CN113984590B - Method for calculating space tortuosity and gas diffusion coefficient distribution of heterogeneous rock - Google Patents
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Abstract
The invention provides a method for calculating the space tortuosity and gas diffusion coefficient distribution of heterogeneous rock, and belongs to the technical field of geology and petroleum engineering. The method of the invention utilizes low-field nuclear magnetic resonance to obtain one-dimensional proton density distribution and space T 2 The distribution fully considers the influence of the heterogeneous characteristics of the rock on the diffusion of the gas in the fully liquid saturated rock, carries out accurate quantitative characterization on the pore structure of each position of the rock, obtains the tortuosity and the gas diffusion coefficient distribution of each position of the heterogeneous rock, has the remarkable advantages of no damage, accuracy, time saving, labor saving, money saving and the like, completely meets the requirements of standardization and batch production of the core analysis industry, and is suitable for popularization and application.
Description
Technical Field
The invention belongs to the technical field of geology and petroleum engineering, and relates to a method for calculating the space tortuosity and gas diffusion coefficient distribution of heterogeneous rocks.
Background
Diffusion is one of the main modes of movement of gas molecules throughout the geologic process of formation, migration, aggregation and loss of subsurface gas resources (natural gas, carbon dioxide, helium, etc.), and is mainly due to diffusion of gas molecules in the rock by concentration differences, as the pores of subsurface rock are typically saturated with fluids (oil, gas, water, etc.). The diffusion coefficient is a physical quantity for measuring the diffusion capacity of gas molecules, and is also one of key parameters for quantitatively describing the underground gas resource hiding and developing process.
Currently, for gas diffusion coefficients in underground rock, mainly through experimental measurement, related industry standards (methods for measuring hydrocarbon gas diffusion coefficients in SY/T6129-2016 rock) have been developed, and Liu et al (New insights into natural gas diffusion coefficient in rocks [ J ]. Petroleum Exploration and Development,2012,39 (5): 597-604.) describe and summarize commonly used measurement methods in detail. However, the measurement experiment method is expensive in equipment, complex in operation, long in time consumption, and relatively large in influence on the accuracy of experimental results due to experimental conditions and personnel operation, and is not suitable for batch rock core experimental measurement (the technical details of hydrocarbon gas diffusion coefficient determination in rock are shallow analysis [ J ]; petroleum and chemical equipment; 2019 in 05). In addition, the core is used as a 'black box' homogeneous model by the measuring method, and the influence of the heterogeneity of the rock structure on the gas diffusion coefficient is not considered. In the lengthy geological history, however, the combined effects of sediments, diagenetic and post-formation effects are experienced such that the spatial distribution of the rock, as well as various internal properties (e.g., porosity, permeability, pore structure, etc.), are of a non-homogeneous nature, and the rock non-homogeneity is absolute, unconditional, infinite, and therefore, in order to improve the accuracy of the gas diffusion coefficient measurements, the rock non-homogeneity effects must be considered.
Disclosure of Invention
In order to solve the problems, the invention provides a method for calculating the spatial tortuosity and the gas diffusion coefficient distribution of heterogeneous rock, and the accuracy of the diffusion coefficient measurement method is improved. To obtain heterogeneous rock heterogeneous characteristics, low-field nuclear magnetic resonance technology is used for measuring one-dimensional proton density distribution and space T of heterogeneous rock core completely saturated by fluid (hydrogen-containing fluid such as water, oil and the like) 2 And (3) distributing to obtain the porosity of each position of the heterogeneous core and the pore distribution of each position. It is assumed that the pore channels in each location in the heterogeneous core consist of parallel channels of the same length and the same pore size, and the pore length and pore size of each location are different. Based on nuclear magnetic resonance theory and porous medium fractal theory, calculating to obtain each position of heterogeneous rock coreAnd calculating the pore number and the average pore diameter of each position of the heterogeneous core through the pore rate of each position of the heterogeneous core to obtain the tortuosity of each position pore channel of the heterogeneous core. And correcting the diffusion coefficient of gas (natural gas, carbon dioxide, helium and the like) in a large-volume medium (such as water, oil, gas and the like) through the tortuosity of pore channels at each position of the heterogeneous rock core to obtain space effective diffusion coefficient distribution. And finally, carrying out integrated calculation on the tortuosity of the pore channels at each position of the heterogeneous core to obtain the overall tortuosity of the heterogeneous core, and correcting the diffusion coefficient of the gas in a large-volume medium through the overall tortuosity of the heterogeneous core so as to obtain the overall effective diffusion coefficient of the gas in the fully saturated heterogeneous core.
