Stratum macroscopic capture cross section calculation method and system based on sliding time window

Abstract

The invention provides a stratigraphic macroscopic capture cross section calculation method and system based on a sliding time window. The method comprises the following steps: acquiring a time spectrum, and initializing thermal neutron decay life tau; generating a time window on the time spectrum according to the thermal neutron decay life tau; calculating a counting ratio of the time window, and judging whether the counting ratio meets a preset condition or not; if the counting ratio does not meet the preset condition, modifying the thermal neutron attenuation life tau, sliding the time window, and recalculating the counting ratio; and if the counting ratio meets the preset condition, calculating the stratum macroscopic capture cross section Sigma according to the counting ratio. By means of the method, the position and time of the time window can be adjusted in a self-adaptive mode, and then the calculation precision of Sigma is improved.

Description

Technical Field

[0001] The present application relates to the field of nuclear well logging technology, and in particular to a method, system and electronic equipment for calculating a formation macroscopic capture cross section based on a sliding time window. Background Art

[0002] Neutron lifetime logging is an important evaluation method in cased wells. The formation lifetime can be used to obtain the formation macroscopic capture cross section Sigma, which plays an important role in obtaining formation mineralization and water saturation. Because the time spectrum decays quickly in an environment with a larger formation Sigma, the traditional method of obtaining Sigma with a fixed time gate results in a low utilization rate of the time spectrum. In an environment with a smaller formation Sigma, the time gate will not be wide enough, making it inconvenient to obtain Sigma. Summary of the invention

[0003] In view of this, the present application proposes a method, system and electronic device for calculating the macroscopic capture cross section of a formation based on a sliding time window to solve the problems reflected in the above-mentioned background technology.

[0004] According to one aspect of the present application, a method for calculating a formation macroscopic capture cross section based on a sliding time window is provided, comprising the following steps:

[0005] Get the time spectrum and initialize the thermal neutron decay lifetime τ;

[0006] Generating a time window on the time spectrum according to the thermal neutron decay lifetime τ;

[0007] Calculating the count ratio of the time window, and determining whether the count ratio meets a preset condition;

[0008] If the counting ratio does not meet the preset condition, modify the thermal neutron decay lifetime τ, slide the time window, and recalculate the counting ratio;

[0009] If the count ratio satisfies the preset condition, the macroscopic capture cross section of the formation is calculated according to the count ratio.

[0010] Further, the time window includes a first time window and a second time window;

[0011] The start time of the first time window is t1, the end time is t2, and t2-t1=τ;

[0012] The start time of the second time window is t3, the end time is t4, and t4-t3=2τ.

[0013] Furthermore, the end time t2 of the first time window is equal to the start time t3 of the second time window.

[0014] Furthermore, the time from the start time t1 of the first time window to the end time of the neutron burst pulse is 2τ.

[0015] Further, the calculating the count ratio of the time window includes:

[0016] Derive expressions for the number of thermal neutrons in the first time window and the second time window;

[0017] The expression of the number of thermal neutrons in the first time window is:

[0018]

[0019] The expression for the number of thermal neutrons in the second time window is:

[0020]

[0021] The ratio of the number of thermal neutrons in the first time window to the number of thermal neutrons in the second time window is calculated to obtain a counting ratio.

[0022] Among them, N0 is the initial value of the number of thermal neutrons, is the average diffusion velocity of thermal neutrons.

[0023] Furthermore, the calculation formula of the counting ratio is:

[0024]

[0025] Furthermore, the preset condition is that the counting ratio is equal to the fixed coefficient or the error between the counting ratio and the fixed coefficient is the smallest, and the fixed coefficient is taken as:

[0026]

[0027] Furthermore, the formation macroscopic capture cross section is calculated according to the counting ratio, and the formula is:

[0028]

[0029] Where Δt is the interval between the middle points of the time window.

