Method for determining content of lost gas in shale gas content test

Abstract

The present invention discloses a method for determining a content of lost gas in a shale gas content test. The method includes: acquiring a shale core and recording the time required for acquiring the shale core; carrying out a desorption experiment on the shale core to obtain desorption data; acquiring a fitting objective function; fitting the desorption data by using the fitting objective function to obtain fitted desorption data; determining fitting parameters according to the desorption data and the fitted desorption data; correcting the time required for acquiring the shale core according to the fitting parameters; and obtaining the content of lost gas according to the fitting parameters and the corrected time required for acquiring the shale core. The present invention can improve the determining precision of the content of the lost gas.

Claims

1. A method for determining a content of lost gas in a shale gas content test, comprising: acquiring a shale core and recording time required for acquiring the shale core; carrying out a desorption experiment on the shale core to obtain desorption data; acquiring a fitting objective function; fitting the desorption data by using the fitting objective function to obtain fitted desorption data; determining fitting parameters according to the desorption data and the fitted desorption data; correcting the time required for acquiring the shale core according to the fitting parameters; and obtaining the content of lost gas according to the fitting parameters and the corrected time required for acquiring the shale core, wherein the time required for acquiring the shale core is corrected by using formula $\overline{t_0}=\frac{k{t}_0+p_0}{p_w}{t}_0,$ wherein t.sub.0 is the corrected time required for acquiring the shale core, k is a depressurization rate in the process of acquiring the shale core, p.sub.0 is a local atmospheric pressure, p.sub.w is a mud water column pressure, and t.sub.0 is the time required for acquiring the shale core.

2. The method for determining a content of lost gas in a shale gas content test according to claim 1, wherein the carrying out a desorption experiment on the shale core to obtain desorption data comprises: putting the shale core into a desorption canister and discharging air in a dead volume of the desorption canister; sealing the desorption canister; heating the sealed desorption canister to a set temperature; acquiring gas output of the desorption canister every set time and recording current acquisition time until the gas output of the desorption canister is stable; and obtaining desorption data accord to the gas output of the desorption canister and the corresponding acquisition time.

3. The method for determining a content of lost gas in a shale gas content test according to claim 2, wherein after the step of carrying out a desorption experiment on the shale core to obtain desorption data, before the step of acquiring a fitting objective function, the method further comprises: preprocessing the acquisition time in the desorption data, so that a difference between adjacent acquisition time is the set time.

4. The method for determining a content of lost gas in a shale gas content test according to claim 1, wherein, the fitting objective function is: $Q=\frac{4\pi k}{D}\underset{n=1}{\overset{\infty }{.Math.}}\frac{\exp \left(-D{\alpha }_n^{2}t\right)-\exp \left(-D{\alpha }_n^2{t}_0\right)}{{\alpha }_n^4}-\frac{2\pi kR}{D}\underset{n=1}{\overset{\infty }{.Math.}}\frac{\exp \left[-D{\alpha }_n^2\left(t-t_0\right)\right]J_2\left(R{\alpha }_n\right)}{{\alpha }_n^3{J}_1\left(R{\alpha }_n\right)}+\frac{k\pi R^4}{8D}$ wherein k is a depressurization rate in the process of acquiring the shale core, D is a diffusion rate of gas in the porous medium core, R is a core radius, t.sub.0 is the time required for acquiring the shale core, α.sub.n is a characteristic value, Q is an accumulated flow, and t is duration of a desorption experiment.

5. The method for determining a content of lost gas in a shale gas content test according to claim 1, wherein the determining fitting parameters according to the desorption data and the fitted desorption data comprises: determining fitting parameters by using formula $\min \underset{n=1}{\overset{N}{.Math.}}{\left[Q\left(t_n\right)-Q_n\right]}^2,$ wherein the fitting parameters comprise the depressurization rate k in the process of acquiring a shale core and the diffusion rate D of gas in the porous medium core, wherein Q(t.sub.n) is the fitted desorption data, Q.sub.n is the desorption data, and N is the number of the desorption data.

6. The method for determining a content of lost gas in a shale gas content test according to claim 1, wherein the obtaining the content of lost gas according to the fitting parameters and the corrected time required for acquiring the shale core comprises: calculating the content of lost gas by using formula $Q_{Lost}=\pi R^{2}k\overline{t_0}-\frac{\pi k{R}^4}{8D}+\frac{4\pi k}{D}\underset{n=1}{\overset{\infty }{.Math.}}\frac{\exp \left(-D{\alpha }_n^2\overline{t_0}\right)}{{\alpha }_n^4},$ wherein k is a depressurization rate in the process of acquiring the shale core, D is a diffusion rate of gas in the porous medium core, R is a core radius, t.sub.0 is the corrected time required for acquiring the shale core, α.sub.n is a characteristic value, and Q.sub.lost is the lost gas volume.

7. The method for determining a content of lost gas in a shale gas content test according to claim 1, wherein the desorption data is fitted by using a least square method to obtain fitted desorption data.

8. The method for determining a content of lost gas in a shale gas content test according to claim 2, wherein the set time is 5 min.

