Development and Validation of a Dynamic Response Model for a Cold

Article pubs.acs.org/IECR

Development and Validation of a Dynamic Response Model for a Cold Flow Circulating Fluidized Bed Esmail R. Monazam,†,‡ Ronald W. Breault,†,* Adam D. Freed,†,‡ Lawrence Shadle,† Larry O. Lawson,† and Steven L. Rowan†,§ †

National Energy Technology Laboratory, U.S. Department of Energy, 3610 Collins Ferry Rd., Morgantown, West Virginia 26507-0880, United States ‡ REM Engineering Services, PLLC, 3537 Collins Ferry Rd., Morgantown, West Virginia 26505, United States § Oak Ridge Institute for Science and Education, 3610 Collins Ferry Rd., Morgantown, West Virginia 26507-0880, United States ABSTRACT: A dynamic response model has been created of the Cold Flow Circulating Fluidized Bed at NETL in Morgantown, WV. The model is considered dynamic, as opposed to steady state, because it is used to predict the transient responses of gas and solids flows throughout the unit as process conditions vary. The model was built in ProTrax with Advanced Continuous Simulation Language (ACSL) custom code. Dynamic experiments, varying both gas and solids flows, in the CFB unit have been used to validate the accuracy of the model. The advantage of this model is its utility in predicting gas hold up and solids flow throughout the unit during transitions of process conditions. Accurate predictions of these phenomena are important in process control and optimization. The dynamic experiments used in validating the model include modulations of the system pressure, move air (solids flow), and riser gas velocity with step and sinusoidal changes.

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INTRODUCTION Fluidized bed technology has become the leading new combustion technology for power generation because of its favorable heat rates, environmental performance, and fuel flexibility.1 In circulating fluidized bed (CFB) systems, the solids hold-up in the riser is estimated from the pressure drop across it. This pressure drop is not independent and is related to the whole CFB system as well as the particle properties, the gas feed and solids circulation rate. This interrelation between these parameters make it necessary to model the entire CFB loop. Breault and Mathur,2 Chen et al.,3 Lei and Horio,4 and Grieco and Marmo5 have presented work on the steady state pressure balances around a circulating fluidized bed loops. These papers have demonstrated the general methodology for preparing the steady state pressure drop model from which the riser solids hold-up can be estimated and used to predict solids or gas conversion in the CFB reactors. However, these steady state models do not address how the system behaves to changes in the input variables as the unit slews from one steady state condition to another as is done with load changes. Therefore, a dynamic response model is needed to simulate that behavior for the development of control systems. Control strategies for circulating fluidized beds have been conservative and simplistic to ensure reliability and maintain guaranteed performance criteria. However, the use of advanced control schemes has the potential to improve the performance and throughput over and above those currently obtained commercially. Hyppanen et al.6 recognized the shortcomings of © 2016 American Chemical Society

CFB control systems during nonsteady conditions. They claimed that when optimization of heat transfer during step changes in load is of high priority, there are many capabilities in a CFB process that are unused because the process models have not been developed. A good dynamic model is required to develop, verify, and test such advanced control systems. The first step in developing a dynamic model of the circulating fluidized bed is to capture the process dynamics associated with the gas−solids hydrodynamics. These hydrodynamics are sufficiently complex that a model portraying the physics should be verified prior to adding the additional complexities of coal combustion chemistry. Complex Computational Fluid Dynamic (CFD) models are too computationally intensive to lend themselves at this time to developing control schemes.7 Previous CFB dynamic model work has mostly been focused on reaction and heat transfer processes.6,8−11 A basic assumption in many of these models is that the hydrodynamics are in steady-state operation. At the 2002 CFB Conference, the need for accurate CFB hydrodynamic modeling techniques was expressed by many researchers. Previous efforts by the authors12,13 exemplify this as they continue to understand operating regimes and process fluctuations around the CFB riser. Received: Revised: Accepted: Published: 288

September 12, 2016 December 6, 2016 December 14, 2016 December 14, 2016 DOI: 10.1021/acs.iecr.6b03536 Ind. Eng. Chem. Res. 2017, 56, 288−300

Article

Industrial & Engineering Chemistry Research

most of the straight sections in order to facilitate qualitative analysis via direct visual observation of the bulk particle motion during experiments. What follows is a brief description of the major hydrodynamic considerations of the CFB system and how these can be associated with components and modeled for this analysis. For a more detailed description of the experimental apparatus see Shadle et al.12

In this paper, a model utilizing the relationships that capture the hydrodynamics of the CFB loop are presented, along with the underlying simplifications necessary for implementation of the relationships. The present model shifts focus from reactions and heat transfer to a more detailed hydrodynamic characterization, including the data required to formulate any empirical relations. Additionally, the parameters required for this dynamic model are identified and the model simulations are validated with experiments. The model utilizes the dynamic simulation package ProTRAX,14 which is ideal for incorporating hydrodynamics developed from a one-dimensional or lumped parameter model. This simulation package, which is also suitable for commercial application due to its ability to run in real time, has been implemented in commercial power plant facilities such as TAMPCO power plant as a process training simulator. The paper presents the methodology, a lumped parameter model, for developing a dynamic response to process changes. The uniqueness of this approach is the simplicity of the lumped model, the ability to capture various operating regimes, and the utility to capture the dynamics for the development of control algorithms. This paper presents the ProTRAX model and compares the prediction with experimental data.

