Harnessing machine learning and data analytics for a real time predictive model for a FCC pre-treatment unit

Abstract

This disclosure provides an apparatus and method for harnessing machine learning and data analytics for a real-time predictive model for a FCC pre-treatment unit. The method includes collecting operating parameters of a pre-treatment unit and fluid catalytic cracking (FCC) unit; evaluating an independent variable of the operating parameters; and adjusting an input to the pre-treatment unit to control the independent variable within specifications in an output of the FCC unit.

Description

TECHNICAL FIELD

This disclosure relates generally to industrial process control and automation systems and other systems using fluidized catalytic cracking (FCC) pre-treatment units. More specifically, this disclosure relates to an apparatus and method for harnessing machine learning and data analytics for a real-time predictive model for a FCC pre-treatment unit.

BACKGROUND

Industrial process control and automation systems are often used to automate large and complex industrial processes. These types of control and automation systems routinely include process controllers and field devices like sensors and actuators. Some of the process controllers typically receive measurements from the sensors and generate control signals for the actuators.

Model-based industrial process controllers are one type of process controller routinely used to control the operations of industrial processes. Model-based process controllers typically use one or more models to mathematically represent how one or more properties within an industrial process respond to changes made to the industrial process. Model-based controllers typically depend on having accurate models of a process's behavior in order to perform well and effectively control the process. As conditions change in the process, a controller's models typically need to be updated.

SUMMARY

This disclosure provides an apparatus and method for harnessing machine learning and data analytics for a real-time predictive model for a fluidized catalytic cracking (FCC) pre-treatment unit.

In a first embodiment, a method provides for harnessing machine learning and data analytics for a real-time predictive model for a FCC pre-treatment unit. The method includes collecting operating parameters of a pre-treatment unit and FCC unit; evaluating an independent variable of the operating parameters; and adjusting an input to the pre-treatment unit to control the independent variable within specifications in an output of the FCC unit.

In a second embodiment, an apparatus provides for harnessing machine learning and data analytics for a real-time predictive model for a FCC pre-treatment unit. The apparatus includes at least one memory and at least one processor operatively coupled to the at least one memory. The at least one processor collects operating parameters of a pre-treatment unit and FCC unit; evaluates an independent variable of the operating parameters; and adjusts an input to the pre-treatment unit to control the independent variable within specifications in an output of the FCC unit.

In a third embodiment, a non-transitory computer readable medium provides for harnessing machine learning and data analytics for a real-time predictive model for a FCC pre-treatment unit. The non-transitory machine-readable medium is encoded with executable instructions that, when executed, cause one or more processors to collect operating parameters of a pre-treatment unit and FCC unit; evaluate an independent variable of the operating parameters; and adjust an input to the pre-treatment unit to control the independent variable within specifications in an output of the FCC unit.

Other technical features may be readily apparent to one skilled in the art from the following figures, descriptions, and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of this disclosure, reference is now made to the following description, taken in conjunction with the accompanying drawings, in which:

FIG. 1 illustrates an example industrial process control and automation system according to this disclosure;

FIG. 2 illustrates an example device for harnessing machine learning and data analytics for a real-time predictive model for a FCC pre-treatment unit of model-based industrial process controllers according to this disclosure;

FIG. 3 illustrates an example schematic for a FCC pre-treatment unit of model-based industrial process controllers according to this disclosure; and

FIG. 4 illustrates an example process for a FCC pre-treatment unit of model-based industrial process controllers according to this disclosure.

DETAILED DESCRIPTION

FIGS. 1-4, discussed below, and the various embodiments used to describe the principles of the present invention in this patent document are by way of illustration only and should not be construed in any way to limit the scope of the invention. Those skilled in the art will understand that the principles of the invention may be implemented in any type of suitably arranged device or system.

Diesel and gasoline specifications require the reduction of sulfur to very low concentrations. The fluid catalytic cracking (FCC) unit is a major source of gasoline in a FCC refinery. A FCC feed pre-treatment operation, placed upstream of the FCC unit, improves the performance of the FCC unit and is an excellent way of meeting the required sulfur levels in gasoline. The degree of desulphurization in a FCC pre-treatment unit is observed by varying the temperature of the reactor, which is controlled by upstream heater firing. However, the FCC pre-treatment reactor temperature variation based on a downstream FCC unit gasoline product sulfur level is currently not available.

