Patent Publication Number: US-8116992-B1

Title: Apparatus and method for determining solids circulation rate

Description:
STATEMENT OF GOVERNMENTAL SUPPORT 
     The United States Government has rights in this invention pursuant to the employer-employee relationship of the Government to the inventors as U.S. Department of Energy employees and site-support contractors at the National Energy Technology Laboratory. 
    
    
     TECHNICAL FIELD 
     A method of determining bed velocity and solids circulation rate in a circulating bed fluidized reactor experiencing a moving packed bed flow in the standpipe section. The method utilizes in-situ measurement of differential pressure over known axial lengths of the standpipe in conjunction with in-situ gas velocity measurement for a novel application of Ergun equations allowing determination of standpipe void fraction and moving packed bed velocity. The method takes advantage of the moving packed bed property of constant void fraction in order to integrate measured parameters into simultaneous solution of Ergun-based equations and conservation of mass equations across multiple sections of the standpipe. The method utilizes measurement techniques that mitigate the aggressive impact of the high temperatures and gas compositions often encountered, are non-intrusive to the flow itself so that systematic errors from changes in the flow itself are minimized, that are capable of operation in large-scale units with minimized calibration requirements, and that are able to cover a broad range of circulation rates with consistent accuracy. 
     BACKGROUND OF THE INVENTION 
     Many processes involve gas and particulate solids flows where the solids are recycled back to the process for further use. Examples of such circulating flow of solids are the flow of solid catalyst in a Circulating Fluidized Bed (CFB) reactor and coating of the particles in a cycle spouted bed. In these systems, the solids circulation rate, which affects both heat and mass transport properties and determines the gas-solid contact time and the performance of the reactor, becomes a highly significant operating parameter. However, measurement challenges abound. The system by its nature promotes highly complex interactions between the gas and the particulates, and simple tracer—response methods produce results that are not unique. Attempts to avoid this complexity concentrate on estimation of the time-averaged solids flow rate across a given section, and assume it to be an estimate of the overall solids circulation rate in the closed loop. However, additional challenges are presented. The high temperatures and gas compositions commonly found in these processes are relatively aggressive to intrusive instruments, and the high pressure with particulate laden flows make the sealing of mechanical motion across the pressure boundary difficult. Further, introduction of intrusive instruments may in turn change the flow itself, leading to a systematic error in the measurement. Additionally, the flow response to specific components which may or may not be present among different circulating systems often demands a-priori calibration that is often difficult to perform in situ. All of this is compounded by the fact that operating conditions vary significantly from application to application. For example, for coal combustion, the gas velocity and solids flux are typically 5-8 m/s and less than 40 kg/m2-s, respectively. For fluid catalytic cracking (FCC), on the other hand, the gas velocity and solids flow rate are considerably higher, e.g. 15-20 m/s (at the riser exit) and greater than 300 kg/m2-s, respectively. As a result, a metering technology generically suitable for gas and particulate solids flows is still lacking. 
     Among the few techniques available for estimating the solids circulation rate in a hot, pressurized solids circulating system, one of the more simple methods involves the measurement of particle velocities at the wall within the packed bed portion of a standpipe. Typically, in a system utilizing circulating solids, the standpipe serves as a component in the solids recirculation loop. In applications involving chemical reactions, the standpipe may also serve as a heat regulator or spent sorbent regenerator. During operations, individual particles are tracked at the wall of the standpipe, and the time needed for an individual particle to travel a known distance is measured in order to determine a particle velocity. This velocity, in conjunction with the cross-sectional area for flow and the solids bulk density, allows a mass circulation rate to be determined. However, this method necessarily assumes that the particles at the wall travel at the same velocity as the bulk, since the presence of the bed material prevents an observer from seeing into the interior of the standpipe. This can introduce significant error. For example, particle slippage due to surface roughness and wall friction can produce a significant velocity deviation between the particle observed at the wall and the bulk flow. Additionally, there may be significant logistical hurdles to this method. For a hot unit at pressure, this technique requires a high temperature window with significant thickness to withstand the operating conditions, which at the same time must be kept sufficiently clean so that individual particles can be seen and tracked. 
     Another method employed involves calorimetric measurements. Many hot systems have heat exchanger equipment in the packed bed portion of the standpipe to control the temperature of the circulating solids. By measuring the temperature change and flow rate of the heat transfer fluid in the heat exchanger while simultaneously measuring the temperature change of the hot circulating solids, the solids circulation rate can be estimated. Clearly, this method is only applicable to systems incorporating submerged heat exchangers and solids at higher temperatures. Additionally, the method assumes that solids temperature is uniformly lowered by the heat exchanger, and that all of the solids flow through the heat exchanger. However, in practicality, because of heat changes driven by seal air and heat radiation, among other factors, the method requires significant plant specific calibration, especially for large systems. As an example, see “Experimental Study on an On-Line Measurement of High Temperature Circulating Ash Flux in a Circulating Fluidized Bed Boiler,” Lu Xiaofeng, et al,  J. of Thermal Science , Vol 10, No. 2 (2001). 
     Another method for estimating the solids circulation rate is based on gas velocity measurement in a riser. Within the riser of a solids circulating system, the gas travels upwards faster than the solids. The difference between the gas velocity and the solids velocity is called the slip velocity. Knowledge of slip velocity and solids concentration in the riser allows determination of a solids mass circulation rate. However, solids flow dynamics in gas-solid risers is inherently complex, and the solids slip velocity is not a simple function of operating conditions. Any measurement of gas velocity using this method will likely be assuming a plug flow through the riser, which can be significantly at odds with the actual situation. See, e.g., “Investigation on slip velocity distributions in the riser of dilute circulating fluidized bed,” Yang Y.-L, et al,  Powder Technology , Vol. 73, pp. 67-73 (1992). Further, solids concentration is not uniform across the diameter of the riser, and shear forces between the riser wall and the particles increase the error in the solids concentration estimate using pressure drop measurements. Additionally, these techniques may introduce invasive probes into the riser, changing the flow itself and leading to a systematic error in the measurement. 
     Another method for estimating the solids circulation rate is based on pressure drop across a specific part of the equipment or across an orifice. In this method, experimentally measured pressure drop, together with the gas velocity, is correlated with the solids mass flux. This technique is effectively non-interfering with the flow in the riser, however, because different combinations of gas and solids flowrates can lead to the same pressure drop, the solids mass flux must be independently estimated using a time-of-descent method or some other method. See, e.g., “Development of a J-shaped Pneumatic Valve to Control the Solid Particle Circulation rate in a Circulating Fluidized Bed,” Terasaka, K. et al.,  Powder Technology , Vol 126, p. 13-21 (2002). This necessitates a calibration process which can be arduous for industrial scale equipment. 