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GENERAL DESCRIPTION OF THE CFB SYSTEM The CFB unit (see Figure 1) consists primarily of a riser, crossover, primary and secondary cyclones, standpipe, and nonmechanical valve (i.e., loopseal or L-valve). The riser section is 15.3 m tall and 0.30 m in diameter with two inlets near the bottom and one outlet near the top. Riser airflow enters through a distributor plate located just below the side port where the solids enter (from the nonmechanical valve). Solids are carried up the riser by a carrier gas and exit through a side port near the top into the crossover. The 0.25 m diameter crossover piping carries the solids from the riser to the primary cyclone. Solids separated by the primary cyclone fall through a freeboard region to the top of the moving packed bed in the standpipe, while the gas separated by the primary cyclone passes through exit piping containing a back pressure valve that controls the absolute pressure of the unit. Generally the process is operated with this valve mostly open such that the operating pressure is near to atmospheric. The standpipe is a reservoir for solids waiting to pass back into the riser where the standpipe freeboard is a variable volume section defined by the volume above the packed moving bed in the standpipe. The dimensions of this important part of the process significantly impact how the whole unit operates. While the length of the standpipe is mostly a function of the length of the riser, the diameter can be varied through a wide range. The two parameters most affected by standpipe diameter are the total solids inventory and the required moveair flow rate. A small diameter will result in low inventory and low move-air requirements and vice versa for a large diameter. With a low solids inventory, the process is constrained to smaller operating ranges. A small change in the riser inventory causes a large change in standpipe inventory; therefore, total system inventory has to be increased to achieve high riser loading. On the other hand, with a large diameter standpipe and the associated large inventory of solids, a high flow of air is required to move the solids from the standpipe to the riser. As the solids freefall from the cyclone into the standpipe, a pressure gradient is generated. A series of eight differential pressure transducers are used to measure the pressure drop across the standpipe. The model treats the standpipe as eight separate sections (ranging from 0.3 m to 6m in height), each corresponding to the pressure tap locations within the unit. In addition, ports for aeration air are located at six heights on the standpipe: −0.24, 0.09, 2.3, 4.7, 6.3, and 8.2 m. The ports at the lowest two heights are the most significant and are referred to as the Base aeration and Move aeration, respectively. The air injected into the process at these points is most commonly used to adjust the rate that solids circulate. One other important measurement made in the standpipe is the solids circulation rate. The rate of solids flow within the standpipe is measured with a spiral device15,16 located in the packed bed region. During steady state operation, this measurement is expected to indicate the flow rate of solids

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CFB PROCESS DESCRIPTION The Cold Flow Circulating Fluidized Bed (CFCFB) at NETL was designed to accommodate hydrodynamic testing applications most similar to transport reactor/gasification in the TRIG process. Figure 1 represents the major components of a CFB system. Realizing the importance of hydrodynamics, the modular design of the CFB incorporates transparent piping for

Figure 1. Schematic of the NETL CFCB unit. 289

DOI: 10.1021/acs.iecr.6b03536 Ind. Eng. Chem. Res. 2017, 56, 288−300

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data, while the process flows remain unchanged. These data are recorded in a database and serve to complement the second-bysecond data which is much more bulky to manage. The following sections describe the different components of the CFB. For each, the output from the model predictions and experimental measured values are compared using two parameters. For example, for the crossover pressure drop, the mean square error (ξ) was calculated by

through all parts of the unit. However, during transients and other dynamics, the measurement reflects only the flow rate of the packed bed. While the common convention for circulation rate is to report mass flux, in this work, rate of mass flow is used because the cross-sectional areas of the components in the unit vary from 0.25 to 0.3 m. As a result, a steady-state mass flow rate translates into many different fluxes depending on the location within the unit. Finally, a loop-seal (nonmechanical valve) is used to transfer the solids from the base of the standpipe back into the bottom of the riser. The experimental nonmechanical valve used here was a 0.25 m diameter 1.5 m tall fluidized loopseal with a 45° downward sloping incline. In this study the bed material used was cork. This is a natural wood product with irregular size and shape that was classified as Geldart Type B particulate. The cork was utilized as the result of applying scaling laws to maintain similar gas: solid density ratio compared to a pressurized coal gasification systems operating at 1255 K and 30 atm. The material properties are presented in Table 1. The size distribution was normally distributed with particles ranging in size from 500 to 1500 μm

Ω=

μm μm m/s m/s

(1)

1

1 N

N

∑ 1

ΔPxo,exp − ΔPxo,calc ΔPxo,exp

× 100 (2)