9. The method for determining a content of lost gas in a shale gas content test according to claim 2, wherein the set temperature is 70° C.

10. The method for determining a content of lost gas in a shale gas content test according to claim 4, wherein the determining fitting parameters according to the desorption data and the fitted desorption data comprises: determining fitting parameters by using formula $\min \underset{n=1}{\overset{N}{.Math.}}{\left[Q\left(t_n\right)-Q_n\right]}^2,$ wherein the fitting parameters comprise the depressurization rate k in the process of acquiring a shale core and the diffusion rate D of gas in the porous medium core, wherein Q(t.sub.n) is the fitted desorption data, Q.sub.n is the desorption data, and N is the number of the desorption data.

11. The method for determining a content of lost gas in a shale gas content test according to claim 3, wherein the set time is 5 min.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) To describe the technical solutions in the embodiments of the present invention or in the prior art more clearly, the following briefly introduces the accompanying drawings required for describing the embodiments. Apparently, the accompanying drawings in the following description show merely some embodiments of the present invention, and a person of ordinary skill in the art may still derive other drawings from these accompanying drawings without creative efforts.

(2) FIG. 1 is a flow chart of a method for determining a content of lost gas in a shale gas content test according to the present invention.

DETAILED DESCRIPTION

(3) The following clearly and completely describes the technical solutions in the embodiments of the present invention with reference to accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are merely some rather than all of the embodiments of the present invention. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

(4) An objective of the present invention is to provide a method for determining a content of lost gas in a shale gas content test, which can improve the determining precision of the content of the lost gas.

(5) In order that the foregoing objectives, features, and advantages of the present invention can be more clearly understood, the present invention will be further described in detail with reference to the accompanying drawings and specific embodiments.

(6) FIG. 1 is a flow chart of a method for determining a content of lost gas in a shale gas content test according to the present invention. As shown in FIG. 1, a method for determining a content of lost gas in a shale gas content test includes:

(7) Step 101: Acquire a shale core and record the time required for acquiring the shale core.

(8) Step 102: Carry out a desorption experiment on the shale core to obtain desorption data.

(9) Step 103: Acquire a fitting objective function.

(10) Step 104: Fit the desorption data by using the fitting objective function to obtain fitted desorption data.

(11) Step 105: Determine fitting parameters according to the desorption data and the fitted desorption data.

(12) Step 106: Correct the time required for acquiring the shale core according to the fitting parameters.

(13) Step 107: Obtain the content of lost gas according to the fitting parameters and the corrected time required for acquiring the shale core.

(14) Specifically, in step 101, the shale core is obtained through a drilled well, and the time required for acquiring the shale core is also the drill string lifting time.

(15) In step 102, the shale core is put into a desorption canister after mud on the surface of the shale core is wiped off. Since the volume V.sub.canister of the desorption canister is greater than the volume V.sub.core of the shale core, there is a dead volume in the desorption canister. It is necessary to exhaust air in the dead volume before the desorbed gas test can be carried out. Therefore, the desorption canister is filled with fine sand to exhaust the air in the dead volume in the desorption canister, and the desorption canister is closed for sealing. After the desorption canister is heated to 70° C. (formation temperature) and the temperature is stable, an air outlet valve installed on the desorption canister is switched on, and gas output of desorbed gas is measured by means of a flow meter. The reading of the flow meter is acquired once every 5 min for the desorption experiment, and the current acquisition time is recorded. The desorption duration of desorbed gas is 20-50 h. Whether desorption is completed can be determined according to whether the readings of the flow meter are stable within a certain period of time. After desorption is stable, desorption section experimental data {(t.sub.n, Q.sub.n)|(n=1, 2, . . . , N)} is obtained through desorption experiments, where t.sub.n denotes time series, and Q.sub.n denotes total flow data series of the desorbed gas corresponding to the time series t.sub.n respectively.

(16) Then the desorption data {(t.sub.n, Q.sub.n)|(n=1, 2, . . . , N)} is preprocessed. Due to the limitation of drilling site conditions, power supply cannot be guaranteed at any time. Desorption experiments cannot be carried out under the condition of power failure, and thus the obtained desorption data is not necessarily uniformly distributed in the recorded time series. Therefore, a breakpoint of the time series is processed, and the power outage time length is deducted, so that the time series is reprocessed for uniform distribution. The processed time series meets t.sub.n−t.sub.n-1=5 min, so that the desorption data is uniformly distributed and conforms to a desorption section model, which facilitates data fitting.

(17) After the shale core desorption experiment is completed, a crushing experiment can be adopted. The shale core is taken out of the desorption canister and put into a crushing device. After the desorption canister is sealed, a crushing switch is turned on to crush the shale core and acquire residual gas. The residual gas content Q.sub.residue is recorded and used for determining the gas content of the shale core.