     In order to avoid the issues associated with the aggressive impact of high temperature and gas compositions, the intrusiveness of measuring instruments leading to systematic error, and the difficulty of extensive calibration in large-scale units, flow correlations such as the Ergun equation have been utilized to correlate moving bed flow with relatively easily obtained pressure measurements. The Ergun equation is well known and traditionally used to describe the pressure drop of a liquid or gas flowing through a stationary packed bed. It relates the pressure drop to a specified flow rate, the flowpath length through the bed, the equivalent spherical diameter of the particles in the bed, the density and dynamic viscosity of the liquid or gas, the velocity of the liquid or gas with respect to the bed, and the void fraction of the bed. See,  Coulson and Richardson&#39;s Chemical Engineering , Richardson, J., et al., Butterworth-Heinemann (2002), among many others. This concept is further extended to moving packed beds where both the liquid or gas and the fixed bed itself are in motion relative to a containing plant component, such as a standpipe in a circulating fluidized bed reactor. For these situations, the Ergun equation and its modified forms utilize the concept of superficial gas velocity, sometimes termed slip velocity, which is simply defined as the relative velocity between the fluid or gas and the moving packed bed. Determination of the superficial gas velocity and separate measurement of the gas velocity with respect to the standpipe is then used to determine bed velocity with respect to the standpipe, and the subsequent solids flowrate. See,  Fluidization, Solids Handling, and Processing: Industrial Applications , Yang, W., Noyes Publications (1999), among many others. Typically in practice, the pressure drop over a length of bed is measured while the equivalent particle diameter, gas density, and gas viscosity is estimated, and the superficial gas velocity and void fraction remain as unknown quantities. At that point, the value of void fraction is often further assumed in order to finalize a superficial gas velocity. For example, see “An Analysis of Loop Seal Operations in a Circulating Fluidized Bed,” Basu, P. et al.,  Trans IChemE , Vol. 78, Part A, p. 991-998 (October 2000); see also “Simultaneous Measurements of Gas-Solid Flow Rates and Pressure Drop in Downcomer of J-Valve in CFB,” Goshima, T., et al,  Chem. BioChem. Eng ., Q 21 (4), p. 357-363 (2007); and see also “Solids Flow Characteristics in Loop-Seal of a Circulating Fluidized Bed,” Sung Won Kim, et al,  Korean J. Chem Eng ., Vol 16, p. 82-88 (1999). Another commonly used approach is to express the void fraction as a linear function of the superficial gas velocity, thereby leaving superficial gas velocity as the only remaining unknown. See, e,g.,  Pneumatic Conveying of Solids: A Theoretical and Practical Approach , Klinzing, G., et al., Springer (1997), among many others. However, this treatment of void fraction, heretofore necessary, can introduce significant error when an Ergun correlation is used to determine a superficial gas velocity. 
     Mathematically, the void fraction typically appears in Ergun correlations as a cubed term and any errors in the void fraction value have a dramatic effect on mathematically determined superficial gas velocities. For example, a 5% error in the void fraction will produce a 55% error in the slip velocity. Therefore, it is necessary to determine void fraction with a great deal of precision. See  Chemical Reactor Design , Harriott, P., CRC Press (2003). In moving bed flow, this is additionally complicated by the fact that the void fraction may not be constant with time, and can change based on changes in operating parameters elsewhere in the system. For example, in a circulating fluidized bed characterized by a riser loop and a recirculating standpipe, under normal operating conditions with a constant mass circulation rate, the pressure drop across the riser is balanced by the pressure drop across the standpipe loop. If a small reduction in gas velocity through the riser takes place, the flow in the riser responds by increasing the pressure drop across the riser. The increase in pressure drop must be balanced by an increase in pressure drop in the standpipe. This increased pressure drop in the standpipe will change the flow of gas through the standpipe and shift the operating value of void fraction in the standpipe. This can introduce further error into the estimated value of void fraction, and further error in the values of superficial gas velocity determined using Ergun correlations. 
     What is needed is a technique for measuring solids flowrate which mitigates the aggressive impact of the high temperatures and gas compositions often encountered, is non-intrusive to the flow itself so that systematic errors from changes in the flow itself are minimized, is capable of operation in large-scale units with minimized calibration requirements, and is able to cover a broad range of circulation rates with consistent accuracy by determination of void fractions and superficial gas velocities based on operating parameters. 
     Accordingly, an object of one embodiment is to provide the bed velocity of a moving packed bed in the standpipe of a circulating bed reactor by measuring the differential pressure and gas velocity in a first section of the standpipe over a first axial distance and in a separate second section of the standpipe over a second axial distance, and determining the void fraction and bed velocity based on an Ergun correlation describing the interaction of measured parameters in the first and second sections. 
     It is another object of one embodiment to provide the bed velocity of a moving packed bed in the standpipe of a circulating bed reactor utilizing a method where the fixed moving bed void fraction is determined based on in-situ measurement of operating conditions, rather than assumed as a constant value or related to other prevailing conditions in the standpipe with empirical relationships, thereby minimizing the impact of void fraction error stemming from initial assumptions or changes in plant operating condition. 
     It is another object of one embodiment to provide the bed velocity of a moving packed bed in the standpipe of a circulating bed reactor utilizing a method which avoids plant specific calibration, by providing a method whereby operating conditions in an instrumented standpipe section are observed and related to bed velocity with Ergun correlations for gas or fluid flow through a moving packed bed applied to that instrumented standpipe section, thereby avoiding a large number of plant specific variables. 
     It is another object of one embodiment to provide the bed velocity of a moving packed bed in the standpipe of a circulating bed reactor utilizing measurement techniques that mitigate the aggressive impact of high temperatures and gas compositions in the circulating bed reactor on measurement instruments. 
     It is another object of one embodiment to provide the bed velocity of a moving packed bed in the standpipe of a circulating bed reactor utilizing measurement techniques that are non-intrusive to the flow itself, mitigating any systematic errors introduced by measurement instruments. 
     SUMMARY OF INVENTION 
     An embodiment of the novel apparatus and method presented herein allows determination of bed velocity and solids circulation rate of a circulating bed fluidized reactor experiencing a moving packed bed flow in the standpipe section. This is accomplished through measurement of differential pressure over known axial sub-lengths of the standpipe in conjunction with gas velocity measurement, allowing novel application of Ergun correlations for determination of standpipe void fraction and moving packed bed velocity. The apparatus and method takes advantage of the moving packed bed property of constant void fraction in order to integrate measured parameters into simultaneous solution of Ergun correlations and conservation of mass equations across multiple sections of the standpipe, and provides void fraction, bed velocity, and solids circulation rate. The method utilizes measurement techniques that mitigate the aggressive impact of the high temperatures and gas compositions often encountered, are non-intrusive to the flow itself so that systematic errors from changes in the flow itself are minimized, are capable of operation in large-scale units with minimized calibration requirements, and are able to cover a broad range of circulation rates with consistent accuracy. 
     The apparatus and method described herein allows determination of solids flowrate in a moving packed bed. In a moving packed bed, a bed of particles moves through a pipe or other flow conduit aided by gas or liquid flow through the conduit. The relative velocity between the gas or liquid and the particles is less than or equal to the minimum fluidization velocity and the particles do not move relative to each other. Correspondingly, void fraction in the moving packed bed, as defined by the volume of gas divided by the total volume of particles and gas, is treated as constant. Such moving packed beds find numerous application in, for example, petrochemical industry in fluid catalytic cracking and the utility industry in coal combustion. 
