CN108729908B - Dense oil flow simulation and permeability prediction method based on pore network model - Google Patents
Dense oil flow simulation and permeability prediction method based on pore network model Download PDFInfo
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Abstract
The invention relates to a dense oil flow simulation and permeability prediction method based on a pore network model, which comprises the following steps: (1) scanning the compact rock core to obtain a two-dimensional electron microscope picture, and acquiring the pore space geometrical information of the porous medium: (2) reconstructing the digital core to obtain a geometric structure data file of the digital core; (3) extracting a pore network model of the digital rock core to obtain a compact rock core pore network model data file; (4) obtaining the pressure at each pore and the volume flow at each pore throat, thereby obtaining the flow condition of the fluid in the nano-scale pore network model; (5) and obtaining the fluid volume flow Q at the outlet end of the pore network model, and calculating the apparent permeability of the pore network model according to Darcy's law. The pore network model which is newly developed in the invention overcomes the defect that the traditional pore network model can not consider the characteristics of boundary slippage, effective viscosity change of fluid and the like when the fluid flows in the nanometer pores.
Description
Technical Field
The invention relates to a dense oil flow simulation and permeability prediction method based on a pore network model, and belongs to the technical field of oil and gas field development engineering numerical simulation.
Background
With the rapid development of various microscopic technologies (scanning electron microscope, CT, etc.) and computer technologies, it is possible to establish a model with good matching degree with the internal characteristics of reservoir rock and to study the flow of fluid in a porous medium by adopting a numerical simulation method. The pore network model is an effective method for researching the fluid flow in the porous medium at a micro-level, and provides an important research platform for simulating the fluid flow in the core. Compared with a physical rock core experiment, the method has the advantages of low experiment cost, simplicity in operation and short experiment period. Compared with a digital core, the pore network model has the characteristic of high calculation efficiency, pores are only used as a fluid storage space but not as a flow space during calculation, and the flow in the pore throat is directly calculated according to the existing flow formula without simulating specific flow details.
The pore network model is to replace pores and throats in the core with simple geometric bodies (such as circular, arbitrary triangular or square columns) and represent the complex pore space of the rock with a spatial network composed of the pores and throats. Many studies have now demonstrated that in certain cases a pore network model can quantitatively predict the flow of fluids in a porous medium. The premise is that the pore network models must physically reflect the true pore structure of the rock they represent, and the first flow equation (the pore throat conductivity equation) input must be able to correctly describe the flow of fluid in each pore throat.
One large hallmark of tight oil, the reservoir, is the presence of a large number of pores on the order of hundreds of nanometers, which makes the interaction of the pore walls with fluid molecules more important than in conventional reservoirs. Numerous experiments have shown that the fluid flow regime in nanochannels deviates significantly from the macroscopic flow equation, e.g., the flow rate of water in nanocubes is significantly higher than the volumetric flow rate predicted by the Hagen-Poiseuille equation. Two significant differences between nanoscale and macroscopic fluid flow are the velocity slip at the solid-liquid interface and the change in the effective viscosity of the fluid due to the presence of the interface layer, which also requires consideration of a wide variety of pore throat shapes when simulating fluid flow in tight reservoir nanoporous networks.
When the traditional pore network model calculates the conductivity of fluid flowing at the pore throat, a finite element method is adopted to solve an N-S equation of a non-slip boundary condition to obtain the flow rate of the fluid of a single tube, so that the conductivity at the pore throat is obtained (Zhao Xiui, digital rock core and pore network model reconstruction method research [ D ]), the flowing characteristic of the fluid in a nano channel is not considered, and the pore network model developed by the traditional pore network model cannot accurately describe the flowing of the fluid in a nano porous medium.
Disclosure of Invention
The invention provides a dense oil flow simulation and permeability prediction method based on a pore network model, which overcomes the defect that the traditional pore network model cannot consider the characteristics of boundary slippage, effective viscosity change and the like of fluid when the fluid flows in nano pores;
the conductivity calculation formula of the single tubes with different cross section shapes under the nanoscale condition is given through computational fluid dynamics modeling analysis, and the speed slippage of the fluid on a solid-liquid interface and the change of the effective viscosity of the fluid are considered. And applied to pore network modeling analysis.
