CN112229754B - Method for calculating adsorption capacity of methane in shale by iterative average method - Google Patents

Method for calculating adsorption capacity of methane in shale by iterative average method Download PDF

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CN112229754B
CN112229754B CN202011056722.0A CN202011056722A CN112229754B CN 112229754 B CN112229754 B CN 112229754B CN 202011056722 A CN202011056722 A CN 202011056722A CN 112229754 B CN112229754 B CN 112229754B
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李相臣
齐冰
林燚
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Southwest Petroleum University
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Abstract

The invention provides a method for calculating the adsorption quantity of methane in shale by an iterative average method, which comprises the following steps of (1) correcting the density of an adsorption phase to obtain an absolute adsorption quantity curve and correcting the volume of the adsorption phase to obtain a pressure point corresponding to the intersection point of the absolute adsorption quantity curve, wherein the pressure point is used as a sectional point of an adsorption unsaturated stage and an adsorption saturated stage; (2) for the stage of adsorption unsaturation, the absolute adsorption quantity (real adsorption quantity) obtained by adopting an adsorption phase volume correction method and the absolute adsorption quantity obtained by adopting an adsorption phase density correction method are used as the upper limit and the lower limit of the real adsorption quantity, and the average adsorption quantity is calculated and used as the average value of the initial absolute adsorption quantity. The method is suitable for correcting the saturated adsorption capacity of methane in all pressure intervals in the shale, and overcomes the error generated by correcting the excessive adsorption capacity of an adsorption unsaturated interval by using the saturated adsorption phase density and the saturated adsorption phase volume in the conventional method.

Description

Method for calculating adsorption capacity of methane in shale by iterative average method
Technical Field
The invention belongs to the technical field of shale oil gas development, and particularly relates to a method for calculating the adsorption quantity of methane in shale by using an iterative average method.
Background
The shale gas is natural gas existing in carbonaceous shale or black shale, is used as an unconventional gas reservoir for self-generation and self-storage, a large amount of shale gas is existing in shale pores in an adsorption state, the proportion of the shale gas can reach 85% at most, and the research on the shale adsorption rule has important significance on gas content calculation, reserve evaluation and yield prediction. The adsorption quantity obtained by the adsorption experiment test is apparent adsorption quantity (excess adsorption quantity), namely the adsorption quantity of the part exceeding the gas density in the adsorption phase cannot reflect the real adsorption quantity (absolute adsorption quantity), the adsorption quantity of shale under the stratum condition can be seriously underestimated according to the prediction of the apparent adsorption quantity, and the absolute adsorption quantity is adopted to indicate that the shale reservoir adsorption is more accurate.
At present, researchers have generally corrected excess adsorption amount by using adsorption phase density or volume based on the formula for defining the excess adsorption amount of Gibbs. Until now, no direct method can obtain the density and volume of the adsorption phase, and the method of fitting experimental data is usually adopted to obtain the density and volume of the adsorption phase in the adsorption saturation stage, so that the adsorption quantity when the adsorption does not reach saturation cannot be accurately corrected. Correcting the excessive adsorption quantity in the stage of adsorption unsaturation by using an adsorption phase density correction method to obtain an absolute adsorption quantity which is smaller than an actual value; the absolute adsorption amount obtained by correcting the excess adsorption amount in the adsorption unsaturated stage by using an adsorption phase volume correction method is larger than the actual value.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides a method for more accurately calculating the methane adsorption capacity in shale based on the principle of testing an isothermal adsorption curve by a gravimetric method on the basis of an adsorption phase density correction method and an adsorption phase volume correction method, wherein in the method, a pressure point corresponding to an intersection point of an absolute adsorption capacity curve obtained by correcting the adsorption phase density and an absolute adsorption capacity curve obtained by correcting the adsorption phase volume is used as a sectional point of an adsorption unsaturated stage and an adsorption saturated stage, and in the adsorption unsaturated stage, an iterative average correction method is provided for calculating the absolute adsorption capacity of the methane in the shale by taking a Gibbs formula as a theoretical basis; in the adsorption saturation stage, the excess adsorption amount is corrected by an adsorption phase density correction method, and thereby the absolute adsorption amount of all pressure stages is obtained. The method overcomes the error generated by correcting the excess adsorption capacity in the unsaturated stage by using the saturated adsorption phase density and the saturated adsorption phase volume in the prior method. The accuracy of the correction result obtained by the method is higher than that of the existing correction method through the fitting verification of the adsorption model.
