CN112098293A - Unsteady gas-water two-phase seepage simulation method based on pore fracture dual-medium gas reservoir - Google Patents
Unsteady gas-water two-phase seepage simulation method based on pore fracture dual-medium gas reservoir Download PDFInfo
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Abstract
The invention relates to a pore fracture-based dual-medium gas reservoir unsteady gas-water two-phase seepage simulation method, which comprises the steps of obtaining a rock core T2 spectrum, and converting to obtain pore throat radius distribution frequency and a pore throat distribution function; obtaining the core pore throat length and coordination number for establishing a disordered pore network model by micro-CT scanning, and adding the number of cracks; establishing a pore crack type double medium model; and introducing an unsteady state seepage theory, and combining a dynamic network simulation algorithm with the unsteady state seepage theory to simulate the gas-water two-phase seepage and pressure propagation process of the fluid double-medium gas reservoir. The invention carries out unsteady gas-water two-phase flow simulation on the basis of a pore crack double-medium model, and can more accurately describe the pore-level gas-water two-phase flow process by considering the dynamic network simulation of the compressibility of the fluid in the traditional gas-water two-phase seepage process; the pressure distribution of gas-water two phases in the dual medium of the pore and the crack can be analyzed, and the propagation of pressure waves is facilitated, so that the flowing rule of fluid in the pore and the crack is researched.
Description
Technical Field
The invention relates to the field of oil and gas field development, in particular to a pore fracture-based dual-medium gas reservoir unsteady-state gas-water two-phase seepage simulation method.
Background
The natural gas reserves in China are large, the application is wide, and the natural gas is one of important clean energy. Through research for many years, the development mode of the conventional gas reservoir tends to be mature, researchers mostly adopt a single pore sandstone structure network model to carry out gas reservoir numerical simulation research, the technology is mature day by day, but research on unsteady state seepage mechanism of the gas reservoir considering hypotonic-dual media is less.
At present, many researchers at home and abroad usually adopt a continuous medium theory to research multiphase seepage of a porous medium, but because viscous force and capillary force have discontinuity on pore size, how the seepage rule changes after considering a crack medium is not clear; practical fluids are often compressible (especially gases) inside the reservoir, which is contrary to the steady state seepage theory where fluid can instantaneously pass from the inlet to the outlet; in the natural gas exploitation process, due to the existence of cracks, the gas reservoir seepage rule (mainly gas-water two-phase flow) is extremely complex, the conventional gas reservoir seepage theory cannot accurately guide the production of the gas reservoir and predict the production dynamics of the gas reservoir, but the research on the unsteady seepage simulation research method of the dual medium with the cracks is limited at present, conventional commercial numerical simulation software can roughly simulate the gas reservoir with the matrix and the microcrack type, but the result of the gas reservoir with the large cracks is often unreliable, the phenomenon of the unsteady seepage is not well known, and the exploitation of the fractured natural gas reservoir is greatly limited. Therefore, it is necessary to provide a non-steady-state seepage simulation method for a pore fracture type network model of a gas reservoir.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a method for simulating unsteady gas-water two-phase seepage of a gas reservoir based on a pore crack dual medium, and overcomes the defects of unsteady seepage simulation research on the pore crack dual medium at present.
The purpose of the invention is realized by the following technical scheme: a pore fracture-based double-medium gas reservoir unsteady gas-water two-phase seepage simulation method comprises the following steps:
obtaining a rock core T2 spectrum obtained through a nuclear magnetic resonance experiment, converting the T2 spectrum according to a preset quantitative relation to obtain pore throat radius distribution frequency, and fitting according to the pore throat radius distribution frequency to obtain a pore throat distribution function;
obtaining the core pore throat length and coordination number for establishing a disordered pore network model through micro-CT scanning, and counting the number of cracks to be added according to a statistical model of the core crack number;
establishing a pore fracture type dual medium model according to the pore throat distribution function, the coordination number, the fracture and the disordered pore network module, wherein the pore fracture type dual medium model accords with the physical property characteristics of the reservoir;
and introducing an unsteady state seepage theory in the pore fracture type network simulation, considering the flow process, the interface movement process and the pore pressure diffusion process of fluid in pores and the flow and pressure diffusion process of fluid in fractures, researching the pore fracture type gas-water two-phase unsteady seepage, and combining a dynamic network simulation algorithm with the unsteady state seepage theory to simulate the gas-water two-phase seepage and pressure propagation process of the fluid dual-medium gas reservoir.
Further, the establishing a pore fracture type dual medium model according to the pore throat distribution function, the coordination number, the fracture and the disordered pore network module and according to the reservoir physical property characteristics comprises the following steps:
let n be a plane normal vector
Obtaining a point method equation A (x-x) according to any two points on the plane0)+B(y-y0)+C(z-z0)＝0；
Taking a random point on the normal vector as a circle center according to a spherical equation (x-a)2+(y-b)2+(z-c)2＝r2Obtaining a plane equation representing the space circular surface crack
Inserting a plane equation into nodes of the disordered pore network model to generate two-dimensional plane cracks, and constructing pore crack dual media;
and (3) generating a pore-fracture dual medium model by taking the pore throat distribution, throat length, coordination number, fracture number and spatial correlation obtained by analyzing the micro-CT scanning experiment as input parameters.
