Method for evaluating reserves of oil and gas products and byproducts of oil and gas products and related device

By determining the sources of oil and gas field by-products and establishing an attribution model, combined with oil and gas field development plans, the problem of existing technologies being unable to assess light hydrocarbon, liquefied gas and ethane reserves has been solved, and accurate and reasonable assessment of oil and gas field by-product reserves has been achieved.

CN120671949APending Publication Date: 2025-09-19PETROCHINA CO LTD
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Patent Information

Application Number
CN202410314771.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-03-19
Publication Date
2025-09-19

AI Technical Summary

Technical Problem

Existing oil and gas field reserve assessment methods are unable to effectively assess the reserves of light hydrocarbons, liquefied gas, and by-products such as ethane, resulting in discrepancies between oil and gas field reserves and commodity volumes.

Method used

By determining the source of by-products, extracting by-products such as light hydrocarbons, liquefied gas and ethane, establishing an attribution model, and combining it with the oil and gas field development plan, using the volume method or decline curve method for evaluation, and using inlet and outlet flow meters to calculate the gas consumption per ton of liquid of the by-products, we ensure the accuracy and reasonable attribution of by-product output.

Benefits of technology

It achieves accurate assessment of oil and gas field by-product reserves, avoids resource waste and misreporting, and improves the accuracy and compliance of reserve assessment.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention discloses an oil and gas product and by-product reserve assessment method and a related device. The method comprises the following steps: determining a by-product source and extracting a by-product; splitting a by-product yield from the extracted by-product; establishing an affiliation model by using the split byproduct yield; and establishing an evaluation method according to the established affiliation model. According to oil and gas production changes, the oil consumption per ton is quantitatively calculated, a reasonable evaluation method is selected in combination with actual production to evaluate reserves, and compliant reasonable evaluation and oil and gas reserves disclosure are achieved.
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Description

Technical Field

[0001] The present invention belongs to the technical field of oil and gas development, and in particular relates to a method for evaluating reserves of oil and gas products and by-products and related devices. Background Art

[0002] Oil and gas field companies must disclose their assessed reserves and annual commodity volume every year. The commodity volume disclosed each year consists of three parts: the output of oil, gas and their associated products, and the output of secondary extracted light hydrocarbons, liquefied gas and ethane by-products. In the current assessment method, only the reserves of oil, gas and their associated products in the oil and gas field are assessed. For oil and gas fields that have not yet entered the decline stage, the volumetric method is generally used to assess the reserves of oil and gas. The volumetric method assessment is combined with the oil and gas field development plan, and the reserves of oil, gas and their associated products are assessed in two stages (stable production stage + decline stage). For oil and gas fields that have entered the decline stage, the decline curve method is used to assess the reserves of oil, gas and their associated products.

[0003] However, existing assessment methods can only assess the reserves of oil, gas and their associated products. They cannot effectively complete the assessment of the reserves of light hydrocarbons, liquefied gas and ethane by-products contained in the natural gas in the oil and gas fields, resulting in discrepancies between the reserves and commodity quantities of the oil and gas fields and the actual production, which affects the assessment work. Summary of the Invention

[0004] The purpose of the present invention is to solve the problems in the prior art and provide a method for evaluating the reserves of oil and gas products and by-products and related devices.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] According to a first aspect of the present invention, a method for evaluating reserves of oil and gas products and their by-products is provided, comprising:

[0007] Identifying the source of by-products and extracting said by-products;

[0008] splitting a by-product yield from the extracted by-product;

[0009] establishing an attribution model using the split by-product yield;

[0010] An evaluation method is established based on the established attribution model.

[0011] Furthermore, before determining the source of the by-product and extracting the by-product, the process further includes:

[0012] Sort out the types of by-products based on the process flow, production equipment, production raw materials and production products.

[0013] Furthermore, the by-product types include light hydrocarbons, liquefied gas and ethane.

[0014] Furthermore, the determining of the source of the by-product and extracting the by-product specifically includes:

[0015] The source oil and gas fields of the by-products are determined in combination with the production equipment, production raw materials and production products, and the by-products are extracted from the oil and gas fields.

