CN113984590A - Method for calculating spatial tortuosity and gas diffusion coefficient distribution of heterogeneous rock - Google Patents

Method for calculating spatial tortuosity and gas diffusion coefficient distribution of heterogeneous rock Download PDF

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CN113984590A
CN113984590A CN202111284191.5A CN202111284191A CN113984590A CN 113984590 A CN113984590 A CN 113984590A CN 202111284191 A CN202111284191 A CN 202111284191A CN 113984590 A CN113984590 A CN 113984590A
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赵越超
宋永臣
黄明星
毛晓坤
张毅
杨明军
郑嘉男
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Dalian University of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
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    • G01N13/00—Investigating surface or boundary effects, e.g. wetting power; Investigating diffusion effects; Analysing materials by determining surface, boundary, or diffusion effects
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    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N15/00—Investigating characteristics of particles; Investigating permeability, pore-volume, or surface-area of porous materials
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    • G01N15/088—Investigating volume, surface area, size or distribution of pores; Porosimetry
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    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N24/00—Investigating or analyzing materials by the use of nuclear magnetic resonance, electron paramagnetic resonance or other spin effects
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    • G01N24/081—Making measurements of geologic samples, e.g. measurements of moisture, pH, porosity, permeability, tortuosity or viscosity
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    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N13/00—Investigating surface or boundary effects, e.g. wetting power; Investigating diffusion effects; Analysing materials by determining surface, boundary, or diffusion effects
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Abstract

The invention provides a method for calculating spatial tortuosity and gas diffusion coefficient distribution of heterogeneous rocks, and belongs to the technical field of geological and petroleum engineering. The method of the invention obtains one-dimensional proton density distribution and space T by using low-field nuclear magnetic resonance2And distribution, wherein the influence of the heterogeneous characteristics of the rock on the diffusion of gas in the completely liquid saturated rock is fully considered, the pore structure of each position of the rock is accurately and quantitatively characterized, the tortuosity and the gas diffusion coefficient distribution of each position of the heterogeneous rock are obtained, the method has the remarkable advantages of no damage, accuracy, time saving, labor saving, money saving and the like, the standardization and batch requirements of the rock core analysis industry are completely met, and the method is suitable for popularization and application.

Description

Method for calculating spatial tortuosity and gas diffusion coefficient distribution of heterogeneous rock
Technical Field
The invention belongs to the technical field of geological and petroleum engineering, and relates to a method for calculating spatial tortuosity and gas diffusion coefficient distribution of heterogeneous rocks.
Background
Diffusion is one of the main modes of movement of gas molecules throughout the geological process of formation, migration, accumulation and dissipation of underground gas resources (natural gas, carbon dioxide, helium, etc.), and since the pores of underground rocks are usually saturated with fluids (oil, gas, water, etc.), the diffusion of gas molecules in rocks is mainly diffusion through these pore fluid media under the action of concentration differences. 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 process of underground gas resource accumulation and development.
At present, the diffusion coefficient of gases in underground rocks is mainly measured through experiments, related industry standards (determination method of the diffusion coefficient of hydrocarbons in SY/T6129-. However, the measurement experiment method is expensive in equipment, complex in operation, long in time consumption, large in influence of experiment conditions and personnel operation on accuracy of experiment results, and not suitable for batch rock core experiment measurement (shallow analysis [ J ] of hydrocarbon gas diffusion coefficient measurement technology details in rock; petroleum and chemical equipment; 2019, 05). In addition, the core is used as a 'black box' homogeneous model in the measuring method, and the influence of the heterogeneity of the rock structure on the gas diffusion coefficient is not considered. In a long geological history, comprehensive influences of deposition, diagenesis and later-period tectonic actions are experienced, so that heterogeneous characteristics exist in spatial distribution of rocks and various internal attributes (such as porosity, permeability, pore structure and the like), and the heterogeneous characteristics of the rocks are absolute, unconditional and infinite, so that the heterogeneous influence of the rocks must be considered in order to improve the accuracy of gas diffusion coefficient measurement.
