Patent Publication Number: US-8527071-B2

Title: Adaptive control system for a sulfur recovery process

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     U.S. Patent Documents: 
                                                        3,026,184   March 1962   Karaser   422/62.           3,312,529   April 1967   Evano   422/62.           3,871,831   March 1975   Andral et al.   422/62.           4,021,201   May 1977   Vautrain et al.   422/110.           4,100,266   July, 1978   Smith   423/574.           4,543,245   September 1985   Peterman et al.   423/574.           5,176,896   January 1993   Bela   423/574.           5,266,274   November 1993   Taggart et al.   422/112.           5,965,100   October 1999   Khanmamedov   423/576.           7,501,111   March 2009   Keller et al.   423/573.           7,754,471   July 2010   Chen   435/266.                        
Foreign Patent Documents:
 
     
       
         
           
               
               
               
               
               
             
               
                   
                   
               
             
            
               
                   
                 1,323,173 
                 October 1993 
                 Lagas 
                 CA 
               
               
                   
                   
               
            
           
         
       
     
     OTHER REFERENCES 
     
         
         J. B. Pfeiffer,  Sulfur Removal and Recovery from Industrial Processes , Washington, D.C., U.S.A., American Chemical Society, 1975. 
         I. Boiko, “Dynamical model of the Claus process and its identification,”  Proc.  2007  American Control Conference , New York, USA, pp. 2260-2264. 
         I. Boiko,  Discontinuous Control Systems: Frequency - Domain Analysis and Design , Boston, Birkhauser, 2009. 
       