Further, the core pore throat length and coordination number used for establishing the disordered pore network model are obtained through micro-CT scanning:
projecting a cone beam X-ray emitted by a micro-focus ray source on a detector after penetrating through a sample, and simultaneously enabling the sample, the ray source and the detector to rotate relatively for 360 degrees to acquire data of each angle of the sample; 3D reconstruction is carried out by utilizing a computed tomography imaging reconstruction method to obtain high-resolution 3D data and images of the internal and external structures of the sample;
carrying out substance differentiation according to different gray levels of the image to realize CT data analysis, wherein a region with low gray level represents low substance density, and carrying out threshold division by referring to the gray level value of pores in a gray level curve, so that the pores are separated in the image;
intercepting a research area with a certain pixel volume in a sample scanning model, extracting pores through binarization segmentation, and calculating the volume percentage of the pores under the current resolution to the total volume of the scanned sample, so as to obtain the porosity required by modeling through comparison with a physical experiment; identifying and extracting connected pores by performing connection simulation on the connectivity of the pores with large data volume, wherein the rest pores are isolated pore groups, and non-connected pores are directly counted by using an equivalent ball;
distinguishing the space occupied by the pores and throats and connectivity in the digital rock core three-dimensional image by using a maximum sphere algorithm, extracting corresponding pore and throat structure network models, and meanwhile, quantitatively extracting pore throat size, pore throat volume, pore throat ratio, coordination number and shape factor by using a mathematical statistics method to obtain parameters for researching rock pore throat representation;
and establishing a pore throat network model through the bat model, counting the pore throat radius, the pore throat volume, the shape factor, the connectivity and the characteristics of each throat communicated with the pore throat network model, and extracting the average pore throat length and the coordination number required by subsequent modeling from the pore throat network model.
Further, the obtaining of a core T2 spectrum obtained through a nuclear magnetic resonance experiment, and the converting of the T2 spectrum according to a preset quantitative relationship to obtain a pore throat radius distribution frequency includes:
washing oil and salt of rock core, drying at certain temperature until weight is unchanged, and performing KCl treatment by vacuum pressure saturator2Carrying out a nuclear magnetic resonance measurement experiment after the rock core is saturated for a certain time by taking saline as a medium;
after the prepared rock core is put into a magnet probe and the parameters are adjusted, series T2 images of different echo times are obtained through a T2 image pulse sequence, and then a nuclear magnetic resonance T2 spectrum is converted into a rock pore throat radius frequency distribution curve.
Further, the preset quantitative relation is rm＝cT2mWherein r ismIs the mth pore throat radius, T2mIs the m-th amplitude value of the T2 spectrum, c is a preset conversion coefficient, and m is a positive integer.
Further, the simulating the gas-water two-phase seepage and pressure propagation process of the fluid dual-medium gas reservoir comprises:
introducing a no-flow boundary condition according to kirchhoff's law to obtain the flow pressure of each node, and further obtaining the average flow velocity of each section; setting the whole flow direction as horizontal direction in the simulation process, and setting the pressure of two points as p for the independent nodes i and j in the modeliAnd pjThe radius and length of the connecting pore passage between two points are respectively rijAnd lijGas viscosity of μg；
If the path between the i and j nodesThe total volume flow of the fluid between two nodes is obtained for the pores
At a gas viscosity of mugThe pore network is viscous to mu before non-wet phase invasionwThe wet phase fluid is filled, the left end of the pore network is injected at a certain speed by the intrusion fluid after the simulation displacement process begins, and the capillary pressure p is solved through the Yang-Laplace equationcij＝2γcosθ/rij；
If the channel between the i and j nodes is a crack, the total volume flow of the fluid between the beam nodes is obtained
Force p of fractured capillarycijw＝2γcosθ/w；
Selecting a time step to make each two-phase interface in the step generate a proper amount of displacement delta x, introducing a minimum time step and a correction time step for this purpose, and selecting a minimum delta tiThe total time step of this calculation is a displacement Δ x of the meniscus other than the meniscus reaching the next nodeij＝vij·ΔtminFrom this, the hydraulic conductivity g at that time can be determinedijAnd the distribution of the two phases in the pore network;
in the actual seepage process, the compressibility of the fluid and the rock is considered to obtain an unsteady state seepage equation
Conversion of unsteady state seepage equation into matrix equation by Taylor expansion and implicit finite difference method
According to the condition that the total volume flow of each node in two-phase seepage meets the conservation law, a linear equation set is constructed
And solving the pressure by adopting a gradient descent method to obtain the pressure of the pore node used at the current moment.
