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CN110530777B - A method for obtaining the permeability of granular samples - Google Patents

A method for obtaining the permeability of granular samples Download PDF

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CN110530777B
CN110530777B CN201910944457.0A CN201910944457A CN110530777B CN 110530777 B CN110530777 B CN 110530777B CN 201910944457 A CN201910944457 A CN 201910944457A CN 110530777 B CN110530777 B CN 110530777B
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江文滨
林缅
周羁
曹高辉
姬莉莉
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Abstract

The embodiment of the invention relates to a method for acquiring the permeability of a particle sample, which can ensure that the square sum of the deviation between a pressure attenuation curve obtained by forward calculation of the determined permeability and an actually measured curve is minimum, and has wider applicability and reliability.

Description

Method for obtaining permeability of particle sample
Technical Field
The embodiment of the invention relates to the technical field of petroleum engineering, in particular to a method for acquiring the permeability of a particle sample.
Background
At present, the amount of the mined resources of the shale gas in China is rich, and the shale gas is one of the most strategic alternative energy sources. Shale reservoir evaluation is an important link of shale gas exploration and development, and permeability is one of important indexes of shale reservoir evaluation.
It can be seen from the scanning electron microscope image that organic matter pores, inter-particle (solution) pores, authigenic mineral intercrystalline pores and bedding seams, joint seams, erosion seams and the like are distributed in the shale, the scale of the shale spans six to seven orders of magnitude, and the difference of the seepage capability of pores (seams) with different scales is obvious. For the convenience of analysis, the void space in shale is generally divided into two stages, namely a matrix and a fracture, the matrix permeability is low, and the fracture permeability is high.
In the related technology, a method for determining permeability by adopting pressure decay curve fitting is adopted, permeability underestimation exists in partial samples during low-pressure testing, permeability underestimation exists in partial samples during high-pressure testing, and permeability underestimation exists in partial samples during low-pressure and high-pressure testing. The uncertainty of the result obtained by the existing method for determining the permeability by fitting the pressure attenuation curve is large, and troubles are brought to the understanding of the real seepage characteristics of the sample.
Disclosure of Invention
In view of this, in order to solve the problems in the prior art, embodiments of the present invention provide a method for obtaining a permeability of a particle sample.
In a first aspect, an embodiment of the present invention provides a method for obtaining permeability of a particle sample, where the method includes:
obtaining a curve P (t) of the pressure over time, the reference chamber volume VbVolume V of the sample chamber before the sample is placed thereinsTotal volume of sample VsbAverage particle radius RaTest temperature T and gas density rho of reference cavity before opening of test valve1And the gas density ρ of the sample chamber0；
Based on helium state equation, pressure decay curve P (t) final stable value P2And temperature T, calculating corresponding gas density ρ2And calculating the pore volume V of the samplePPorosity phi, volume ratio K of outer space to inner space of particle samplecAnd the average gas density ρ of the space outside the particles when the test valve is not openc0；
Determining the pressure P corresponding to the beginning of gas entry into the sample3Determining the pressure P from the curve P (t) of the pressure over time3Corresponding time t3；
Selecting all of the time points t greater than the time point3Based on the helium state equation, calculating the gas density rho (t) and the mass fraction FR(t) for ln (F)R(t)) all of which are greater than the time t3Linear fitting is carried out on the measured point and the time t to obtain a slope s1Obtaining a slope s from said1Calculation of the Permeability k0；
Determine permeability K', set K1 to K0And K' is the minimum value, K3 is K0And K', wherein K2 ═ (K1+ K3)/2;
respectively inputting K1, K2 and K3 into a preset mass fraction calculation algorithm, calculating pressure values FR1(T), FR2(T) and FR3(T) of all measuring points at the moment greater than T3, and respectively calculating FR1(T), FR2(T) and FR3(T) and the measured FRThe sum of the squares of the differences (t), denoted as D1, D2, and D3;
if D2 is the minimum of D1, D2 and D3 and the maximum two-by-two relative deviation of D1, D2 and D3 is less than the set value, the permeability is determined to be K2.
In one possible embodiment, the final stable value P is based on the helium state equation, the pressure decay curve P (t), using the following formula2And temperature T, calculating corresponding gas density ρ2Sample pore volume VPPorosity phi, volume ratio K of outer space to inner space of particle samplecAnd the mean gas density ρ of the space outside the particles (containing the reference chamber) when the test valve is not openc0：
Figure BDA0002223778590000031
Figure BDA0002223778590000032
Figure BDA0002223778590000033
Figure BDA0002223778590000034
In one possible embodiment, the pressure P corresponding to the beginning of the gas entering the sample is determined3The method comprises the following steps:
determination using a formula
Figure BDA0002223778590000035
Based on helium state equation, from rho3And temperature Tcalculated P3。
In one possible embodiment, the mass fraction FR(t) comprising:
Figure BDA0002223778590000036
in one possible embodiment, the slope s is obtained from the equation1Calculation of the Permeability k0：
Figure BDA0002223778590000037
Wherein R isaIs the radius of the particle sample; μ is the viscosity coefficient of the gas, cgIs the gas compression factor; alpha is alpha1Is a transcendental equation
Figure BDA0002223778590000038
1 root of (1).