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     Not Applicable 
     REFERENCE TO SEQUENCE LISTING, A TABLE, OR A COMPUTER PROGRAM LISTING COMPACT DISK APPENDIX 
     Not Applicable 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates to an apparatus and method for controlling the combustion of acid gas containing hydrogen sulfide in sulfur recovery units (Claus plants). 
     2. Prior Art 
     Sulfur is present in natural gas principally as hydrogen sulfide H 2 S and in other fossil fuels as sulfur-containing compounds which are converted to H 2 S during processing. The H 2 S is removed from the natural gas or refinery gas by means of one of the gas treating processes. The resulting H 2 S-containing acid gas is processed to recover sulfur. The recovery of free sulfur from gaseous streams containing hydrogen sulfide has become a valuable procedure in the petroleum gas industries. The Claus process is widely used for sulfur recovery from H 2 S. Conventional Claus plant consists of a thermal conversion section, and a few stages of catalytic conversion section, in series. Acid gas feed entering sulfur recovery unit consists of H 2 S and other uncombustible gases (nitrogen, CO 2 ) and sometimes, in small amounts, combustible gases. The combustion in the thermal section is controlled by adding a controlled amount of air, required for burning one-third of the H 2 S to react with oxygen to produce SO 2 . The balance of the conversion is achieved in the presence of catalyst in the catalytic conversion stages provided via the reaction of two-thirds of H 2 S and SO 2 , to produce sulfur and water. Liquid sulfur is then collected in sulfur concentrators. However, not all the amounts of H 2 S and SO 2  react. Some residual amounts remain in a tail gas. Very strict requirements to the residual H 2 S and SO 2  make the control of the Claus reaction a difficult problem. Unlike the conventional combustion process, which allows for the use of different fuel-air ratios, the Claus reaction requires the stoichiometric values of H 2 S and air. Most commonly, the residual H 2 S is further burned and converted into environmentally less harmful SO 2  and the latter is emitted. For that reason, excess of either H 2 S or SO 2  compared to the stoichiometric values increases emissions, and only optimal H 2 S to SO 2  ratio (corresponding to stoichiometric combustion), which is achieved by proper air-to-acid gas ratio, provides minimal SO 2  emissions. Conventional control of the Claus reaction includes an air-to-acid gas ratio controller that generates a command for a main air flow controller, which manipulates a main air flow valve, and an analyzer controller of proportional-integral-derivative (PID) type that generates a command for a trim air flow controller, which manipulates a trim air flow valve. The set point (ratio value) for the ratio controller is entered by an operator. The analyzer controller uses the measurements of residual H 2 S and SO 2  in a tail gas to generate a command for the trim air flow controller, so that it generates a command to bring tail gas H 2 S-to-SO 2  ratio to the set point  2 . This control scheme may provide a satisfactory performance of the control system if the acid gas flow is relatively steady. If the acid gas flow fluctuates (which is normally the case) it becomes very difficult to achieve a satisfactory performance of the control. As a result, in many cases a very expensive additional treatment of the tail gas aimed at removing the residual H 2 S and SO 2  may be needed to reduce emissions. 
     U.S. Pat. No. 3,985,864 (1976) of Lucien H. Vautrain, et al. discloses an automatic control system for a Claus sulfur plant. The flow rate of the oxygen-containing gas to a process for the oxidation of hydrogen sulfide is regulated so as to be responsive to changes in pressure in the hydrogen sulfide feedstream. In both patents, the overall ratios of oxygen to hydrogen sulfide are adjusted to maintain the desired ratio of hydrogen sulfide to oxygen feed. In carrying out stoichiometric control of the hydrogen sulfide gas stream and oxygen-containing gas stream, there are five objectives cited. These objectives are (1) maintain the quantity of oxygen below that stoichiometrically required for the oxidation of the hydrogen sulfide in order to prevent the formation of sulfates; (2) maintain the oxygen quantity as close as possible to the stoichiometry required in order to promote the highest possible efficiency of oxidizing the hydrogen sulfide-containing gas stream and to reduce the sulfur content of the gaseous effluent from the process; (3) maintain stable control of the process while achieving the above two objectives, even though the gas flow may vary; (4) maintain stable control, even though the hydrogen sulfide content of the hydrogen sulfide gas-containing stream may vary; and (5) effect stable control of the process while achieving the above four objectives, even though there is a time between the occurrence of a variation in one or both of the process feedstreams and the occurrence of the measurement of the effect of that variation on the gaseous effluent from the process. In summary, both patents disclose an automated flow control scheme to maintain the required stoichiometry of the Claus reaction. 
     U.S. Pat. No. RE 28,864 of Andral, et al. (with a foreign priority date, application No. 70.45812 in France) discloses process and apparatus for automated regulation of sulfur production units. The process incorporates oxidation of hydrogen sulfide, in which the flow of gas carrying oxygen into the unit is regulated so as to keep an operating parameter, based on measurement of the sulfurous compound of the residual gases, level with a reference value. It is characterized by the fact that the control signal, used to regulate the flow of gas containing oxygen at the unit inlet, is a combination of a signal based on measurements taken at the inlet, and representing the theoretical flow of this gas needed to keep the operating parameter at its reference level and another signal representing the correction needed in this flow to adjust the instantaneous value of the parameter to the reference level. The disclosed process claims better control of the sulfur unit, with increased efficiency and reduced atmospheric pollution. 
     U.S. Pat. No. 4,100,266 of Smith (1978) discloses an automatic control system for a Claus sulfur plant, in which control of a process is accomplished by manipulating the flow rate of a feed stream containing oxygen to a furnace in such a manner that a desired proportion of the hydrogen sulfide fed to the furnace is converted to sulfur dioxide. The flow rate of a feed stream containing hydrogen sulfide to a tail gas cleanup process is also manipulated utilizing feedforward and feedback control to maintain the hydrogen sulfide and sulfur dioxide concentrations in the gas stream from the tail gas cleanup process at acceptable levels. Some other variations of the described principle were disclosed in U.S. Pat. No. 5,965,100 of Khanmamedov (1999), and 7,754,471 of Chen (2010). The described control principle may provide a satisfactory performance of the control system if the acid gas flow to the sulfur recovery process is a relatively constant value. If the acid gas flow fluctuates (which is normally the case) it becomes very difficult to achieve a satisfactory performance of the control. As a result, in many cases a very expensive additional treatment of the tail gas aimed at removing the residual H 2 S and SO 2  is normally needed. Control performance has a significant effect on the emissions of environmentally harmful substances, which can be substantially mitigated by the disclosed adaptive ratio control. 
     U.S. Pat. No. 5,176,896 of Bela discloses apparatus and method for generation of control signal for Claus process optimization. It incorporates generation of a control signal for the optimization of sulfur removal in a Claus process unit that comprises oxidizing a portion of the tail gas stream exiting the Claus unit by contacting a portion of the tail gas with an oxygen-containing gas in the presence of a catalyst which oxidizes H 2 S to SO 2 , measuring the temperature rise associated with the oxidation reaction, converting the measurement to an appropriate control signal, and using the signal to control the rate of air flow into the Claus unit. Canadian Pat. No. CA 1323173 to Lagas et al. discloses a process for the recovery of sulfur from a hydrogen sulfide containing gas (acid gas), which comprises oxidizing hydrogen sulfide with oxygen, and then reacting the product gas of this oxidation further by using at least two catalytic stages, in accordance with the equation: 2H 2 S+SO 2 =2H 2 O+3/n S n . In order to improve the process and the process control, the invention is characterized in that the H 2 S concentration in the gas leaving the last catalytic stage is controlled to have a value ranging between 0.8 and 3% by volume by reducing the quantity of combustion or oxidation air passed to the oxidation stage and/or causing a portion of the hydrogen sulfide containing feedstock gas to bypass the oxidation stage and to be added to the gas flowing to a catalytic stage. As described, typical control of the Claus reaction includes an air-to-acid gas ratio controller that uses measurements of acid gas flow and generates a command for a main air flow controller, which in turn manipulates a main air flow valve, and an analyzer controller