Further, the simulation method further comprises the step of establishing a disordered pore network model on the basis of the SC model before obtaining a core T2 spectrum obtained through a nuclear magnetic resonance test.
Further, the step of establishing the disordered pore network model on the basis of the SC model comprises the following steps:
determining the size and the number of nodes of a network model, constructing an X multiplied by Y multiplied by Z three-dimensional simple cubic grid, wherein each node represents a pore, the nodes are connected with each other through throats, six throats are arranged around each node representing a pore in the established network, and each throat is connected with two adjacent pores;
calculating the coordinates of each node in the network model according to a calculation formula (x, y, z) [ (i-1) l, (j-1) l, (k-1) l ];
setting probability as a probability function of p, and determining whether tube bundles are communicated among adjacent nodes in the x, y and z directions through a random number generator;
and generating a random network from the coordinates of the central node through central displacement correction.
Further, when the penetration probability p is 50%, the probability of 50% of the randomly generated integers of the rand () function is less than 50%, and the probability of the other 50% is more than 50%, and bundle connection with the probability p being 50% can be realized, that is, when a number less than 50 is generated, the expression if (rand ()% 100 < p × 100) is true, and the task of allocating the bundle radius is executed; otherwise, false, no operation is performed.
The invention has the beneficial effects that:
1. the pore fracture filling heavy medium modeling method disclosed by the invention combines a CT (computed tomography) experiment and a nuclear magnetic resonance experiment in a rock core analysis technology on the basis of a pore network model, the modeling method is scientific and has physical significance, and the established model meets the reservoir characteristics and meets the production requirement of a pore-fracture type reservoir;
2. the gas-water unsteady simulation method suitable for the pore fracture dual medium provided by the invention is characterized in that unsteady gas-water two-phase flow simulation is carried out on the basis of a pore fracture dual medium model, and the dynamic network simulation considering the compressibility of fluid in the traditional gas-water two-phase seepage process can more accurately describe the pore-level gas-water two-phase flow process; the pressure distribution of gas-water two phases in the dual medium of the pore and the crack can be analyzed, and the propagation of pressure waves can help to research the flowing rule of fluid in the pore and the crack.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of nuclear magnetic T2 spectrum conversion pore throat radius according to the method of the present invention;
FIG. 3 is a schematic diagram of a percolation in which the channel between the i and j nodes is porous;
FIG. 4 is a schematic view of a seepage flow in which the channel between the i and j nodes is a fracture;
FIG. 5 is a schematic diagram of a simulation result of unsteady-state gas-water two-phase seepage;
FIG. 6 is a schematic diagram of the result of unsteady-state gas-water two-phase seepage simulation 2.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are only a part of the embodiments of the present application, and not all the embodiments. The components of the embodiments of the present application, generally described and illustrated in the figures herein, can be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present application, as presented in the figures, is not intended to limit the scope of the claimed application, but is merely representative of selected embodiments of the application. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present application without making any creative effort, shall fall within the protection scope of the present application. The invention is further described below with reference to the accompanying drawings.
As shown in figure 1, the invention relates to a pore fracture-based dual-medium gas reservoir unsteady gas-water two-phase seepage simulation method, which specifically comprises a step of establishing a disordered pore network model, a step of counting coordination numbers and core fracture numbers through a micro-CT scanning experiment, a step of analyzing, testing and counting pore throat radius distribution through nuclear magnetic resonance core analysis, a step of establishing a pore fracture type dual-medium network model and a step of simulating gas-water unsteady two-phase seepage.
S1, step of establishing unordered pore network model
Generation of disordered structure network by displacement of central point based on SC network model
(1) And determining the size and the number of nodes (or grids) of the network model, and constructing an X multiplied by Y multiplied by Z three-dimensional simple cubic grid. Each node represents a pore, and the nodes are connected by a throat. Six throats are connected around each node representing pore in the network established by the method; similarly, each throat is connected to two adjacent apertures. The spacing distance between nodes in each direction (namely the x direction, the y direction and the z direction) is set to be l, the number of the nodes is set to be d, and the side length of the model is (d-1) multiplied by l.
(2) And calculating the coordinates of each node in the network model. The calculation formula is as follows: (x, y, z) [ (i-1) l, (j-1) l, (k-1) l ], where i, j, and k are node numbers in the x, y, and z directions, respectively, and take values of 1,2, and 3 …, respectively.
(3) A random network (3 × 3 × 3 for example) is generated by displacing the center node coordinates from the center point. Move each node coordinate (x, y, z) as follows:
(x,y,z)＝[(i-1)l±rand()％(0.5l),(j-1)l±rand()％(0.5l),(k-1)l±rand()％(0.5l)]。
(4) and setting a probability function with the probability p in a program, and determining whether the pipe bundles are communicated between every two adjacent nodes in the x direction through a (pseudo) random number generator. In the C/C + + programming language, random numbers can be generated using the rand () function, thereby generating random probabilities. The specific C/C + + code is: if (% rand () < p.times.100), rand ()% 100-computer randomly generates any integer in the range of 0-99.