In one possible embodiment, the permeability k' is determined using the following equation, including:
Figure BDA0002223778590000039
in one possible embodiment, the preset quality score calculating algorithm includes:
Figure BDA0002223778590000041
wherein alpha isnIs a transcendental equation
Figure BDA0002223778590000042
N times root.
According to the technical scheme provided by the embodiment of the invention, the curve P (t) of the pressure changing along with the time and the reference cavity volume V are obtainedbVolume V of the sample chamber before the sample is placed thereinsTotal volume of sample VsbAverage particle radius RaTest temperature T and gas density rho of reference cavity before opening of test valve1And the gas density ρ of the sample chamber0(ii) a Based on helium state equation, pressure decay curve P (t) final stable value P2And temperature T, calculating corresponding gas density ρ2And calculating the pore volume V of the samplePPorosity phi, volume ratio K of outer space to inner space of particle samplecAnd the average gas density ρ of the space outside the particles when the test valve is not openc0(ii) a Determining the pressure P corresponding to the beginning of gas entry into the sample3Determining the pressure P from the curve P (t) of the pressure over time3Corresponding time t3(ii) a Selecting all of the time points t greater than the time point3Based on the helium state equation, calculating the gas density rho (t) and the mass fraction FR(t) for ln (F)R(t)) all ofGreater than said time t3Linear fitting is carried out on the measured point and the time t to obtain a slope s1Obtaining a slope s from said1Calculation of the Permeability k0(ii) a Determine permeability K', set K1 to K0And K' is the minimum value, K3 is K0And K', wherein K2 ═ (K1+ K3)/2; respectively inputting K1, K2 and K3 into a preset mass fraction calculation algorithm, calculating pressure values FR1(T), FR2(T) and FR3(T) of all measuring points at the moment greater than T3, and respectively calculating FR1(T), FR2(T) and FR3(T) and the measured FRThe sum of the squares of the differences (t), denoted as D1, D2, and D3; if D2 is the minimum of D1, D2 and D3 and the maximum two-by-two relative deviation of D1, D2 and D3 is less than the set value, the permeability is determined to be K2. The method can ensure that the square sum of the deviation of the pressure attenuation curve obtained by the determined permeability forward calculation and the actually measured curve is minimum, and has wider applicability and reliability.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments described in the embodiments of the present invention, and it is also possible for a person skilled in the art to obtain other drawings based on the drawings.
Fig. 1 is a schematic flow chart of an implementation of a method for obtaining permeability of a particle sample according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
For the convenience of understanding of the embodiments of the present invention, the following description will be further explained with reference to specific embodiments, which are not to be construed as limiting the embodiments of the present invention.
As shown in fig. 1, an implementation flow diagram of a method for obtaining a permeability of a particle sample according to an embodiment of the present invention is shown, and the method specifically includes the following steps:
step 1, obtaining a curve P (t) of pressure changing along with time and a reference cavity volume VbVolume V of the sample chamber before the sample is placed thereinsTotal volume of sample VsbAverage particle radius RaTest temperature T and gas density rho of reference cavity before opening of test valve1And the gas density ρ of the sample chamber0；
Step 2, based on a helium state equation and a pressure attenuation curve P (t), obtaining a final stable value P2And temperature T, calculating corresponding gas density ρ2Sample pore volume VPPorosity phi, volume ratio K of outer space to inner space of particle samplecAnd the mean gas density ρ of the space outside the particles (containing the reference chamber) when the test valve is not openc0Wherein the calculation formula is as follows:
Figure BDA0002223778590000061
Figure BDA0002223778590000062
Figure BDA0002223778590000063
Figure BDA0002223778590000064
step 3, determining the corresponding pressure P of the gas entering the sample3Wherein is determined by a formula
Figure BDA0002223778590000065
Equation of state based on helium consisting of rho3And temperature Tcalculated P3。
Determining the pressure P from the curve P (t) of the pressure over time3Corresponding time t3All measured point time values are expressed as t3For zero point recalculation, take time greater than t3The first measurement point of (1), the time of which is denoted as t4The corresponding pressure is denoted as P4。
Step 4, all the time points greater than the time t are selected3Is measured (i.e. all time is selected to be greater than or equal to t)4Measure point) of the helium gas, calculating the gas density ρ (t) and the mass fraction F based on the helium gas state equationR(t) for ln (F)R(t)) all of which are greater than the time t3Measure point (i.e., all times greater than or equal to t)4Measured point) and time t to obtain slope s1Obtaining a slope s from said1Calculation of the Permeability k0Wherein the permeability k is calculated according to the formula0；
Figure BDA0002223778590000066
Figure BDA0002223778590000067
Wherein R isaIs the radius of the particle sample; μ is the viscosity coefficient of the gas, cgIs the gas compression factor; alpha is alpha1Is a transcendental equation
Figure BDA0002223778590000068
1 root of (1).