Interpretation of terms:
1. conductivity: volumetric flow rate per unit pressure gradient as the fluid flows along the capillary tube.
2. Form factor: the method is used for representing the cross-sectional shapes of pores and throats in a pore network model, and the expression is as follows:
wherein P is the cross-sectional perimeter and A is the cross-sectional area.
3. The sliding length is as follows: the extrapolated length of the velocity vector with a tangential component of 0 is a measure of the effect of slip on fluid flow in the pipe, expressed as LsAnd (4) showing.
4. Dimensionless slip length: the ratio of the slip length to the 1/2 th power of the cross-sectional area of the channel is expressed as:
the technical scheme of the invention is as follows:
a dense oil flow simulation and permeability prediction method based on a pore network model comprises the following steps:
(1) scanning the compact rock core through a scanning electron microscope to obtain a two-dimensional electron microscope picture, and acquiring the geometrical information of the porous medium pore space: the geometrical information of the pore space of the porous medium comprises the shape, the size and the connection relation of pore throats;
(2) reconstructing the digital core by adopting a Markov chain-Monte Carlo (MCMC) numerical value based on the two-dimensional electron microscope picture obtained in the step (1) to obtain a geometric structure data file of the digital core; the geometric structure data file comprises each pixel point and a geometric structure corresponding to the pixel point, and the geometric structure comprises a rock core pore and a rock framework; for example, each pixel point in the geometric structure data file corresponds to 0 and 1, 0 represents that the current pixel point is a pore space, and 1 represents that the current pixel point is a rock skeleton. Among the references to the digital core reconstruction technique of markov chain-Monte Carlo Method (MCMC) are: wu K, Dijke MIJV, coupling G D, et al, 3D storage modeling of heterologous ports Media-Applications to memories Rocks [ J ]. Transport in ports Media,2006,65(3): 443-.
(3) Extracting the pore network model of the digital rock core in the step (2) by using a maximum sphere method to obtain a compact rock core pore network model data file; the pore network model data file comprises a pore throat section shape factor, a pore throat radius, a pore throat length, a pore throat position, a pore throat connection relation and a pore throat average coordination number; among the references of the maximum sphere algorithm are: morning, carbonate rock medium double-pore network model construction theory and method [ D ]. Qingdao, China university of Petroleum (east China), 2013, Chapter 2 of doctor thesis;
(4) for each pore in the pore network model to conserve mass, for incompressible fluids, volume conservation must be met, as shown in equation (I):
in the formula (I), I and j refer to any two adjacent pores in the pore network model; q. q.sijIs the volume flow, P, flowing from the adjacent aperture j into the aperture i through its interconnected throatsiIs the pressure in the pore i, gijIs the hydraulic conductivity connecting pore i and pore j throat; pjIs the pressure in the pore j;
solving the system of equations to obtain the pressure at each pore and the volume flow at each pore throat, thereby obtaining the flow condition of the fluid in the nano-scale pore network model; as shown in FIG. 2, LsIs the slip length.
(5) And obtaining the fluid volume flow Q at the outlet end of the pore network model, and calculating the apparent permeability of the pore network model according to Darcy's law.
Preferably, in step (4), the hydraulic conductivity g of the channel connecting the pore i and the pore j isijThe method is obtained by computational fluid dynamics modeling analysis, the speed slippage of a solid-liquid boundary and the change of the effective viscosity of the fluid caused by the existence of an interface layer are considered in the modeling process, and the calculation formula is shown as the formula (II):
in formula (II), A is the cross-sectional area of the channel, and μ is the fluid bulk viscosity; g is the shape factor, k is the thickness of the interface layer, P is the circumference of the throat section, LsdIs the dimensionless slip length, h is the viscosity coefficient, which is the ratio of the boundary layer fluid viscosity to the macroscopic fluid viscosity; a. b, c, d, e, f are empirical constants obtained by fitting the data, and when G is equal to or greater than 0.04, a is-0.16, b is 0.12, c is 6.4, d is-0.0055, e is-50, f is 1.7, and when G is equal to or greater than 0.04, G is equal to or greater than-0.16, d is equal to or greater than-0.4, e is equal to or greater than-50, and f is equal to or greater than 1.7<0.04, a ═ 0.012, b ═ 0.057, c ═ 2, d ═ 0.0052, e ═ 38, and f ═ 3.2.