When the percolation probability p is 50%, 50% of the randomly generated integers of the rand () function have a probability (probability) of less than 50 and the other 50% have a probability (probability) of more than 50. Therefore, the expression can realize bundle connection with a probability p of 50%, that is, when a number smaller than 50 is generated, the expression is true, all values are assigned to 1, the value which does not satisfy the condition is assigned to 0, and the task of allocating the bundle radius (allocating the bundle radius r) is executed; otherwise, false, no operation is performed.
(5) And establishing a connection probability function through a (pseudo) random number generator to determine whether tube bundle connection exists between adjacent nodes in the y and z directions. The method is the same as the x-direction tube bundle distribution process,
s2, and carrying out micro CT scanning experiment statistics on coordination number and core fracture number
The method comprises the steps of projecting a cone beam X-ray emitted by a micro-focus ray source on a detector after penetrating a sample, enabling the sample, the ray source and the detector to rotate relatively by 360 degrees, collecting data of thousands of frame angles, and then performing 3D reconstruction by using a computed tomography imaging reconstruction method to obtain high-resolution 3D data and images of internal and external structures of the sample.
Intercepting a research area with the volume of 1000 multiplied by 1000 pixels from a sample scanning model, extracting pores through binary segmentation, and calculating the volume percentage of the pores under the current resolution ratio in the total volume of the scanned sample, so as to obtain the porosity required by modeling through comparison with a physical experiment, performing communication simulation on the connectivity of the pores with large data volume through a computer, identifying and extracting the communicated pores, wherein the rest pores are isolated pore groups, and counting the non-communicated pores by using the equivalent sphere diameter.
And simultaneously, quantitative extraction of pore structures such as pore throat size, pore throat volume, pore throat ratio, coordination number, shape factor and the like can be realized by applying a mathematical statistical method, so that parameters for researching the pore throat characteristics of the rock are obtained.
And establishing a pore-throat network model through a bat model, counting characteristic parameters such as radius, volume, shape factor, connectivity (coordination number) and throat characteristics (throat length and shape factor) communicated with the model, and extracting the average pore-throat length and coordination number required by subsequent modeling from the statistical parameters.
The number of cracks needing to be added through a statistical model of the number of physical core cracks
The method specifically comprises the following steps: based on a computer high-resolution tomography imaging technology (MicroCT scans a sample and 3D reconstruction of a digital core respectively constructs a pore network by an equivalent sphere method and a maximum sphere method, and performs structural feature analysis on a reservoir, wherein the roar length can be calculated by the following formula:
L＝D-R1-R2
in the formula, R1，R2The radius of two pores connected with the roar channel is mum respectively; d is the actual coordinate distance of the central points of the two holes, and is mum.
The coordination number is automatically counted by software.
S3, and performing nuclear magnetic resonance core analysis test to count pore throat radius distribution
Washing carbonate rock core collected from stratum with oil, washing salt, drying at 80 deg.C until weight is unchanged, and performing vacuum pressure saturation with KCl2Brine is used as a medium, a nuclear magnetic resonance measurement experiment is carried out after a carbonate rock core is saturated for 48 hours, the prepared core is placed in a magnet probe, the resonance frequency is adjusted, a T2 Image pulse sequence is selected, system parameters and acquisition parameters are set, T2 Image pulse sequences are used for obtaining T2 images of different echo time series, and finally a nuclear magnetic resonance T2 spectrum is converted into a rock pore throat radius frequency distribution curve.
The method specifically comprises the following steps: as shown in fig. 2, the nuclear magnetic resonance signal intensity is positively correlated with the number of fluid hydrogen nuclei inside the saturated rock sample. The measuring method comprises the following steps: measuring a group of sample calibration, wherein the porosity values of the calibration samples are respectively 2%, 4%, 8%, 15% and 30%, and after a series of T2 images of each calibration sample with different nuclear magnetic echo times are obtained, curve fitting is performed on the data by taking the proton density image signal of the unit volume of the calibration sample as an abscissa and the porosity of the calibration sample as an ordinate, so as to obtain a nuclear magnetic porosity scale relation:
wherein a and b are fitting parameters,
Porosity, S the size of the magnetic image signal, V the sample volume. And then measuring the target rock core, and substituting the measured image signal value into the scale relation to obtain the rock core porosity and the whole porosity distribution value.
Meanwhile, the nuclear magnetic resonance relaxation time distribution is combined with the conventional rock mercury intrusion pore size distribution, a conversion coefficient c (which is obtained by mercury intrusion experiments and has regional experience) value can be obtained, and the pore size distribution can be obtained by multiplying the abscissa of the T2 spectrum by c.