     In the numerous applications utilizing moving packed beds, the solids circulation rate, which affects both heat and mass transport properties and determines the gas-solid contact time and the performance of the reactor, becomes a highly significant operating parameter. The method described herein provides for determination of solids circulation rate through observation of operating parameters in the standpipe section and subsequent calculation of mass flow using Ergun correlations known in the art. The apparatus utilizes two sections of a standpipe separated by at least one aeration port, where each section has a differential pressure means for the measurement of differential pressure over a known length, and a gas velocity means, for measurement of a gas velocity through the sections. In operation, when the standpipe contains a contiguous moving packed bed over the two sections and the at least one aeration port provides aeration air between the two sections, Ergun correlations having the form dP/dL=A V R +B ρ GAS  V R   2  are formulated for each section and the formulations are solved to determine the moving packed bed velocity and void fraction, and subsequently the solids circulation rate. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a typical CFB having riser, a particulate collection system, a standpipe, and solids flow control valve. 
         FIG. 2  illustrates a standpipe receiving solids experiencing a superficial gas flow and forming a moving packed bed. 
         FIG. 3  illustrates a standpipe containing a first section and a second section for determination of void fraction and bed velocity. 
         FIG. 4  illustrates a gas tracer device using helium as a trace gas. 
         FIG. 5  illustrates a standpipe containing a first section and a second section and containing a moving packed bed flow and gas flows in the standpipe. 
         FIG. 6  illustrates an online system for the determination of solids circulation rate using one embodiment of the method. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The following description is provided to enable any person skilled in the art to use the invention and sets forth the best mode contemplated by the inventor for carrying out the invention. Various modifications, however, will remain readily apparent to those skilled in the art, since the principles of the present invention are defined herein specifically to provide a technique for measuring solids flowrate which mitigates the aggressive impact of the high temperatures and gas compositions often encountered, is non-intrusive to the flow itself so that systematic errors from changes in the flow itself are minimized, is capable of operation in large-scale units with minimized calibration requirements, and is able to cover a broad range of circulation rates with consistent accuracy through utilization of Ergun correlations. 
     As used herein, the term “Ergun correlation” means a formulation relating pressure drop, superficial gas or liquid velocity, void fraction, and parameters which may be estimated or measured in flow across moving packed beds. Ergun correlations often take the form dP/dL=A V R +B ρ GAS  V R   2 , where V R  describes a relative velocity between a gas or liquid and a particulate bed, and A and B are formulations tailored to the specifics of the flow situation, including situations where either A or B may have a zero value. Those skilled in the art recognize that alternate formulations tailored to specific flow situations is a long standing and continued effort. See, e.g., Macdonald, et al, “Flow Through Porous Media—The Ergun Equation Revisited,”  Ind. Eng. Chem. Fundamen.,  1979, 18(3), among many others. The alternative formulations tailored to specific flow situations may be utilized without invalidating the method presented herein. 
     As used herein, the term “standpipe” means a pipe situated to enclose a flow of incompressible solid particles and having substantially uniform cross-section over a standpipe axial length, where the standpipe axial length is some contiguous portion of the standpipe longitudinal axis. 
     As used herein, the term “packed bed” means a layer of incompressible particles or objects enclosed in a standpipe and experiencing intimate contact between individual incompressible particles or objects within the layer of incompressible particles or objects. 
     As used herein, the term “moving packed bed” means a packed bed moving over a standpipe axial length and having a bed velocity with respect to the standpipe, such that the mass flow rate of the packed bed is substantially equivalent at all points along the standpipe axial length. 
     Principles 
     The apparatus and method described herein allows determination of solids flowrate in a moving packed bed. In a moving packed bed, a bed of particles moves through a pipe or other flow conduit aided by gas or liquid flow through the conduit. The relative velocity between the gas or liquid and the particles is less than or equal to the minimum fluidization velocity and the particles do not move relative to each other. Correspondingly, void fraction in the moving packed bed, as defined by the volume of gas divided by the total volume of particles and gas, is treated as constant. See  Handbook of Fluidization and Fluid - particle Systems , Wen-Ching Yang, CRC Press (2003). Such moving packed beds find numerous application in, for example, petrochemical industry in fluid catalytic cracking and the utility industry in coal combustion. 
     As an example of a process utilizing a moving packed bed, consider a circulating fluidized bed (CFB) reactor. A CFB reactor can function as a heavy oil cracker, combustor or gasifier to process carbonaceous materials. For all of these applications, the CFB reactor typically comprises similar components, namely a riser, a particulate collections system, a standpipe and a solids flow control valve. This is illustrated at  FIG. 1 , showing a CFB  100  having riser  101 , particulate collection system  102 , standpipe  103 , and solids flow control valve  104 . CFB  100  circulates the solids comprising moving packed bed  105  contained in standpipe  103  by injecting solids from moving packed bed  105  through the solids flow control valve  104  into the riser  101  with aeration air injected through aeration port  106 . Riser air is injected through riser port  107  to produce an upward flow of gas-solids mixture in the riser  101 . The gas-solids mixture flows from the riser to particulate collection system  102 , where the gas and solids are separated. The gas exits CFB  100  through gas exit  108 . The solids exit particulate collection system  102  and enter standpipe  103 , and gravitationally flow down standpipe  103  back to moving packed bed  105 , to begin the recirculation process anew, so that moving packed bed  105  is depleted of solids via solids flow control valve  104  while simultaneously receiving solids from the particulate collection system  102 , and the solids comprising moving packed bed  105  are simultaneously moving through moving packed bed  105 . Aeration air is supplied to standpipe  103  through aeration port  109  to assist the solids in moving down standpipe  103  through moving packed bed  105 . 
     In the numerous applications utilizing systems similar to that illustrated in  FIG. 1 , the solids circulation rate, which affects both heat and mass transport properties and determines the gas-solid contact time and the performance of the reactor, becomes a highly significant operating parameter. The method described herein provides for determination of solids circulation rate through observation of operating parameters in the standpipe section and subsequent calculation of mass flow using Ergun correlations known in the art. 
       FIG. 2  demonstrates a detailed view of standpipe  203 . Standpipe  203  contains particles  210  received from a particulate collection system (not shown). The particles  210  collect in the standpipe  203  and form a moving packed bed between axis AA′ and axis BB′. In the region between axis AA′ and BB′, the moving packed bed moves at a velocity V BED  with respect to standpipe  203 . However, as discussed infra, the particles  210  comprising the moving packed bed do not move relative to each other, and void fraction in the moving packed bed is treated as having a constant, though unknown, value. The moving packed bed is assisted in moving down standpipe  203  by aeration air supplied through aeration ports  209  and  212 . Aeration ports  209  and  212  are constructed for fluid communication with the interior of standpipe  203 . At the base of standpipe  203 , particles  210  detach from the moving packed bed aided by aeration air from air port  206  and move into the riser (not shown). Throughout this process, gas flow  211  flows through standpipe  203  and through the moving packed bed at a velocity V GAS  with respect to standpipe  203 . Although represented in  FIG. 2  as a flow in the upward direction, gas flow  211  may flow either up or down in standpipe  203 . 
     When the gas flows through the moving packed bed of solids it exerts a drag force on the particles, causing a pressure drop across the bed in the nominal direction of the gas flow. The pressure drop over the moving packed bed can be related to operating conditions in standpipe  203  using Ergun correlations for flow through a packed column with modification for moving packed beds. Once such Ergun correlation takes the form: 
     