Step 5, determining the permeability k', and solving the following equation:
Figure BDA0002223778590000071
step 6, setting K1 as K0And K' is the minimum value, K3 is K0And K', wherein K2 ═ (K1+ K3)/2;
step 7, inputting K1, K2 and K3 into a preset mass fraction calculation algorithm, calculating pressure values FR1(T), FR2(T) and FR3(T) of all measuring points at the moment of being greater than T3 by taking T3 as a starting point, and calculating FR1(T), FR2(T) and FR3(T) and an actually measured FR(t) the sum of the squares of the differences, denoted as D1, D2, and D3, wherein the predetermined mass fraction calculation algorithm comprises:
Figure BDA0002223778590000072
wherein alpha isnIs a transcendental equation
Figure BDA0002223778590000073
N times root.
Figure BDA0002223778590000074
m is the total number of measuring points.
Step 8, if D2 is the minimum value of D1, D2 and D3 and the maximum pairwise relative deviation of D1, D2 and D3 is less than the set value (relative deviation is defined as the ratio of the absolute value of the difference between the two variables to the mean value of the two variables), determining the permeability as K2
Step 9, if D2 is the minimum value among D1, D2 and D3, but the maximum pairwise relative deviation of the three is greater than a set value, setting K1 to (K1+ K2)/2 and K3 to (K3+ K2)/2, and continuing to execute step 7;
step 10, if D1 is the minimum value among D1, D2 and D3, setting K3 to K2, K2 to K1, and K1 to 2 to K2 to K3, and continuing to execute step 7;
and 11, if the D3 is the minimum value of the D1, the D2 and the D3, setting K1 to K2, setting K2 to K3, setting K3 to 2 to K2 to K1, and continuing to execute the step 7.
In the embodiment of the invention, aiming at the problem that the permeability is underestimated when the existing method for determining the permeability by fitting the pressure attenuation curve in the permeability test of the particle sample is applied to a part of samples under a certain pressure condition, the invention provides a new analysis method, which can ensure that the square sum of the deviation between the pressure attenuation curve obtained by forward calculation of the determined permeability and an actually measured curve is minimum, and has wider applicability and reliability.
Those of skill would further appreciate that the various illustrative components and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative components and steps have been described above generally in terms of their functionality in order to clearly illustrate this interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied in hardware, a software module executed by a processor, or a combination of the two. A software module may reside in Random Access Memory (RAM), memory, Read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (7)

1.一种颗粒样品渗透率的获取方法，其特征在于，所述方法包括：1. a method for obtaining the permeability of a particle sample, wherein the method comprises: 获得压力随时间变化的曲线P(t)，基准腔体积Vb、放入样品前样品腔体积Vs、样品总体体积Vsb、颗粒平均半径Ra、测试温度T、测试阀开启前基准腔的气体密度ρ1和样品腔的气体密度ρ0；Obtain the curve P(t) of pressure versus time, the reference cavity volume V b , the sample cavity volume V s before placing the sample, the overall sample volume V sb , the average particle radius Ra , the test temperature T, and the reference cavity before the test valve is opened The gas density ρ 1 of the sample cavity and the gas density ρ 0 of the sample cavity; 基于氦气状态方程、压力衰减曲线P(t)最终稳定值P2和温度T，计算对应的气体密度ρ2，并计算样品孔隙体积VP、孔隙度φ、颗粒样品外部空间和内部孔隙空间的体积比Kc和测试阀未开启时颗粒外部空间的气体平均密度ρc0；Based on the helium equation of state, the final stable value P 2 of the pressure decay curve P (t), and the temperature T, the corresponding gas density ρ 2 is calculated, and the sample pore volume VP , porosity φ, outer space and inner pore space of the particle sample are calculated The volume ratio K c and the gas average density ρ c0 of the outer space of the particle when the test valve is not opened; 确定气体开始进入样品对应的压力P3，从所述压力随时间变化的曲线P(t)中确定压力P3对应的时刻t3；Determine the pressure P 3 corresponding to the gas beginning to enter the