This disclosure applies a predictive model by harnessing data analytics and machine learning concepts with real time operating data to vary the pre-treatment reactor temperature with product sulfur level/specification. The disclosure describes controlling the FCC pre-treatment reactor temperature by using FCC gasoline product sulfur levels with the use of a real time algorithm, and not within the unit. This disclosure also describes predicting the FCC gasoline product sulfur level based on FCC pre-treatment feed sulfur levels by the use of a model algorithm built using real time data.

FIG. 1 illustrates an example industrial process control and automation system 100 according to this disclosure. As shown in FIG. 1, the system 100 includes various components that facilitate production or processing of at least one product or other material. For instance, the system 100 can be used to facilitate control over components in one or multiple industrial plants. Each plant represents one or more processing facilities (or one or more portions thereof), such as one or more manufacturing facilities for producing at least one product or other material. In general, each plant may implement one or more industrial processes and can individually or collectively be referred to as a process system. A process system generally represents any system or portion thereof configured to process one or more products or other materials in some manner.

In FIG. 1, the system 100 includes one or more sensors 102a and one or more actuators 102b. The sensors 102a and actuators 102b represent components in a process system that may perform any of a wide variety of functions. For example, the sensors 102a could measure a wide variety of characteristics in the process system, such as flow, pressure, or temperature. Also, the actuators 102b could alter a wide variety of characteristics in the process system, such as valve openings. Each of the sensors 102a includes any suitable structure for measuring one or more characteristics in a process system. Each of the actuators 102b includes any suitable structure for operating on or affecting one or more conditions in a process system.

At least one network 104 is coupled to the sensors 102a and actuators 102b. The network 104 facilitates interaction with the sensors 102a and actuators 102b. For example, the network 104 could transport measurement data from the sensors 102a and provide control signals to the actuators 102b. The network 104 could represent any suitable network or combination of networks. As particular examples, the network 104 could represent at least one Ethernet network (such as one supporting a FOUNDATION FIELDBUS protocol), electrical signal network (such as a HART network), pneumatic control signal network, or any other or additional type(s) of network(s).

The system 100 also includes various controllers 106. The controllers 106 can be used in the system 100 to perform various functions in order to control one or more industrial processes. For example, a first set of controllers 106 may use measurements from one or more sensors 102a to control the operation of one or more actuators 102b. A second set of controllers 106 could be used to optimize the control logic or other operations performed by the first set of controllers. A third set of controllers 106 could be used to perform additional functions. The controllers 106 could therefore support a combination of approaches, such as regulatory control, advanced regulatory control, supervisory control, and advanced process control.

Each controller 106 includes any suitable structure for controlling one or more aspects of an industrial process. At least some of the controllers 106 could, for example, represent proportional-integral-derivative (PID) controllers or multivariable controllers, such as controllers implementing model predictive control (MPC) or other advanced predictive control (APC). As a particular example, each controller 106 could represent a computing device running a real-time operating system, a WINDOWS operating system, or other operating system.

At least one network 108 couples the controllers 106 and other devices in the system 100. The network 108 facilitates the transport of information between components. The network 108 could represent any suitable network or combination of networks. As particular examples, the network 108 could represent at least one Ethernet network.

Operator access to and interaction with the controllers 106 and other components of the system 100 can occur via various operator consoles 110. Each operator console 110 could be used to provide information to an operator and receive information from an operator. For example, each operator console 110 could provide information identifying a current state of an industrial process to the operator, such as values of various process variables and warnings, alarms, or other states associated with the industrial process. Each operator console 110 could also receive information affecting how the industrial process is controlled, such as by receiving setpoints or control modes for process variables controlled by the controllers 106 or other information that alters or affects how the controllers 106 control the industrial process. Each operator console 110 includes any suitable structure for displaying information to and interacting with an operator. For example, each operator console 110 could represent a computing device running a WINDOWS operating system or other operating system.

Multiple operator consoles 110 can be grouped together and used in one or more control rooms 112. Each control room 112 could include any number of operator consoles 110 in any suitable arrangement. In some embodiments, multiple control rooms 112 can be used to control an industrial plant, such as when each control room 112 contains operator consoles 110 used to manage a discrete part of the industrial plant.

