Prediction System and Method for Delayed Coking Product Distribution
By using a delayed coking product distribution prediction system, a reference device is selected and data deviations are corrected using the Euclidean distance function, thus solving the problem of the universality of delayed coking product distribution prediction and achieving accurate prediction for any raw material.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- PETROCHINA CO LTD
- Filing Date
- 2021-07-20
- Publication Date
- 2026-06-30
AI Technical Summary
Existing methods for predicting the distribution of delayed coking products lack universality and cannot accurately predict the product distribution of unconventional raw materials.
A delayed coking product distribution prediction system was established. Through a delayed coking unit library, a heavy oil thermal processing performance evaluation device, and a reference unit selection module, the Euclidean distance was calculated using the Euclidean distance function. The delayed coking unit with the smallest Euclidean distance was selected as the reference unit, and data processing was performed to correct data deviations, thereby obtaining reliable product distribution prediction results.
It improves the accuracy and adaptability of product distribution forecasting for any conventional or unconventional industrial raw materials, corrects data biases, and provides reliable product distribution forecasts.
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Figure CN115936160B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of petroleum processing technology, and more specifically, to a prediction system and method for the distribution of delayed coking products. Background Technology
[0002] Delayed coking is a process in which heavy oil is rapidly heated to the reaction temperature in a coking furnace, and then fed into a coking tower to complete a deep thermal reaction, producing gaseous, liquid, and solid (coke) products. Due to its advantages such as strong feedstock adaptability, mature and reliable technology, and low equipment investment, delayed coking remains one of the main methods for heavy oil processing in refining and chemical enterprises, especially for processing low-quality residue oil. Currently, with the increasing demand for processing refinery waste oil and sludge oil using delayed coking units, higher requirements are being placed on the deterioration and diversification of feedstocks and the accuracy of product distribution in delayed coking processes.
[0003] Product distribution in delayed coking units is a crucial indicator affecting the unit's economic efficiency and provides significant reference value for feedstock processing scheme formulation, operating parameter optimization, and techno-economic evaluation. The reaction process of heavy oil within the coking tower is complex, and the reaction mechanism is not yet fully understood, resulting in poor accuracy of conventional empirical prediction models. Therefore, accurately predicting the product distribution of specific feedstocks in delayed coking units for which there is no prior processing experience is of significant practical guiding importance.
[0004] Currently, methods for predicting the product distribution of delayed coking mainly fall into two categories: experimental evaluation and correlation model prediction. Experimental evaluation involves evaluating the raw materials under set reaction temperatures and times, and then collecting and measuring the post-reaction products to obtain the product distribution. This method has advantages such as low raw material consumption, controllable reaction conditions, and the ability to further analyze product properties. However, because experimental conditions cannot fully simulate the reaction conditions of industrial plants, especially the actual residence time within the coke tower, there is still a significant deviation between the experimentally evaluated product distribution and the results of actual industrial plants. Correlation model prediction methods are based on the correlation calculation of product distribution using industrial or experimental data on raw material composition, reaction conditions, and product distribution. These are black-box models, and due to limitations in the range of the underlying correlation data, their applicability is also very limited, with significant deviations in prediction results for unconventional raw materials for which there is no processing experience.
[0005] The primary influencing factor on the product distribution of delayed coking is the property of the feedstock, followed by reaction conditions (reaction temperature, pressure, recycle ratio, etc.). Experimental evaluation methods focus on the impact of feedstock properties, while correlation modeling, although considering both feedstock properties and reaction conditions, is limited by the complexity of feedstock composition and reaction mechanisms, making it unsuitable for predicting unconventional feedstocks. Therefore, establishing a product distribution prediction model with high universality is urgently needed to expand the feedstock adaptability of delayed coking units and leverage their technological advantages. Summary of the Invention
[0006] The main objective of this invention is to provide a prediction system and method for the distribution of delayed coking products, in order to solve the problem that the existing methods for predicting the distribution of delayed coking products lack universality.