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 the heterogeneous rock, and the accuracy of the diffusion coefficient measuring method is improved. In order to obtain the heterogeneous characteristics of the heterogeneous rock, the one-dimensional proton density distribution and the space T of the completely saturated heterogeneous rock core of the fluid (hydrogen-containing fluid such as water, oil and the like) are measured by using the low-field nuclear magnetic resonance technology2And (4) distribution, namely respectively obtaining the porosity and the pore distribution of each position of the heterogeneous rock core. Assuming that the pore channels in each location in the heterogeneous core are composed of parallel channels of the same length and the same pore diameter, the pore length and pore diameter at each location differ. Based on the nuclear magnetic resonance theory and the porous medium fractal theory, the number of pores and the average pore diameter of each position of the heterogeneous core are calculated, and then the tortuosity of pore channels of each position of the heterogeneous core is calculated through the porosity of each position 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 core to obtain the spatial effective diffusion coefficient distribution. And finally, integrating and calculating the tortuosity of pore channels at each position of the heterogeneous rock core to obtain the integral tortuosity of the heterogeneous rock core, and correcting the diffusion coefficient of the gas in a large-volume medium through the integral tortuosity of the heterogeneous rock core so as to obtain the integral effective diffusion coefficient of the gas in the fully saturated heterogeneous rock core.
The technical scheme adopted by the invention is as follows:
a method for calculating spatial tortuosity and gas diffusion coefficient distribution of heterogeneous rocks comprises the following steps:
step 1: core sample preparation
Preparing a plunger-shaped core sample from the rock to be measured, putting the core into a constant temperature box to remove water in the core, cooling to room temperature, and measuring the diameter and length parameters of the core. And putting the core into a fluid (water, oil and other hydrogen-containing fluids), and vacuumizing until the core is completely saturated.
Step 2: obtaining one-dimensional proton density distribution and space T of completely fluid saturated heterogeneous rock core2Distribution of
Acquiring one-dimensional proton density distribution and space T of the completely fluid saturated heterogeneous rock core obtained in the step 1 by using low-field nuclear magnetic resonance2Distributing; one-dimensional proton density distribution and space T2The distribution divides the heterogeneous rock core to be measured into n layers, the thickness of each layer is the same, wherein n is a positive integer; the one-dimensional proton density distribution reflects the distribution of the water content of the rock core, and each data point represents the water content V of the lamella at the positionw,iI is each position of the heterogeneous core, i is 1,2, …, n; space T2Distribution reflects core content1Spatial transverse relaxation time distribution of H proton fluid, passing through space T2Distributed to obtain different layers in the core1The content distribution of the H proton fluid in the pores with different sizes.
In addition, the volume V of each position of the heterogeneous core is calculated by the diameter of the heterogeneous core and the thickness of each layeriAnd then the porosity of each position of the heterogeneous core is as follows:
Figure BDA0003332365130000031
and step 3: calculating the fractal dimension of the pores at each position of the heterogeneous rock core
Space T using heterogeneous cores2Distribution, calculating T of each position by formula (2)2,iCorresponding fluid volume VT2,iTotal fluid volume V occupied at the locationw,iPercentage of (S)v,i：
Figure BDA0003332365130000032
As known from the transverse relaxation mechanism of nuclear magnetic resonance,relaxation time T when core porosity is saturated with a fluid2Positive correlation with pore radius r:
Figure BDA0003332365130000033
according to rock physics, the relationship between rock capillary pressure and pore size exists:
Figure BDA0003332365130000034
obtaining rock capillary pressure P through formulas (3) and (4)cAnd relaxation time T2The relationship between:
Figure BDA0003332365130000035
in the formula, FsIs a geometric form factor; ρ is T of the pore surface2Relaxation intensity (μm/ms); r is the pore radius (cm); pcIs the capillary pressure (Mpa) when the pore size is r; σ 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 expression of the capillary pressure curve of the known rock core is shown as a formula (6), and the fractal expressions of different positions of the heterogeneous rock core are obtained based on the formulas (5) and (6) and are shown as a formula (7):
Figure BDA0003332365130000041
Figure BDA0003332365130000042
wherein, PcminIs the capillary pressure at a pore diameter r, T2max,iTransverse relaxation time, D, corresponding to the largest pore in the coref,iThe fractal dimension of the pores at each position of the core.
Taking logarithm on two sides of the formula (7):
lgSv,i＝(3-Df,i)lgT2,i+(Df,i-3)lgT2max,i (8)
passing through a low-field nuclear magnetic resonance space T2Distributing to obtain T of each position of heterogeneous core2Distribution, and obtaining the pore fractal dimension D of each position of the heterogeneous rock core through the cyclic calculation of a formula (8)f,iAnd accurately and quantitatively characterizing the complex pore channel structure of the heterogeneous rock core.
And 4, step 4: calculating the tortuosity of pore channels at each position of the heterogeneous rock core
It is assumed that the pore channels in each location in the heterogeneous core are composed of parallel channels of the same length and the same pore size. Through space T2The pore structure information of different positions of the heterogeneous rock core is obtained through distribution, and the relaxation time T is obtained through the formula (3)2Equation of relation with pore diameter λ, T2Theoretically in direct proportion to the pore diameter λ:
Figure BDA0003332365130000043
wherein, λ is a pore diameter,
Figure BDA0003332365130000044
are conversion coefficients.