S4, establishing a pore crack type dual medium network model
Inserting a plane equation into the nodes of the constructed disordered pore network module to generate a two-dimensional plane crack, and constructing a pore crack dual medium; let n be the plane normal vector:
M(x，y，z)，N(x0，y0，z0) Two arbitrary points on the plane are as follows:
the point-normal equation for the plane is thus:
A(x-x0)+B(y-y0)+C(z-z0)＝0
the spatial circular face crack can be generated by the following method:
taking a random point on a normal vector as a circle center o (a, B, C), wherein a is a random number from 0 to A, B is a random number from 0 to B, and C is a random number from 0 to C, firstly calculating a spherical equation:
(x-a)2+(y-b)2+(z-c)2＝r2
wherein the radius r is the radius of the sphere; so that the equation of the plane where the circle is located satisfies
From both, the equation of the circular plane (circular plane fracture) can be derived. The number of the cracks is determined by the number of the plane equations, the number i of the cracks in the rock core with the diameter of 2.5cm and the length of 3cm of a plurality of samples is counted through the physical rock core, and the cracks approximately trend; with niThe normal vector is used as a reference (generating random point coordinates) to control the angle and the distribution position of the cracks, and the number of generated cracks is controlled by the cycle number.
And finally, generating a pore and fracture dual medium model by taking the pore throat distribution, the roar length, the coordination number, the fracture number, the spatial correlation and the like obtained by the CT experimental analysis as input parameters.
The radius of the pore throat of a reservoir is modeled to be in lognormal distribution (obtained by nuclear magnetic T2 spectrum), and the mean value mu and the standard deviation sigma of the distribution are obtained by fitting a frequency distribution curve through Matlab, so that a lognormal distribution random function is obtained:
wherein x >0, represents the pore throat radius.
S5 simulation step of gas-water unsteady two-phase seepage
In a real core, due to the viscous action of the fluid, the fluid mass points adhere to the surface of the object, and a fluid non-slip phenomenon (i.e. the relative velocity is zero) is formed, so that frictional resistance and energy dissipation are generated. Therefore, assuming that the fluid flow in the pore network follows the principle of lowest energy dissipation, the mass conservation law followed by the pore network model in the flow process is described by kirchhoff's law, namely the volume of the inflow fluid is equal to the volume of the outflow fluid, so that the real core matrix flow is simplified into the pore network model flow, and the gas-water two-phase unsteady seepage simulation can be carried out in the disordered structure network model.
And introducing a no-flow boundary condition according to kirchhoff's law, solving the flow pressure of each node, and thus obtaining the average flow velocity of each section. The overall flow direction was set to the horizontal direction during the simulation. In the model, for the independent nodes i and j, two point pressures are respectively set as piAnd pjThe radius and length of the connecting pore passage between two points are respectively rijAnd lijGas viscosity of μg(ii) a The total volume flow q of the fluid between the two nodesijThe method can be divided into the following steps:
as shown in fig. 3, if the channel between the i and j nodes is a pore:
in the formula, gijrIs the gas conductance of the tube bundle between nodes i and j, BgIs the gas volume coefficient, Z and ZscGas deviation factors, T and T, underground and surface respectivelyscThe temperature of the ground and the temperature of the ground respectively,<p>pressure of underground gas, pscIs the ground atmospheric pressure; mu.seffIs the effective viscosity (Pa s) of two phases in a single pipe, and only in the pipeEffective viscosity mu in the presence of a two-phase concave surfaceeffCan be calculated by the following equation.
μeff＝Bgμgxij+μw(1-xij)
Where x isijIs a dimensionless number (0. ltoreq. x) related to the position of the meniscusijLess than or equal to 1), i.e. the abscissa of the position of the concave liquid surface is divided by the length of the whole pore network, when only single-phase fluid exists in the pipeline, pc＝0。
At a viscosity of μg(Pa s) before non-wet invasion, the pore network is rendered viscous to μw(Pa · s) is occupied by a wet phase fluid. After the simulated displacement process begins, the invading fluid is injected from the left end of the pore network at a certain rate, and the capillary pressure pc(MPa) solved using the young-laplace equation (tunnel capillary force formula):
pcijr＝2γcosθ/rij
where γ is the interfacial tension (N/m) and θ is the wetting contact angle.
As shown in fig. 4-6, if the channel between the i and j nodes is a crack:
wherein b is the depth of the crack, w is the opening of the crack, and l is the length of the crack.
Wherein p iscijwIs a crack capillary force formula:
pcijw＝2γcosθ/w
in the simulation process, a time step is selected to ensure that each two-phase interface in the step generates a proper displacement delta x, and a minimum time step and a correction time step are introduced for the purpose, wherein the minimum time step delta ti(i-1, 2, …) refers to the time at which the meniscus in all the channels reaches the next nodeIn (1), the minimum Deltat is selectediThe total time step of this calculation is a displacement Δ x of the meniscus other than the meniscus reaching the next nodeij＝vij·ΔtminFrom this, the hydraulic conductivity g at that time can be determinedijAnd the distribution of the two phases in the pore network. It is clear that the time step Δ t in the minimum time step methodiDepending on the pressure drop Δ p and the meniscus position, the step size of each iteration depends on the specifics of the calculation, and is not all equal. The introduction of the minimum time step enables the model to obtain a simulation result by using the iteration times as few as possible, so that the calculation efficiency is greatly improved while the precision is ensured.