[0016] Furthermore, the by-product yield is split from the extracted by-product, specifically comprising:

[0017] The extracted by-products are split according to the proportion of each component in the by-products during extraction.

[0018] Furthermore, an attribution model is established using the split by-product yield, specifically including:

[0019] A by-product production attribution model is established based on the weighted proportion of the product of natural gas production and component content.

[0020] Furthermore, the evaluation method is established based on the established attribution model, specifically including:

[0021] Establishing evaluation principles;

[0022] According to the established evaluation principles, by-products are included as independent product items in the corresponding units to participate in the calculation of economic limit output;

[0023] For oil and gas fields that have not yet entered the decline phase, the volumetric method is used for evaluation, and condensate oil and secondary extraction by-products are evaluated simultaneously as associated products;

[0024] For oil and gas fields that have entered the decline stage, the decline curve method is used to evaluate the reserves of oil, gas and their associated products;

[0025] The natural gas loss and the corresponding by-product output are obtained using the inlet and outlet flow meters. The gas consumption per ton of liquid of the by-product is calculated by dividing the natural gas loss by the by-product output.

[0026] According to a second aspect of the present invention, there is provided a system for evaluating reserves of oil and gas products and their by-products, comprising:

[0027] An extraction module, used for extracting by-products;

[0028] A splitting module, used for splitting the output of the extracted by-products;

[0029] A model building module for building an attribution model using the split by-product yields;

[0030] The evaluation method establishment module is used to establish an evaluation method based on the established attribution model.

[0031] According to a third aspect of the present invention, an electronic device is provided, comprising a memory, a processor, and a computer program stored in the memory and executable in the processor, wherein the processor implements the steps of the above-described method for assessing reserves of oil and gas products and their by-products when executing the computer program.

[0032] According to a fourth aspect of the present invention, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method for evaluating reserves of oil and gas products and their by-products as described above are implemented.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] 1. This invention quantitatively calculates gas consumption per ton of oil based on changes in oil and gas production, assuming reasonable configuration of output, units, and gas sources. It also uses a reasonable assessment method based on actual production to assess reserves, thereby achieving the goal of compliant and reasonable assessment and disclosure of oil and gas reserves.

[0035] 2. The sources and extraction processes of by-products are clarified, making the splitting of by-product output more accurate and reliable. By determining the sources of by-products and extracting them, it can be ensured that the by-product data is accurate and complete in the subsequent reserve assessment process. At the same time, the precise splitting of by-product output also helps to avoid waste of resources and misreporting, and improves the accuracy of reserve assessment.

[0036] 3. By establishing an attribution model, the by-product output can be reasonably attributed to the corresponding oil and gas products, thereby achieving an accurate assessment of reserves. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0038] Figure 1 A flow chart of a method for evaluating reserves of oil and gas products and by-products provided by the present invention;

[0039] Figure 2 A flow chart of the gas field where the by-products originate in a method for evaluating the reserves of oil and gas products and by-products provided by the present invention;

[0040] Figure 3 This is a schematic diagram of a reserve assessment system for oil and gas products and their by-products provided by the present invention. DETAILED DESCRIPTION

[0041] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

[0042] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort shall fall within the scope of protection of the present invention.

[0043] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0044] In the description of the embodiments of the present invention, it should be noted that if the terms "upper," "lower," "horizontal," "inner," etc. appear, the orientation or positional relationship indicated is based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the inventive product is typically placed when in use. These terms are merely for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or component referred to must have a specific orientation, be constructed, or operate in a specific orientation. Therefore, they should not be construed as limitations on the present invention. In addition, the terms "first," "second," etc. are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0045] In addition, if the term "horizontal" appears, it does not mean that the component must be absolutely horizontal, but can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0046] In the description of the embodiments of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "disposed," "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0047] The present invention is described in further detail below with reference to the accompanying drawings:

[0048] The embodiment of the present invention provides a method for evaluating the reserves of oil and gas products and by-products and a related device.