[0030] The present application also provides a formation macroscopic capture section calculation system based on a sliding time window, comprising:

[0031] A time spectrum acquisition module is used to acquire the time spectrum and initialize the thermal neutron decay lifetime τ;

[0032] A time window generating module, used for generating a time window on the time spectrum according to the thermal neutron decay lifetime τ;

[0033] A counting ratio module, used to calculate the counting ratio of the time window and determine whether the counting ratio meets a preset condition;

[0034] An iteration module, used for modifying the thermal neutron decay lifetime τ, sliding the time window, and recalculating the count ratio when the count ratio does not meet the preset condition;

[0035] The output module is used to calculate the formation macroscopic capture cross section according to the counting ratio when the counting ratio meets the preset condition.

[0036] The present application also provides an electronic device, including:

[0037] processor;

[0038] a memory for storing processor-executable instructions;

[0039] Wherein, the processor is configured to implement any of the above-mentioned methods for calculating the macroscopic capture cross section of the formation based on a sliding time window when executing the executable instructions.

[0040] Beneficial effects of this application:

[0041] The present application obtains a time spectrum to initialize the thermal neutron decay lifetime τ; generates a time window on the time spectrum according to the thermal neutron decay lifetime τ; calculates the count ratio of the time window to determine whether the count ratio meets a preset condition; if the count ratio does not meet the preset condition, modifies the thermal neutron decay lifetime τ, slides the time window, and recalculates the count ratio; if the count ratio meets the preset condition, calculates the macroscopic capture cross section Sigma of the formation according to the count ratio, so that the position and time of the time window can be adaptively adjusted, thereby improving the calculation accuracy of Sigma. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a flow chart of a method for calculating a formation macroscopic capture cross section based on a sliding time window according to an embodiment of the present application;

[0043] Figure 2 A schematic diagram of modeling PNST in Geant4 according to an embodiment of the present application;

[0044] Figure 3 This is a schematic diagram of a sliding time window according to an embodiment of the present application;

[0045] Figure 4 A schematic diagram of Δt setting according to an embodiment of the present application;

[0046] Figure 5 This is a scatter plot of logarithmic counts changing over time at different porosities when the mineralization is 0 kppm in one embodiment of the present application;

[0047] Figure 6 This is a scatter plot of logarithmic counts changing over time at different porosities when the salinity is 600 kppm in one embodiment of the present application;

[0048] Figure 7 This is a scatter plot of logarithmic counts changing over time at different mineralizations in one embodiment of the present application;

[0049] Figure 8 This is a schematic diagram of a sliding time window calculation result based on a fixed coefficient according to an embodiment of the present application;

[0050] Fig. 9 This is a schematic diagram of comparison results of a fixed time window and a sliding time window according to an embodiment of the present application;

[0051] Fig.10 A system block diagram of a system for calculating a formation macroscopic capture cross section based on a sliding time window according to an embodiment of the present application. DETAILED DESCRIPTION

[0052] Various exemplary embodiments, features and aspects of the present application will be described in detail below with reference to the accompanying drawings. The same reference numerals in the accompanying drawings represent elements with the same or similar functions. Although various aspects of the embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless otherwise specified.

[0053] Among them, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise", "axial", "radial", "circumferential" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present application or simplifying the description, and do not indicate or imply that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present application.

[0054] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of this application, the meaning of "plurality" is two or more, unless otherwise clearly and specifically defined.

[0055] The word “exemplary” is used exclusively herein to mean “serving as an example, example, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.

[0056] In addition, in order to better illustrate the present application, numerous specific details are provided in the following specific embodiments. It should be understood by those skilled in the art that the present application can also be implemented without certain specific details. In some examples, methods, means, components and circuits well known to those skilled in the art are not described in detail in order to highlight the subject matter of the present application.

[0057] The solution of the present application is applied to the field of nuclear well logging technology. In a nuclear well logging experiment or a simulation experiment of Monte Carlo software, the captured gamma time spectrum is analyzed, the time gate position is adaptively adjusted, and the macroscopic capture cross section Sigma of the formation is calculated.