[0007] To achieve the above objectives, according to one aspect of the present invention, a prediction system for the distribution of delayed coking products is provided, comprising: a delayed coking unit library, the delayed coking unit library including multiple delayed coking units and delayed coking product yield data of at least one industrial raw material on each delayed coking unit; a heavy oil thermal processing performance evaluation device, which performs delayed coking treatment on each industrial raw material under set test conditions to obtain test product yield data; a reference device selection module, which calculates the Euclidean distance between the test product yield data and the delayed coking product yield data of the same industrial raw material using an Euclidean distance function, and selects the delayed coking unit corresponding to the minimum Euclidean distance of any industrial raw material as the reference device for that industrial raw material; and a data processing module, used to calculate the ratio of the delayed coking product yield data of the reference device for each delayed coking product to the test product yield corresponding to the test conditions, and to calculate the product of each test product yield and the ratio corresponding to each product and perform normalization processing to obtain the predicted product distribution.
[0008] Furthermore, the aforementioned delayed coking products include gaseous products, liquid products, and coke products.
[0009] Furthermore, the above-mentioned test conditions include a coking reaction temperature of 400–500°C, a coking reaction time of 30–200 min, and a coking reaction pressure of 0.1–1.5 MPa.
[0010] Furthermore, the above Euclidean distance function is:
[0011]
[0012] Among them, X g0 1 X l0 1 X s0 1 These represent the gaseous product yield, liquid product yield, and coke product yield under the experimental conditions, respectively; X g0 2 X l0 2 X s0 2 These represent the gas product yield, liquid product yield, and coke product yield in the delayed coking unit's storage area, respectively.
[0013] Further immediate normalization is achieved through Formula III.
[0014] X ip =(X i0 P i ) / ∑(X i0 P i )×100%
[0015] Formula III
[0016] Among them, X ip X represents the predicted yield for any product; i0 P represents the yield of any product under the experimental conditions. i =Xipr / Xi0r, where Xipr is the product yield of any product from the reference unit, and Xi0r is the product yield of the delayed coking product corresponding to the test conditions.
[0017] According to another aspect of this application, a method for predicting the distribution of delayed coking products is provided. This method includes: collecting delayed coking product yield data of industrial raw materials processed by each delayed coking unit; performing delayed coking on each industrial raw material under set test conditions using a heavy oil thermal processing performance evaluation device to obtain test product yield data; calculating the Euclidean distance between the test product yield data and the delayed coking product yield data of the same industrial raw material using an Euclidean distance function, wherein the delayed coking unit corresponding to the minimum Euclidean distance for any industrial raw material is used as a reference unit for that industrial raw material; calculating the ratio of the delayed coking product yield data of the reference unit to the product yield corresponding to the test conditions; and calculating the product of each test product yield and the corresponding ratio, and performing normalization processing to obtain the predicted product distribution.
[0018] Furthermore, the aforementioned delayed coking products include gaseous products, liquid products, and coke products.
[0019] Furthermore, the above-mentioned test conditions include a coking reaction temperature of 400–500°C, a coking reaction time of 30–200 min, and a coking reaction pressure of 0.1–1.5 MPa.
[0020] Furthermore, the above Euclidean distance function is:
[0021]
[0022] Among them, X g0 1 X l0 1 X s0 1 These represent the gaseous product yield, liquid product yield, and coke product yield under the experimental conditions, respectively; X g02 X l0 2 X s0 2 These represent the gas product yield, liquid product yield, and coke product yield in the delayed coking unit's storage area, respectively.
[0023] Furthermore, the above ratio is calculated using Formula II: Pi = Xipr / Xi0r, where Xipr is the product yield of any product from the reference unit, and Xi0r is the product yield of the delayed coking product corresponding to the test conditions;
[0024] Normalization is achieved through Formula III.
[0025] X ip =(X i0 P i ) / ∑(X i0 P i )×100%
[0026] Formula III
[0027] Among them, X ip X represents the predicted yield for any product; i0 The yield of any product under the test conditions.