Based on porous medium fractal theory and core space T2Calculating the number N of pore channels of the rock core at each position in a distributed manneri：
Figure BDA0003332365130000045
In the formula, NiNumber of pores at each position of heterogeneous core, lambdamax,i、λmin,iThe maximum pore channel diameter and the minimum pore channel diameter of each position of the heterogeneous core are respectively.
Probability formula (11) of pore distributionObtaining the average pore diameter lambda of each position of the heterogeneous core according to the formula (11) when the number of pores with the pore diameter lambda accounts for the percentage of the number of poresav,iAs shown in formula (12):
Figure BDA0003332365130000051
Figure BDA0003332365130000052
obtaining average pore diameter lambda of each position of the heterogeneous coreav,iAnd number of pores NiAnd calculating the pore volume of each position of the heterogeneous core to obtain the average pore channel length of each position of the heterogeneous core, and further obtaining the pore channel tortuosity of each position of the heterogeneous core:
Figure BDA0003332365130000053
in the formula, τiTortuosity of pore channel for each position of heterogeneous core, Lav,iIs the average length of pore channels, L, of each position of the heterogeneous coreiThe length of each position of the heterogeneous core,
Figure BDA0003332365130000054
the porosity of each position of the heterogeneous core is shown, and A is the cross-sectional area of the heterogeneous core.
Porosity and T at various positions of heterogeneous core2The distribution is different, and the number of pores at each position, the average pore radius and the porosity of pore channels of the obtained heterogeneous rock core have larger difference. Therefore, the problem of gas diffusion in the rock needs to fully consider the influence of heterogeneous pore structure of the core.
And 5: calculating the effective diffusion coefficient distribution of gas in the heterogeneous core
And 4, obtaining the tortuosity of pore channels at each position of the heterogeneous core, obtaining the diffusion coefficients of gases (natural gas, carbon dioxide, helium and the like) in the large-volume pure fluid (oil, gas, water and the like) under different temperature and pressure conditions by looking up data, and correcting the diffusion coefficients of the gases in the large-volume pure fluid medium by using the tortuosity of the pore channels at each position of the heterogeneous core to obtain the distribution of the space effective diffusion coefficient as shown in the formula (14):
Figure BDA0003332365130000055
in the formula, De,iFor each location the effective diffusion coefficient of the gas in the fluid saturated core, 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 cores are in a serial connection mode at each position, the tortuosity tau of the pore channel at each position of the heterogeneous cores is obtained through a formula (15)iPerforming integrated calculation to obtain the tortuosity tau of the integral pore channel of the heterogeneous rock core:
Figure BDA0003332365130000061
the effective diffusion coefficient of the gas in the core is as follows:
Figure BDA0003332365130000062
in the formula, DeIs the effective diffusion coefficient of gas in a fluid saturated core.
The invention has the beneficial effects that: the invention discloses a method for calculating spatial tortuosity and gas diffusion coefficient distribution of heterogeneous rocks, which is used for obtaining one-dimensional proton density distribution and spatial T by utilizing low-field nuclear magnetic resonance2Distribution, fully considering the influence of rock heterogeneous characteristics on the diffusion of gas in the completely liquid saturated rock, and carrying out accurate quantitative characterization on the pore structure of each position of the rockThe tortuosity and gas diffusion coefficient distribution at each position of the heterogeneous rock are obtained, the method has the remarkable advantages of no damage, accuracy, time saving, labor saving, money saving and the like, completely meets the standardization and batch requirements of the core analysis industry, and is suitable for popularization and application.
Drawings
FIG. 1 is a block diagram of a process flow.
Fig. 2 heterogeneous core porosity distribution.
FIG. 3 shows NMR space T of heterogeneous core under full brine saturation2And (4) distribution.
Fig. 4 is a fractal dimension for each location of a heterogeneous core.
Fig. 5 is a graph of the number of pores at each location of the heterogeneous core.
Fig. 6 is an average pore radius for each location of the heterogeneous core.
Fig. 7 shows the tortuosity at each location of the heterogeneous core.
Fig. 8 is a non-homogeneous core diffusion coefficient distribution.
Detailed Description
The invention is further explained with reference to the drawings and technical solutions.