[0058] Example 1

[0059] Figure 1 The flowchart of a method for calculating the formation macroscopic capture cross section based on a sliding time window in an embodiment of the present application is shown. By using this method, the position and time of the time window can be adaptively adjusted, thereby improving the accuracy of calculating Sigma. Figure 1 , the flow chart includes:

[0060] Step S100, obtaining a time spectrum and initializing a thermal neutron decay lifetime τ.

[0061] Specifically, see Figure 2 , the pulsed neutron spectrum saturation logging tool (PNST) was used to carry out Monte Carlo modeling and calculation in Geant4.

[0062] Among them, Geant4 (Geometry and Tracking 4) is a high-performance computing software developed by CERN to simulate the interaction between particles and matter. It is one of the most widely used Monte Carlo programs in nuclear detection technology. Geant4 is powerful and flexible, and is widely used in many fields and scientific research such as medical radiology, nuclear reactor design, space radiation protection, and semiconductor physics.

[0063] Specifically, PNST uses three NaI crystal detectors, of which the ultra-far detector and the far detector are 1 inch * 6 inches, and the near detector is 1 inch * 4 inches. PNST emits 14MeV fast neutrons into the formation, the near and far source detectors collect gamma energy spectra and time spectra for C / O and Sigma measurements, and the ultra-far source detector collects inelastic and captured gamma counts for gas saturation evaluation, thereby providing C / O, saturation and Sigma measurements.

[0064] After high-energy fast neutrons undergo inelastic and elastic scattering processes with the nuclei of some elements in the formation, they decay into thermal neutrons. The average time from the decay into thermal neutrons to the capture of the thermal neutrons by the nuclei of elements in the formation is called the thermal neutron decay lifetime τ. The thermal neutron decay lifetime τ is initialized to 0.

[0065] Through the above steps, the gamma time spectrum can be obtained and the thermal neutron decay lifetime τ can be initialized to facilitate subsequent calculations.

[0066] Step S200: generating a time window on the time spectrum according to the thermal neutron decay lifetime τ.

[0067] Specifically, see Figure 3 , the time window includes a first time window and a second time window.

[0068] The start time of the first time window is t1, the end time is t2, and t2-t1=τ;

[0069] The start time of the second time window is t3, and the end time is t4, where t4-t3=2τ.

[0070] Optionally, the end time t2 of the first time window is equal to the start time t3 of the second time window, that is, t2=t3.

[0071] Optionally, the time from the start time t1 of the first time window to the end of the neutron pulse burst is 2τ.

[0072] Through the above steps, a time window can be generated according to the thermal neutron decay lifetime τ, which is convenient for subsequent recalculation of τ and adjustment of the time window.

[0073] Step S300, calculating the count ratio of the time window, and determining whether the count ratio meets a preset condition.

[0074] Specifically, the steps include:

[0075] Step S310, deriving expressions for the number of thermal neutrons in the first time window and the second time window.

[0076] Specifically, the calculation formula of thermal neutron decay lifetime τ is:

[0077]

[0078] in, is the average diffusion velocity of thermal neutrons, in cm / s; S is the average value of the free motion distance of thermal neutrons from generation to absorption.

[0079]

[0080] Where Σ is the macroscopic capture cross section of the rock.

[0081]

[0082] Here, Σ is the capture cross section.

[0083] Since the number of neutrons at any time satisfies the form of exponential decay, the starting times t1 and t2 of the first time window and the second time window are specified, and the number of thermal neutrons can be expressed as:

[0084] The expression for the number of thermal neutrons in the first time window is:

[0085]

[0086] The expression for the number of thermal neutrons in the second time window is:

[0087]

[0088] Among them, N0 is the initial value of the number of thermal neutrons, is the average diffusion velocity of thermal neutrons.

[0089] Step S320, calculating the ratio of the number of thermal neutrons in the first time window to the number of thermal neutrons in the second time window to obtain a counting ratio.

[0090] Specifically, divide the expressions for the number of thermal neutrons in the first time window and the second time window and substitute them into The count ratio is:

[0091]

[0092] Step S330, determining whether the counting ratio satisfies a preset condition.

[0093] The preset conditions are: the counting ratio is equal to the fixed coefficient or the error between the counting ratio and the fixed coefficient is the smallest.