[0028] Applying the technical solution of this invention, the aforementioned prediction system includes a delayed coking unit library, which can collect data on the raw materials processed by delayed coking units in various industrial applications and the yields of each product from those raw materials, thereby forming a database that can generate raw material and delayed coking product yields. Furthermore, this application utilizes a typical heavy hot oil processing performance evaluation device to perform delayed coking treatment on the aforementioned industrial raw materials under set test conditions, obtaining test product yield data. A reference device selection module processes the aforementioned test product yield data and delayed coking product yield data to calculate the Euclidean distance, and selects a suitable reference device for each industrial raw material based on this distance. A data processing module corrects for data deviations caused by the reference device and experimental conditions, thereby obtaining reliable product distribution prediction results. The aforementioned prediction system is applicable to any conventional industrial raw material as well as any unconventional industrial raw material, and the data reliability is improved after correction, demonstrating the high adaptability and accuracy of the prediction system in this application. Attached Figure Description
[0029] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:
[0030] Figure 1A schematic diagram of the prediction process for delayed coking product distribution according to Embodiment 1 of the present invention is shown; and
[0031] Figure 2 The variation curves of test conditions for delayed coking according to Embodiment 1 of the present invention are shown. Detailed Implementation
[0032] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.
[0033] As analyzed in the background section of this application, the existing methods for predicting the distribution of delayed coking products are not universally applicable. To address this issue, this application provides a prediction system and method for predicting the distribution of delayed coking products.
[0034] In one embodiment of this application, a prediction system for the distribution of delayed coking products is provided. The prediction system includes: a delayed coking unit library, a heavy oil thermal processing performance evaluation device, a reference device selection module, and a data processing module. The delayed coking unit library includes multiple delayed coking units and delayed coking product yield data for each delayed coking unit containing at least one industrial raw material. The heavy oil thermal processing performance evaluation device performs delayed coking treatment on each industrial raw material under set test conditions to obtain test product yield data. The reference device selection module uses a Euclidean distance function to calculate the Euclidean distance between the test product yield data and the delayed coking product yield data for the same industrial raw material, and selects the delayed coking unit corresponding to the minimum Euclidean distance for any industrial raw material as the reference device for that industrial raw material. The data processing module calculates the ratio of the delayed coking product yield data of the reference device for each delayed coking product to the test product yield corresponding to the test conditions, calculates the product of each test product yield and the ratio corresponding to each product, and performs normalization processing to obtain the predicted product distribution.
[0035] The aforementioned prediction system includes a delayed coking unit library, which can collect data on the raw materials processed by delayed coking units in various industrial applications and the yields of each product from those raw materials, thereby forming a database that can generate raw material and delayed coking product yields. Furthermore, this application utilizes a typical heavy hot oil processing performance evaluation device to perform delayed coking treatment on the aforementioned industrial raw materials under set test conditions, obtaining test product yield data. A reference device selection module processes the aforementioned test product yield data and delayed coking product yield data to calculate the Euclidean distance, and uses this as a basis to select a suitable reference device for each industrial raw material. A data processing module corrects for data deviations caused by the reference device and experimental conditions, thereby obtaining reliable product distribution prediction results. The aforementioned prediction system is applicable to any conventional industrial raw material as well as any unconventional industrial raw material, and the data reliability is improved after correction, demonstrating the high adaptability and accuracy of the prediction system in this application.
[0036] The heavy heat oil processing performance evaluation device of this application is a conventional heavy heat oil processing performance evaluation device in this field, such as the heavy heat oil processing performance evaluation device designed by China University of Petroleum (East China).
[0037] The delayed coking product distribution prediction system of this application predicts delayed coking products in the same way as the prior art, by clustering the products and then performing cluster analysis. In order to simplify the analysis method, the aforementioned delayed coking products include gaseous products, liquid products and coke products.
[0038] In some embodiments of this application, typical experimental conditions are summarized based on current delayed coking process conditions, including a coking reaction temperature of 400–500°C, a coking reaction time of 30–200 min, and a coking reaction pressure of 0.1–1.5 MPa. These experimental conditions are universally applicable. More specifically, a coking reaction temperature of 450°C, a coking reaction time of 60 min, and a coking reaction pressure of 0.1–1.5 MPa.
[0039] Since the delayed coking products of this application are widely distributed and fall within the scope of Euclidean distance function calculation in n-dimensional space, the preferred Euclidean distance function is:
[0040]
[0041] Among them, X g0 1 X l0 1 X s0 1 These represent the gaseous product yield, liquid product yield, and coke product yield under the experimental conditions, respectively; X g0 2 X l02 X s0 2 These represent the gas product yield, liquid product yield, and coke product yield in the delayed coking unit's storage area, respectively.