sample, and determine the time t 3 corresponding to the pressure P 3 from the curve P(t) of the pressure changing with time; 选择所有大于所述时刻t3的测点，基于氦气状态方程计算气体密度ρ(t)和质量分数FR(t)，对ln(FR(t))中所有大于所述时刻t3的测点和时间t进行线性拟合，得到斜率s1，根据所述得到斜率s1计算渗透率k0；Select all measuring points greater than the time t 3 , calculate the gas density ρ(t) and mass fraction F R (t) based on the helium state equation, for all the points in ln(FR ( t)) greater than the time t 3 Perform linear fitting at the measured points and time t to obtain the slope s 1 , and calculate the permeability k 0 according to the obtained slope s 1 ; 确定渗透率k′，设定K1为k0和k′的最小值，K3为k0和k′的最大值，其中，K2＝(K1+K3)/2；Determine the permeability k', set K1 as the minimum value of k 0 and k', and K3 as the maximum value of k 0 and k', wherein, K2=(K1+K3)/2; 将K1、K2、K3分别输入预设的质量分数计算算法，计算大于T3时刻的所有测点的质量分数值FR1(t)、FR2(t)和FR3(t)，并分别计算FR1(t)、FR2(t)和FR3(t)与实测FR(t)之差的平方和，记为D1、D2和D3；Input K1, K2, K3 into the preset quality score calculation algorithm respectively, calculate the quality score values FR1(t), FR2(t) and FR3(t) of all measuring points greater than T3 time, and calculate FR1(t) respectively , FR2(t) and FR3(t) and the square sum of the difference between the measured FR ( t ), denoted as D1, D2 and D3; 如果D2为D1、D2和D3中的最小值且D1、D2和D3中的最大两两相对偏差小于设定值，则确定渗透率为K2。If D2 is the minimum value among D1, D2, and D3 and the maximum pairwise relative deviation among D1, D2, and D3 is less than the set value, the permeability is determined to be K2. 2.根据权利要求1所述的方法，其特征在于，利用下述公式，基于氦气状态方程、压力衰减曲线P(t)最终稳定值P2和温度T，计算对应的气体密度ρ2、样品孔隙体积VP、孔隙度φ、颗粒样品外部空间和内部孔隙空间的体积比Kc和测试阀未开启时颗粒外部空间的气体平均密度ρc0：2. method according to claim 1, is characterized in that, utilize following formula, based on helium gas state equation, pressure decay curve P (t) final stable value P 2 and temperature T, calculate corresponding gas density ρ 2 , Sample pore volume V P , porosity φ, volume ratio K c of the outer space and inner pore space of the particle sample, and the gas average density ρ c0 of the outer space of the particle when the test valve is not opened:
Figure FDA0003351467980000021
Figure FDA0003351467980000021
 3.根据权利要求1所述的方法，其特征在于，所述确定气体开始进入样品对应的压力P3，包括：3 . The method according to claim 1 , wherein the determining the pressure P 3 corresponding to the gas beginning to enter the sample comprises: 3 . 利用公式确定
Figure FDA0003351467980000022
Determined using the formula
Figure FDA0003351467980000022
 基于氦气状态方程，由ρ3和温度T计算P3。P 3 is calculated from ρ 3 and temperature T based on the helium equation of state. 4.根据权利要求1所述的方法，其特征在于，利用下述公式计算质量分数FR(t)：4. method according to claim 1, is characterized in that, utilize following formula to calculate mass fraction F R (t):
Figure FDA0003351467980000023
Figure FDA0003351467980000023
 5.根据权利要求1所述的方法，其特征在于，利用下述公式，根据所述得到斜率s1计算渗透率k0：5. The method according to claim 1, characterized in that, the following formula is used to calculate the permeability k 0 according to the obtained slope s 1 :
Figure FDA0003351467980000024
Figure FDA0003351467980000024
 其中Ra为颗粒样品的半径；μ为气体的粘性系数，cg为气体压缩系数；α1为超越方程
Figure FDA0003351467980000025
的1次根。where R a is the radius of the particle sample; μ is the viscosity coefficient of the gas, c g is the gas compressibility; α 1 is the transcendental equation
Figure FDA0003351467980000025
1 root of . 6.根据权利要求5所述的方法，其特征在于，利用下述公式，确定渗透率k′：6. The method according to claim 5, wherein the permeability k' is determined by using the following formula:
Figure FDA0003351467980000031
Figure FDA0003351467980000031
 其中αn为超越方程
Figure FDA0003351467980000032
的n次根，t4为大于时间零点的第一个测点。where α n is the transcendental equation
Figure FDA0003351467980000032
The nth root of , t 4 is the first measurement point greater than time zero. 7.根据权利要求6所述的方法，其特征在于，所述预设的质量分数计算算法，包括：7. The method according to claim 6, wherein the preset quality score calculation algorithm comprises:
Figure FDA0003351467980000033
Figure FDA0003351467980000033
 其中，αn为超越方程
Figure FDA0003351467980000034
的n次根。where α n is the transcendental equation
Figure FDA0003351467980000034
the nth root of .
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