MPa;
inner boundary conditions:
P w (x d ,y d ,t)＝P jd,t (29)
P w (x d ,y d t) -in the production process, at the moment of t, the liquid phase pressure at the near position of the bottom of the well is MPa;
P jd,t the bottom hole pressure is the acid pressure construction bottom hole pressure at the moment t and is MPa;
s7, calculating the accumulated output of the gas well according to seepage data of the acid fracturing process in the step S5 and pressure and liquid phase saturation parameters of the whole production process obtained by the gas well production model in the step S6, and drawing an accumulated output graph.
Wherein:
x i,j ,y i,j the length and the width of the grid unit at the coordinate position i and the coordinate position j are respectively m;
h is the height of the acid etched crack, m
Q is the accumulated output from the production of the gas well to the time t, m 3 ；
m i ,n j The total number of grids in the x direction and the y direction of the grid of the structured reservoir respectively;
for the end of acid press construction (t=t end ) The total number of acid etched crack units is dimensionless;
W F,tend for the end of acid press construction (t=t end ) The width of the acid etching crack is dimensionless;
N D,tend for the end of acid press construction (t=t end ) When the total number of karst cave units is communicated, the method has no dimension
D, F is the number of a karst cave unit and a crack unit, and is dimensionless;
L F the length of the acid etching crack is m;
k is an overcurrent correction coefficient, dimensionless, and the embodiment is defined as 0.9;
t end d, the time of ending the acid pressing process;
φ m (i, j, t) is the porosity of the matrix grid at the i, j position at the time t of gas well production, dimensionless;
φ f (F, t) is the porosity of an acid etched fracture unit of the F section from the production of the gas well to the time t, and is dimensionless;
S mw (i, j, t) is the liquid phase saturation of the matrix grid at the i, j position from the production of the gas well to the time t, dimensionless;
S fw (F, t) is the liquid phase saturation of an acid etched crack unit of the F-th section from the production of the gas well to the time t, and is dimensionless;
S mw (D, t) is the liquid phase saturation of a D-stage karst cave unit from the production of the gas well to the time t, and is dimensionless;
V b,D the volume of the karst cave unit in the D section, m 3 ；
S8, calculating the accumulated yield-increasing ratio of the construction scheme according to the accumulated yield of the gas well, wherein the larger the accumulated yield-increasing ratio of the construction scheme is, the better the acid fracturing effect is.
The calculation mode of the accumulated yield increase multiple ratio is as follows:
wherein:
s, accumulating the yield increase multiple ratio, and having no dimension;
Q t after acid fracturing construction, the simulated accumulated yield of the gas well after the production time t, m 3 ；
t is the time when the daily gas yield of the gas well after the acid fracturing construction is equal to the daily gas yield before the construction, and d;
Q 0,t to predict the cumulative yield from the production of the gas well to the time t when acid fracturing construction is not adopted, m 3 。
Taking an X well of a carbonate fracture-cavity reservoir in the southwest area as an example, the acid fracturing effect of the well is evaluated by adopting the method. The buried depth of the X-well stratum is 3958.2-3976.3 m, which mainly consists of dolomite and calcite, also contains trace clay and silicate minerals, has complex macroscopic and microscopic fracture-cavity networks, and is mainly distributed in a deep dolomite layer. The porosity of the reservoir is 2.4-8.7%, and the average porosity of the reservoir is 5.7%. The permeability of the reservoir is 0.43-1.2 md. The average permeability of the reservoir was 0.72md. Because the block contains large karst cave, the local permeability can reach 800-900 md, the gas saturation range is 28.43-36.72%, and the average gas saturation is 33.45%. The temperature of the stratum at the well depth (3968.63 m) in the middle of the production layer is 97.6 ℃, the stratum pressure is 39.7MPa, the Young modulus of a core sample of the reservoir is 23.67GPa, the Poisson ratio is 0.32, and the compressive strength is 195.63MPa. The condition of the communication of the fracture-cavity system after acid fracturing has great influence on the acid fracturing effect. To increase single well production, the present method is now intended to evaluate acid fracturing effects and to prefer acid fracturing protocols. The alternative scheme is as follows:
scheme one: construction liquid: guanidine gum 110m 3 200 m+gelled acid 3 +temporary plugging agent 170m 3 Pumping mode: and (3) three-stage temporary plugging acidification.
Scheme II: construction liquid: slick water 100m 3 +thickening acid 180m 3 +turning acid 140m 3 Pumping mode: stage injection.
The invention is used for respectively simulating and calculating the single well yield of the X well by adopting the acid fracturing scheme I, the acid fracturing scheme II and the acid fracturing transformation not. The specific operation method is as follows:
1. simulation was performed using acid fracturing scheme one.