The invention adopts the following technical scheme:
a method for calculating the adsorption quantity of methane in shale by an iterative averaging method comprises the following steps:
step (1): correcting the density of the adsorption phase to obtain an absolute adsorption capacity curve and correcting the volume of the adsorption phase to obtain a pressure point corresponding to the intersection point of the absolute adsorption capacity curve, wherein the pressure point is used as a sectional point of an adsorption unsaturated stage and an adsorption saturated stage;
step (2): for the unsaturated adsorption stage, the absolute adsorption quantity (real adsorption quantity) obtained by adopting an adsorption phase volume correction method and the absolute adsorption quantity obtained by adopting an adsorption phase density correction method are used as the upper limit and the lower limit of the real adsorption quantity, and the average adsorption quantity is calculated and used as the average value of the initial absolute adsorption quantity;
and (3): substituting the upper limit and the lower limit of the real adsorption quantity and the average value of the upper limit and the lower limit of the real adsorption quantity into a proper isothermal adsorption model for fitting to obtain a fitting result; (characterization methods include fitness, sum of squares of residuals, etc.);
and (4): taking two groups of adsorption quantities with the optimal fitting result as the upper limit and the lower limit of the new real adsorption quantity, calculating the average value, and repeating the step (3) to start the first iterative computation;
and (5): repeating the step (4) until the fitting precision of the n +1 th iteration begins to decrease, and considering that the absolute adsorption quantity of the n-th fitting result which is optimal is the absolute adsorption quantity of the unsaturated adsorption stage;
and (6): and calculating the absolute adsorption quantity by using an adsorption phase density correction method after the segmentation point to obtain the real adsorption quantity in the saturated adsorption stage.
The invention has the beneficial effects that:
1. according to the invention, the correction value of the saturated adsorption phase volume to the excess adsorption quantity and the correction value of the saturated adsorption phase density to the excess adsorption quantity are respectively the upper limit and the lower limit of the true adsorption quantity of the shale in the adsorption unsaturated stage. Correcting the excessive adsorption amount by using a segmented correction method and adopting an iterative average method before a segmentation point (adsorption unsaturated stage); the excess adsorption amount is corrected after the segmentation point using the adsorption phase density method. The Langmuir volume of the sample can be obtained by fitting the isothermal adsorption curve, compared with the correction results of the adsorption phase density and the adsorption phase volume, the accuracy of obtaining the Langmuir volume can be effectively improved by adopting a segmentation method for correction, and the accuracy improvement rate can reach 7.053% to the maximum. The method has important significance for evaluating shale gas reservoir reservoirs.
Drawings
FIG. 1 is a graphical representation of an iterative averaging method;
FIG. 2 is a graph of the excess adsorption capacity of the experimental test;
FIG. 3(a) is a plot of L-1 sample fitness as a function of iteration number;
FIG. 3(b) is a plot of the sum of squares of the fitted residuals for the L-1 sample as a function of iteration number;
FIG. 4(a) is a plot of L-2 sample fitness as a function of iteration number;
FIG. 4(b) is a plot of the sum of squares of the fitted residuals for the L-2 sample as a function of iteration number;
FIG. 5 is a schematic diagram of a piecewise correction method;
FIG. 6(a) is a graph showing the results of L-1 calibration;
FIG. 6(b) is a graph showing the L-2 calibration result;
FIG. 7(a) is a comparison graph of fitting degrees of different calibration methods;
FIG. 7(b) is a plot of residual square sum correction contrast for different correction methods;
Detailed Description
To make the objects, technical solutions and advantages of the present invention clearer, the following description is given for clarity and completeness in conjunction with the technical solutions of the present invention, and it is obvious that the described embodiments are a part of the embodiments of the present invention, not all of the embodiments. 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.