of proportional-integral-derivative (PID) type that uses measurements of H 2 S and SO 2  in a tail gas and generates a command for a trim air flow controller, which in turn manipulates a trim air flow valve. The main drawback of the available controls is related to possible fluctuations of acid gas flow and slow response of the tail gas concentrations to changes in a tail gas flow and air flow. If a tail gas flow changes the main air flow controller responds to this change very quickly incrementing air flow. However, the air-to-acid gas flow ratio demand is entered by an operator and is not optimal, so that the air flow increment would not fully correspond to the acid gas flow increment, and the increment of air flow will be either smaller or larger than the optimal necessary for a stoichiometric combustion. As a result, after all the reactions occur the concentrations of H 2 S and SO 2  in a tail gas will change. Yet, it will only be measured with some delay, after this reaction has already happen, which results in insufficiently high quality of control, observed as high fluctuations in a tail gas H 2 S-to-SO 2  ratio. Another drawback is related to uncoordinated motion of the two air valves, so that one valve may have a command to open, thus increasing air flow, and the other valve to have the command to close, thus decreasing air flow, while in fact no change may be required in terms of total air required. This uncoordinated motion of the two air valves contributes to the deterioration of the control performance, as the valves respond to their commands not instantaneously but with some lag, which differs between the two valves. Those lags result in the deviations of the total air flow from the total air flow demand (sum of the two demands) and overall performance deterioration. 
     It would be desirable to calculate and use an optimal value for the air-to-acid gas ratio demand, so that any fluctuation in an acid gas flow should be immediately matched by corresponding amount of air-through the action of the ratio controller. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention improves performance of the control of the sulfur recovery process in the conditions of variable flow rate of acid gas and variable H 2 S concentration in acid gas by using an adaptive ratio control principle. In accordance with an embodiment of this invention, H 2 S-to-SO 2  ratio fluctuations (molar amounts) in the tail gas are substantially reduced by generating the air flow demand that is calculated as a sum of the principal air flow demand and the supplemental air flow demand, where the principal air flow demand is calculated via multiplication of the acid gas flow by the optimal air-to-acid gas ratio demand value, and the supplemental air flow demand is calculated by a proportional-integral-derivative (PID) algorithm, with process variable of the PID algorithm based on measurements of molar amounts of residual H 2 S and SO 2  in the tail gas. An optimal value of the air-to-acid gas ratio demand is determined through learning (adaptation), which allows for the best possible rejection of disturbances coming to the control system in the form of acid gas flow fluctuations, while slow changes in the concentration of H 2 S in the acid gas are compensated for by adaptation aimed at finding a varying optimal value of the air-to-acid gas ratio, which changes with changes of H 2 S concentration. Through this principle, combustion of hydrogen sulfide is precisely controlled by the control system to maintain the hydrogen sulfide and sulfur dioxide concentrations in the tail gas at the desired ratio and acceptable levels to minimize the environmental pollution. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
         FIG. 1  is an illustration of a Claus sulfur plant with associated controls (preferred embodiment A); 
         FIG. 2  is a schematic of a processor-based control system means for the calculation of the principal air flow demand, supplemental air flow demand and total air flow demand ((a)—preferred embodiment A, (b)—preferred embodiment B); 
         FIG. 3  is a schematic of a processor-based control system means for the calculation of commands to main air control valve and trim air control valve for preferred embodiment A; 
         FIG. 4  is a schematic of a processor-based control system means of the adaptive control (preferred embodiments A and B) 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention relates to method and apparatus to control the ratio of air to hydrogen sulfide (H 2 S) in the acid gas in Claus (sulfur recovery) reaction. In one specific aspect the invention relates to a method and apparatus for obtaining near optimum performance of a sulfur plant where free sulfur is produced from hydrogen sulfide. In a second specific aspect, this invention relates to a method and apparatus for reducing air pollution produced by the production of free sulfur from hydrogen sulfide. In a third specific aspect, the invention relates to a method and apparatus for controlling the ratio of hydrogen sulfide to oxygen fed to a reaction of hydrogen sulfide and oxygen to form free sulfur. In a fourth specific aspect, the invention relates to a method and apparatus for maintaining a desired hydrogen sulfide to sulfur dioxide ratio in a sulfur plant tail gas. Other possible applications of the same control principle are as follows (but not limited to those): control of fuel combustion in utility boilers by measuring O 2  concentration in the flue gas and manipulating the air flow on the basis of the measurements obtained; control of SO x  passivation by means of ammonia injection into the gas/liquid; control of desuperheated steam temperature in utility boilers by means of spraying water into steam; control of air-fuel ratio in internal combustion engines. 
     Sulfur is present in natural gas principally as H 2 S and in other fossil fuels as sulfur-containing compounds which are converted to H 2 S during processing. The H 2 S is removed from the natural gas or refinery gas by means of one of the gas treating processes. The resulting H 2 S-containing acid gas is processed to recover sulfur. The recovery of free sulfur from gaseous streams containing hydrogen sulfide has become a valuable procedure in the petroleum gas industries. Such an operation results in both the recovery of valuable free sulfur and a reduction of atmospheric pollution. The Claus process is widely used for sulfur recovery from H 2 S. The Claus process as used today is a modification of a process first used in 1883 in which H 2 S was reacted over a catalyst with air (oxygen) to form elemental sulfur and water. A modification of the Claus process was developed in 1936 in which the overall reaction was separated into a highly exothermic combustion reaction section and a moderately exothermic catalytic reaction section in which sulfur dioxide formed in the combustion section reacts with unburned H 2 S to form elemental sulfur. 
     In practice, the control of the reaction is usually implemented with the use of measurements of the acid gas flow and the ratio of residual H 2 S and SO 2  in the tail gas after the reaction, and by means of two air valves with respective controllers (loops) that utilize the above measurements. This control scheme may provide a satisfactory performance of the control system if the acid gas flow is a relatively constant value. If the acid gas flow fluctuates (which is normally the case) it becomes very difficult to achieve a satisfactory performance of the control. As a result, in many cases a very expensive additional treatment of the tail gas aimed at removing the residual H 2 S and SO 2  is normally needed. Control performance has a significant effect on the emissions of environmentally harmful substances, and therefore, development of process model suitable for controller design and tuning may have a high environmental impact. 
     In many aspects the Claus process is no different than a regular combustion process of the fuel gas in utility boilers, for example. However, very strict requirements to the residual H 2 S and SO 2  make the control of the Claus reaction a much more difficult problem. Unlike the conventional combustion process, which allows for the use of different air-to-fuel ratios, the Claus reaction requires the stoichiometric values of H 2 S and air. Commonly, the residual H 2 S is further burned and converted into environmentally less harmful SO 2  and the latter is emitted into the atmosphere. For that reason, excess of either H 2 S or SO 2  compared to the stoichiometric values increases emissions, and only optimal H 2 S to SO 2  ratio (corresponding to stoichiometric combustion) provides minimal SO 2  emissions. Another difference that complicates the control of the Claus reaction is uncontrolled acid gas flow (all available acid gas must be incinerated) versus regulated fuel flow in other types of combustion. The main objective of the control quality enhancement is to ensure the conversion of all available H 2 S into relatively neutral and environmentally safe sulfur; increase of sulfur production is usually a secondary objective only. 
     The free sulfur generally is produced by a process which involves the following two reactions. The reaction in the thermal or combustion reaction section is given by the following expression (J. B. Pfeiffer,  Sulfur Removal and Recovery from Industrial Processes , Washington, D.C., U.S.A., American Chemical Society, 1975):
 