The control and automation system 100 here also includes at least one historian 114 and one or more servers 116. The historian 114 represents a component that stores various information about the system 100. The historian 114 could, for instance, store information that is generated by the various controllers 106 during the control of one or more industrial processes. The historian 114 includes any suitable structure for storing and facilitating retrieval of information. Although shown as a single component here, the historian 114 could be located elsewhere in the system 100, or multiple historians could be distributed in different locations in the system 100.

Each server 116 denotes a computing device that executes applications for users of the operator consoles 110 or other applications. The applications could be used to support various functions for the operator consoles 110, the controllers 106, or other components of the system 100. Each server 116 could represent a computing device running a WINDOWS operating system or other operating system. Note that while shown as being local within the control and automation system 100, the functionality of the server 116 could be remote from the control and automation system 100. For instance, the functionality of the server 116 could be implemented in a computing cloud 118 or a remote server communicatively coupled to the control and automation system 100 via a gateway 120.

At least one component of the system 100 could support a mechanism for harnessing machine learning and data analytics for a real-time predictive model for a FCC pre-treatment unit. For example, this functionality could be implemented in an operator console 110, a server 116, or a computing cloud 118 or remote server.

Although FIG. 1 illustrates one example of an industrial process control and automation system 100, various changes may be made to FIG. 1. For example, the system 100 could include any number of sensors, actuators, controllers, networks, operator consoles, control rooms, historians, servers, and other components. Also, the makeup and arrangement of the system 100 in FIG. 1 is for illustration only. Components could be added, omitted, combined, further subdivided, or placed in any other suitable configuration according to particular needs. Further, particular functions have been described as being performed by particular components of the system 100. This is for illustration only. In general, control and automation systems are highly configurable and can be configured in any suitable manner according to particular needs. In addition, FIG. 1 illustrates one example operational environment where harnessing machine learning and data analytics for a real-time predictive model for a FCC pre-treatment unit of model-based industrial process controllers can be used. This functionality can be used in any other suitable system.

FIG. 2 illustrates an example device 200 for harnessing machine learning and data analytics for a real-time predictive model for a FCC pre-treatment unit of model-based industrial process controllers according to this disclosure. The device 200 could, for example, denote an operator console 110, server 116, or device used in the computing cloud 118 described above with respect to FIG. 1. However, the device 200 could be used in any other suitable system.

As shown in FIG. 2, the device 200 includes at least one processor 202, at least one storage device 204, at least one communications unit 206, and at least one input/output (I/O) unit 208. Each processor 202 can execute instructions, such as those that may be loaded into a memory 210. The instructions could harness machine learning and data analytics for a real-time predictive model for a FCC pre-treatment unit of model-based industrial process controllers. Each processor 202 denotes any suitable processing device, such as one or more microprocessors, microcontrollers, digital signal processors, application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), or discrete circuitry.

The memory 210 and a persistent storage 212 are examples of storage devices 204, which represent any structure(s) capable of storing and facilitating retrieval of information (such as data, program code, and/or other suitable information on a temporary or permanent basis). The memory 210 may represent a random access memory or any other suitable volatile or non-volatile storage device(s). The persistent storage 212 may contain one or more components or devices supporting longer-term storage of data, such as a read only memory, hard drive, Flash memory, or optical disc. The persistent storage 212 could store operating parameters 214, independent variables 216, real-time models 218, and specifications 220.

The communications unit 206 supports communications with other systems or devices. For example, the communications unit 206 could include a network interface card or a wireless transceiver facilitating communications over a wired or wireless network. The communications unit 206 may support communications through any suitable physical or wireless communication link(s).

The I/O unit 208 allows for input and output of data. For example, the I/O unit 208 may provide a connection for user input through a keyboard, mouse, keypad, touchscreen, or other suitable input device. The I/O unit 208 may also send output to a display, printer, or other suitable output device.

Although FIG. 2 illustrates one example of a device 200 for harnessing machine learning and data analytics for a real-time predictive model for a FCC pre-treatment unit of model-based industrial process controllers, various changes may be made to FIG. 2. For example, components could be added, omitted, combined, further subdivided, or placed in any other suitable configuration according to particular needs. Also, computing devices can come in a wide variety of configurations, and FIG. 2 does not limit this disclosure to any particular configuration of computing device.