       
         
           
             
               
                 
                   
                     
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     Where the superficial gas velocity, V SUP ) is:
 
 V   SUP =ε( V   GAS   −V   BED )  (2)
 
     and: 
     ΔP/ΔL is the pressure drop of the gas flow  211  through the moving packed bed per unit length of standpipe  203 , 
     ε is the void fraction, defined by the volume of gas in the moving packed bed divided by the total volume of the moving packed bed, 
     D p  is the effective diameter of particles  210 , 
     μ is the dynamic viscosity of gas flow  211  flowing through the moving packed bed, and 
     ρ is the density of gas flow  211  flowing through the moving packed bed. 
     In equation (1), |V SUP | represents the absolute value of the vector quantity V SUP . The second term of equation (1) is often represented containing V SUP   2 , however the product of V SUP  and |V SUP | is utilized within the method presented herein in order to preserve the vector property. 
     As is well known, equations (1) and (2) or variants thereof are commonly used in the characterization of gas or liquid flow through packed beds, both moving and stationary. In practice, typically, a differential pressure is measured, the gas and particle properties are estimated based on prevailing operating conditions, and void fraction ε and superficial gas velocity V SUP  are remaining unknowns. The void fraction ε is then eliminated as an unknown by either assigning a constant value or relating it to the superficial gas velocity with an empirical correlation. See, e.g.,  Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions , Gidaspow, D., Academic Press (1994). The result allows determination of superficial gas velocity V SUP ) and subsequent determination of moving packed bed velocity and mass flow rate. However, the validity of any results determined in this practice clearly depends strongly on the proper characterization of void fraction ε, since any errors in the characterization are carried forward to the final determination of moving packed bed velocity. For example, a 5% error in the void fraction will produce a 55% error in the slip velocity. See  Chemical Reactor Design , Harriott, p. 361. This is further complicated in moving bed flow in the standpipe of a CFB, because the void fraction ε is impacted by changes in operating parameters elsewhere in the system. In a CFB where system pressures provide the motive force for solids movement rather than a direct feeding device, the pressure gradient along the standpipe axis is hydrodynamically coupled with the pressure gradient along the riser axis. Further, the pressure gradient across the riser is strongly impacted by changes in CFB operating conditions such as solids inventory within the riser. As a result, changes in CFB operating conditions impact the pressure gradient in the standpipe, which impacts the void fraction E. See  Solids Handling, and Processing: Industrial Applications , Yang, p. 111. This further exacerbates inaccuracies in moving packed bed velocity determination based on assumed and correlated void fraction values. 
     The apparatus and method presented herein utilizes Ergun correlations in two sections of the standpipe separated by at least one aeration port in order to relate operating conditions in the sections and determine both superficial gas velocity V SUP  and void fraction ε based on measured operating parameters. This minimizes the impact of void fraction errors discussed supra and allows accurate determination of superficial gas velocity V SUP  and solids mass flow rate. The apparatus and method utilizes measured differential pressure across sections of interest and measured gas velocity V GAS  through the moving packed bed in those sections. Aeration points between the sections avoid mathematically trivial relationships from section to section, and Ergun correlations in conjunction with conservation equations allow determination of void fraction ε and superficial gas velocity V SUP  based on observed operating parameters. It is recognized that although the method is illustrated by reference to a CFB utilizing gas flow, the method is equally applicable to situations using a liquid medium rather than gas, and that the term “aeration point” may refer to the injection of either a gaseous or liquid medium provided to the standpipe between sections in order to assist solids flow down the standpipe. 
     As will be understood by those skilled in the art, this method is based on formulations of pressure drop across moving packed beds taking the traditional form dP/dL=A V R +B ρ GAS  V R   2 , where V R  describes a relative velocity between a gas and a particulate bed, and A and B are formulations tailored to the specifics of the flow situation, including situations where either A or B may have a zero value. Here equations (1) and (2) are utilized as representations of this traditional form, however alternate formulations tailored to specific flow situations may be utilized without invalidating the method presented herein. 
     Description of a Preferred Embodiment 
       FIG. 3  illustrates a standpipe  303  having a standpipe axial length along the longitudinal axis of the standpipe from AA′ to BB′. Standpipe  303  has a first axial sub-length from CC′ to axis DD′, and has a second axial sub-length from EE′ to FF′. As illustrated in  FIG. 3 , the first axial sub-length from CC′ to DD′ and the second axial sub-length from EE′ to FF′ are separate segments of the standpipe axial length from AA′ to BB′. The first axial sub-length and the second axial sub-length define a first section  318  and a second section  319  respectively, where first section  318  is that portion of standpipe  303  surrounding the first axial sub-length from CC′ to DD′, and the second section  319  is that portion of standpipe  303  surrounding the second axial sub-length from EE′ to FF′. 
     Standpipe  303  has one or more aeration ports, illustrated in  FIG. 3  as aeration ports  309  and  312 . At least one of the aeration ports, illustrated in  FIG. 3  as aeration port  309 , is connected to standpipe  303  between first section  318  and second section  319 , such that aeration port  309  fluidly communicates with the interior of standpipe  303  between the first section  318  and the second section  319 . Remaining aeration ports, represented in  FIG. 3  as aeration port  312 , are connected to standpipe  303  outside the volume bounded by first section  318  and second section  319 . Standpipe  303  may have any number of aeration ports, provided that at least one fluidly communicates with standpipe  303  between first section  318  and second section  319 , and provided that none of the aeration ports fluidly communicate with standpipe  303  within the volume bounded by first section  318  or second section  319 . 