[0042] In some embodiments, the above normalization process is implemented using Formula III.
[0043] X ip =(X i0 P i ) / ∑(X i0 P i )×100%
[0044] Formula III
[0045] Among them, X ip X represents the predicted yield for any product; i0 P represents the yield of any product under the experimental conditions. i =Xipr / Xi0r, where Xipr is the product yield of any product from the reference unit, and Xi0r is the product yield of the delayed coking product corresponding to the test conditions.
[0046] The above normalization method effectively corrects for data deviations caused by the reference device and experimental conditions, and the accuracy of the results has been verified in practical applications.
[0047] In another typical embodiment of this application, a method for predicting the distribution of delayed coking products is provided. This method includes: collecting delayed coking product yield data of industrial raw materials processed by each delayed coking unit; performing delayed coking on each industrial raw material under set test conditions using a heavy oil thermal processing performance evaluation device to obtain test product yield data; calculating the Euclidean distance between the test product yield data and the delayed coking product yield data of the same industrial raw material using an Euclidean distance function, wherein the delayed coking unit corresponding to the minimum Euclidean distance for any industrial raw material is used as the reference unit for that industrial raw material; calculating the ratio of the delayed coking product yield data of the reference unit for each delayed coking product to the product yield corresponding to the test conditions; and calculating the product of each test product yield and the corresponding ratio, and performing normalization processing to obtain the predicted product distribution.
[0048] The aforementioned prediction method collects data on the raw materials processed by delayed coking units in various industrial applications and the yields of each product from those raw materials, thereby forming a library of delayed coking units that can generate yields of both raw materials and delayed coking products. Furthermore, this application utilizes a typical heavy hot oil processing performance evaluation device to perform delayed coking treatment on the aforementioned industrial raw materials under set test conditions, obtaining test product yield data. Then, the aforementioned test product yield data and delayed coking product yield data are processed to calculate the Euclidean distance, and based on this, a suitable reference unit is selected for each industrial raw material. Finally, data deviations caused by the reference unit and experimental conditions are corrected to obtain reliable product distribution prediction results. The aforementioned prediction method is applicable to any conventional industrial raw material as well as any unconventional industrial raw material, and the data reliability is improved after correction, demonstrating the high adaptability and accuracy of the prediction method in this application.
[0049] The delayed coking product distribution prediction system of this application predicts delayed coking products in the same way as the prior art, by clustering the products and then performing cluster analysis. In order to simplify the analysis method, the aforementioned delayed coking products include gaseous products, liquid products and coke products.
[0050] In some embodiments of this application, typical test conditions are summarized based on current delayed coking process conditions, including a coking reaction temperature of 400–500°C, a coking reaction time of 30–200 min, and a coking reaction pressure of 0.1–1.5 MPa.
[0051] Since the delayed coking products of this application are widely distributed and fall within the scope of Euclidean distance function calculation in n-dimensional space, the preferred Euclidean distance function is:
[0052]
[0053] Among them, X g0 1 X l0 1 X s0 1 These represent the gaseous product yield, liquid product yield, and coke product yield under the experimental conditions, respectively; X g0 2 X l0 2 X s0 2 These represent the gas product yield, liquid product yield, and coke product yield in the delayed coking unit's storage area, respectively.
[0054] In some embodiments, the above ratio is calculated using Formula II: P i=Xipr / Xi0r, where Xipr is the product yield of any product from the reference unit, and Xi0r is the product yield of the delayed coking product corresponding to the test conditions; normalization is achieved through Formula III.
[0055] X ip =(X i0 P i ) / ∑(X i0 P i )×100%
[0056] Formula III
[0057] Among them, X ip X represents the predicted yield for any product; i0 The yield of any product under the test conditions.
[0058] The following description, in conjunction with embodiments and accompanying drawings, illustrates the implementation steps of a delayed coking product distribution prediction method provided by the present invention. This is intended to help readers better understand the essence and characteristics of the present invention and is not intended to limit the scope of implementation of this invention.