The prior art adsorbent phase density correction method comprises the following steps:
1. the isothermal adsorption experiment is carried out on the shale sample by adopting a magnetic suspension high-temperature high-pressure adsorption instrument, the changes of the temperature, the pressure and the sample mass of the environment in the adsorption process are measured by a magnetic suspension balance, and the excessive adsorption quantity under the corresponding temperature and pressure is calculated.
2. Fitting the experimental data of the high-pressure section, calculating the density of a saturated adsorption phase, and substituting the density of the saturated adsorption phase into a Gibbs formula to correct the excess adsorption capacity of the full-pressure section to obtain the absolute adsorption capacity.
According to the Gibbs formula:
Figure BDA0002711055990000041
in the above formula, nadsAbsolute adsorption amount, g; n isexExcess adsorption, g; rho a is the density of the adsorption phase, g/cm3;ρgIs free gas density, g/cm3. Free gas density ρgThe excess adsorption n can be obtained by searching in a databaseexObtained by testing an isothermal adsorption experiment, and rho is obtained when the temperature and the pressure are fixedg、nexAll are constants, and the absolute adsorption amount n is setadsIs y, ρaDensity of adsorbed phase x, density of free gas rhogWith a constant a and an excess adsorption amount b, the above formula can be expressed as:
Figure BDA0002711055990000042
derivation of x in formula:
Figure BDA0002711055990000043
obviously, the free gas density is constantly greater than 0, so the derivative is constantly less than 0, i.e. the value of y decreases as the density of the adsorbed phase increases. As can be seen from the adsorption phase density acquisition method, the adsorption phase density at the adsorption saturation stage is higher than that at the adsorption non-saturation stage. Therefore, the absolute adsorption amount obtained by correcting the excess adsorption amount in the adsorption unsaturated zone using the saturated adsorption phase density inevitably leads to a smaller result.
The prior art adsorbent phase volume correction method comprises the following steps:
1. the isothermal adsorption experiment is carried out on the shale sample by adopting a magnetic suspension high-temperature high-pressure adsorption instrument, the changes of the temperature, the pressure and the sample mass of the environment in the adsorption process are measured by a magnetic suspension balance, and the excessive adsorption quantity under the corresponding temperature and pressure is calculated.
2. Fitting the experimental data of the high-pressure section, calculating the volume of a saturated adsorption phase, and correcting the volume of the saturated adsorption phase for the excess adsorption capacity of the full-pressure section to obtain the absolute adsorption capacity.
From the definition of the excess adsorption:
nex=nabsgVa=Vaag) (4)
obtaining:
nabs=nex+Vaρg (5)
wherein, VaIs volume of adsorption phase, cm3. According to the method for obtaining the volume of the adsorption phase, the volume of the saturated adsorption phase is larger than the volume of the real adsorption phase in the adsorption unsaturated interval. Therefore, the absolute adsorption amount obtained by correcting the excess adsorption amount in the adsorption unsaturated zone using the saturated adsorption phase volume must be large as a result.
From the above analysis, it was found that the absolute adsorption amount in the adsorption unsaturated zone was between the absolute adsorption amount obtained by the adsorption phase density correction method and the absolute adsorption amount obtained by the adsorption phase volume correction method.
Analysis of prior art calibration results
At present, the excess adsorption capacity is usually corrected by obtaining the saturated adsorption phase volume and the saturated adsorption phase density by a method aiming at experimental data fitting, and the excess adsorption capacity cannot be accurately corrected in an adsorption unsaturated zone by an adsorption phase volume correction method and an adsorption phase density correction method for the following reasons:
(1) the result of the absolute adsorption amount obtained by correcting the excess adsorption amount in the adsorption unsaturated zone using the saturated adsorption phase density is small.