[0049] like Figure 1 As shown, in a first aspect, an embodiment of the present invention provides a method for evaluating reserves of oil and gas products and by-products, comprising:

[0050] S101. Determine the source of by-products and extract them. For example, first sort out the types of by-products based on the process flow, production equipment, production raw materials and production products. Currently, the types of by-products extracted include light hydrocarbons, liquefied gas and ethane. Some of the light hydrocarbons come from crude oil, and the other two mainly come from natural gas. When extracting the above three by-products, it is necessary to determine the source oil and gas fields of the by-products based on the production equipment, production raw materials and production products, and extract the by-products from the oil and gas fields. For example, Figure 2 As shown, gas production area A contains two main product phases of oil and gas, and the by-products are extracted from natural gas, including one by-product, light hydrocarbons; gas production area B also contains two main product phases of oil and gas, and the by-products are also extracted from natural gas, including three by-products, light hydrocarbons, liquefied gas, and ethane. The light hydrocarbons, liquefied gas, and ethane extracted from the natural gas in gas production area B are divided into two parts: the first part is the light hydrocarbons and liquefied gas extracted from the natural gas at the oil and gas processing plant in gas production area B; the second part is the light hydrocarbons, liquefied gas, and ethane extracted from the natural gas in gas production area B through deep processing. In this embodiment, the by-products are mainly derived from light hydrocarbons and liquefied gas extracted from natural gas through dehydrogenation and light hydrocarbons, liquefied gas, and ethane extracted from natural gas through deep processing.

[0051] S102, splitting the by-product yield from the extracted by-product; splitting the extracted by-product according to the proportion of each component in the by-product during extraction. For example, Figure 2As shown, the sources of by-products include two parts. One part is the natural gas processing plants. Light hydrocarbons and liquefied gas extracted from the natural gas processing plants are each equipped with a separate metering device, which can directly obtain the output of light hydrocarbons and liquefied gas extracted from natural gas in the natural gas processing plant in this gas-producing area; the other part is the light hydrocarbons, liquefied gas and ethane extracted from the deep processing of natural gas. However, the natural gas sources include six gas-producing areas, namely A, B, C, D, E and F. Therefore, the output of light hydrocarbons, liquefied gas and ethane extracted from the natural gas of each gas-producing area in the recovery device needs to be split according to the proportion of natural gas received by the recovery device from each gas-producing area. For example, the total receiving capacity of the energy recovery device is 813.09 million cubic meters for deep processing to extract light hydrocarbons, liquefied gas and ethane. The receiving capacity of gas-producing area A is 142.36 million cubic meters, accounting for 17.5%; the receiving capacity of gas-producing area B is 152.39 million cubic meters, accounting for 18.7%; the receiving capacity of gas-producing area C is 356.24 million cubic meters, accounting for 43.8%; the receiving capacity of gas-producing area D is 85.75 million cubic meters, accounting for 10.5%; the receiving capacity of gas-producing area E is 62.86 million cubic meters, accounting for 7.7%; and the receiving capacity of gas-producing area A is 13.50 million cubic meters, accounting for 1.7%. For example, the output of light hydrocarbons and liquefied gas extracted by the oil and gas processing plant in Gas Area B is directly read through their respective flow meters; the output of light hydrocarbons, liquefied gas and ethane extracted from the natural gas in Gas Area B through deep processing is split according to the proportion of natural gas received by the recovery device from Gas Area B. The output of these two parts of by-products is added together to obtain the output of light hydrocarbons, liquefied gas and ethane extracted from the natural gas in Gas Area B.

[0052] S103. Establish an attribution model using the split by-product production. For example, since the price difference between light hydrocarbons and liquefied gas is small, while the price difference between ethane is large, based on the principle of simplifying the assessment work as much as possible, light hydrocarbons and liquefied gas are considered as one by-product, and ethane is considered as one by-product. The prices of light hydrocarbons and liquefied gas are taken as the weighted average of the prices of light hydrocarbons and liquefied gas. For example, if the price of light hydrocarbons is RMB 3,650 / ton, the production of light hydrocarbons is 580,000 tons, the price of liquefied gas is RMB 3,520 / ton, the production of light hydrocarbons is 650,000 tons, and the price of light hydrocarbons and liquefied gas is RMB 3,538.86 / ton. The differences in components between different gas reservoirs result in different production of by-products extracted from crude oil and natural gas in different blocks. A by-product production attribution model is established based on the weighted proportion of the product of natural gas production and component content. The specific calculation is as follows:

[0053] Calculate the weighted average gas composition:

[0054] r: component content in the gas production area; v: component content in different gas fields / blocks in the gas production area; q: production of different gas fields / blocks in the gas production area.