Preferably, in the step (5), the apparent permeability of the pore network model is calculated according to Darcy's law; the calculation formula is shown in formula (III):
in formula (III), K is the apparent permeability of the pore network model, μ is the bulk fluid viscosity, L is the model length, A is the flow cross-sectional area, and Δ P is the flow pressure differential.
The invention has the beneficial effects that:
1. the invention provides a conductivity calculation formula of single tubes with different cross-sectional shapes under the condition of nano scale, considers the speed slippage of a solid-liquid boundary and the influence of the change of the effective viscosity of fluid caused by the existence of an interface layer on the flow of the fluid, and uses the conductivity calculation formula for the modeling analysis of a pore network. The newly developed pore network model overcomes the defects that the traditional pore network model cannot consider the characteristics of boundary slippage, effective viscosity change of fluid and the like when the fluid flows in the nanometer pores.
2. The pore network model established by the invention has been developed to simulate the flow of single-phase Newtonian fluid in compact rock and the prediction of permeability, and the predicted apparent permeability considers the slip effect of the liquid and the influence of the change of the effective viscosity of the fluid, thereby more accurately describing the flow of the liquid in the nano-porous medium.
Drawings
FIG. 1 is a block flow diagram of a dense oil flow simulation and permeability prediction method based on a pore network model according to the present invention;
FIG. 2 is a comparison graph of the flow effect of a simulated single-phase Newtonian fluid in a nano-channel obtained by respectively considering the flow characteristics of the fluid at the nano-scale in comparison with the flow characteristics of the fluid at the nano-scale in the prior art and the flow characteristics of the fluid at the nano-scale in the prior art;
FIG. 3 is a schematic diagram comparing the velocity field of the flow in the nanochannel for comparative and example examples.
FIG. 4 is a schematic diagram showing the permeability of the pore network model established in the example in comparison with the permeability of the comparative example.
Detailed Description
The invention is further defined in the following, but not limited to, the figures and examples in the description.
Examples
A method for simulating flow of dense oil and predicting permeability based on a pore network model is applied to simulating single-phase fluid flow and permeability prediction in dense rock, as shown in figure 1, an initial simulation state is set as saturated water in the pore network model, then a periodic pressure boundary condition is set in an X direction, and no flow boundary exists in a Y direction and a Z direction, and comprises the following steps:
(1) scanning the compact rock core through a scanning electron microscope to obtain a two-dimensional electron microscope picture, and acquiring the geometrical information of the porous medium pore space: the geometrical information of the pore space of the porous medium comprises the shape, the size and the connection relation of pore throats;
(2) reconstructing the digital core by adopting a Markov chain-Monte Carlo (MCMC) numerical value based on the two-dimensional electron microscope picture obtained in the step (1) to obtain a geometric structure data file of the digital core; the geometric structure data file comprises each pixel point and a geometric structure corresponding to the pixel point, and the geometric structure comprises a rock core pore and a rock framework; for example, the geometric structure data file includes that each pixel point corresponds to 0 and 1, 0 represents that the current pixel point is a pore space, and 1 represents that the current pixel point is a rock skeleton. Among the references to the digital core reconstruction technique of markov chain-Monte Carlo Method (MCMC) are: wu K, Dijke MIJV, coupling G D, et al, 3D storage modeling of heterologous ports Media-Applications to memories Rocks [ J ]. Transport in ports Media,2006,65(3): 443-.