The technical scheme adopted by the invention is as follows:
a method for calculating the spatial tortuosity and gas diffusion coefficient distribution of heterogeneous rock comprises the following steps:
step 1: core sample preparation
And (3) preparing the rock to be tested into a plunger-shaped core sample, putting the core into an incubator to remove water in the core, cooling to room temperature, and measuring parameters of the diameter and length of the core. And then placing the core into a fluid (hydrogen-containing fluid such as water, oil and the like), and vacuumizing until the core is completely saturated.
Step 2: acquiring one-dimensional proton density distribution and space T of completely fluid saturated heterogeneous rock core 2 Distribution of
Obtaining one-dimensional proton density distribution and space T of the completely fluid saturated heterogeneous core obtained in step 1 by using low-field nuclear magnetic resonance 2 Distribution; one-dimensional proton density distribution and space T 2 The heterogeneous rock core to be measured is divided into n layers, wherein each layer has the same thickness, and n is a positive integer; the one-dimensional proton density distribution reflects the distribution condition of the water content of the core, and each data point represents the water content V of the sheet layer at the position w,i I is each position of the heterogeneous core, i=1, 2, …, n; space T 2 Distribution reflects the content of the core 1 Spatial transverse relaxation time distribution of H proton fluid through space T 2 Distribution to obtain the contents of different slices in the core 1 H proton fluid at different scalesDistribution of content in porosity.
In addition, the volume of each position of the heterogeneous core is calculated to be V from the diameter of the heterogeneous core and the thickness of each layer i The porosity of each position of the heterogeneous core is:
step 3: calculating fractal dimension of pore at each position of heterogeneous core
Space T using heterogeneous cores 2 Distribution, T of each position is calculated by formula (2) 2,i Corresponding fluid volume V T2,i The total fluid volume V of the position w,i Percentage S of (2) v,i ：
From the nuclear magnetic resonance transverse relaxation mechanism, when the core pores are saturated with a fluid, the relaxation time T 2 Positive correlation with pore radius r:
from petrophysics, there is a relationship between rock capillary pressure and pore size:
obtaining the rock capillary pressure P through formulas (3) and (4) c And relaxation time T 2 Relationship between:
wherein F is s Is a geometric form factor; ρ is the holeT of the clearance surface 2 Relaxation intensity (μm/ms); r is the pore radius (cm); p (P) c Is the capillary pressure (Mpa) at an aperture r; σ is the surface tension (mN/m) of the pore fluid; θ is the contact angle between the pore fluid and the pore surface.
The fractal expressions of the capillary pressure curve of the known core are shown as a formula (6), and the fractal expressions of different positions of the heterogeneous core obtained based on the formulas (5) and (6) are shown as a formula (7):
wherein P is cmin Is the capillary pressure at a pore diameter r, T 2max,i For the transverse relaxation time corresponding to the maximum pore in the core, D f,i Fractal dimension of pores for each position of the core.
Taking the logarithm of two sides of the formula (7):
lgS v,i ＝(3-D f,i )lgT 2,i +(D f,i -3)lgT 2max,i (8)
by low-field nuclear magnetic resonance space T 2 Distribution to obtain T of each position of heterogeneous rock core 2 The distribution is circularly calculated by a formula (8) to obtain the pore fractal dimension D of each position of the heterogeneous rock core f,i And accurately and quantitatively characterizing the complex pore channel structure of the heterogeneous rock core.
Step 4: calculating tortuosity of pore channels at each position of heterogeneous core
It is assumed that the pore channels in each location in the heterogeneous core consist of parallel channels of the same length and the same pore size. Through space T 2 Obtaining pore structure information of different positions of the heterogeneous rock core by distribution, and obtaining relaxation time T by a formula (3) 2 Formula T related to pore diameter lambda 2 Theoretically proportional to the pore diameter lambda:
where lambda is the pore diameter,
is a conversion coefficient.
Based on porous medium fractal theory and core space T 2 Distribution calculating the number N of pore channels of each position core i ：
Wherein N is i Is the pore number lambda of each position of the heterogeneous rock core max,i 、λ min,i The maximum pore channel diameter and the minimum pore channel diameter of each position of the heterogeneous core are respectively.