FIG. 3 illustrates an example schematic for a FCC system 300 with a FCC pre-treatment unit 305 of model-based industrial process controllers according to this disclosure. The embodiment of the FCC system 300 illustrated in FIG. 3 is for illustration only. FIG. 3 does not limit the scope of this disclosure to any particular implementation of an FCC system.

The FCC system 300 receives feed 301 and furnace fuel 302 and outputs gasoline product 303. The FCC system 300 includes an FCC pre-treatment unit 305, an FCC unit 310, a sulfur sensor 315, an operating parameter controller 320, a real-time model algorithm controller 325, a split controller 330, a boiler 335, a boiler input valve 340, a heat exchanger 345, a heat exchanger bypass valve 350, a boiler temperature controller 355 and a reactor temperature controller 360. The FCC system 300 receives heavy hydrocarbons (feed 301) and through the cracking process produce lighter products that are more valuable (gasoline products 303). The controllers described herein can be implemented as processors.

The FCC pre-treatment unit 305 is upstream before the FCC unit 310 and after the boiler 335. The FCC pre-treatment unit 305 provides a level of desulphurization based on a input temperature of the feed 301 output from the boiler 335. The FCC pre-treatment unit can include a reactor or a fractionator.

The FCC unit 310 performs fluid catalytic cracking (FCC). In the FCC process, the feed 301 is heated to a high temperature and pressurized to a moderate pressure for the FCC unit 310 and brought into contact with a catalyst. Vapor is collected when the catalysts break down the long-chain molecules of the feed 301.

The sulfur sensor 315 is located downstream of the FCC unit 310. The sulfur sensor determines an amount or percentage of sulfur that is contained within the gasoline product 303. The sulfur sensor 315 transmits the sulfur level to the real-time model algorithm controller 325

The operating parameter controller 320 receives the operating parameters of the FCC pre-treatment unit 305. The operating parameter controller 320 uses the operating parameters to estimate a sulfur level of the gasoline product 303. The estimated sulfur level is then sent to the real-time model algorithm with the operating parameters of the FCC pre-treatment unit 305

The real-time model algorithm controller 325 receives the operating parameters and the estimated sulfur level from the operating parameter controller 320 and the actual sulfur level. The algorithm controller 325 processes the parameters, estimated sulfur level and actual sulfur level to determine the operating parameters of the boiler input valve 340, the heat exchanger bypass valve 350, the boiler temperature controller 355 and the reactor temperature controller 360. The algorithm controller 325 transmits the operating parameters to the split controller 330.

The split controller 330 operates the bypass valve 350, the boiler temperature controller 355, the boiler input valve 340, and the reactor temperature controller 360 according to the output of the real-time model algorithm controller 325. The split controller 330 receives the operating parameters from the algorithm controller 325 and determines which component of the FCC system is controlled by each operating parameter. The split controller 330 transmits the respective operating parameters to each of the bypass valve 350, the boiler temperature controller 355, the boiler input valve 340, and the reactor temperature controller 360.

The boiler 335 receives the feed 301 after the heat exchanger 345 and bypass valve 350 and receives oil fuel (F_O) or gas fuel (F_G) through the boiler input valve 340. The boiler 335 is controlled by the boiler temperature controller 355. The temperature is based on the algorithm controller 325 determining an optimal temperature or temperature adjustment for reducing the sulfur level in the gasoline product 303.

The boiler input valve 340 controls the amount of fuel 302 that is received by the boiler 335. The boiler input valve 340 is controlled by the operating parameters determined by the algorithm controller 325.

The heat exchanger 345 adjusts the temperature of the feed before the boiler 335. The heat exchanger 345 receives a portion of the feed 301. The portion could be an entire portion or no portion. The heat exchanger 345 outputs the treated feed 301 to the boiler 335.

The heat exchanger bypass valve 350 controls the amount of the feed 301 that passes through the heat exchanger 345. The bypass valve 350 can allow a remaining portion of the feed to flow to the boiler 335 without passing through the heat exchanger 345. The output of the bypass valve 350 can be combined with the output of the heat exchanger 345 before being input to the boiler 335, or separately input to the boiler 335 and combined in the boiler 335 itself.

The boiler temperature controller 355 adjusts the temperature in the boiler 335. The boiler temperature can be constantly adjusted in real-time according to the results of the algorithm controller 325. The temperature of the boiler 335 in combination with the FCC pre-treatment unit 305 affects the sulfur level of the gasoline product 303.