 H   2   S+ 1½ O   2   →SO   2   +H   2   O   (1)
 
     The reaction in the combustion and catalytic reaction sections is given as follows:
 
2 H   2   S+SO   2 →3 /×S   x +2 H   2   O   (2)
 
     If high H 2 S/SO 2  conversion levels are to be reached in the Claus reaction, this ratio should be kept as close as possible to the stoichiometric value of two. 
     The first reaction generally takes place in the combustion chamber of a boiler. Since this reaction is highly exothermic, the substantial amount of heat which is released is recovered in the form of steam production. One third of the source hydrogen sulfide is combined with air to form sulfur dioxide in this reaction. The reaction of the hydrogen sulfide is combined with the reaction products from the combustion chamber to carry out the second reaction in the furnace. The effluent from the furnace is cooled, and the free sulfur product is recovered as a liquid. 
     All the hydrogen sulfide and sulfur dioxide gases will not be converted in the furnace. The remaining unconverted gases are passed through a catalytic sulfur removal reactor to further convert the unreacted hydrogen sulfide and sulfur dioxide to free sulfur. The effluent from the reactor is cooled, and the free sulfur product is removed as a liquid. 
     Let q H2S  be the molar amount (flow) of H 2 S and q O2  be the molar amount (flow) of O 2 . Then assuming that all oxygen is reacted in the combustion reaction we can write an expression for the molar amount of SO 2  obtained as a result:
 
 q   (1)   SO2 =⅔ q   O2   (3)
 
where superscript “1” refers to the combustion reaction. In this reaction the amount of H 2 S equal to ⅔ of the amount of the oxygen is consumed, and the remaining H 2 S is:
 
 q   (1)   H2S   =q   H2S −⅔ q   O2   (4)
 
     In the combustion and catalytic reaction section, not all available H 2 S and SO 2  react but only a certain amount. We describe the percentage of H 2 S and SO 2 , reacted in the catalytic reaction section, with respect to the stoichiometric amounts of H 2 S and SO 2 , by the sulfur recovery factor k r . The value of the sulfur recovery factor would, therefore, normally be slightly below 1. The remaining amounts of H 2 S and SO 2  after the catalytic section would be as follows:
 
 q   (2)   H2S =(1 −k   r ) q   (1)   H2S  and  q   (2)   SO2   =q   (1)   SO2 −0.5 k   r   q   (1)   H2S  if  q   (2)   H2S &lt;=2 q   (1)   SO2   (5)
 
where superscript “2” refers to the catalytic reaction or
 
 q   (2)   H2S   =q   (1)   H2S −2 k   r   q   (1)   SO2  and  q   (2)   SO2 =(1 −k   r ) q   (1)   SO2  if  q   (2)   H2S &gt;2 q   (1)   SO2   (6)
 
     Usually the control utilizes the ratio of the two values, which shows how far the amounts of the reagents are from the stoichiometric values:
 
ρ= q   (2)   H2S   /q   (2)   SO2   (7)
 
     Considering oxygen content in the air of 21% the air flow q air  is related to the oxygen flow as follows:
 
 q   O2 =0.21 q   air   (8)
 
     From the above formulas, we can obtain the relationship between the air/H 2 S ratio r at the process input and H 2 S/SO 2  ratio in the tail gas p as follows (I. Boiko, “Dynamical model of the Claus process and its identification,”  Proc.  2007  American Control Conference , New York, USA, pp. 2260-2264): 
     
       
         
           
             
               
                 
                   
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     In the past, the noncondensed material from the catalytic sulfur removal reactor (tail gas) was simply passed to as incinerator. Recently various processes have been developed to clean up the tail gas from the catalytic sulfur removal reactor, resulting in less air pollution and in additional free sulfur recovery. When a tail gas cleanup process is utilized, close control of the desired ratios between the gases to be reacted also must be maintained. Sometimes it is also desirable to be able to change the ratio of the hydrogen sulfide and the sulfur dioxide in the tail gas to conserve the catalyst in the tail gas cleanup process. 
     The main idea of the present invention is to use an adaptive ratio control principle that is first introduced in the present invention. The use of this principle is based on the supposition that there are two main types of disturbances that come to the control system for this process: the acid gas flow fluctuations and the acid gas composition (mainly H 2 S concentration). This supposition totally agrees with the practice of sulfur recovery control. The adaptive part of the adaptive ratio control is aimed at determination of the optimal value of the necessary air-to-acid gas ratio (ratio ser point), so that when an acid gas fluctuation occurs an equivalent increment or decrement of air flow demand is calculated immediately by the ratio controller (through multiplication of the actual acid gas flow by the ratio set point). If the ratio set point is not optimal then there always exists an unmatched portion in the acid gas flow fluctuation, and proper proportion between air and acid gas will be disturbed, which in turn will results in improper proportion between H 2 S and SO 2  in the tail gas. On the other hand, the optimal value of the necessary air-to-acid gas ratio is not constant and depends on the acid gas composition. However, at relatively slow changes of the composition the optimal value of the necessary air-to-acid gas ratio (ratio set point) can be successfully determined through adaptation (learning), which is done with involvement of proper low-pass filtering of the actual air-to-acid gas ratio and additional inhibiting/permissive and nonlinear logic. 
     Accordingly, it is an objective of this invention to provide a method and apparatus for controlling the production of free sulfur from hydrogen sulfide. A second objective of this invention is to provide a method and apparatus for obtaining near optimum performance of a sulfur plant where free sulfur is produced from hydrogen sulfide. A third objective of this invention is to provide a method and apparatus for reducing air pollution produced by the sulfur plant. A fourth objective of this invention is to provide a method and apparatus for maintaining a desired hydrogen sulfide to sulfur dioxide ratio in a tail gas. 
     In accordance with the present invention, an improved method and apparatus for controlling the production of free sulfur from hydrogen sulfide is provided wherein a processor-based control system means (distributed control system or programmable logic controller, for example) is utilized to obtain near optimum performance from a sulfur plant by maintaining the H 2 S/SO 2  ratios in the tail gas at desired value. The desired H 2 S/SO 2  ratio in the tail gas is maintained at a desired value by controlling the air flow to the furnace in such a manner that enough H 2 S in the acid gas feed is converted to SO 2  to give the desired H 2 S/SO 2  ratio in the gas stream flowing from the furnace to the catalytic sulfur removal reactors. 
     For the sake of simplicity, the invention is illustrated and described in terms of a sulfur plant wherein the catalytic sulfur converters are Claus converters. 
     Although the invention is illustrated and described in terms of a specific embodiment, the applicability of the use of the invention described herein extends to sulfur plants using different types of catalytic sulfur converters. 
     Controllers shown may utilize the various modes of control such as proportional (P), proportional-integral (PI), proportional-derivative (PD), or proportional-integral-derivative (PID). In a preferred embodiment proportional-integral-derivative controllers are utilized. All other variations of the PID controller can be obtained from the PID controller by setting respective gains to zero. The operation of these types of controllers is well known in the art. The output control signal of a proportional-integral-derivative controller may be represented as 
     