The probability formula (11) of pore distribution shows the percentage of the number of pores to the number of pores with the pore diameter lambda, and the average pore diameter lambda of each position of the heterogeneous core is obtained according to the formula (11) av,i As formula (12):
by obtaining the average pore diameter lambda of each position of the heterogeneous core av,i And the number of pores N i And calculating the pore volume of each position of the heterogeneous core to obtain the average length of the pore channel of each position of the heterogeneous core, thereby obtaining the tortuosity of the pore channel of each position of the heterogeneous core:
wherein τ i Tortuosity of pore channel at each position of heterogeneous rock core, L av,i Average length of pore channel at each position of heterogeneous core, L i For the length of each location of the heterogeneous core,
the porosity of each position of the heterogeneous core is represented by A, and the cross-sectional area of the heterogeneous core is represented by A.
Due to the porosity and T at various locations of the heterogeneous core 2 The obtained heterogeneous core has larger differences in pore numbers, average pore radius and pore channel tortuosity at each position. Therefore, the problem of gas diffusion in rock needs to be fully considered on the influence of the heterogeneity of the core pore structure.
Step 5: calculating effective diffusion coefficient distribution of gas in heterogeneous rock core
And 4, obtaining the tortuosity of the pore channel at each position of the heterogeneous core, obtaining the diffusion coefficient of gas (natural gas, carbon dioxide, helium and the like) in a large-volume pure fluid (oil, gas, water and the like) under different temperature and pressure conditions through checking data, and correcting the diffusion coefficient of the gas in the large-volume pure fluid medium by utilizing the tortuosity of the pore channel at each position of the heterogeneous core to obtain the space effective diffusion coefficient distribution as shown in the formula (14):
wherein D is e,i For the effective diffusion coefficient of the gas in the fluid saturation core at each location, D is the diffusion coefficient of the gas in the bulk pure fluid.
Step 6: integrated calculation of tortuosity and diffusion coefficient of integral pore channel of heterogeneous core
Because the heterogeneous core is in a serial form at each position, the tortuosity tau of the pore channel at each position of the heterogeneous core is calculated by the formula (15) i Proceeding withIntegrating calculation to obtain tortuosity tau of the integral pore channel of the heterogeneous core:
the effective diffusion coefficient of the gas in the core is:
wherein D is e Is the effective diffusion coefficient of gas in the fluid saturation core.
The invention has the beneficial effects that: the invention relates to a method for calculating the space tortuosity and gas diffusion coefficient distribution of heterogeneous rock, which utilizes low-field nuclear magnetic resonance to obtain one-dimensional proton density distribution and space T 2 The distribution fully considers the influence of the heterogeneous characteristics of the rock on the diffusion of the gas in the fully liquid saturated rock, carries out accurate quantitative characterization on the pore structure of each position of the rock, obtains the tortuosity and the gas diffusion coefficient distribution of each position of the heterogeneous rock, has the remarkable advantages of no damage, accuracy, time saving, labor saving, money saving and the like, completely meets the requirements of standardization and batch production of the core analysis industry, and is suitable for popularization and application.
Drawings
Fig. 1 is a flow chart of a method.
FIG. 2 heterogeneous core porosity distribution.
FIG. 3 shows the nuclear magnetic resonance space T of a heterogeneous core in a fully brine saturated state 2 Distribution.
Fig. 4 is a fractal dimension for various locations of a heterogeneous core.
Fig. 5 is a graph of the number of pores at various locations of the heterogeneous core.
Fig. 6 shows the average pore radius for each location of the heterogeneous core.
Fig. 7 is tortuosity for various locations of a heterogeneous core.
Fig. 8 is a heterogeneous core diffusion coefficient profile.
Detailed Description
The invention is further described with reference to the drawings and the technical scheme.
As shown in fig. 1, a method for calculating the tortuosity and gas diffusion coefficient of heterogeneous rock comprises the following steps:
step 1: core sample preparation
Selecting typical outcrop sandstone Berea (permeability of 250-350 md) as rock to be measured, preparing the rock to be measured into a plunger-shaped rock core, putting the rock core into an incubator, heating the rock core to 110 ℃, drying the inside water to constant weight, then putting the rock core into a dryer, cooling to room temperature, and measuring the diameter of the rock core to be 2.52cm and the length of the rock core to be 4.40cm. And then the core is put into salt water, the core is vacuumized by a vacuum pump until no bubbles overflow, the vacuum is maintained for more than 48 hours, the core is fully saturated with the salt water, and the core which is fully saturated with the salt water is taken out.