[0055] Calculate the ethane production of light hydrocarbon liquefied gas in each gas production area:

[0056] X: ethane production of light hydrocarbon liquefied gas in the gas production area; r: component content in the gas production area; x: production of different gas fields / blocks in the gas production area; t: total ethane production of light hydrocarbon liquefied gas.

[0057] Calculate the light hydrocarbon liquefied gas ethane production of each oil and gas production area assessment unit:

[0058]

[0059] q: ethane production of light hydrocarbon liquefied gas in the assessment unit of the gas production area; m: component content of the assessment unit of the gas production area; y: production of the assessment unit of the gas production area; X: total ethane production of light hydrocarbon liquefied gas in the gas production area.

[0060] S104. Establish an evaluation method based on the established attribution model; for example, establish evaluation principles; the evaluation principle is that light hydrocarbons, liquefied gas, ethane and other secondary extraction by-products are derived from oil and gas. The source of oil and gas is stable, and the output of light hydrocarbons, liquefied gas and ethane and other secondary extraction by-products is relatively stable. The output of by-products is controlled by the oil and gas source. The reserves of light hydrocarbons, liquefied gas and ethane and other secondary extraction by-products should be quantitatively evaluated in coordination with oil and gas. The production life of by-products should be consistent with that of main products such as oil and gas. They should be added to the corresponding evaluation unit as independent product items for evaluation; the output of corresponding light hydrocarbons, liquefied gas and ethane, light hydrocarbon and liquefied gas output superimposed as a by-product, ethane as a separate by-product, verify the output of natural gas and condensate oil, etc., and according to the established evaluation principles, the by-products (light hydrocarbons, liquefied gas and ethane) should be included as independent product items in the corresponding unit to participate in the calculation of economic limit output. The evaluation curve of light hydrocarbons, liquefied gas and ethane in the by-products has a decreasing trend and an economic cut-off date. The primary product of each assessment unit remains consistent with natural gas. For oil and gas fields that have not yet entered the decline phase, the volumetric method is used for assessment, with natural gas as the primary product and associated condensate, along with secondary light hydrocarbons, liquefied gas, and ethane byproducts, assessed simultaneously as associated products. In conjunction with the field development plan, the reserves of gas and its associated products are assessed in two stages (stable production stage + decline stage). For oil and gas fields entering the decline phase, the decline curve method is used to assess the reserves of oil, gas, and their associated products. Based on actual production trends, the decline type (APS decline, hyperbolic, or harmonic) is determined through comprehensive analysis. The monthly production on the assessment base date is generally the starting point for the assessment. Finally, based on material balance theory, using inlet and outlet flowmeters, the natural gas loss and the corresponding byproduct production are calculated. The gas consumption per ton of byproduct liquid is calculated by dividing the natural gas loss by the byproduct production. The gas consumption for the light hydrocarbon + liquefied gas and ethane reserve assessments is calculated based on the volume of natural gas consumed per ton of liquid hydrocarbon recovered. This consumption is deducted from the annual natural gas production and reserves during the assessment.

[0061] For example, taking the two assessment units A and B as examples, the main product of assessment unit A is natural gas, and the by-products are condensate oil, light hydrocarbons, liquefied gas and ethane. The volumetric method is used for annual reserve assessment. The main product assessment curve is a two-stage curve with stable production first and then decreasing. The assessment curve trends of by-products light hydrocarbons, liquefied gas and ethane are consistent with those of the main products.

[0062] Annual reserve assessment results of assessment unit A: annual production of light hydrocarbons and liquefied gas is 130,300 tons, with reserves of 1,033,500 tons; annual production of ethane is 150,200 tons, with reserves of 1,240,200 tons; annual production and reserves of natural gas minus the corresponding gas consumption are 1.773 billion cubic meters.