In the actual seepage process, gas is compressible fluid, and the rock skeleton has micro compressibility. If fluid and rock compressibility are considered, an unsteady state seepage equation can be obtained:
the above equation can be converted into a matrix equation by taylor expansion and implicit finite difference method techniques:
in the formula, CtThe compression factor is the comprehensive compression factor (mainly the gas compression factor), Q is the gas production speed, and delta t is the time step.
Setting a pore medium as 1 and a crack medium as 2, adopting a judgment statement, if the medium is a pore, selecting 1 and having common conductivityFormula (II) is as followsijrIf the medium is a crack, 2 is selected, and the conductivity formula adopts gijw。
In a two-phase flow pore fracture medium model, the total volume flow of each node and the fracture still meets the conservation law, namely sigmajqijFrom this, a system of linear equations can be constructed:
the above equation can be simplified into a matrix solution formula Ax ═ B, where a is a symmetric sparse matrix with dominant diagonal dominance, B is a set of vectors, and x is the global pressure field vector to be solved. The matrix can be solved by adopting a gradient descent method, wherein the gradient descent method comprises the following steps:
f(p)＝Ap-B
f′(p)＝A
the calculation of the key physical parameters of the natural gas comprises the calculation of gas reservoir temperature, pressure and relative density, deviation factors, volume coefficients and isothermal compression coefficients.
1. Gas reservoir temperature, pressure and relative density
Underground natural gas is a mixed product of multiple gas components, the temperature and pressure of which are typically treated with pseudo-critical parameters:
ppc＝∑yipci，Tpc＝∑yiTci
in the formula, ppc,TpcSimulating critical pressure and temperature for natural gas; p is a radical ofci,TciCritical pressure and critical temperature of gas component i; y isiIs the mole fraction of component i.
Relative density gamma of natural gashRepresenting natural gas density ρg(ii) a And air density rhoairThe ratio of.
Therefore, the pseudo-critical pressure and the pseudo-critical temperature can be obtained by the relative density:
the apparent contrast pressure p of the natural gas can be obtained from the pressure p and the temperature T of the natural gasprTemperature T in contrast to apparentpr：
2. Deviation factor
The natural gas deviation factor z is a coefficient for quantitatively describing the degree of deviation between real gas (natural gas) and ideal gas, and is an important parameter for calculating other physical properties of the natural gas, calculating the geological reserves of the natural gas reservoir and designing the yield of the natural gas of the pipeline. The natural gas deviation factor is calculated by a plurality of methods, and the deviation factor is calculated by adopting a Dranchuk and Abou-Kassem-11 parameter method.
z＝0.27ppr/(ρprTpr)
And is
Wherein a1 ═ 0.3265; a2 ═ -1.07; a3 ═ -0.5339; a4 ═ 0.01569；A5＝-0.05165；A6＝0.5475； A7＝-0.7361；A8＝0.1844；A9＝0.1056；A10＝0.6134；A11＝0.721，TprIs the apparent contrast temperature under given conditions; pprIs the apparent contrast pressure under given conditions; rhoprFor intermediate parameters, newton's iteration method can be used to solve:
let the primitive function be:
the first derivative is:
the K order derivative and the K +1 order derivative have the following relation:
and setting iteration precision (the error is less than 0.05 percent in this time) to meet the requirement to obtain the deviation factor z.
3. Volume factor
The volume coefficient of the natural gas is the volume V of the underground natural gas and the volume V of the ground natural gas under the standard conditionscThe formula of the ratio is as follows:
Bg＝V/Vsc
under the condition of an oil-gas reservoir, the pressure is p, the temperature is T, the natural gas state equation and the ground condition are substituted into the formula, and the natural gas volume coefficient calculation formula can be obtained:
Bg＝3.458×10-4zT/p
wherein p and T are formation pressure and temperature, and z is a deviation factor.
4. Coefficient of isothermal compression
Natural gas isothermal compressibility factor CgThe change rate of the volume along with the pressure change under the isothermal condition is shown as the following mathematical expression:
after considering the apparent contrast pressure:
in the formula ppcTo approximate pressure, pprTo look at the contrast pressure, z is the bias factor.