[0059] Example 1
[0060] Figure 1 The specific implementation steps of Embodiment 1 are shown, mainly including: establishing a delayed coking device library, setting experimental conditions to perform delayed coking of the industrial raw materials of this embodiment to obtain the experimental product yield, selecting a reference device, and correcting the experimental product yield data based on the reference device. Specifically:
[0061] Establish a delayed coking unit library: Mark the distribution of industrial raw materials and products on the industrial units and record it in Table 1. Industrial unit 1 is the delayed coking unit of Liaohe Petrochemical, industrial unit 2 is the delayed coking unit of Jinzhou Petrochemical, and industrial unit 3 is the delayed coking unit of Jinxi Petrochemical.
[0062] Delayed coking of the aforementioned calibrated industrial raw materials was carried out under set test conditions: The raw materials were subjected to a thermal reaction experiment under the set test conditions in a heavy oil thermal processing performance evaluation device. The mass of the products (gas, liquid, and coke) after the reaction was collected and measured. The yield of the test products was calculated using the following formula and recorded in Table 1:
[0063] Experimental product yield Xi0 = mass of product obtained after reaction mi / mass of raw material before reaction M × 100%.
[0064] The experimental conditions were as follows: first-stage reaction temperature 450℃, total time 60 min; second-stage reaction temperature 500℃, total time 60 min; reaction pressure 0.1 MPa. Specific reaction temperature conditions are detailed in [link to relevant documentation]. Figure 2 .
[0065] The Euclidean distance function was used as a measure of sample data similarity. The Euclidean distance between the experimental product yield of the evaluated raw material and the product distribution of existing raw materials in the equipment database was calculated, with industrial equipment 3, which had the smallest Euclidean distance, serving as the reference equipment. The formula for calculating the Euclidean distance is as follows:
[0066]
[0067] Among them, X g0 1 X l0 1 X s0 1 These represent the gaseous product yield, liquid product yield, and coke product yield under the experimental conditions, respectively; X g0 2 X l0 2 X s0 2 These represent the gas product yield, liquid product yield, and coke product yield in the delayed coking unit's storage area, respectively.
[0068] The data correction method is as follows:
[0069] a) First, calculate Pi, the ratio of the product distribution of the reference device to the product distribution of the experiment under specific conditions.
[0070] P i =Xipr / Xi0r
[0071] Xipr is the product yield of any product from the reference unit, and Xi0r is the product yield of the delayed coking product corresponding to the test conditions.
[0072] b) Then, the device product distribution Xi0 and Pi of the evaluation raw material are multiplied sequentially and normalized to obtain the device product distribution Xip of the evaluation raw material:
[0073] X ip =(X i0 P i ) / ∑(X i0 P i )×100%
[0074] X ip X represents the predicted yield for any product; i0 The yield of any product under the test conditions is recorded in Table 1, and the product yield and corrected data of the test product are calculated according to the above calculation formula.
[0075] Table 1
[0076] Gas yield / % Liquid yield / % Coke yield / % Industrial Unit 1 7.76 61.56 30.68 Industrial Unit 2 9.79 60.56 29.65 Industrial Unit 3 9.92 64.79 25.29 Industrial Unit 4 8.79 62.76 28.45 test products 10.82 60.34 28.84 Corrected data 7.67 65.84 26.49
[0077] As can be seen from the above description, the embodiments of the present invention achieve the following technical effects:
[0078] The aforementioned prediction system includes a delayed coking unit library, which can collect data on the raw materials processed by delayed coking units in various industrial applications and the yields of each product from those raw materials, thereby forming a database that can generate raw material and delayed coking product yields. Furthermore, this application utilizes a typical heavy hot oil processing performance evaluation device to perform delayed coking treatment on the aforementioned industrial raw materials under set test conditions, obtaining test product yield data. A reference device selection module processes the aforementioned test product yield data and delayed coking product yield data to calculate the Euclidean distance, and uses this as a basis to select a suitable reference device for each industrial raw material. A data processing module corrects for data deviations caused by the reference device and experimental conditions, thereby obtaining reliable product distribution prediction results. The aforementioned prediction system is applicable to any conventional industrial raw material as well as any unconventional industrial raw material, and the data reliability is improved after correction, demonstrating the high adaptability and accuracy of the prediction system in this application.