(18) The fitting objective function in step 103 is as follows:

(19) $Q=\frac{4\pi k}{D}\underset{n=1}{\overset{\infty }{.Math.}}\frac{\exp \left(-D{\alpha }_n^{2}t\right)-\exp \left(-D{\alpha }_n^2{t}_0\right)}{{\alpha }_n^4}-\frac{2\pi kR}{D}\underset{n=1}{\overset{\infty }{.Math.}}\frac{\exp \left[-D{\alpha }_n^2\left(t-t_0\right)\right]J_2\left(R{\alpha }_n\right)}{{\alpha }_n^3{J}_1\left(R{\alpha }_n\right)}+\frac{k\pi R^4}{8D}$

(20) where k is a depressurization rate in the process of acquiring the shale core, D is a diffusion rate of gas in the porous medium core, R is a core radius, t.sub.0 is the drill string lifting time, α.sub.n is a characteristic value, Q is an accumulated flow, and t is desorption time. It is analyzed according to the convergence of series summation that the foregoing summation form is stable convergence. On the premise of meeting the existing computer precision, summation results of first 50 items can be used to characterize an objective function within the precision range.

(21) The fitting method used in step 104 is a least square method.

(22) In step 105, parameter values in the objective function through the given experimental data sequence {(t.sub.n, Q.sub.n)|(n=1, 2, . . . , N)} of desorbed gas with reference to the fitting objective function, so that the sum of squared differences between the desorption data and the fitted desorption data is minimized. The specific data processing formula is shown below:

(23) $\min \underset{n=1}{\overset{N}{.Math.}}{\left[Q\left(t_n\right)-Q_n\right]}^2$

(24) where Q(t.sub.n) is a value of the time series substituted into the objective function, namely the fitted desorption data; Q.sub.n is a desorption experimental data value corresponding to the time series, namely the desorption data. The parameters D and k in the objective function are obtained by solving the optimization problem.

(25) Strictly, for the correction process in step 106, the drill string lifting time starts from the time when the shale pore pressure and the mud water column pressure are balanced. The relationship between the mud water column pressure and the drill string lifting time is calculated in combination with the drilling depth, the shale pore pressure is calculated by fitting the obtained parameter k. As a result, the time when the shale pore pressure and the mud water column pressure are balanced is calculated, thereby obtaining corrected drill string lifting time data t.sub.o.

(26) $\overline{t_0}=\frac{k{t}_0+p_0}{p_w}{t}_0$

(27) t.sub.o is the corrected time required for acquiring the shale core, k is a depressurization rate in the process of acquiring the shale core, t.sub.0 is the time required for acquiring the shale core. p.sub.0 is the local atmospheric pressure, and p.sub.w is the mud water column pressure. When the data error is large, t.sub.0=0.5t.sub.0 can be used as the corrected drill string lifting time data.

(28) In step 107, the obtained parameters D and k and the time t.sub.o required for acquiring the shale core are substituted into the following objective function:

(29) $Q_{Lost}=\pi R^{2}k\overline{t_0}-\frac{\pi k{R}^4}{8D}+\frac{4\pi k}{D}\underset{n=1}{\overset{\infty }{.Math.}}\frac{\exp \left(-D{\alpha }_n^2\overline{t_0}\right)}{{\alpha }_n^4}$

(30) where k is a depressurization rate in the process of acquiring the shale core, D is a diffusion rate of gas in the porous medium core, R is a core radius, t.sub.o is the corrected drill string lifting time, α.sub.n is a characteristic value, and Q.sub.lost is the lost gas volume.

(31) Specifically, the estimated content Q.sub.Lost of lost gas, experimental data Q.sub.N of the content of desorbed gas, and experimental data Q.sub.residue of the content of residual gas are added to obtain the shale gas content based on a segmented estimation method. The formula is as follows:
Q.sub.total=Q.sub.Lost+Q.sub.N+Q.sub.residue.

(32) The present invention also discloses the following technical effects:

(33) 1. Compared with the method for estimating the content of lost gas through a straight line method in the prior art, the method for determining the content of lost gas provided by the present invention is also based on desorption experimental data, but nonlinear fitting is carried out, and the fitting precision is higher.

(34) 2. According to the present invention, the pore pressure of the shale reservoir can be obtained by fitting according to the fitting objective function, and then the corrected shale core drill string lifting time t.sub.o can be calculated according to the mud water column pressure. Compared with the fixed parameters in the prior art, the method for calculating the drill string lifting time provided by the patent is more accurate, and is suitable for different reservoirs and different coring conditions.

(35) 3. According to the present invention, the relationship between the lost gas volume and time in the shale coring process and the relationship between the desorbed gas volume and time in the desorption experiment are distinguished and fitted segmentally. Compared with the mode of unified treatment of the two in the prior art, the method provided by the present invention is more suitable for actual engineering conditions and more formation conditions (including pore pressure and gas content) can be obtained by fitting.

(36) Each embodiment of the present specification is described in a progressive manner, each embodiment focuses on the difference from other embodiments, and the same and similar parts between the embodiments may refer to each other.

(37) Several examples are used herein for illustration of the principles and embodiments of the present invention. The description of the embodiments is used to help illustrate the method and its core principles of the present invention. In addition, a person of ordinary skill in the art can make various modifications in terms of specific embodiments and scope of application in accordance with the idea of the present invention. In conclusion, the content of the present specification shall not be construed as a limitation to the present invention.