       
         
           
             
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     where 
     t is time, 
     u is output control signal; 
     e is difference between two input signals (error), 
     and K p , K i  and K d  are proportional gain, integral gain and derivative gain, respectively. 
     Referring now to the drawings and in particular to  FIG. 1 , which illustrates a preferred embodiment that involves two (main and trim) air control valves (preferred embodiment A), an acid-gas feed stream containing H 2 S passes from supply conduit means  1  through conduit means  2  into the reaction furnace  3 . The reaction furnace  3  is also supplied with air from supply  4  through air conduit means  5 . In another embodiment, the reaction furnace  3  is supplied with air from supply  4  through air conduit means  5 , primary air supply conduit means  6  and trim air conduit means  7 . Sufficient air is mixed with the acid-gas feed in the furnace to convert one-third of the H 2 S fed to the furnace to SO 2  and also burn any hydrocarbons present in the acid-gas feed. The well-known stoichiometric reaction in the furnace is given by formula (1). Burning of one-third of the H 2 S to SO 2  yields a desired H 2 S/SO 2  mol ratio of 2.0 in the reaction effluent gas which leaves the reaction furnace  3  via conduit means  8 . 
     The flame temperature in the reaction furnace may reach temperatures of 2450° F. At such temperature some of the unburned H 2 S can react with the SO 2  formed by the reaction given in equation (1), to form free sulfur vapor in accordance with the reaction of equation (2). This will decrease the temperature of the hot gases to about 2300° F. Heat can be removed from the hot gases by heat exchange with water passed through the reaction furnace  3 . The hot gases in the reaction furnace are typically cooled to 550° F. before exiting the furnace. 
     The hot gases pass from the reaction furnace  3  through conduit means  8  to a catalytic section  9 , which comprises a series of reactors, reheaters and condensers. The free sulfur vapor formed in the reaction furnace  9  is condensed in the condensers and the resulting liquid sulfur can then be separated from the main gas stream containing unreacted H 2 S and SO 2 . The separated liquid free sulfur flows through conduit means  10  to sulfur collection and storage means. 
     The Claus reaction proceeds to a further degree of completion in the presence of the Claus catalyst in the Claus catalytic converters contained in the catalytic section  9 . The reaction involved is given by formula (2). The gas stream which now contains free sulfur plus the unreacted H 2 S and SO 2  flows out of the Claus catalytic converter to sulfur condenser where the free sulfur is condensed. The condensed free sulfur flows through conduit means  10  to sulfur collection and storage means. 
     The Claus tail gas, containing the remaining unreacted H 2 S and SO 2  which are still in a H 2 S/SO 2  mol ratio of about 2.0, flows through conduit means  11  to further processing (cleaning) or is released to the atmosphere. 
     It is desirable to have an H 2 S/SO 2  mol ratio of slightly greater than 2.0 if the tail gas is further processed. 
     As has been stated, one object of this invention is to optimize the performance of a sulfur plant by maintaining the H 2 S/SO 2  ratio to the sulfur removal reactors at least substantially at 2.0. 
     The H 2 S/SO 2  mol ratio to the catalytic section  9  can be maintained by manipulating the flow of air through conduit  5  to the reaction furnace  3 . 
     Control of the process is accomplished by providing processor-based control system means  12  with measured process variables as inputs. These process variables are then utilized by processor-based control system means  12  to generate signals to the valves which are used to maintain the various controlled flow rates at desired levels. 
     The following sensors (transmitters) are used by the processor-based control system means  12  to measure the process variables. Flow sensor  13 , located in supply conduit means  2 , measures the actual flow rate of acid gas through conduit means  2  to furnace  3 . Flow transducer  14 , associated with flow sensor  13 , transmits this information to control system means  12  via data signal  15 . Flow sensor  16 , located in the primary air supply conduit means  6 , measures the actual flow rate of air through conduit means  6 . Flow transducer  17 , associated with flow sensor  16 , transmits this information to control system means  12  via data signal  18 . Flow sensor  19 , located in trim air conduit means  7 , measures the actual flow rate of the trim air. Flow transducer  20 , associated with flow sensor  19 , transmits this information to control system means  12  via data signal  21 . 
     An analyzer  22 , such as a gas chromatograph, analyzes the Claus tail gas flowing from the catalytic section  9  through conduit means  11 . Analyzer  22  provides the control system means  12  with data signal  23  which is representative of the H 2 S concentration in the tail gas. An analyzer  24 , such as a gas chromatograph, analyzes the Claus tail gas flowing from the catalytic section  9  through conduit means  11 . Analyzer  24  provides the control system means  12  with data signal  25  which is representative of the SO 2  concentration in the tail gas. Optionally, both measurements: the H 2 S concentration and the SO 2  concentration in the tail gas can be performed by one analyzer (chromatograph). 
     Control system means  12  is also supplied with certain H 2 S/SO 2  ratio setpoint value through setpoint entry means  59  (operator entry or coding). Signal  26  is representative of the required H 2 S/SO 2  ratio in the tail gas stream and has a value of 2.0 in this preferred embodiment. 
     Based on the described input data, control system means  12  calculates the required flow rate of the main air and trim air. Signal  31 , representative of the required flow rate of the trim air, is supplied to the current to pneumatic transducer  32 . Control valve  33  is manipulated in response to signal  34  to provide the desired trim air flow rate. Signal  27 , representative of the required flow rate of the main air, is supplied to the current to pneumatic transducer  28 . Control valve  29  is manipulated in response to signal  30  to provide the desired main air flow rate. It should be noted that main air flow  18  and trim air flow  21  are not the same flows as principal air and supplemental air, which are parts of the calculation of the total air flow demand. Moreover, supplemental air can be positive, zero or negative value, while main air and trim air are always positive values. However, the sum of main air and the trim air is supposed to be equal to the total air demand, which in turn is the sum of principal air demand and the supplemental air demand. Therefore, ideally (when both main air and trim air are equal to the set points for respective air flow controllers) the sum of main air and the trim air is equal to the sum of principal air and supplemental air demands. 