[0094] The fixed coefficients are:

[0095]

[0096] Through the above steps, the count ratios of the two time windows are calculated and the count ratio judgment is performed to facilitate the subsequent sliding of the time window and calculation of the macroscopic capture cross section of the formation.

[0097] Step S400: if the counting ratio does not meet the preset condition, modify the thermal neutron decay lifetime τ, slide the time window, and recalculate the counting ratio.

[0098] Specifically, when the count ratio does not meet the preset condition, the τ value is adjusted, the time window is slid according to the adjusted τ value, and the count ratio is recalculated according to the adjusted time window to re-judge whether the count ratio meets the preset condition.

[0099] Optionally, the τ value may be adjusted by presetting a step length, gradually increasing the τ value according to the step length, and traversing the τ value until a preset condition is met.

[0100] Step S500: If the count ratio satisfies the preset condition, a macroscopic capture cross section of the formation is calculated according to the count ratio.

[0101] Specifically, when the count ratio is equal to the fixed coefficient or the error between the count ratio and the fixed coefficient is the smallest, Sigma is calculated based on the τ value that satisfies the count ratio condition by the relationship between τ and Σ:

[0102]

[0103] Optionally, the formation macroscopic capture cross section Sigma can also be calculated according to the counting ratio using the following formula:

[0104]

[0105] Where Δt is the interval between the middle points of the time window, see Figure 4 ; N1 / N2 is the counting ratio of the first time window and the second time window.

[0106] Through the above steps, using the counting ratio closest to the fixed coefficient to calculate Sigma can improve the calculation accuracy and the method has strong adaptability.

[0107] Example 2

[0108] Based on the same principle as the above method, a specific implementation method of a formation macroscopic capture cross section calculation method based on a sliding time window at a depth of 3132-3139m in a certain measured well is proposed, including the following steps:

[0109] Step A1, obtaining a gamma time spectrum.

[0110] Specifically, the formation macroscopic capture cross section can be combined with C / O to evaluate the formation saturation, which is an important reservoir parameter. In the formation, because the capture cross section of chlorine is large and exists in the pore water in a free ion state, when the formation water salinity is high, measuring the Sigma of the formation can assist in evaluating the water saturation content. Under different porosities, the volume ratio of the formation to the porosity changes, so the measured capture cross section will also change.

[0111] Take the 60us burst pulse as an example. Figure 5 and Figure 6The variation of the captured gamma-ray time spectrum collected at different porosities in the capture mode is shown. Figure 5 When the mineralization is 0kppm, the time spectrum is mainly divided into two intervals. In the first interval, the captured gamma count increases. This area is generated by the absorption of thermal neutrons formed by the slowing down of the environment when the fast neutrons explode. The second interval is the captured gamma generated by the slowing down of the neutrons after the explosion period of 60us. The attenuation of this area can reflect the neutron capture ability of the formation, that is, the Sigma value of the formation can be measured. Figure 6 , when the mineralization is 600kppm, with the increase of mineralization, different porosity The difference in the time spectrum attenuation becomes increasingly obvious.

[0112] Figure 7 It shows the variation of different mineralization under the same porosity. Figure 7 , with the increase of mineralization, the neutron capture ability of the formation is enhanced, resulting in faster decay of the captured gamma. At 600kppm, the gamma statistics deteriorate after 300us, and the time spectrum gradually disperses. At 0kppm, the formation Sigma is small, so the gamma time spectrum decays slowly. Therefore, it can be seen here that if the traditional windowing method of calculating Sigma is used, the time spectrum will decay quickly in a larger Sigma environment, resulting in low utilization of the time spectrum and poor statistics. However, in an environment with a smaller formation Sigma, the time gate will not be wide enough, resulting in errors in the calculation of Sigma.

[0113] The SGA measurement values ​​at the depth of 3132-3139m in a well of PNST were selected. The time spectrum collected by the PNST tool is divided into 100 channels, and each channel is separated by 10us.

[0114] Step A2, calculate the formation macro capture cross section Sigma.