The foregoing is illustrative of the preferred embodiments of this invention, and it is to be understood that the invention is not limited to the precise form disclosed herein and that various other combinations, modifications, and environments may be resorted to, falling within the scope of the concept as disclosed herein, either as described above or as apparent to those skilled in the relevant art. And that modifications and variations may be effected by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (9)
1. The unsteady gas-water two-phase seepage simulation method based on the pore fracture dual-medium gas reservoir is characterized by comprising the following steps of: the simulation method comprises the following steps:
obtaining a rock core T2 spectrum obtained through a nuclear magnetic resonance experiment, converting the T2 spectrum according to a preset quantitative relation to obtain pore throat radius distribution frequency, and fitting according to the pore throat radius distribution frequency to obtain a pore throat distribution function;
obtaining the core pore throat length and coordination number for establishing a disordered pore network model through micro-CT scanning, and counting the number of cracks to be added according to a statistical model of the core crack number;
establishing a pore fracture type dual medium model according to the pore throat distribution function, the coordination number, the fracture and the disordered pore network module, wherein the pore fracture type dual medium model accords with the physical property characteristics of the reservoir;
and introducing an unsteady state seepage theory in the pore fracture type network simulation, considering the flow process, the interface movement process and the pore pressure diffusion process of fluid in pores and the flow and pressure diffusion process of fluid in fractures, researching the pore fracture type gas-water two-phase unsteady seepage, and combining a dynamic network simulation algorithm with the unsteady state seepage theory to simulate the gas-water two-phase seepage and pressure propagation process of the fluid dual-medium gas reservoir.
2. The pore fracture-based dual-medium gas reservoir unsteady-state gas-water two-phase seepage simulation method of claim 1, characterized in that: the establishing of the pore fracture type dual medium model according to the pore throat distribution function, the coordination number, the fracture and the disordered pore network module, wherein the pore fracture type dual medium model accords with the physical property characteristics of the reservoir, comprises the following steps:
let n be a plane normal vector
Obtaining a point method equation A (x-x) according to any two points on the plane0)+B(y-y0)+C(z-z0)＝0；
Taking a random point on the normal vector as a circle center according to a spherical equation (x-a)2+(y-b)2+(z-c)2＝r2Obtaining a plane equation representing the space circular surface crack
Inserting a plane equation into nodes of the disordered pore network model to generate two-dimensional plane cracks, and constructing pore crack dual media;
and (3) generating a pore-fracture dual medium model by taking the pore throat distribution, throat length, coordination number, fracture number and spatial correlation obtained by analyzing the micro-CT scanning experiment as input parameters.
3. The pore fracture-based dual-medium gas reservoir unsteady-state gas-water two-phase seepage simulation method of claim 1, characterized in that: obtaining the pore throat length and coordination number of a rock core for establishing a disordered pore network model through micro-CT scanning:
projecting a cone beam X-ray emitted by a micro-focus ray source on a detector after penetrating through a sample, and simultaneously enabling the sample, the ray source and the detector to rotate relatively for 360 degrees to acquire data of each angle of the sample; 3D reconstruction is carried out by utilizing a computed tomography imaging reconstruction method to obtain high-resolution 3D data and images of the internal and external structures of the sample;
carrying out substance differentiation according to different gray levels of the image to realize CT data analysis, wherein a region with low gray level represents low substance density, and carrying out threshold division by referring to the gray level value of pores in a gray level curve, so that the pores are separated in the image;
intercepting a research area with a certain pixel volume in a sample scanning model, extracting pores through binarization segmentation, and calculating the volume percentage of the pores under the current resolution to the total volume of the scanned sample, so as to obtain the porosity required by modeling through comparison with a physical experiment; identifying and extracting connected pores by performing connection simulation on the connectivity of the pores with large data volume, wherein the rest pores are isolated pore groups, and non-connected pores are directly counted by using an equivalent ball;
distinguishing the space occupied by the pores and throats and connectivity in the digital rock core three-dimensional image by using a maximum sphere algorithm, extracting corresponding pore and throat structure network models, and meanwhile, quantitatively extracting pore throat size, pore throat volume, pore throat ratio, coordination number and shape factor by using a mathematical statistics method to obtain parameters for researching rock pore throat representation;
and establishing a pore throat network model through the bat model, counting the pore throat radius, the pore throat volume, the shape factor, the connectivity and the characteristics of each throat communicated with the pore throat network model, and extracting the average pore throat length and the coordination number required by subsequent modeling from the pore throat network model.
4. The pore fracture-based dual-medium gas reservoir unsteady-state gas-water two-phase seepage simulation method of claim 1, characterized in that: the obtaining of the core T2 spectrum obtained through the nuclear magnetic resonance experiment, and the converting of the T2 spectrum according to the preset quantitative relation to obtain the distribution frequency of the pore throat radius comprises the following steps:
the rock core is dried under the condition of certain temperature after being washed with oil and saltUntil the weight is unchanged, and using a vacuum pressure saturator with KCl2Carrying out a nuclear magnetic resonance measurement experiment after the rock core is saturated for a certain time by taking saline as a medium;
after the prepared rock core is put into a magnet probe and the parameters are adjusted, series T2 images of different echo times are obtained through a T2 image pulse sequence, and then a nuclear magnetic resonance T2 spectrum is converted into a rock pore throat radius frequency distribution curve.