     A first differential pressure sensor  314  is connected to standpipe  303  within the first section  318 . First differential pressure sensor  314  serves as a means for providing differential pressure between two discrete points separated by a first pressure length within the first axial sub-length between CC′ and DD′. The first pressure length is contained within the first section and is parallel to or a segment of the first sub-axial length. In a preferred embodiment, the first pressure length is substantially equivalent to the first axial sub-length between CC′ and DD′. The first differential pressure sensor  314  may be an instrument designed to measure the difference in pressure between two discrete points and present the resultant differential pressure directly, or may be a set of instruments indicating static pressure at two discrete points, with the differential pressure calculated as the difference. The first differential pressure sensor  314  may be a bellows, diaphragm, semiconductor strain sensor, or other sensors well known in the art, and may relay pressures of interest using an analog pneumatic, analog electronic, digital electronic signal, or using other methods well known in the art. A suitable first differential pressure sensor  314  and first pressure length is a pressure transmitter capable of measuring 0.25-2.0 psid over a 2-4 feet first pressure length, manufactured by ROSEMOUNT, Inc., Chanhassen, Minn. 
     A first gas velocity sensor  315  is connected to standpipe  303  within the first section  318 . First gas velocity sensor  315  serves as a means for providing a first gas velocity over a first gas length within the axial sub-length between CC′ and DD′. The first gas length is contained within the first section and is parallel to or a segment of the first sub-axial length. In a preferred embodiment, the first gas length is substantially equivalent to the first axial sub-length between CC′ and DD′. The first gas velocity sensor  315  may be a gas tracer device, a laser device, a hot wire anemometer device, or other devices known in the art for determination of gas velocity through a moving packed bed. 
     A second differential pressure sensor  316  is connected to standpipe  303  within the second section  319 . Second differential pressure sensor  316  acts in second section  319  in a manner similar to that described for first differential pressure sensor  314  in first section  318 . Second differential pressure sensor  316  serves as a means for providing differential pressure between two discrete points separated by a second pressure length within the second axial sub-length between EE′ and FF′. The second pressure length is contained within the second section and is parallel to or a segment of the second sub-axial length. In a preferred embodiment, the second pressure length is substantially equivalent to the second axial sub-length between EE′ and FF′. The second differential pressure sensor  316  may be an instrument designed to measure the difference in pressure between two discrete points and present the resultant differential pressure directly, or may be a set of instruments indicating static pressure at two discrete points, with the differential pressure calculated as the difference. The second differential pressure sensor  316  may be a bellows, diaphragm, semiconductor strain sensor, or other sensors well known in the art, and may relay pressures of interest using an analog pneumatic, analog electronic, digital electronic signal, or using other methods well known in the art. A suitable second differential sensor  314  and second pressure length is a pressure transmitter capable of measuring 0.25-2.0 psid over a 2-4 feet second pressure length, manufactured by ROSEMOUNT, Inc., Chanhassen, Minn. 
     A second gas velocity sensor  317  is connected to standpipe  303  within the second section  319 . Second gas velocity sensor  317  acts in second section  319  in a manner similar to that described for first gas velocity sensor  315  in first section  318 . Second gas velocity sensor  317  serves as a means for providing a second gas velocity over a second gas length within the second axial sub-length between EE′ and FF′. The second gas length is contained within the second section and is parallel to or a segment of the second sub-axial length. In a preferred embodiment, the second gas length is substantially equivalent to the second axial sub-length between EE′ and FF′. The second gas velocity sensor  317  may be a gas tracer device, a laser device, a hot wire anemometer device, or other devices known in the art for determination of gas velocity through a moving packed bed. 
     For standpipes utilizing gas flow, a gas tracer device developed at the National Energy Technology Laboratory (NETL) which utilizes helium as the trace gas is particularly suited for use as the first gas velocity sensor  315  and the second gas velocity sensor  317 . This gas tracer device is illustrated at  FIG. 4 . As illustrated, helium injection probe  426  is inserted through standpipe  403  and into gas flow  411 . Helium injection probe  426  is connected to solenoid valve  431  and is tipped with first filter  428 . Similarly, thermistor probe  432  is inserted through standpipe  403  and into gas flow  411 , however thermistor probe  432  is inserted such that thermistor probe  432  is upstream of helium probe  426  in gas flow  411 . Thermistor probe  432  is connected to vacuum pump  434  and tipped with second filter  433 . Additionally, thermistor probe  432  contains thermistor  421 . Thermistor  421  is connected in a Wheatstone bridge with first variable resistor  422 , second variable resistor  423 , and reference resistor  424 . DC source  425  supplies power to the Wheatstone bridge and gage  426  provides indication of bridge balance. In operation, gas flow  411  flows in standpipe  429  over helium injection probe  426  then thermistor probe  432 . Vacuum pump  434  operates to cause a flow of gas from gas flow  411  to be drawn through second filter  433  and over thermistor  421 . Vacuum pump  434  maintains a critical pressure ratio across second filter  433  to insure the flow of gas through second filter  433  is relatively constant relative to any fluctuating conditions in gas flow  411 . Then, first variable resistor  422  and second variable resistor  423  are adjusted to balance the Wheatstone bridge as indicated by gage  426 . Exact balancing is not required, as the gas tracer device relies on variations in bridge balance rather than specific magnitudes. Solenoid valve  431  then momentarily opens to allow a helium pulse from helium flow He through helium probe  426  and into gas flow  411 . First filter  427  assists in dispersing the helium pulse into gas flow  411 . 
     The helium pulse is carried by gas flow  411  from helium injection probe  426  to thermistor probe  432 . As the helium pulse reaches thermistor probe  423 , some portion of the helium pulse is drawn through second filter  433 . This alters the heat transfer characteristics of the gas flowing past thermistor  421 , altering the temperature and the resistive characteristics of thermistor  421 , and altering the bridge balance indicated by gage  426 . Gas velocity is determined by the separation between helium injection probe  426  and thermistor probe  432  and the time elapsed between operation of solenoid valve  431  and detection of the bridge imbalance, taking into account the intrinsic time delays of the gas tracer device. 