     In the preferred embodiment that involves one air control valve (preferred embodiment B) the following elements of the diagram are not present: as numbered by 19, 20, 21, 31, 32, 33, and 34. 
       FIG. 2  illustrates a part of the control system, in which calculations of the total air demand for the air flow controller(s) are done. In the preferred embodiments it is realized through a software module in the processor-based control system. The method and apparatus shown in  FIG. 2  is only one of many such configurations which could be utilized to perform the required calculations. It should also be recognized that a processor-based control system could easily be programmed to perform the required calculations. 
     Signal  23 , representative of the actual H 2 S concentration in the tail gas measured by analyzer  22 , is provided to multiplying means  40 . Multiplying means  40  is also provided with set point signal  26 , representative of the required H 2 S/SO 2  ratio in the tail gas. Signal  23  is multiplied by signal  26  to produce signal  41 . Signal  25 , representative of the actual SO 2  concentration in the tail gas measured by analyzer  24 , is provided to summing means  42 . Signal  41  is summed with negative signal  25  to produce signal  43 , which is supplied to controller  44 . In a preferred embodiment, controller  44  is a proportional-integral-derivative controller. However, controller  44  can be a relay controller or a different type of controller, for example a relay type of controller well-known in the art (I. Boiko,  Discontinuous Control Systems: Frequency - Domain Analysis and Design , Boston, Birkhauser, 2009). The output signal  45  of such a controller is well known in the art, as has been previously stated. Signal  45  is the supplemental air demand. It can be a positive, zero or negative quantity. It is supplied to summing means  50 . Signal  43  is also supplied to an adaptive controller  46 . Signal  15 , representative of the actual acid gas flow measured by flow transducer  14 , is provided to the adaptive controller  46 . 
     In the preferred embodiment that involves two (main and trim) air control valves (preferred embodiment A; as illustrated by  FIG. 2   a ), signal  18 , representative of the actual main air flow measured by the flow transducer  17 , is provided to a summing means  52 . Signal  21 , representative of the actual trim air flow measured by the flow transducer  20 , is provided to a summing means  52  too. Signals  18  and  21  are summed together producing the output signal  53 , which is the actual total air flow representative. Signal  53  is supplied to the adaptive controller  46 . The output signal  47  of the adaptive controller  46  is produced as per the algorithm that is described below. Signal  47  is supplied to multiplying means  48 . Signal  15 , representative of the actual acid gas flow, is also supplied to multiplying means  48 . The output signal  49  of the multiplying means  48  is the principal air demand. It is supplied to the summing means  50 . The output signal  51  of the summing means  50  is the total air demand. It is supplied to a part of the control system means for the calculation of commands to main air control valve and trim air control valve as illustrated by  FIG. 3  and described below, which in the preferred embodiment A is a combination of two proportional-integral-derivative controllers. 
     In the preferred embodiment that involves one air control valve (preferred embodiment B; as illustrated by  FIG. 2   b ), signal  18 , representative of the actual air flow measured by flow transducer  17 , is provided to the adaptive controller  46 . Signal  18  is also supplied with the negative sign to a summing means  54 . The output signal  47  of the adaptive controller  46  is produced as per the algorithm that is described below. Signal  47  is supplied to multiplying means  48 . Signal  15 , representative of the actual acid gas flow, is also supplied to multiplying means  48 . The output signal  49  of the multiplying means  48  is the principal air demand. It is supplied to the summing means  50 . The output signal  51  of the summing means  50  is the total air demand. It is supplied to a summing means  54 . The output signal  55  of the summing means  54  is supplied to an air flow controller  56 . In a preferred embodiment B, controller  56  is a proportional-integral-derivative controller. The output signal  27  of the controller  56  is provided to the current-to-pneumatic transducer  28  described above (see  FIG. 1 ). 
       FIG. 3  illustrates a preferred embodiment that involves two (main and trim) air control valves (preferred embodiment A) of an air flow controller, which is realized as a software module in the processor-based control system. It should also be recognized that a processor-based control system could easily be programmed to perform the required calculations. 
     The total air demand signal  51  is supplied to a low-pass filter  60 , to a summing means  62 , and to a summing means  69 . The low-pass filter  60  performs low-pass filtering of signal  51  in accordance with the transfer function of the filter and provides an output signal  61 . In a preferred embodiment, the transfer function of the filter is W LPF1 (s)=1/[(T 1 s+1)(T 2 s+1)] where T 1  and T 2  are the time constants, s is the Laplace variable. Transfer function means of description of a filter is well known in the art. Output signal  61  with negative sign is supplied to a summing means  62 , which produces the output signal  63 . Signal  63  is the difference between the total air demand and low-pass filtered total air demand signal and, therefore, contains the fast component of the total air demand. Signal  63  is supplied to a summing means  65 . Constant bias signal  64  generated with the use of biasing means  77  within the air flow controller is supplied to the second input of the summing means  65 . The constant bias signal value  64  is selected in such a way that it approximately corresponds to the trim air flow at the 50% opening position of the trim air flow valve, so that in average the trim air flow valve will travel around 50% opening (which usually represents a linear part of the air flow control characteristic). If necessary, the constant bias value can be adjusted to ensure optimal travel range of the trim air valve. Output signal  66  of the summing means  65  is supplied to a limiter  67 , which limits the signal  66  from below and above producing the output signal  68 , which is the set point for the trim air flow controller. Signal  66  is limited from below by a certain non-negative value to prevent the set point for the trim air flow controller to be a negative value or a too small positive value, when the trim air valve has to go to nearly closed position to provide the required air flow. Signal  66  is also limited from above by a certain positive value to prevent the set point for the trim air flow controller to be a too high value, when the trim air valve has to go to nearly open position to provide the required air flow or the air flow goes to saturation. The trim air flow set point  68  is supplied with the negative sign to a summing means  69  that provides the output signal  70 , which is the set point for the main air flow controller. The set point for the main air flow controller is, therefore, produced as the difference between the total air demand  51  and the trim air flow controller set point  68 . Thus the sum of the set points for the main air flow controller and the trim air flow controller is always equal to the total air flow demand. This system allows the faster trim air adjustment to prevail over the shorter term with the main air controls prevailing over the longer term. 