5. The pore fracture-based dual-medium gas reservoir unsteady-state gas-water two-phase seepage simulation method of claim 1, characterized in that: the preset quantitative relation is rm＝cT2mWherein r ismIs the mth pore throat radius, T2mIs the m-th amplitude value of the T2 spectrum, c is a preset conversion coefficient, and m is a positive integer.
6. The pore fracture-based dual-medium gas reservoir unsteady-state gas-water two-phase seepage simulation method of claim 1, characterized in that: the simulation of the gas-water two-phase seepage and pressure propagation process of the fluid double-medium gas reservoir comprises the following steps:
introducing a no-flow boundary condition according to kirchhoff's law to obtain the flow pressure of each node, and further obtaining the average flow velocity of each section; setting the whole flow direction as horizontal direction in the simulation process, and setting the pressure of two points as p for the independent nodes i and j in the modeliAnd pjThe radius and length of the connecting pore passage between two points are respectively rijAnd lijGas viscosity of μg；
If the channel between the node i and the node j is a pore, the total volume flow of the fluid between the two nodes is obtained
At a gas viscosity of mugThe pore network is viscous to mu before non-wet phase invasionwThe wet phase fluid is filled, the invading fluid is injected at the left end of the pore network at a certain speed after the simulation displacement process begins, and the wool is solved through the Yang-Laplace equationPipe pressure pcij＝2γcosθ/rij；
If the channel between the i node and the j node is a crack, the total volume flow of the fluid between the two nodes is obtained
Force p of fractured capillarycijw＝2γcosθ/w；
Selecting a time step to make each two-phase interface in the step generate a proper amount of displacement delta x, introducing a minimum time step and a correction time step for this purpose, and selecting a minimum delta tiThe total time step of this calculation is a displacement Δ x of the meniscus other than the meniscus reaching the next nodeij＝vij·ΔtminFrom this, the hydraulic conductivity g at that time can be determinedijAnd the distribution of the two phases in the pore network;
in the actual seepage process, the compressibility of the fluid and the rock is considered to obtain an unsteady state seepage equation
Conversion of unsteady state seepage equation into matrix equation by Taylor expansion and implicit finite difference method
According to the condition that the total volume flow of each node in two-phase seepage meets the conservation law, a linear equation set is constructed
And solving the pressure by adopting a gradient descent method to obtain the pressure of the pore node used at the current moment.
7. The pore fracture-based dual medium gas reservoir unsteady-state gas-water two-phase seepage simulation method according to any one of claims 1 to 6, characterized in that: the simulation method further comprises the step of establishing a disordered pore network model on the basis of the SC model before obtaining a core T2 spectrum obtained through a nuclear magnetic resonance test.
8. The pore fracture-based dual-medium gas reservoir unsteady-state gas-water two-phase seepage simulation method of claim 7, characterized in that: the step of establishing the disordered pore network model on the basis of the SC model comprises the following steps:
determining the size and the number of nodes of a network model, constructing an X multiplied by Y multiplied by Z three-dimensional simple cubic grid, wherein each node represents a pore, the nodes are connected with each other through throats, six throats are arranged around each node representing a pore in the established network, and each throat is connected with two adjacent pore pores;
calculating the coordinates of each node in the network model according to a calculation formula (x, y, z) [ (i-1) l, (j-1) l, (k-1) l ];
setting probability as a probability function of p, and determining whether tube bundles are communicated among adjacent nodes in the x, y and z directions through a random number generator;
and generating a random network from the coordinates of the central node through central displacement correction.
9. The pore fracture-based dual-medium gas reservoir unsteady-state gas-water two-phase seepage simulation method of claim 8, characterized in that: when the penetration probability p is 50%, the probability of 50% of the randomly generated integers of the rand () function is less than 50%, the probability of the other 50% is more than 50, and the bundle connection with the probability p of 50% can be realized, namely when a number less than 50 is generated, the expression if (rand ()% 100 < p × 100) is true, and the task of distributing the bundle radius is executed; otherwise, false, no operation is performed.
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| CN117057271A (en) * | 2023-08-15 | 2023-11-14 | 西南石油大学 | VOF-based multiphase fluid seepage process simulation method |
| CN117057271B (en) * | 2023-08-15 | 2024-03-01 | 西南石油大学 | VOF-based multiphase fluid seepage process simulation method |
| CN117929238A (en) * | 2024-03-19 | 2024-04-26 | 西南石油大学 | Method for testing pore volume compression coefficient of hypotonic rock based on gaseous medium |
| CN117929238B (en) * | 2024-03-19 | 2024-05-28 | 西南石油大学 | Method for testing pore volume compression coefficient of hypotonic rock based on gaseous medium |
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| CN112098293B (en) | 2021-06-01 |
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