(3) Extracting the pore network model of the digital rock core in the step (2) by using a maximum sphere method to obtain a compact rock core pore network model data file; the pore network model data file comprises a pore throat section shape factor, a pore throat radius, a pore throat length, a pore throat position, a pore throat connection relation and a pore throat average coordination number; among the references of the maximum sphere algorithm are: morning, carbonate rock medium double-pore network model construction theory and method [ D ]. Qingdao, China university of Petroleum (east China), 2013, Chapter 2 of doctor thesis;
(4) for each pore in the pore network model to conserve mass, for incompressible fluids, volume conservation must be met, as shown in equation (I):
in the formula (I), I and j refer to any two adjacent pores in the pore network model; q. q.sijIs the volume flow, P, flowing from the adjacent aperture j into the aperture i through its interconnected throatsiIs the pressure in the pore i, gijIs the hydraulic conductivity connecting pore i and pore j throat; pjIs the pressure in the pore j.
Solving a system of equations to obtainObtaining the pressure of each pore and the volume flow of each pore throat, thereby obtaining the flow condition of the fluid in the nano-scale pore network model; as shown in fig. 2, b in fig. 2 is a schematic diagram of the effect of the simulated single-phase newtonian fluid flow in the nanoporous medium obtained by the embodiment; l issIs the slip length. As shown in fig. 3, b in fig. 3 is a schematic diagram of the velocity field flowing in the nanochannel according to the present embodiment;
(5) and obtaining the fluid volume flow at the outlet end of the pore network model, and calculating the apparent permeability of the pore network model according to Darcy's law. The calculation formula is shown in formula (III):
in formula (III), K is the apparent permeability of the pore network model, μ is the bulk fluid viscosity, L is the model length, A is the flow cross-sectional area, and Δ P is the flow pressure differential.
In the step (4), the hydraulic conductivity g of a channel connecting the pore i and the pore jijThe method is obtained by computational fluid dynamics modeling analysis, the speed slippage of a solid-liquid boundary and the change of the effective viscosity of the fluid caused by the existence of an interface layer are considered in the modeling process, and the calculation formula is shown as the formula (II):
in formula (II), A is the cross-sectional area of the channel, and μ is the fluid bulk viscosity; g is the shape factor, k is the critical thickness, P is the circumference of the throat section, LsdIs the dimensionless slip length, h is the viscosity coefficient, which is the ratio of the boundary layer fluid viscosity to the macroscopic fluid viscosity; a. b, c, d, e, f are empirical constants obtained by fitting the data, and when G is equal to or greater than 0.04, a is-0.16, b is 0.12, c is 6.4, d is-0.0055, e is-50, f is 1.7, and when G is equal to or greater than 0.04, G is equal to or greater than-0.16, d is equal to or greater than-0.4, e is equal to or greater than-50, and f is equal to or greater than 1.7<0.04, a ═ 0.012, b ═ 0.057, c ═ 2, d ═ 0.0052, e ═ 38, and f ═ 3.2.
Comparative example
According to the embodiment, the method for simulating the flow of the dense oil and predicting the permeability based on the pore network model is characterized in that,
the hydraulic conductivity of the channel connecting pore i and pore j is:
the formula for solving the hydraulic conductivity of the circular capillary is shown as the formula (IV):
the formula for solving the hydraulic conductivity of the square capillary is shown as the formula (V):
the formula for solving the hydraulic conductivity of the triangular capillary is shown as the formula (VI):
as shown in FIG. 2, a in FIG. 2 is a schematic diagram illustrating the effect of simulating the flow of a single-phase Newtonian fluid in a nano-scale porous medium obtained by a comparative example without considering the flow characteristics of the fluid at the nano-scale; the liquid flow rate at the solid-liquid interface was 0.
As shown in fig. 3, a in fig. 3 is a schematic diagram of the velocity field flowing in the nanochannel according to the present comparative example; all other conditions were the same, and the single-tube flow for the comparative example was about 1/2 for the example flow, with only the slip boundary conditions being different.
The capillary conductivity does not take into account the characteristics of the fluid flowing at the nanoscale, i.e., the boundary slip and the effect of the effective viscosity of the fluid on the flow. The permeability of nanoporous media (e.g., tight oil reservoirs) cannot be accurately predicted by virtue of pore network models developed by the model.