The reactor temperature controller 360 adjust the temperature of the FCC pre-treatment unit 305. The reactor or fractionation temperatures can both be constantly and independently adjusted in real-time according to the results of the algorithm controller 325. The temperature of the FCC pre-treatment unit 305 in combination with the boiler 335 affects the sulfur level of the gasoline product 303.

FIG. 4 illustrates an example process 400 for a FCC pre-treatment unit of model-based industrial process controllers according to this disclosure. For example, the process depicted in FIG. 4 may be performed by the device 200 in FIG. 2. The process may also be implemented by the system 300 in FIG. 3.

In operation 405, device 200 collects operating parameters of a pre-treatment unit and a fluid catalytic cracking (FCC) unit.

In operation 410, device 200 evaluates an independent variable of the operating parameters. The independent variable can be evaluated for being within a range of specifications. The specifications require

A real-time model can be developed to evaluate the independent variable. The real-time model can be developed using data analytics to develop a correlation between a change of the input and the independent variable. The real-time model can be updated with the operating parameters in real-time. The input can be adjusted using a machine learning capability based on the real-time model.

In certain embodiments, the independent variable is a concentration of sulfur in FCC gasoline.

An estimated sulfur level can be determined from the operating parameters. The estimated sulfur level can also be determined based on the following equation:Ln(Sg)=0.905*Ln(Sf)−2.5where Sg is an estimated sulfur level by weight percentage in a gasoline product and Sf is a sulfur level measured by weight percentage in a feed.

In operation 415, device 200 adjusts an input to the pre-treatment unit to control the independent variable within specifications in an output of the FCC unit. The input can include a percentage of feed flow diverted from the heat exchanger, a temperature adjustment in the boiler, a fuel flow adjustment to the boiler, a temperature adjustment for the pre-treatment unit, etc. The adjustments to the input affect the level of sulfur that is output from the FCC unit.

The input can include a pre-treatment reactor temperature. The temperature is adjusted by varying an inlet exchanger bypass valve and a heater fuel gas valve.

Although FIG. 4 illustrates an example process 400 for a FCC pre-treatment unit of model-based industrial process controllers, various changes could be made to FIG. 4. For example, while shown as a series of steps, various steps in each figured could overlap, occur in parallel, occur in a different order, or occur multiple times.

In some embodiments, various functions described in this patent document are implemented or supported by a computer program that is formed from computer readable program code and that is embodied in a computer readable medium. The phrase “computer readable program code” includes any type of computer code, including source code, object code, and executable code. The phrase “computer readable medium” includes any type of medium capable of being accessed by a computer, such as read only memory (ROM), random access memory (RAM), a hard disk drive, a compact disc (CD), a digital video disc (DVD), or any other type of memory. A “non-transitory” computer readable medium excludes wired, wireless, optical, or other communication links that transport transitory electrical or other signals. A non-transitory computer readable medium includes media where data can be permanently stored and media where data can be stored and later overwritten, such as a rewritable optical disc or an erasable storage device.

It may be advantageous to set forth definitions of certain words and phrases used throughout this patent document. The terms “application” and “program” refer to one or more computer programs, software components, sets of instructions, procedures, functions, objects, classes, instances, related data, or a portion thereof adapted for implementation in a suitable computer code (including source code, object code, or executable code). The term “communicate,” as well as derivatives thereof, encompasses both direct and indirect communication. The terms “include” and “comprise,” as well as derivatives thereof, mean inclusion without limitation. The term “or” is inclusive, meaning and/or. The phrase “associated with,” as well as derivatives thereof, may mean to include, be included within, interconnect with, contain, be contained within, connect to or with, couple to or with, be communicable with, cooperate with, interleave, juxtapose, be proximate to, be bound to or with, have, have a property of, have a relationship to or with, or the like. The phrase “at least one of,” when used with a list of items, means that different combinations of one or more of the listed items may be used, and only one item in the list may be needed. For example, “at least one of: A, B, and C” includes any of the following combinations: A, B, C, A and B, A and C, B and C, and A and B and C.