     Signal  70  is supplied to a summing means  71 , and signal  18 , which is a representative of the main air flow, is supplied with the negative sign to the second input of the summing means  71 , producing the difference between the main air flow controller set point and the actual main air flow. The output  72  of the summing means  71  is supplied to a main air flow controller  73 . Controller  73  is a proportional-integral controller in a preferred embodiment. The output  27  of the controller is supplied to the current-to-pneumatic transducer (see  FIG. 1 ). 
     Set point  68  for the trim air flow controller is supplied to a summing means  74 , and signal  21 , which is a representative of the trim air flow, is supplied with the negative sign to the second input of the summing means  74 , producing the difference between the trim air flow controller set point and the actual trim air flow. The output  75  of the summing means  74  is supplied to a trim air flow controller  76 . Controller  76  is a proportional-integral controller in a preferred embodiment. The output  31  of the controller is supplied to the current-to-pneumatic transducer (see  FIG. 1 ). 
       FIG. 4  illustrates a preferred embodiment of an adaptive controller, which in the preferred embodiment is a software module in the processor-based control system. It should also be recognized that a processor-based control system could easily be programmed to perform the required calculations. 
     The objective of the adaptive controller is to provide the control system with an optimal value of the required air-to-acid gas ratio (ratio set point). The adaptation (learning) is carried out through low-pass filtering of the actual air-to-acid gas ratio subject to the permissive signal provided by an additional logic that uses H 2 S/SO 2  ratio in the tail gas as a signal witnessing proper air-to-acid gas ratio. 
     The total actual air flow signal  53  either measured by the flow transducer  17  (for the preferred embodiment B) or obtained by the summation of the main air flow signal  18  and trim air flow signal  21  (for the preferred embodiment A; see also  FIG. 1  and  FIG. 2 ) is supplied to the dividing means  81 . The actual acid gas flow signal  15  measured by the acid gas flow transducer  14  (see also  FIG. 1  and  FIG. 2 ) is supplied to the second input of the dividing means  81 . The dividing means  81  perform the division of signal  18  by signal  15  producing the output  82 . Signal  82  is supplied to the first input of the selector  87 , which produces the output signal  88  as a result of the selection between signals supplied to the first and the second inputs. Signal  88  is supplied to a low-pass filter  89 . The low-pass filter  89  is used for the determination of the actual averaged (on a relatively long period of time suitable for learning) air-to-acid gas ratio, subject to the condition of the closeness to optimal H 2 S-to-SO 2  ratio in the tail gas. The low-pass filter  89  performs low-pass filtering of signal  88  in accordance with the transfer function of the filter and provides an output signal  90 . In both preferred embodiments, the transfer function of the filter is W LPF2 (s)=1/[(T 3 s+1)(T 4 s+1)], where T 3  and T 4  are the time constants, s is the Laplace variable. Transfer function means of description of a filter is well known in the art. Time constants T 3  and T 4  of the low-pass filter should be selected large enough, so that the filter is capable of filtering out fluctuations of air-to-acid gas flow caused by the action of the controller  44 . But these time constants should not be too large, so that the adaptive controller could adjust the air-to-acid gas ratio set point  47  quickly enough to changes in the concentration of H 2 S in the acid gas. Signal  90  is supplied to the second input of selector  87 . The signal  43  produced by the summing means  42  (see also  FIG. 2 ) is supplied to a means for computing the absolute value  83 , which in turn produces an output signal  84 . Signal  84  is supplied to a compactor  85 , which compares the input to the threshold value producing a logical (Boolean) output signal  86  in dependence on the results of this comparison. If the input signal  84  is greater than or equal to the threshold value Δ then the output signal  86  is 1, if the input signal  84  is smaller than the threshold value Δ then the output signal  86  is 0. Logical signal  86  is supplied to the control input of the selector  87 . Selector  87  produces the output signal  88  according to the following algorithm: if signal  86  is equal to 0 then the first input (signal  82 ) is selected, if signal  86  is equal to 1 then the second input (signal  90 ) is selected. The signal selection provided by the selector  87  and associated logic is intended for the purpose of learning (adaptation), so that only acceptable values of air-to-acid gas ratio, which is witnessed by signal  43  being within assigned limits, are processed by the low-pass-filter  89 . 
     The output signal  90  of the low-pass filter is supplied to a summing means  91 . The output of the adaptive controller (which is the air-to-acid gas ratio set point)  47  is supplied with the negative sign to the second input of the summing means  91 . The summing means  91  produces the output signal  92 , which is the difference between signal  90  and signal  47 . Signal  92  is supplied to a nonlinear block  93 , which produces an output signal  94  in accordance with the following equation: 
               x   94     =     {             x   92     -   δ             if   ⁢           ⁢     x   92       &gt;   δ             0           if   -   δ     ≤     x   92     ≤   δ                 x   92     +   δ             if   ⁢           ⁢     x   92       &lt;     -   δ                     
where x 92  is signal  92 , x 94  is signal  94 , δ is a positive quantity (air-to-acid gas ratio update tolerance). Nonlinear block  93  is introduced with the purpose to increase stability of the adaptive ratio control through the introduction of the deadband nonlinearity, so that no adaptation happens if the error signal  92  is within the dead band. This slightly reduces the accuracy of the adaptive ratio control (because small nonzero errors in the air-to-acid gas ratio are allowed) but improves the stability via elimination of interactions between the adaptive ratio control and the proportional-integral-derivative control.
 