[0115] Specifically, when calculating Sigma, the step size of the τ value needs to be small enough to sensitively reflect the change of Sigma. For the measured time spectrum data, the interval is 10us, and the Sigma calculated based on the τ value can only reflect the change of Sigma under this interval. Since the time spectrum is longer when Sigma is smaller, the time spectrum needs to be long enough to obtain the best calculated value. However, the measured time spectrum has no information after 1000us, which limits the calculation range of Sigma.

[0116] Figure 8 shows the direct measurement results of the sliding time window, see Figure 8Sigma cannot be calculated when the count is lower than 19 c.u., and the step-like change also reflects the poor resolution caused by the measured 10us interval. The above problem can be improved by obtaining the count ratio of the two time windows and calculating Sigma based on the count ratio.

[0117] The calculation formula of Sigma is:

[0118]

[0119] Fig. 9 The comparison results of sliding time window and fixed time window are shown in Fig. 9 , where the absolute error calculated by the sliding time window is overall low; while the fixed time window shows insufficient absolute error when the Sigma changes at a higher level. In addition, the root mean square error of the sliding time window method is 0.7405; the root mean square error of the fixed time window method is 1.0480.

[0120] This method does not rely on prior knowledge to calculate Sigma. It is easy to calculate and has strong adaptability. It can obtain better results than a fixed time window.

[0121] Example 3

[0122] Based on the same principle as the above method, a formation macroscopic capture cross section calculation system based on sliding time window is also proposed, see Fig.10 The formation macroscopic capture section calculation system based on sliding time window of the embodiment of the present application includes:

[0123] A time spectrum acquisition module 100 is used to acquire a time spectrum and initialize the thermal neutron decay lifetime τ;

[0124] A time window generating module 200, configured to generate a time window on the time spectrum according to the thermal neutron decay lifetime τ;

[0125] The counting ratio module 300 is used to calculate the counting ratio of the time window and determine whether the counting ratio meets a preset condition;

[0126] An iteration module 400, configured to modify the thermal neutron decay lifetime τ, slide the time window, and recalculate the count ratio when the count ratio does not meet the preset condition;

[0127] The output module 500 is used to calculate the formation macroscopic capture cross section according to the counting ratio when the counting ratio meets the preset condition.

[0128] Obviously, those skilled in the art should understand that all or part of the processes in the above-mentioned embodiment method can be implemented by instructing the relevant hardware through a computer program. The program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above-mentioned control methods. The modules or steps of the present invention can be implemented by a general-purpose computing device. They can be concentrated on a single computing device or distributed on a network composed of multiple computing devices. Optionally, they can be implemented by program codes executable by computing devices, so that they can be stored in a storage device and executed by the computing device, or they can be made into individual integrated circuit modules respectively, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. In this way, the present invention is not limited to any specific combination of hardware and software.

[0129] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment method can be implemented by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above-mentioned control methods. Among them, the storage medium can be a disk, an optical disk, a read-only memory (ROM), a random access memory (RAM), a flash memory (Flash Memory), a hard disk (Hard Disk Drive, abbreviated as: HDD) or a solid-state drive (SSD), etc.; the storage medium can also include a combination of the above-mentioned types of memory.

[0130] Example 4

[0131] Furthermore, an electronic device is proposed, comprising:

[0132] processor;

[0133] a memory for storing processor-executable instructions;

[0134] The processor is configured to implement the method for calculating the formation macroscopic capture cross section based on a sliding time window of the above embodiment when executing the executable instructions.

[0135] The electronic device of the embodiment of the present application includes a processor and a memory for storing processor executable instructions, wherein the processor is configured to implement any of the above-mentioned methods for calculating the formation macroscopic capture cross section based on a sliding time window when executing the executable instructions.

[0136] It should be noted that the number of processors may be one or more. At the same time, the electronic device in the embodiment of the present application may also include an input device and an output device. The processor, memory, input device, and output device may be connected via a bus or in other ways, which are not specifically limited here.