Step 2: acquisition of one-dimensional proton density distribution and space T of fully fluid saturated heterogeneous core by nuclear magnetic resonance 2 Distribution of
The heterogeneous core has a length of 4.40cm and is divided into 40 layers, and the thickness of each layer is 0.11cm. Obtaining one-dimensional proton density distribution and space T of the completely fluid saturated heterogeneous core obtained in step 1 by using low-field nuclear magnetic resonance 2 Distribution, and further obtaining the water content and T of each layer of the heterogeneous rock core 2 Distribution. Calculating to obtain the volume of each layer of core to be 2.20cm 3 And obtaining the porosity of each layer of the rock core through the water content of each layer of the heterogeneous rock core and the volume of each layer of the rock core.
Step 3: calculating pore fractal dimension of each position of heterogeneous core
Through the space T of the heterogeneous core under the full salt water saturation state measured in the step 2 2 Distributing to obtain each layer of core T 2 Distribution. Respectively calculating different T of each layer 2 Corresponding fluid volume V at value T2 The total fluid volume V of the layer w,i Percentage S of (2) v,i . Directly for each layer of core T 2 Distributed lgT 2,i And lgS v,i The data is subjected to linear regression analysis, and the slope K of a straight line is fitted i ＝3-D f,i Solving to obtain fractal dimension D of each layer of rock core pore f,i 。
Step 4: calculating tortuosity of pore channels at each position of heterogeneous core
According to the nuclear magnetic resonance principle, the T of the completely saline saturated heterogeneous rock core 2 The distribution can reflect the internal structure of the rock and the transverse relaxation time T 2 Is in linear proportion to the theory of the aperture r. Thus, by saturating the heterogeneous core space T 2 And obtaining the pore size distribution of the core at each position by distribution. Based on porous medium fractal theory and core space T 2 And (3) calculating the distribution to obtain the number and average pore diameter of pores at each position in the heterogeneous core, and then calculating the tortuosity of each position in the heterogeneous core.
Step 5: calculating effective diffusion coefficient distribution of gas in heterogeneous rock core
According to literature (Guo HR, chen Y, lu WJ, et al in situ Raman spectroscopic study of diffusion coefficients of methane in liquid water under high pressure and wide temperatures), when the subsurface depth is 3km, the pressure is 31Mpa, the temperature is 403K, and the diffusion coefficient of methane in pure brine d=9.34×10 -9 (m 2 And/s), calculating the effective diffusion coefficient of methane at each position in the pure brine saturated heterogeneous core under the condition by using the tortuosity of the pore channel at each position of the heterogeneous core obtained in the step 4.
Step 6: integrated calculation of tortuosity and diffusion coefficient of integral pore channel of heterogeneous core
And (3) integrating and calculating the tortuosity of the pore channel of each position of the heterogeneous core obtained in the step (4) to obtain the tortuosity tau=6.63 of the whole pore channel of the heterogeneous core.
In addition, the overall tortuosity of the core is 6.77 measured by a resistivity method, and the core is well matched with the calculation result of the method. Correcting the diffusion coefficient of methane in pure brine at the pressure of 31Mpa and the temperature of 403K when the underground depth is 3km by using the tortuosity of the integral pore channel of the heterogeneous core to obtain the integral diffusion coefficient D of methane in the pure brine saturated heterogeneous core under the condition e ＝1.41*10 -9 (m 2 /s)。
Claims (1)
1. A method of calculating the spatial tortuosity and gas diffusion coefficient distribution of a heterogeneous rock, the method comprising the steps of:
step one: core sample preparation
Preparing a plunger-shaped core sample from rock to be measured, heating and drying the core to constant weight, cooling to room temperature, and measuring parameters of the diameter and length of the core; then placing the core into fluid, and vacuumizing until the core is completely saturated;
step two: acquiring one-dimensional proton density distribution and space T of completely fluid saturated heterogeneous rock core 2 Distribution the one-dimensional proton density distribution and the space T of the completely fluid saturated heterogeneous core obtained in the first step are obtained by using low-field nuclear magnetic resonance 2 Distribution; one-dimensional proton density distribution and space T 2 The heterogeneous rock core to be measured is divided into n layers, wherein each layer has the same thickness, and n is a positive integer; the one-dimensional proton density distribution reflects the water content V of each sheet w,i I is each position of the heterogeneous core, i=1, 2, …, n; the water content V of each position of the heterogeneous rock core w,i Volume V of each position i Obtaining the porosity of each position