A structured reservoir grid near the x-well is established, an initial artificial fracture is added, and a matrix grid replica grid is added. And modifying karst cave parameters on the replica grids, wherein positions of karst cave exist, the permeability of the modified karst cave grids is equal to M times of that of the matrix grids, and M is a very natural constant. Its corresponding matrix grid is defined as karst cave unit. The position without karst cave modifies the karst cave grid to an empty grid. The karst cave grid and the crack grid are regarded as fluid circulation channels when the matrix grid is communicated, and the influence of the porosity of the karst cave is compensated by adding an overcurrent correction coefficient k when the flow is calculated. When the crack extends into the karst cave unit, the crack is regarded as the crack-cave communication. The M value is 1000, the k value is 0.9, and the technical personnel can determine the M value according to the needs. And numbering the initial fracture unit and the karst cave unit.
The initial conditions and the boundary conditions are set according to formulas (16) to (20).
And (3) calculating the width and the pressure of the artificial crack at a certain moment in the acid fracturing process according to the formulas (1) - (4).
And (5) simulating and calculating the permeability, the porosity, the liquid phase pressure and the liquid phase saturation of the acid pressure transformation area at the time t according to formulas (5) to (15). The fracture pressure of the position of the well bore is equal to the pumping pressure during simulation, and the acid liquid concentration in the initial fracture is equal to the acid liquid concentration in pumping liquid.
Judging whether the acid etching crack is expanded at the moment t or not according to formulas (21) - (23), and if so, entering a karst cave unit, and repeating the steps until the acid fracturing process is finished. Obtaining the total number of artificial crack units; the width, length, intra-slit pressure, porosity, permeability, liquid phase saturation and vapor phase saturation of each slit unit; the porosity, permeability, liquid phase pressure, liquid phase saturation and vapor phase saturation of each matrix grid; each location of a karst cave unit common to the fracture.
According to the calculated data, the gas well production initial conditions and the initial boundaries given by formulas (27) to (29) are combined, and when different production moments are calculated by using the gas well production models given by formulas (24) to (26), the porosity distribution and the liquid phase saturation distribution of the gas reservoir are calculated.
And (3) calculating the accumulated output and the accumulated production multiplying ratio of the gas well production simulation process according to the formulas (30) and (31).
The above process is repeated by acid pressure method, and the accumulated yield and the accumulated production multiple ratio of the two schemes are compared, preferably acid pressure scheme.
The cumulative yield results of the two acid fracturing schemes are shown in FIG. 1, and it can be seen from FIG. 1 that the maximum daily yield of an X-well single well after modification by using the acid fracturing scheme is 22.48 multiplied by 10 4 m 3 After 900d production, the cumulative yield was 9.127X 10 7 m 3
Maximum daily production of single well of X-well after modification of acid fracturing scheme II is 21.13 multiplied by 10 4 m 3 After 900d production, the cumulative yield was 7.608X 10 7 m 3
The maximum daily production value of an X-well single well is 11.53 multiplied by 10 without acid fracturing 4 m 3 After 900d production, the cumulative yield was 4.357X 10 7 m 3 。
The results show that the cumulative yield increase ratios of the first acid fracturing scheme and the second acid fracturing scheme are 2.1 and 1.75 respectively, and the yield is increased by 109% and 74.6% respectively compared with the case of not adopting acid fracturing modification. A pair of x-well acid fracturing is preferred. After modification, the actual cumulative yield and the simulated cumulative yield are compared with each other, for example, as shown in FIG. 2, and after 900d, the actual cumulative yield is 8.542 ×10 7 m 3 The difference between the two is 6.8%, the error is small, and the production example proves that the method can effectively evaluate the acid fracturing effect of the fracture-cavity type reservoir, and has practical guiding significance for the acid fracturing effect evaluation of the fracture-cavity type reservoir.
Claims (8)
1. The fracture-cavity type reservoir acid fracturing effect evaluation method based on embedded discrete fracture is characterized by comprising the following steps of:
s1, determining the position of a large karst cave through a drilling method and a seismic wave method, acquiring target terrain parameters, constructing a reservoir geological model, and setting an initial crack unit, an initial matrix grid and a karst cave grid; the reservoir geological model adopts an embedded discrete fracture model;
s2, establishing a crack expansion model considering a karst cave system; the crack extension model comprises a crack width calculation model, a channeling calculation model among cracks, karst cave and reservoir matrixes, a discrete fracture cavity model acid liquor convection diffusion model and a reservoir matrix crack seepage model;
s3, carrying out numerical simulation by combining the crack expansion model in the S2 according to different acid fracturing schemes on the basis of the reservoir grid, and obtaining seepage parameters at a certain moment in the acid fracturing construction process;
s4, judging whether the crack is expanded at a certain moment according to the expansion of the acid etching crack, and if the crack is not expanded, determining the total number N of the crack units F Unchanged; if the expansion occurs, the total number of the crack units is +1, and whether the karst cave unit is entered is judged;
and S5, judging whether the crack is expanded to the karst cave unit, if so, ending the acid fracturing, otherwise, updating the total number of the crack units according to the crack expansion condition of S4, taking the updated total number of the crack units and the seepage parameters of the step S3 as initial values, and repeating the steps S3-S5 to calculate the crack expansion condition at the next moment until the crack is expanded to the karst cave unit and ending the acid fracturing.