As shown in fig. 1, a method for calculating the tortuosity and the gas diffusion coefficient of the 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 detected, preparing the rock to be detected into a plunger-shaped core, putting the core into a constant temperature box, heating to 110 ℃, drying the internal water to constant weight, then putting the core into a dryer, cooling to room temperature, and measuring the diameter of the core to be 2.52cm and the length to be 4.40 cm. And then putting the core into the brine, vacuumizing the core by using a vacuum pump until no bubbles overflow, keeping the vacuum for more than 48 hours to ensure that the core is fully saturated with the brine, and taking out the core which is fully saturated with the brine.
Step 2: obtaining one-dimensional proton density distribution and space T of completely fluid saturated heterogeneous rock core by utilizing nuclear magnetic resonance2Distribution of
The length of the heterogeneous core is 4.40cm, the heterogeneous core is divided into 40 layers in total, and the thickness of each layer is0.11 cm. Acquiring one-dimensional proton density distribution and space T of the completely fluid saturated heterogeneous rock core obtained in the step 1 by using low-field nuclear magnetic resonance2Distributing to obtain the water content and T of each layer of the heterogeneous rock core2And (4) distribution. Calculating to obtain the volume of each layer of the rock core of 2.20cm3And obtaining the porosity of each layer of the core through the water content of each layer of the heterogeneous core and the volume of each layer of the core.
And step 3: calculating the fractal dimension of pores at each position of heterogeneous rock core
The space T of the heterogeneous rock core in the complete brine saturation state measured in the step 22Distributing to obtain each layer of rock core T2And (4) distribution. Respectively calculate different T of each layer2Fluid volume V corresponding to the valueT2Volume V of total fluid in the layerw,iPercentage of (S)v,i. Directly for each core T2Distributed lgT2,iAnd lgSv,iPerforming linear regression analysis on the data, and fitting the slope K of a straight linei＝3-Df,iSolving to obtain the fractal dimension D of the core hole of each layerf,i。
And 4, step 4: calculating the tortuosity of pore channels at each position of the heterogeneous rock core
T of fully brine saturated heterogeneous core according to nuclear magnetic resonance principle2The distribution can reflect the internal structure of the rock and transverse relaxation time T2Is theoretically linearly proportional to the aperture r. Thus, by saturating the heterogeneous core space T2And (4) distribution, wherein the pore size distribution of the core at each position can be obtained. Based on porous medium fractal theory and core space T2And (4) calculating distribution to obtain the number of pores at each position in the heterogeneous core and the average pore diameter, and then calculating the tortuosity at each position in the heterogeneous core.
And 5: calculating the effective diffusion coefficient distribution of gas in the heterogeneous core
According to the literature (Guo HR, Chen Y, Lu WJ, et al. in situ Raman spectroscopic study of diffusion coeffectives of methane in liquid water under high pressure and gas temperature), at a depth of 3km underground, a pressure of 31MPa, a temperature of 403K, and a methane diffusion in pure brineCoefficient of dispersion D9.34 x 10-9(m2And/s) calculating the effective diffusion coefficient of the 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 (4) integrating and calculating the tortuosity of the pore channel at each position of the heterogeneous core obtained in the step (4) to obtain the whole pore channel tortuosity tau of the heterogeneous core, which is 6.63.
In addition, the integral tortuosity of the rock core is measured to be 6.77 by a resistivity method, and the calculation result is better matched with the method. Correcting the diffusion coefficient of methane in pure saline water saturated heterogeneous core under the condition that the local depth is 3km, the pressure is 31Mpa, the temperature is 403K and the diffusion coefficient of methane in pure saline water is corrected to obtain the integral diffusion coefficient D of methane in the pure saline water saturated heterogeneous core under the conditione＝1.41*10-9(m2/s)。

Claims (3)

1. A method for calculating spatial tortuosity and gas diffusion coefficient distribution of heterogeneous rock, the method comprising the steps of:
the method comprises the following steps: core sample preparation
Preparing a plunger-shaped core sample from a rock to be measured, heating and drying the core to constant weight, cooling to room temperature, and measuring the diameter and length parameters of the core; putting the core into fluid, and vacuumizing until the core is completely saturated;
step two: obtaining one-dimensional proton density distribution and space T of completely fluid saturated heterogeneous rock core2Distribution of
Acquiring one-dimensional proton density distribution and space T of the completely fluid saturated heterogeneous rock core obtained in the first step by utilizing low-field nuclear magnetic resonance2Distributing; one-dimensional proton density distribution and space T2The distribution divides the heterogeneous rock core to be measured into n layers, the thickness of each layer is the same, wherein n is a positive integer; one-dimensional proton density distribution reflects the water content V of each sheetw,iI is each position of the heterogeneous core, i is 1,2,…, n; from water content V of heterogeneous core at various positionsw,iAnd volume V of each positioniObtaining the porosity of each position