FIG. 4 compares the difference between the permeability of the pore network model established in the examples and the permeability of the comparative examples, and shows the effect of boundary slip and fluid effective viscosity change on the apparent permeability of the nanoporous media. The apparent permeability of the pore network model obtained in the comparative example is the comparative basis for the normalized permeability. In comparison, the apparent permeability of the porous medium under the slip condition is much higher than that under the no-slip condition. And under slip conditions, changes in the effective viscosity of the fluid caused by the presence of the interfacial layer will have a significant effect on the apparent permeability of the porous media. Boundary slip is the main reason why the permeability of dense porous media (nanoporous media) is higher than that predicted by darcy's law.
Claims (5)
1. A dense oil flow simulation and permeability prediction method based on a pore network model is characterized by comprising the following steps:
(1) scanning the compact rock core to obtain a two-dimensional electron microscope picture, and acquiring the pore space geometrical information of the porous medium: the geometrical information of the pore space of the porous medium comprises the shape, the size and the connection relation of pore throats;
(2) numerically reconstructing the digital core based on the two-dimensional electron microscope picture obtained in the step (1) to obtain a geometric structure data file of the digital core; the geometric structure data file comprises each pixel point and a geometric structure corresponding to the pixel point, and the geometric structure comprises a rock core pore and a rock framework;
(3) extracting the pore network model of the digital rock core in the step (2) to obtain a compact rock core pore network model data file; the pore network model data file comprises a pore throat section shape factor, a pore throat radius, a pore throat length, a pore throat position, a pore throat connection relation and a pore throat average coordination number;
(4) for each pore in the pore network model to conserve mass, for incompressible fluids, volume conservation must be met, as shown in equation (I):
in the formula (I), I and j refer to pore network modelsAny two adjacent apertures; q. q.sijIs the volume flow, P, flowing from the adjacent aperture j into the aperture i through its interconnected throatsiIs the pressure in the pore i, gijIs the hydraulic conductivity connecting pore i and pore j throat; pjIs the pressure in the pore j;
solving the system of equations to obtain the pressure at each pore and the volume flow rate at each pore throat, thereby obtaining the flow condition of the fluid in the nano-scale pore network model;
in the step (4), the hydraulic conductivity g of the channel connecting the pore i and the pore jijThe fluid dynamic modeling analysis is carried out to obtain the fluid dynamic modeling analysis, and the calculation formula is shown as the formula (II):
in formula (II), A is the cross-sectional area of the channel, and μ is the fluid bulk viscosity; g is the shape factor, k is the critical thickness, P is the circumference of the throat section, LsdIs the dimensionless slip length, h is the viscosity coefficient, which is the ratio of the boundary layer fluid viscosity to the macroscopic fluid viscosity; a. b, c, d, e, f are empirical constants obtained by fitting the data, and when G is equal to or greater than 0.04, a is-0.16, b is 0.12, c is 6.4, d is-0.0055, e is-50, f is 1.7, and when G is equal to or greater than 0.04, G is equal to or greater than-0.16, d is equal to or greater than-0.4, e is equal to or greater than-50, and f is equal to or greater than 1.7<0.04, a ═ 0.012, b ═ 0.057, c ═ 2, d ═ 0.0052, e ═ 38, and f ═ 3.2;
(5) and obtaining the fluid volume flow Q at the outlet end of the pore network model, and calculating the apparent permeability of the pore network model according to Darcy's law.
2. The method for dense oil flow simulation and permeability prediction based on a pore network model is characterized in that in the step (5), the apparent permeability of the pore network model is calculated according to Darcy's law; the calculation formula is shown in formula (III):
in formula (III), K is the apparent permeability of the pore network model, μ is the bulk fluid viscosity, L is the model length, A is the flow cross-sectional area, and Δ P is the flow pressure differential.
3. The method for simulating flow of dense oil and predicting permeability of the pore network model according to claim 1, wherein in the step (1), the dense core is scanned by a scanning electron microscope to obtain a two-dimensional electron microscope picture.
4. The method for simulating dense oil flow and predicting permeability based on a pore network model according to claim 1, wherein in the step (2), the digital core is reconstructed by using a Markov chain-Monte Carlo method numerical value to obtain a geometric data file of the digital core.
5. The method for simulating dense oil flow and predicting permeability based on the pore network model according to claim 1, wherein the pore network model of the digital core in the step (2) is extracted by a maximum sphere method to obtain a dense core pore network model data file.
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