     Signal  92  is also supplied to a comparator  97 , which compares the input to the threshold value δ (air-to-acid gas ratio update tolerance) producing a logical (Boolean) output signal  98  in dependence on the results of this comparison. If the input signal  92  is greater than the threshold value δ or input signal  92  is smaller than the negative threshold value −δ then the output signal  98  is 1, if the input signal  92  is within the range [−δ; δ] then the output signal  98  is 0. Logical signal  98  is supplied to a logical AND block  101 . The system has means of sampling  99 . Means of sampling  99  produces logical (Boolean) signal  100 , which is short pulses of predefined frequency that can be equal to or lower than the frequency of the algorithm execution in the control system. Output signal  100  of the sampling means is supplied to the logical AND block  101 . Logical AND block  101  produces logical (Boolean) output signal in accordance with the following logic. If both input signals  98  and  100  are 1 then the output signal  102  is 1; all other combinations of the input signals produce the output signal  102  value of 0. Signal  102  is supplied to the control input of a selector  103 . 
     Output signal  94  of the nonlinear block  93  is supplied to the summing means  95 . The output of the adaptive controller (which is the air-to-acid gas ratio set point)  47  is supplied to the second input of the summing means  95 . Summing means  95  produces an output signal  96 , which is the sum of signal  47  and signal  94 . Output signal  96  is supplied to the second input of the selector  103 . Selector  103  produces the output signal  104  according to the following algorithm: if signal  102  is equal to 0 then the first input (signal  106 ) is selected, if signal  102  is equal to 1 then the second input (signal  96 ) is selected. Signal  104  is supplied to a memory block  105 , which stores the value until another input value (signal  104 ) comes and produces an output signal  106 . The values stored in the memory block are updated with the frequency generated by the sampling means  99 , subject to the logical 1 value of signal  98 . Signal  98  serves as a permissive to update a value in the memory block  105 . This value is, therefore, updated only if the difference between the output of the low-pass filter  89  and the current the air-to-acid gas ratio set point  47  is large enough (larger than δ). Output signal  106  is supplied to the first input of a selector  109 . 
     The system comprises a means of entry of a manual air-to-acid gas ratio set point  107 , with the output signal representative of the manual set point  108 . Manual set point can be used primarily for the start-up of the system, when learning through low-pass filtering using filter  89  is not yet done. Output signal  108  is supplied to the second input of a selector  109 . The system comprises an operator switch  110  allowing the operator to select between the manual (with a manual air-to-acid gas ratio set point) or automatic (with the air-to-acid gas ratio set point produced automatically through adaptation) modes of operation. If the selected mode is “automatic” the switch  110  produces a logical (Boolean) output signal  111  of 0; if the selected mode is “manual” the switch  110  produces a logical (Boolean) output signal  111  of 1. Selector  109  produces the output signal  47  according to the following algorithm: if signal  111  is equal to 0 then the first input (signal  106 ) is selected, if signal  111  is equal to 1 then the second input (signal  108 ) is selected. Output signal  47  of the selector  109  is the output signal of the whole adaptive controller. 
     In  FIG. 4 , selectors  87 ,  103  and  109  are shown in the position corresponding to the control signal  86 ,  102  and  111  (respectively) equal to zero. 
     The invention has been described in terms of a presently preferred embodiment as shown in  FIG. 1 ,  FIG. 2 ,  FIG. 3 , and  FIG. 4 . Specific components which can be used in the practice of the invention as shown in  FIG. 1  are as follows: 
     In the preferred embodiment, analyzer  22  and  24  is Ametek 880-NSL; flow sensors  13 ,  16 , and  19  and associated transducers  14 ,  17 , and  20 ; control valves  29 , and  33 , and current to pressure transducers  28 , and  32  are each well known, commercially available control components such as are described at length in Béla G. Lipták, INSTRUMENT ENGINEERS&#39; HANDBOOK, 4th Edition, Vol. 1 and 2, CRC Press, 2003. 
     While the invention has been described in terms of the presently preferred embodiment, reasonable variations and modifications are possible, by those skilled in the art, within the scope of the described invention and the appended claims.