(2) The result of the absolute adsorption amount obtained by correcting the excess adsorption amount in the adsorption unsaturated zone using the saturated adsorption phase volume is large.
The invention provides a correction method applicable to the whole isothermal adsorption curve, namely a sectional correction method, wherein an iterative average method is adopted before sectional points; and (3) using an adsorption phase density method after the segmentation point, wherein the segmentation point is a pressure point corresponding to the intersection point of the calibration curves of the adsorption phase volume method and the adsorption phase density method.
As shown in fig. 1, it can be known from the above analysis that the accurate absolute adsorption amount is necessarily between the results of the adsorption phase density correction method and the adsorption phase volume correction method, so the present invention proposes a method for calculating the methane adsorption amount in shale by using an iterative average method:
step (1), correcting the density of an adsorption phase to obtain an absolute adsorption capacity curve and correcting the volume of the adsorption phase to obtain a pressure point corresponding to an intersection point of the absolute adsorption capacity curve, wherein the pressure point is used as a sectional point of an adsorption unsaturated stage and an adsorption saturated stage;
step (2), for the unsaturated adsorption stage, taking the absolute adsorption quantity (real adsorption quantity) obtained by adopting an adsorption phase volume correction method and the absolute adsorption quantity obtained by adopting an adsorption phase density correction method as the upper limit and the lower limit of the real adsorption quantity, and calculating the average adsorption quantity as the average value of the initial absolute adsorption quantity;
step (3), substituting the upper limit and the lower limit of the real adsorption quantity and the average value of the upper limit and the lower limit into a proper isothermal adsorption model (the isothermal adsorption model is the existing model) for fitting to obtain a fitting result;
step (4), taking two groups of adsorption quantities with the optimal fitting results as the upper limit and the lower limit of the new real adsorption quantity, calculating the average value, and repeating the step (2) to start the first iterative computation;
step (5) repeating the step (3) until the fitting precision of the n +1 th iteration begins to decline, and considering that the absolute adsorption quantity of the n-th fitting result which is optimal is the absolute adsorption quantity of the unsaturated adsorption stage;
and (6) calculating the absolute adsorption quantity by using an adsorption phase density correction method after the segmentation point to obtain the real adsorption quantity in the saturated adsorption stage.
Examples
As shown in fig. 2, in order to test the excessive adsorption amount of the shale sample in methane by using the magnetic suspension balance, at a low pressure, the adsorption amount increases with the increase of the experimental pressure, and after reaching a maximum value, the adsorption amount gradually decreases with the increase of the experimental pressure. The adsorption capacity obtained by the gravimetric method is the excess adsorption capacity (apparent adsorption capacity), and cannot reflect the real adsorption condition of the stratum, and if the gas content of the shale reservoir is not corrected, the gas content of the shale reservoir can be greatly underestimated.
The excess adsorption capacity of the shale samples of No. L-1 and L-2 is corrected by respectively using an adsorption phase volume correction method, an adsorption phase density correction method and an iterative average method, and a Langmuir-Freundlich (L-F) model is selected to perform fitting comparison on the correction results, and the results are shown in Table 1. The fitting degree of the initial average value of the sample No. L-1 is smaller than the correction result of the volume method and larger than the correction result of the density method, and the fitting degree of the 1 st iteration result exceeds the volume method and reaches the maximum value; the fitting degree of the initial average value of the sample No. L-2 is smaller than the correction result of the density method and larger than the correction result of the volume method, the fitting degree of the 1 st iteration result is consistent with the correction result of the density method, the fitting degree is unchanged along with the increase of the iteration times, probably because the precision of fitting software is limited, and the fitting degree R is2The value of (A) can only be calculated to the last 5 decimal places, and the fitting degree of two samples is closer and tends to be stable after iteration is carried out for a certain number of times.