S6, establishing a gas well production model, and taking seepage parameters at the end of acid fracturing as initial parameters of the gas well production model to obtain pressure and liquid phase saturation parameters of the whole production process;
s7, calculating the accumulated output of the gas well according to seepage data of the acid pressure process in the step S5 and pressure and liquid phase saturation parameters of the whole production process obtained by the gas well production model in the step S6, and drawing an accumulated output graph;
s8, calculating the accumulated yield-increasing ratio of the construction scheme according to the accumulated yield of the gas well, wherein the larger the accumulated yield-increasing ratio of the construction scheme is, the better the acid fracturing effect is.
2. The fracture-cavity reservoir acid fracturing effect evaluation method based on embedded discrete fracture according to claim 1, wherein the fracture width calculation model is as follows:
W(x,t)＝Mδ md (x,t)+w(x,t)+w s (x,t)
wherein W (x, t) is the width of the acid etching crack at the x position and m at the time t in the acid pressing process; m is a constant; delta md (x, t) is a karst cave communication judgment function, if the x position at time t belongs to the karst caveUnit then delta md (x, t) =1, otherwise δ md (x, t) =0; w (x, t) is the width of the reservoir fracture at the x position at time t, m; w (w) s And (x, t) is the width of the crack at the x position at the time of acid fracturing construction t caused by acid rock reaction, and m.
3. The method for evaluating the acid fracturing effect of a fracture-cavity type reservoir based on embedded discrete fracture according to claim 1, wherein a calculation model of channeling between the fracture, the karst cavity and the reservoir matrix is as follows:
in which Q mf (x,t)、Q fd (x,t)、Q md (x, t) is the flow of the matrix and the crack, the crack and the karst cave and the cross flow between the matrix and the karst cave at the position x at the moment t, m 3 /s；T mf (x,t)、T fd (x,t)、T md (x, t) are the flow coefficients of the matrix and the crack, the crack and the karst cave, and the matrix and the karst cave at the position x at the moment t, m 3 /(s·MPa)；P f (x,t)、P m (x,t)、P d (x, t) are respectively the pressures of the fluid in the crack, the matrix and the karst cave at the position x at the moment t in the acid fracturing process and MPa; a is that mf 、A md The contact areas of the matrix unit and the crack unit, the contact area of the matrix unit and the karst cave unit are respectively m 2 ；k mf 、k fd 、k md The average permeability, mD, of the matrix unit and the crack unit, the crack unit and the karst cave unit, and the matrix unit and the karst cave unit respectively; l (L) fd The intersection length of the crack unit and the karst cave unit is m;the characteristic distance from the crack to the matrix grid where the crack is located is m; k is an overcurrent correction coefficient; v l The acid liquid filtration speed is m/s; s is S mwg For matrix grid cell area, m 2 The method comprises the steps of carrying out a first treatment on the surface of the Mu is the viscosity of the acid liquor and MPa.s.