Figure FDA0003332365120000011
Step three: based on nuclear magnetic resonance theory and porous medium fractal theory, the method passes through a rock core space T2Calculating the fractal dimension of pores at each position in a distributed manner;
step four: calculating the tortuosity of pore channels at each position of the heterogeneous rock core
Through space T2Distributing to obtain the pore radius distribution of different positions of the heterogeneous rock core; based on porous medium fractal theory and space T2The number of pores and the average pore diameter of each position of the heterogeneous rock core are calculated in a distributed mode; obtaining the average length of pore channels of each position of the heterogeneous core according to 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 channels of each position of the heterogeneous core;
step five: calculating the effective diffusion coefficient distribution of gas in the heterogeneous core
Correcting the diffusion coefficient of the gas in the large-volume pure fluid through the diffusion coefficients of the gas in the large-volume pure fluid under different temperature and pressure conditions and the tortuosity of pore channels at each position of the heterogeneous core to obtain the effective diffusion coefficient distribution of the gas in the saturated heterogeneous core:
Figure FDA0003332365120000021
in the formula, De,iFor each location the effective diffusion coefficient of the gas in the fluid saturated core, D is the diffusion coefficient of the gas in the bulk pure fluid; tau isiThe tortuosity of pore channels at each position of the heterogeneous rock core;
step six: integrated calculation of tortuosity and diffusion coefficient of integral pore channel of heterogeneous core
Due to heterogeneous coreThe positions are in series connection, and the tortuosity tau of the pore channel at each position of the heterogeneous rock core is obtained through the formula (2)iPerforming integrated calculation to obtain the tortuosity tau of the integral pore channel of the heterogeneous rock core:
Figure FDA0003332365120000022
the effective diffusion coefficient of the gas in the core is as follows:
Figure FDA0003332365120000023
in the formula, DeIs the effective diffusion coefficient of gas in a fluid saturated core.
2. The method according to claim 1, wherein the calculation process of the step three is as follows:
space T using heterogeneous cores2Distribution, calculating T at each position2,iCorresponding fluid volume VT2,iTotal fluid volume V occupied at the locationw,iPercentage of (S)v,i：
Figure FDA0003332365120000024
Rock capillary pressure PcAnd relaxation time T2The relationship between:
Figure FDA0003332365120000025
in the formula, FsIs a geometric form factor; ρ is T of the pore surface2Relaxation strength, μm/ms; r is the pore radius, cm; pcIs 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 expression of the capillary pressure curve of the known rock core is shown as a formula (6), and the fractal expressions of different positions of the heterogeneous rock core are obtained based on the formulas (5) and (6) and are shown as a formula (7):
Figure FDA0003332365120000026
Figure FDA0003332365120000031
wherein, PcminIs the capillary pressure at a pore diameter r, T2max,iTransverse relaxation time, D, corresponding to the largest pore in the coref,iForming fractal dimension of pores at each position of the rock core;
taking logarithm on two sides of the formula (7):
lgSv,i＝(3-Df,i)lgT2,i+(Df,i-3)lgT2max,i (8)
circularly calculating by a formula (8) to obtain the fractal dimension D of the pores at each position of the heterogeneous rock coref,iAnd accurately and quantitatively characterizing the complex pore channel structure of the heterogeneous rock core.
3. The method according to claim 1 or 2, wherein the calculation process of the step four is as follows:
setting pore passages in each position of the heterogeneous rock core to be composed of parallel passages with the same length and the same aperture; based on porous medium fractal theory and core space T2Calculating the number N of pore channels of the rock core at each position in a distributed manneri：
Figure FDA0003332365120000032
In the formula, NiNumber of pores at each position of heterogeneous core, lambdamax,i、λmin,iRespectively the maximum pore channel diameter and the minimum pore channel diameter of each position of the heterogeneous rock core;
calculating the average pore diameter lambda of each position of the heterogeneous rock coreav,i：
Figure FDA0003332365120000033
Obtaining average pore diameter lambda of each position of the heterogeneous coreav,iAnd number of pores NiAnd calculating the pore volume of each position of the heterogeneous core to obtain the average pore channel length of each position of the heterogeneous core, and further obtaining the pore channel tortuosity of each position of the heterogeneous core:
Figure FDA0003332365120000034
in the formula, τiTortuosity of pore channel for each position of heterogeneous core, Lav,iIs the average length of pore channels, L, of each position of the heterogeneous coreiThe length of each position of the heterogeneous core,
Figure FDA0003332365120000035
the porosity of each position of the heterogeneous core is shown, and A is the cross-sectional area of the heterogeneous core.
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