     An advantage of the gas tracer device as described herein when used for first gas velocity sensor  315  and the second gas velocity sensor  317  is the ability to insert helium injection probe  426  and thermistor probe  432  into gas flow  411  a sufficient distance from standpipe  403  such that the gas velocities obtained accurately reflect typical plug flow assumptions in the standpipe. Additionally, the critical pressure ratio across second filter  433  maintains a relatively constant flow of gas past thermistor  421  such that any thermistor  421  response can be attributed to gas composition changes rather than any fluctuating conditions in gas flow  411 . Additionally, the gas tracer device may be sufficiently small such that intrinsic time delays are short, alteration of inherent flow characteristics in the standpipe are negligible, and the time scale of each helium injection is reduced such that constant temperature in the system can be assumed. In one gas tracer device constructed and operated by NETL as a gas velocity means, thermistor  421  is a SENSOR SCIENTIFIC S14A10225 manufactured by Sensor Scientific, Inc., Fairfield, N.J. Solenoid valve  431  is a PETER/PAUL PN 52N8DGB, manufactured by Peter Paul Electronics, Inc., New Britain, Conn. Operation of solenoid valve  431  is controlled using a CRYDOM DO061A relay manufactured by Crydom, Inc., San Diego, Calif., driven by a computer generated square wave. The helium injection probe  426  and the thermistor probe  432  are 9.5 mm nominal diameter, 0.3 m long, stainless steel tubes, and first filter  428  and second filter  433  are 6.4 mm diameter, 25.4 mm long, 20 μm pore size sintered metal filters. First variable resistor  422  is variable between 0-2000 ohms and second variable resistor  423  is variable between 0-1000 ohms. DC source  425  supplies 5.5 VDC to the wheatstone bridge. This gas tracer device has an intrinsic time delay of 14.6 ms, determined in a 4.6 m/s flow with helium injection probe  426  and thermistor probe  432  separated by 15.3 cm. 
       FIG. 4  illustrates a 2-wire Wheatstone bridge as an exemplary bridge circuit with thermistor  426  as the active element, however the bridge circuit may be 3-wire or 4-wire Wheatstone bridge, or may be an alternative bridge circuit typically utilized for resistance measurement such as a Kelvin double bridge, a Maxwell bridge, or other suitable bridge circuits known in the art. 
     Operation of a Preferred Embodiment 
     A method of operation using the particular embodiment discussed supra is illustrated with reference to  FIG. 5 .  FIG. 5  illustrates standpipe  503  containing moving packed bed  505  over the standpipe axial length from AA′ to BB′. In the region between AA′ and BB′, the moving packed bed  505  moves at a velocity V BED  with respect to standpipe  503 . Moving packed bed  505  is comprised of particles having an equivalent particle diameter. The particles comprising moving packed bed  505  do not move relative to each other, and the void fraction in moving packed bed  505  is assumed to have a constant, though unknown, value. Standpipe  503  has aeration ports  509  and  512  injecting air into standpipe  503  in order to assist the movement of moving packed bed  505  down standpipe  503 . Gas flow  511  flows axially in standpipe  503  and through moving packed bed  505  at a velocity V GAS  with respect to standpipe  503 . Although represented in  FIG. 5  as a flow in the upward direction, gas flow  511  may flow either up or down in standpipe  503 . 
     A standpipe axial length of the standpipe experiencing moving packed bed flow, represented in  FIG. 5  as the axial length of standpipe  503  from axis AA′ to axis BB′, will typically be known to standpipe operators. This standpipe axial length is necessarily within what is often referred to as the dense phase of the standpipe, where the free-falling particles begin to accumulate in the standpipe and form a distinct bed level. Numerous methods exist for determining the onset of dense phase standpipe operation based on operating conditions within the standpipe itself. See, e.g., “The control of bed height and solids circulation rate in the standpipe of a cold flow circulating fluidized bed”, Park, J., et al.,  Powder Technology , Vol 150, Issue 3 (February 2005). Similarly, the equivalent particle diameter of the particles may be determined experimentally, or may be may be obtained based on existing reference materials. See  Chemical Reactor Analysis and Design , Froment, F. Wiley, (1990), and see  Industrial Catalysis: Optimizing Catalysts and Processes , Ruud, J., et al., Wiley-VCH (1998). 
     Referring to  FIG. 5 , first section  518  is identified within the standpipe axial length of standpipe  503  from axis CC′ to axis DD′ such that aeration by aeration ports  512  and  509  does not occur within first section  518  volume. This is a significant requirement, as subsequent steps in the methodology presented herein assume the mass flow of gas entering and exiting the first section  518  at axes CC′ and DD′ are equivalent. First section has first differential pressure sensor  514  providing differential pressure indication of gas flow  511  as gas flow  511  flows through moving packed bed  505  over a first pressure length, and has first gas velocity sensor  515 . Gas flow  511  has a first gas density and a first gas viscosity in the first section  518  determined by the operating conditions in first section  518 . 
     Similarly, second section  519  is identified within the standpipe axial length of standpipe  503  from axis EE′ to axis FF′ such that aeration by aeration ports  512  and  509  does not occur within second section  519  volume, but such that at least one aeration port, here illustrated as aeration port  509 , provides aeration to standpipe  503  between first section  518  and second section  519 . This is additionally a significant requirement, as subsequent steps in the methodology presented herein assume that gas velocity of the gas flow  511  through second section  519  is altered from the gas velocity of gas flow  511  through first section  518 . Second section  519  has second differential pressure sensor  516  providing differential pressure indication of gas flow  511  as gas flow  511  flows through moving packed bed  505  over a second pressure length, and second gas velocity sensor  517 . Gas flow  511  has a second gas density and a second gas viscosity in the second section  519  determined by the operating conditions in second section  519 . 
     Referring to  FIG. 5 , a first differential pressure per unit length is determined using first differential pressure sensor  514  and the first pressure length. First gas velocity with respect to the standpipe  503  is measured using first gas velocity sensor  515 . Similarly, a second differential pressure per unit length is determined using second differential pressure sensor  516  and the second pressure length. Second gas velocity with respect to the standpipe  503  is measured using second gas velocity sensor  515 . 
     Using equations (1) and (2), an Ergun correlation is formulated for the first section: 
                       Δ   ⁢           ⁢     P   1         Δ   ⁢           ⁢     L   1         =         150   ⁢       μ   1     ⁡     [     ɛ   (           ⁢       V     GAS   ⁢           ⁢   1       -     V   BED       )     ]       ⁢       (     1   -   ɛ     )     2           D   p   2     ⁢     ɛ   3         +       1.75   ⁢     ρ   1     ⁢       ɛ   2     (           ⁢       V     GAS   ⁢           ⁢   1       -     V   BED       )     ⁢          (           ⁢       V     GAS   ⁢           ⁢   1       -     V   BED       )          ⁢     (     1   -   ɛ     )           D   p     ⁢     ɛ   3                   (   3   )               
Using;
 