4. The method for evaluating the acid fracturing effect of the fracture-cavity type reservoir based on the embedded discrete fracture as claimed in claim 1, wherein the discrete fracture model acid convection diffusion model is as follows:
wherein d is the crack opening; c f ,c d Respectively, the acid liquor concentration in cracks and karst cave, mol/m 3 ；φ f Crack porosity,%; d (D) f ,D d Respectively the effective diffusion coefficient of the acid liquor in the cracks, m 2 /s。
5. The method for evaluating the acid fracturing effect of a fracture-cavity type reservoir based on embedded discrete fractures according to claim 1, wherein the reservoir matrix fracture seepage model is as follows:
wherein k is m Is reservoir matrix permeability, mD; mu (mu) w mPa.s as the viscosity of the liquid phase in the reservoir matrix; mu (mu) g mPa.s for the gas phase viscosity in the reservoir matrix; p (P) mw 、P mg The pressure of liquid phase and gas phase in the reservoir matrix are respectively MPa; k (k) x ,k y The permeability of the acid etched cracks in the x and y directions and mD are respectively shown; k (k) rmg ，k rmw The relative permeability of the gas phase and the liquid phase of the reservoir matrix is dimensionless; mu is the viscosity of the acid liquor in the reservoir matrix and is dimensionless; b is the volume coefficient of acid liquor in the reservoir matrix, and is dimensionless; s is S g ,S w The saturation of gas phase and liquid phase in the reservoir matrix is dimensionless; b (B) g ,B w The volume coefficients of the gas phase and the liquid phase in the reservoir matrix are dimensionless; phi (phi) f ,φ m Porosity of the acid etched fracture and reservoir matrix unit,%; v (V) f ,V b The volumes of the acid etched cracks and the reservoir matrix units, m 3 ；δ mf (x, t) is the fracture communication constant, delta if there are fracture cells in the matrix grid at x-position at time t mf(x,t) =1, otherwise δ mf (x,t)＝0。
6. The method for evaluating the acid fracturing effect of the fracture-cavity type reservoir based on the embedded discrete fracture according to claim 1, wherein the judgment standard of the acid etching fracture expansion is as follows:
if the stress intensity factor of the crack tip of the crack unit is larger than the fracture toughness of the rock crack, fracture occurs, otherwise, fracture does not occur, wherein the fracture toughness of the crack unit is calculated by adopting a type II fracture toughness calculation model if the next grid in the extending direction of the crack unit is a karst cave unit grid, and the fracture toughness of the crack unit is calculated by adopting a type I fracture toughness calculation model if the next grid in the extending direction of the crack unit is not the karst cave unit grid;
the calculation formula of the crack tip stress intensity factor is as follows:
the type I fracture toughness calculation model is as follows:
K ΙCI1 ＝0.4868ρ r -0.1502exp(V n )+0.09531ln(DT)-0.5041
the type II fracture toughness calculation model is as follows:
wherein k is 11,t When the acid fracturing process is carried out at the time t, the stress intensity factor of the tip of the crack is calculated; y is i,j The width of the matrix grid at position i, j; Δx is the width of the tip of the artificial crack at the acid fracturing construction time t, m; k (K) ICI1 、K ICI2 I, II fracture toughness, MPa.m, of matrix reservoir rock, respectively 1/2 ；ρ r Dan Midu for matrix reservoir rock, kg/m 3 ；V n Average shale content,%; DT is the matrix reservoir average sonic moveout, μs/m.
7. The method for evaluating acid fracturing effect of a fracture-cavity type reservoir based on embedded discrete fractures according to claim 1, wherein the gas well production model comprises the following seepage differential equation:
S fg +S fw ＝1,S mg +S mw ＝1
wherein:
k x ,k y the permeability of the acid etched cracks in the x and y directions and mD are respectively shown; k (k) rfg ,k rfw The relative permeability of the gas phase and the liquid phase of the acid etching cracks is dimensionless; ρ g ,ρ w Density of gas phase and liquid phase in acid etched crack, kg/m 3 ；q fg ,q fw Respectively the source and sink items of gas phase and liquid phase in the acid etched cracks, m 3 /s；μ g ,μ w The viscosity of the gas phase and the liquid phase in the reservoir matrix are dimensionless; s is S fg ,S fw ,S mg ,S mw The saturation of gas phase and liquid phase in acid etched cracks and reservoir matrixes respectively has no dimension.
8. The method for evaluating the acid fracturing effect of a fracture-cavity type reservoir based on embedded discrete fractures according to claim 1, wherein the calculation model of the accumulated yield is as follows:
wherein x is i,j ,y i,j The length and the width of the grid unit at the coordinate position i and the coordinate position j are respectively m; h is the cell matrix grid height; q is the accumulated output from the production of the gas well to the time t, m 3 ；m i ,n j The total number of grids in the x direction and the y direction of the grid of the structured reservoir respectively;the total number of acid etching crack units at the end of acid fracturing construction is dimensionless; />The total number of communicated karst cave units at the end of acid fracturing construction is dimensionless; d, F are numbers of karst cave units and fracture units respectively, and are dimensionless; l (L) F The length of the acid etching crack is m; k is a flow correction coefficient, dimensionless; t is t end D, the time of ending the acid pressing process; phi (phi) m (i, j, t) is the porosity of the matrix grid at the i, j position at the time t of gas well production, dimensionless; phi (phi) f (F, t) is the porosity of an acid etched fracture unit of the F section from the production of the gas well to the time t, and is dimensionless; s is S mw (i, j, t) is the liquid phase saturation of the matrix grid at the i, j position from the production of the gas well to the time t, dimensionless; s is S fw (F, t) is the liquid phase saturation of an acid etched crack unit of the F-th section from the production of the gas well to the time t, and is dimensionless; s is S mw (D, t) is the liquid phase saturation of a D-stage karst cave unit from the production of the gas well to the time t, and is dimensionless; v (V) b,D The volume of the karst cave unit in the D section, m 3 The method comprises the steps of carrying out a first treatment on the surface of the k is a flow correction coefficient; />The width of the acid etching crack at the end of the acid fracturing construction is dimensionless.
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