[0063] The main product of assessment unit B is natural gas, and the by-products are condensate oil, light hydrocarbons, liquefied gas and ethane. The dynamic method is used for annual PD reserve assessment. The assessment curve of the main product is a one-stage decreasing curve, and the assessment curve trends of by-products light hydrocarbons, liquefied gas and ethane are consistent with those of the main products.

[0064] The annual reserve assessment results of assessment unit B are as follows: the annual production of light hydrocarbons and liquefied gas is 36,000 tons, and the reserves are 57,800 tons; the annual production of ethane is 59,600 tons, and the reserves are 90,000 tons; the annual production and reserves of natural gas minus the corresponding gas consumption is 173 million cubic meters.

[0065] like Figure 3 As shown, in a second aspect, an embodiment of the present invention provides a system for evaluating reserves of oil and gas products and their by-products, including:

[0066] An extraction module, used for extracting by-products;

[0067] A splitting module, used for splitting the output of the extracted by-products;

[0068] A model building module for building an attribution model using the split by-product yields;

[0069] The evaluation method establishment module is used to establish an evaluation method based on the established attribution model.

[0070] In a third aspect, an embodiment of the present invention provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable in the processor, wherein the processor implements the steps of the above-described method for assessing reserves of oil and gas products and their by-products when executing the computer program.

[0071] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the method for assessing reserves of oil and gas products and their by-products as described above.

[0072] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be considered as equivalent replacement methods and are included in the scope of protection of the present invention.

[0073] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0074] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0075] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0076] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0077] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A method for evaluating reserves of oil and gas products and their by-products, characterized in that: include: Identifying the source of by-products and extracting said by-products; splitting a by-product yield from the extracted by-product; establishing an attribution model using the split by-product yield; An evaluation method is established based on the established attribution model.

2. The evaluation method according to claim 1, wherein: Before determining the source of by-products and extracting the by-products, it also includes: Sort out the types of by-products based on the process flow, production equipment, production raw materials and production products.

3. The evaluation method according to claim 2, wherein: The types of by-products include light hydrocarbons, liquefied gas and ethane.

4. The evaluation method according to claim 1, wherein: Determining the source of the by-product and extracting the by-product specifically includes: The source oil and gas fields of the by-products are determined in combination with the production equipment, production raw materials and production products, and the by-products are extracted from the oil and gas fields.

5. The evaluation method according to claim 1, wherein: The by-product yield is split from the extracted by-products, specifically including: The extracted by-products are split according to the proportion of each component in the by-products during extraction.

6. The evaluation method according to claim 1, wherein: The split by-product yield is used to establish an attribution model, specifically including: A by-product production attribution model is established based on the weighted proportion of the product of natural gas production and component content.

7. The evaluation method according to claim 1, wherein: The evaluation method is established based on the established attribution model, specifically comprising: Establishing evaluation principles; According to the established evaluation principles, by-products are included as independent product items in the corresponding units to participate in the calculation of economic limit output; For oil and gas fields that have not yet entered the decline phase, the volumetric method is used for evaluation, and condensate oil and secondary extraction by-products are evaluated simultaneously as associated products; For oil and gas fields that have entered the decline stage, the decline curve method is used to evaluate the reserves of oil, gas and their associated products; The natural gas loss and the corresponding by-product output are obtained using the inlet and outlet flow meters. The gas consumption per ton of liquid of the by-product is calculated by dividing the natural gas loss by the by-product output.

8. A system for evaluating reserves of oil and gas products and their by-products, characterized in that: include: An extraction module, used for extracting by-products; A splitting module, used for splitting the output of the extracted by-products; A model building module for building an attribution model using the split by-product yields; The evaluation method establishment module is used to establish an evaluation method based on the established attribution model.

9. An electronic device, characterized in that: The method comprises a memory, a processor, and a computer program stored in the memory and executable in the processor, wherein when the processor executes the computer program, the steps of the method for evaluating reserves of oil and gas products and their by-products according to any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method for evaluating reserves of oil and gas products and their by-products according to any one of claims 1 to 7 are implemented.