     ΔP 1 =first differential pressure determined by first differential pressure sensor  514 , 
     ΔL 1 =first pressure length, 
     V GAS1 =first gas velocity determined by first gas velocity sensor  515 , 
     D p =equivalent particle diameter of particles comprising fixed moving bed  505 , 
     μ 1 =first gas viscosity of gas flow  511  in first section  518 , 
     ρ 1 =first gas density of gas flow  511  in first section  518 . 
     Similarly, using equations (1) and (2), an Ergun correlation is formulated for the second section: 
                       Δ   ⁢           ⁢     P   2         Δ   ⁢           ⁢     L   2         =         150   ⁢       μ   2     ⁡     [     ɛ   (           ⁢       V     GAS   ⁢           ⁢   2       -     V   BED       )     ]       ⁢       (     1   -   ɛ     )     2           D   p   2     ⁢     ɛ   3         +       1.75   ⁢     ρ   2     ⁢       ɛ   2     (           ⁢       V     GAS   ⁢           ⁢   2       -     V   BED       )     ⁢          (           ⁢       V     GAS   ⁢           ⁢   1       -     V   BED       )          ⁢     (     1   -   ɛ     )           D   p     ⁢     ɛ   3                   (   4   )               
Using;
 
     ΔP 2 =second differential pressure determined by second differential pressure sensor  516 , 
     ΔL 2 =second pressure length, 
     V GAS2 =second gas velocity determined by second gas velocity sensor  517 , 
     D p =equivalent particle diameter of particles comprising fixed moving bed  505 , 
     μ 2 =second gas viscosity of gas flow  511  in second section  519 , 
     ρ 2 =second gas density of gas flow  511  in second section  519 . 
     As discussed previously, since the moving packed bed  505  extends from axis AA′ to axis BB′, the void fraction ε and bed velocity V BED  of moving packed bed  505  are constant, though unknown. Additionally, because aeration port  509  injects air into standpipe  503  between the first instrumented section and the second instrumented section, this alters the operating conditions in first section  518  from the operating conditions in second section  519 , and equations (3) and (4) present a solvable set of equations. Void fraction ε may therefore be determined based on the operating standpipe conditions measured, as well as bed velocity V BED , using appropriate mathematical methods known to those skilled in the art. For example, Equations (3) and (4) may be solved for void fraction ε and bed velocity V BED  using EXCEL SOLVER. 
     It is important to note that the presence of at least one aeration port between the first section and the second section is critical to the success of this particular technique. Otherwise, V GAS1  will approximately equal V GAS2 , and formulations of equations (3) and (4) as above will reflect substantially similar conditions. In that situation, solution of equations (3) and (4) will not produce useful results for void fraction E, and consequently for bed velocity V BED . Note, however, that when determining void fraction ε using a first and second section, it is not necessary that the mass flow rate of aeration air through aeration ports  509  and  512  be known values. It is only necessary that the aeration air mass flow rate be sufficient to alter the first gas velocity through first section  518  from the second gas velocity through second section  519  such that the simultaneous solution produces a meaningful result. Preferably, the mass flow rate of aeration air is at least 5% of the total aeration mass flow supplied to the standpipe  503 . Having determined void fraction ε and bed velocity V BED , the solids circulation rate (SCR) can determined by:
 