Step three: based on nuclear magnetic resonance theory and porous medium fractal theory, the core space T is passed through 2 Calculating the fractal dimension of the pore at each position of the distribution; the calculation process is as follows:
space T using heterogeneous cores 2 Distribution, calculate T of each position 2,i Corresponding fluid volume V T2,i The total fluid volume V of the position w,i Percentage S of (2) v,i ：
Rock capillary pressure P c And relaxation time T 2 Relationship between:
wherein F is s Is a geometric form factor; ρ is T of the pore surface 2 Relaxation intensity, μm/ms; r is pore radius, cm; p (P) c Is the capillary pressure, mpa, when the pore size is r; sigma is the surface tension of the pore fluid, mN/m; θ is the contact angle between the pore fluid and the pore surface;
the fractal expressions of the capillary pressure curve of the known core are shown as a formula (6), and the fractal expressions of different positions of the heterogeneous core obtained based on the formulas (5) and (6) are shown as a formula (7):
wherein P is cmin Is the capillary pressure at a pore diameter r, T 2max,i For the transverse relaxation time corresponding to the maximum pore in the core, D f,i Fractal dimension of pores for each position of the core;
taking the logarithm of two sides of the formula (7):
lgS v,i ＝(3-D f,i )lgT 2,i +(D f,i -3)lgT 2max,i (8)
circularly calculating according to a formula (8) to obtain pore fractal dimension D of each position of the heterogeneous rock core f,i Accurately and quantitatively characterizing the complex pore channel structure of the heterogeneous rock core;
step four: calculating tortuosity of pore channels at each position of heterogeneous core
Through space T 2 Obtaining pore radius distribution of different positions of the heterogeneous rock core by distribution; based on porous medium fractal theory and space T 2 Distribution calculationThe number of pores and the average pore diameter of each position of the heterogeneous core; obtaining the average length of the pore channel of each position of the heterogeneous core through the average pore diameter, the number of pores and the pore volume of each position of the heterogeneous core, and further obtaining the tortuosity of the pore channel of each position of the heterogeneous core; the calculation process is as follows:
the pore channels in each position in the heterogeneous rock core are formed by parallel channels with the same length and the same aperture; based on porous medium fractal theory and core space T 2 Distribution calculating the number N of pore channels of each position core i ：
Wherein N is i Is the pore number lambda of each position of the heterogeneous rock core max,i 、λ min,i The maximum pore channel diameter and the minimum pore channel diameter of each position of the heterogeneous rock core are respectively;
calculating the average pore diameter lambda of each position of the heterogeneous rock core av,i ：
By obtaining the average pore diameter lambda of each position of the heterogeneous core av,i And the number of pores N i And calculating the pore volume of each position of the heterogeneous core to obtain the average length of the pore channel of each position of the heterogeneous core, thereby obtaining the tortuosity of the pore channel of each position of the heterogeneous core:
wherein τ i Tortuosity of pore channel at each position of heterogeneous rock core, L av,i Average length of pore channel at each position of heterogeneous core, L i For the length of each location of the heterogeneous core,
the porosity of each position of the heterogeneous core, A is the cross-sectional area of the heterogeneous core;
step five: calculating effective diffusion coefficient distribution of gas in heterogeneous rock core
The diffusion coefficient of the gas in the large-volume pure fluid is corrected through the tortuosity of pore channels at each position of the heterogeneous rock core under different temperature and pressure conditions, so that the effective diffusion coefficient distribution of the gas in the saturated heterogeneous rock core is obtained:
wherein D is e,i For each position, the effective diffusion coefficient of the gas in the fluid saturated core is D, the diffusion coefficient of the gas in the large-volume pure fluid; τ i Tortuosity of pore channels at each position of the heterogeneous core;
step six: integrated calculation of tortuosity and diffusion coefficient of integral pore channel of heterogeneous core
Because the heterogeneous core is in a serial form at each position, the tortuosity tau of the pore channel at each position of the heterogeneous core is calculated by the formula (2) i And (3) carrying out integration calculation to obtain tortuosity tau of the integral pore channel of the heterogeneous core:
the effective diffusion coefficient of the gas in the core is:
wherein D is e Is a gasEffective diffusion coefficient in fluid saturated core.
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