The description in the present application should not be read as implying that any particular element, step, or function is an essential or critical element that must be included in the claim scope. The scope of patented subject matter is defined only by the allowed claims. Moreover, none of the claims invokes 35 U.S.C. § 112(f) with respect to any of the appended claims or claim elements unless the exact words “means for” or “step for” are explicitly used in the particular claim, followed by a participle phrase identifying a function. Use of terms such as (but not limited to) “mechanism,” “module,” “device,” “unit,” “component,” “element,” “member,” “apparatus,” “machine,” “system,” “processor,” or “controller” within a claim is understood and intended to refer to structures known to those skilled in the relevant art, as further modified or enhanced by the features of the claims themselves, and is not intended to invoke 35 U.S.C. § 112(f).

While this disclosure has described certain embodiments and generally associated methods, alterations and permutations of these embodiments and methods will be apparent to those skilled in the art. Accordingly, the above description of example embodiments does not define or constrain this disclosure. Other changes, substitutions, and alterations are also possible without departing from the spirit and scope of this disclosure, as defined by the following claims.

Claims

1. A method comprising: collecting operating parameters of a pre-treatment unit and fluid catalytic cracking (FCC) unit;developing a real-time model to evaluate an independent variable of the operating parameters;adjusting an input to the pre-treatment unit to control the independent variable within specifications in an output of the FCC unit,wherein the real-time model is developed using data analytics to develop a correlation between a change of the input and the independent variable;the real-time model is updated with the operating parameters in real-time; andthe input is adjusted using a machine learning capability based on the real-time model.

2. The method of claim 1, wherein the independent variable is a concentration of sulfur in FCC gasoline.

3. The method of claim 2, wherein: an estimated sulfur level is determined from the operating parameters, andthe estimated sulfur level is determined by the following equation: Ln(Sg)=0.905*Ln(Sf)−2.5,where Sg is an estimated sulfur level by weight percentage in a gasoline product and Sf is a sulfur level measured by weight percentage in a feed.

4. The method of claim 1, wherein: the input includes a pre-treatment reactor temperature; andthe pre-treatment reactor temperature is adjusted by varying an inlet exchanger bypass valve and a heater fuel gas valve.

5. An apparatus comprising: at least one memory; andat least one processor operatively coupled to the at least one memory, the at least one processor configured to: collect operating parameters of a pre-treatment unit and fluid catalytic cracking (FCC) unit;develop a real-time model to evaluate an independent variable of the operating parameters;adjust an input to the pre-treatment unit to control the independent variable within specifications in an output of the FCC unit,wherein the real-time model is developed using data analytics to develop a correlation between a change of the input and the independent variable;the real-time model is updated with the operating parameters in real-time; andthe input is adjusted using a machine learning capability based on the real-time model.

6. The apparatus of claim 5, wherein the independent variable is a concentration of sulfur in FCC gasoline.

7. The apparatus of claim 6, wherein: an estimated sulfur level is determined from the operating parameters, andthe estimated sulfur level is determined by the following equation: Ln(Sg)=0.905*Ln(Sf)−2.5,where Sg is an estimated sulfur level by weight percentage in a gasoline product and Sf is a sulfur level measured by weight percentage in a feed.

8. The apparatus of claim 5, wherein: the input includes a pre-treatment reactor temperature; andthe pre-treatment reactor temperature is adjusted by varying an inlet exchanger bypass valve and a heater fuel gas valve.

9. A non-transitory computer readable medium containing instructions that, when executed by at least one processing device, cause the at least one processing device to: collect operating parameters of a pre-treatment unit and fluid catalytic cracking (FCC) unit;a real-time model to evaluate an independent variable of the operating parameters;adjust an input to the pre-treatment unit to control the independent variable within specifications in an output of the FCC unit,wherein the real-time model is developed using data analytics to develop a correlation between a change of the input and the independent variable;the real-time model is updated with the operating parameters in real-time; andthe input is adjusted using a machine learning capability based on the real-time model.

10. The non-transitory computer readable medium of claim 9, wherein the independent variable is a concentration of sulfur in FCC gasoline.

11. The non-transitory computer readable medium of claim 10, wherein: an estimated sulfur level is determined from the operating parameters, andthe estimated sulfur level is determined by the following equation: Ln(Sg)=0.905*Ln(Sf)−2.5,where Sg is an estimated sulfur level by weight percentage in a gasoline product and Sf is a sulfur level measured by weight percentage in a feed.