SCR= V   BED   A   BED (1−ε)ρ SOLID   (5)
 
where:
 
     A BED  is the cross-sectional area of the moving packed bed  505 , and 
     ρ SOLID  is the density of a particle comprising moving packed bed  505 . 
     Thus, solids circulation rate is determined using superficial gas velocity and void fraction based on measured parameters within the standpipe, rather than reliance on tabulated values or empirical correlations relating the two quantities. The method relies on application of the Ergun correlations across multiple sections of a standpipe separated by at least one aeration port. Aeration from the aeration port between the sections alters operating conditions from section to section, and Ergun correlations in conjunction with conservation equations allow solvable equations for superficial gas velocity V SUP  and void fraction ε based on observed operating parameters. 
     It can be recognized that a point of novelty in this method is the manner in which Ergun correlations relating pressure drop and gas velocity are applied to specific standpipe sections to produce descriptive equations that allow determination of void fraction and bed velocity based on in-situ measurement. Once standpipe sections are identified and measurements obtained under the conditions specified, the mathematical operations necessary for determination of void fraction and bed velocity are straightforward and consistent. As such, this methodology lends itself to an online system which samples measured parameters periodically and provides an updated indication of solids circulation rate based on the sampled measurement. 
     One such system is represented schematically at  FIG. 6  for the standpipe shown in  FIG. 5  discussed supra. Referring to  FIG. 6 , a first instrumented section  618  and a second instrumented section  619  is in communication with a Solution Module to provide respective values of differential pressure per unit axial length and gas velocity. Gas densities and gas viscosities for the first and second instrumented sections are determined and provided to the Solution Module based on actual or estimated pressure and temperature conditions in the first instrumented section, and equivalent particle diameter D P  is determined for the bed material and provided to the Solution Module. The Solution Module receives the inputs, formulates equations relating pressure drop and gas velocity similar to equations (3) and (4), and determines the resulting void fraction ε and bed velocity V BED . 
     Having described the basic concept of the invention, it will be apparent to those skilled in the art that the foregoing detailed disclosure is intended to be presented by way of example only, and is not limiting. Various alterations, improvements, and modifications are intended to be suggested and are within the scope and spirit of the present invention. Additionally, the recited order of elements or sequences, or the use of numbers, letters, or other designations therefore, is not intended to limit the claimed processes to any order except as may be specified in the claims. Accordingly, the invention is limited only by the following claims and equivalents thereto. 
     All publications and patent documents cited in this application are incorporated by reference in their entirety for purposes to the same extent as it each individual publication or patent document were so individually denoted.