Based on the reasons, the invention introduces the residual square sum for comparative analysis, and finds out from the experimental result that the residual square sum of the 1 st iteration result of the sample No. L-1 reaches the minimum value and is lower than the correction results of the density method and the volume method, as shown in Table 1. As the iteration progresses, the sum of squared residuals tends to increase, as shown in fig. 3(a) -3 (b), which shows that the result of iteration 1 is closest to the true adsorption amount, and the iteration result deviates from the true adsorption amount more and more as the number of iterations increases. After the sample L-2 is subjected to the first iterative calculation, the fitting degree is kept unchanged; as the number of iterations increases, the sum of squared residuals decreases and then increases, as shown in fig. 4(a) -4 (b), and reaches a minimum value at iteration 3, indicating that the result of iteration 3 is closest to the absolute adsorption capacity.
TABLE 1 model fitting cases
Figure BDA0002711055990000071
As is clear from fig. 5, when the pressure reaches about 13MPa, the calibration curves of the volume method and the density method intersect at a point, and thereafter the calibration curve of the volume method tends to be flat while the calibration curve of the density method exceeds the former.
Combining the analysis, a correction method suitable for the whole adsorption, namely a method for calculating the adsorption quantity of methane in the shale by an iterative average method, is provided. As shown in fig. 6(a) and 6(b), the whole adsorption process is divided into an adsorption unsaturated zone and an adsorption saturated zone, the intersection point of the density method and the volume method correction curve is used as a segmentation point, an iterative averaging method is adopted before the segmentation point,
the method avoids the error caused by the fact that the density and the volume of the adsorption phase can not be accurately obtained, the adsorption phase density method is used after the segmentation point, the defect of the iterative average method after the segmentation point is overcome, and the L-F method is adopted
The model was fitted to 70 experimental points obtained by the 3 calibration methods, and the results showed that the curves corrected by the segmentation method were superior to the density method and volume method calibration curves in both the fitting degree and the sum of the squares of the residuals, as shown in the following table and fig. 7(a) and 7 (b).
Comparison of correction results by three methods
Figure BDA0002711055990000081
The Langmuir volume of the sample can be obtained by fitting the isothermal adsorption curve, and the following table shows that the accuracy of obtaining the Langmuir volume can be effectively improved by adopting a segmentation method for correction, and the accuracy improvement rate can reach 7.053% to the maximum. The method has important significance for evaluating shale gas reservoir reservoirs.
Langmuir volume relative deviation analysis obtained by different correction methods
Figure BDA0002711055990000082
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (1)

1. A method for accurately calculating the true adsorption quantity of methane in shale by an iterative averaging method is characterized by comprising the following steps:
step (1): correcting the density of the adsorption phase to obtain an absolute adsorption capacity curve and correcting the volume of the adsorption phase to obtain a pressure point corresponding to the intersection point of the absolute adsorption capacity curve, wherein the pressure point is used as a sectional point of an adsorption unsaturated stage and an adsorption saturated stage;
step (2): for the stage of adsorption unsaturation, the absolute adsorption quantity obtained by adopting an adsorption phase volume correction method and the absolute adsorption quantity obtained by adopting an adsorption phase density correction method are used as the upper limit and the lower limit of the real adsorption quantity, and the average adsorption quantity is calculated as the average value of the initial absolute adsorption quantity;
and (3): substituting the upper limit and the lower limit of the real adsorption quantity and the average value of the upper limit and the lower limit of the real adsorption quantity into a proper isothermal adsorption model for fitting to obtain a fitting result;
and (4): taking two groups of adsorption quantities with the optimal fitting result as the upper limit and the lower limit of the new real adsorption quantity, calculating the average value, and repeating the step (3) to start the first iterative computation;
and (5): repeating the step (4) until the fitting precision of the n +1 th iteration begins to decrease, and considering that the absolute adsorption quantity of the n-th fitting result which is optimal is the absolute adsorption quantity of the unsaturated adsorption stage;
and (6): and calculating the absolute adsorption quantity by using an adsorption phase density correction method after the segmentation point to obtain the real adsorption quantity in the saturated adsorption stage.
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