[0079] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A prediction system for the distribution of delayed coking products, characterized in that, include: A library of delayed coking units, comprising multiple delayed coking units and yield data of delayed coking products from each unit containing at least one industrial raw material; A heavy oil thermal processing performance evaluation device, wherein the heavy oil thermal processing performance evaluation device performs delayed coking treatment on each of the industrial raw materials under set test conditions to obtain test product yield data; The reference device selection module uses the Euclidean distance function to calculate the Euclidean distance between the experimental product yield data and the delayed coking product yield data of the same industrial raw material, and selects the delayed coking device corresponding to the minimum Euclidean distance of any industrial raw material as the reference device for that industrial raw material. The data processing module is used to calculate the ratio of the delayed coking product yield data of the reference device for each delayed coking product to the yield of the test product corresponding to the test conditions, and to calculate the product of each test product yield and the ratio corresponding to each product and perform normalization processing to obtain the predicted product distribution.
2. The prediction system according to claim 1, characterized in that, The delayed coking products include gaseous products, liquid products, and coke products.
3. The prediction system according to claim 1, characterized in that, The test conditions include a coking reaction temperature of 400–500°C, a coking reaction time of 30–200 min, and a coking reaction pressure of 0.1–1.5 MPa.
4. The prediction system according to claim 1, characterized in that, The Euclidean distance function is: Among them, X g0 1 X l0 1 X s0 1 These are the gas product yield, liquid product yield, and coke product yield under the aforementioned test conditions, respectively. X g0 2 X l0 2 X s0 2 These are the gas product yield, liquid product yield, and coke product yield in the delayed coking unit, respectively.
5. The prediction system according to any one of claims 1 to 4, characterized in that, The normalization process is achieved through Formula III. X ip =(X i0 P i ) / ∑(X i0 P i )×100% Formula III Among them, X ip For the predicted yield of any product; X i0 The yield of any product under the aforementioned test conditions; P i =Xipr / Xi0r, where Xipr is the product yield of any product of the reference device, and Xi0r is the product yield of the delayed coking product corresponding to the test conditions.
6. A method for predicting the distribution of delayed coking products, characterized in that, The prediction method includes: Collect data on the yield of delayed coking products from industrial raw materials processed by each delayed coking unit; The industrial raw materials were subjected to delayed coking under set test conditions using a heavy oil thermal processing performance evaluation device to obtain the yield data of the test products. The Euclidean distance function is used to calculate the Euclidean distance between the experimental product yield data and the delayed coking product yield data of the same industrial raw material, wherein the delayed coking device corresponding to the minimum Euclidean distance of any industrial raw material is used as the reference device for that industrial raw material. Calculate the ratio of the delayed coking product yield data of the reference device for each delayed coking product to the product yield corresponding to the test conditions; The predicted product distribution is obtained by calculating the product of the yield of each of the test products and the corresponding ratio, and then normalizing the product.
7. The prediction method according to claim 6, characterized in that, The delayed coking products include gaseous products, liquid products, and coke products.
8. The prediction method according to claim 6, characterized in that, The test conditions include a coking reaction temperature of 400–500°C, a coking reaction time of 30–200 min, and a coking reaction pressure of 0.1–1.5 MPa.
9. The prediction method according to claim 6, characterized in that, The Euclidean distance function is: Among them, X g0 1 X l0 1 X s0 1 These are the gas product yield, liquid product yield, and coke product yield under the aforementioned test conditions, respectively. X g0 2 X l0 2 X s0 2 These are the gas product yield, liquid product yield, and coke product yield in the delayed coking unit, respectively.
10. The prediction method according to any one of claims 6 to 9, characterized in that, The ratio is calculated using Formula II: P i =Xipr / Xi0r, where Xipr is the product yield of any product of the reference device, and Xi0r is the product yield of the delayed coking product corresponding to the test conditions; The normalization process is achieved through Formula III. X ip =(X i0 P i ) / ∑(X i0 P i )×100% Formula III Among them, X ip For the predicted yield of any product; X i0 The yield of any product under the stated test conditions.