[0137] The memory, as a computer-readable storage medium for implementing the formation macroscopic capture cross-section calculation method based on a sliding time window, can be used to store software programs, computer executable programs, and various modules, such as: the program or module corresponding to the formation macroscopic capture cross-section calculation method based on a sliding time window in the embodiment of the present application. The processor executes various functional applications and data processing of the electronic device by running the software program or module stored in the memory.

[0138] The input device can be used to receive input numbers or signals. The signal can be a key signal related to user settings and function control of the device / terminal / server. The output device can include a display device such as a display screen.

[0139] The embodiments of the present application have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The selection of terms used herein is intended to best explain the principles of the embodiments, practical applications, or technical improvements in the market, or to enable other persons of ordinary skill in the art to understand the embodiments disclosed herein.

Claims

1. A method for calculating the macroscopic capture cross section of a formation based on a sliding time window, characterized in that: The following steps are involved: Get the time spectrum and initialize the thermal neutron decay lifetime τ; Generating a time window on the time spectrum according to the thermal neutron decay lifetime τ; Calculating the count ratio of the time window, and determining whether the count ratio meets a preset condition; If the counting ratio does not meet the preset condition, modify the thermal neutron decay lifetime τ, slide the time window, and recalculate the counting ratio; If the count ratio satisfies the preset condition, the macroscopic capture cross section of the formation is calculated according to the count ratio.

2. The method for calculating the formation macroscopic capture cross section based on a sliding time window according to claim 1, characterized in that: The time window includes a first time window and a second time window; The start time of the first time window is t1, the end time is t2, and t2-t1=τ; The start time of the second time window is t3, the end time is t4, and t4-t3=2τ.

3. The method for calculating the formation macroscopic capture cross section based on a sliding time window according to claim 2, characterized in that: The end time t2 of the first time window is equal to the start time t3 of the second time window.

4. The method for calculating the formation macroscopic capture cross section based on a sliding time window according to claim 3 is characterized in that: The time between the start time t1 of the first time window and the end time of the neutron burst pulse is 2τ.

5. The method for calculating the formation macroscopic capture cross section based on a sliding time window according to claim 3 or 4, characterized in that: The calculating the count ratio of the time window includes: Derive expressions for the number of thermal neutrons in the first time window and the second time window; The expression for the number of thermal neutrons in the first time window is: The expression for the number of thermal neutrons in the second time window is: The ratio of the number of thermal neutrons in the first time window to the number of thermal neutrons in the second time window is calculated to obtain a counting ratio. Among them, N0 is the initial value of the number of thermal neutrons, is the average diffusion velocity of thermal neutrons.

6. The method for calculating the formation macroscopic capture cross section based on a sliding time window according to claim 5, characterized in that: The calculation formula of the counting ratio is:

7. The method for calculating the formation macroscopic capture cross section based on a sliding time window according to claim 1, characterized in that: The preset condition is that the count ratio is equal to the fixed coefficient or the error between the count ratio and the fixed coefficient is the smallest, and the fixed coefficient is:

8. The method for calculating the formation macroscopic capture cross section based on a sliding time window according to claim 1, characterized in that: The formula for calculating the formation macroscopic capture cross section according to the counting ratio is: Where Δt is the interval between the middle points of the time window.

9. A formation macroscopic capture cross section calculation system based on sliding time window, characterized in that: include: A time spectrum acquisition module is used to acquire the time spectrum and initialize the thermal neutron decay lifetime τ; A time window generating module, used for generating a time window on the time spectrum according to the thermal neutron decay lifetime τ; A counting ratio module, used to calculate the counting ratio of the time window and determine whether the counting ratio meets a preset condition; An iteration module, used for modifying the thermal neutron decay lifetime τ, sliding the time window, and recalculating the count ratio when the count ratio does not meet the preset condition; The output module is used to calculate the formation macroscopic capture cross section according to the counting ratio when the counting ratio meets the preset condition.

10. An electronic device, characterized in that: include: processor; a memory for storing processor-executable instructions; Wherein, the processor is configured to implement the method for calculating the macroscopic capture cross section of the formation based on a sliding time window as described in any one of claims 1 to 8 when executing the executable instructions.

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