Riser. The riser operating conditions of interest for this analysis include gas velocities above which a fixed or fluidized bed can be produced, resulting in superficial gas velocities much greater than the terminal velocity of the particles. Under these conditions, solids introduced into the riser from the loopseal are accelerated up the riser toward the gas/solids exit. Depending on the superficial gas velocity and the solids flow rate, various operating regimes can be established in the riser.17 While there have been some experimental attempts to show that frictional sheer forces can account for up to 25% of the apparent riser pressure drop18 and attempts are underway to measure shear forces at NETL, it is commonly assumed that the mass of solids in the riser is proportional to the pressure drop measured across the riser.19 Until reliable measurements are made, the aforementioned assumption of negligible shear will be used for this development and riser inventory will be related to pressure drop by the following equation.

cork characteristics kg/m3 kg/m3

N

∑ (ΔPxo,exp − ΔPxo,calc)2

and the mean relative error (Ω) was calculated by

Table 1. Bed Material Properties ρs ρb εb dp50 dsv Ut Umf εmf ϕ

1 N

ξ=

189 95 0.45 1170 812 0.86 0.17 0.50 0.69

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ΔPr =

DISCUSSION OF THE PHYSICS (MODEL EQUATIONS) ProTrax is a tool to convert the state functions and dependencies of the lump model into the time domain. Dynamic models built in ProTRAX utilize steady state behavior functions for each component that relate the pressure drop to flow rates and particle properties. The model uses fundamental equations to describe the hydrodynamic phenomena within the CFB components. For example, the expression for pressure drop in the standpipe is derived from the conservation of mass, ideal gas law, and the Ergun equation. For the riser, however, an empirical relationship was used to relate the desired property to two measurable variables using data from 321 experiments spanning riser operating regimes from fast fluidization through core annular to dilute homogeneous. The use of this correlation from this data eliminates the need to model the riser slip to get riser inventory. The dynamics of the riser inventory during process changes is captured from the differences in the solids flow in and out of the riser. When used the form of the empirical relation was chosen to be as simple as possible without sacrificing the integrity of the overall model. In either case, the constants for fundamental and empirical equations are fit using the least-squares technique with data obtained during steady state operations of the CFB unit. Because of noise in the data sampled at 1 Hz, steady state data points are calculated by averaging 1 to 5 min of experimental

M rg Ar

(3)

where Mr (kg) is the mass of solids in the riser, Ar (m2) is the cross sectional area of the riser, and g is the acceleration of gravity (m2/s) Operating experience has revealed that solids inventory in the riser and riser air flow rate most directly influence the solids flux exiting the riser. The following correlation was developed to relate the rate of mass leaving the riser, Ṁ s,o with riser inventory and the velocity of air through the riser. ⎛ ⎛ 3.905 ⎞2.8707 ⎞ 0.12 ⎟ ⎜ ̇ ⎟ − ⎜⎜ Ms,o = 0.00467exp 8.529 × ΔPr ⎟ ⎜ Ug ⎟⎠ ⎝ ⎠ ⎝ (4)

where ΔPr (kPa) is the pressure drop across the riser and Ug (m/s) is the superficial gas velocity. The equation was the best fit of data from 321 steady state experiments where the Froude ⎛G ⎞ ⎛ Ug2 ⎞ number ⎜ gD ⎟ varied from 2 to 40, load ratio ⎜ ρ Us ⎟ from 0.28 to ⎝ ⎠ ⎝ g g⎠ ⎛ ρg Ugd p ⎞ 1.8, Reynold number ⎜ μ ⎟ from 131 to 582 and Archimedes ⎝ g ⎠ number (Ar) 3593. It was selected because it yielded the highest correlation for equations with five parameters or less using the software TableCurve 2D, available from SPSS. This correlation was least 290


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Figure 2. Comparison of the measured solids circulation rates, from cork experiments ck-5 through II-50 (total of 321 experiments), to the calculated values with varying riser pressure drop and gas velocity. Gas velocity ranged from 3 to 10 m/s.

accurate for the case of low gas velocity and low solids inventory. The correlation was developed for air velocity ranging from 3 to 10 m/s and riser pressure drop ranging from 0 to 3.5 kPa. A riser pressure drop of 3.5 kPa with cork material represents a bulk volume of 0.28 m3 of material, or 3.8 m of stationary bed. With regard to the 321 data points, the gas velocity in the riser was varied with values ranging between 2.5 and 10.87 m/s. The transport velocity and solid flux at the onset of fast fluidization for the cork material are 2.2 m/s and 2 kg/m2 s. The gas velocity at the onset of the homogeneous or dilute regime (which includes core-annular flow) is 3.6 m/s. Therefore, operation between 2.5 and 10.87 m/s results in operation in the fast fluidization and homogeneous regimes in which 110 tests were in fast fluidization regime with a solids mass flow rate of 0.09 to 0.45 kg/s and 211 tests were in the homogeneous regime with the solids mass flow rate ranging from 0.06 to 1.7 kg/s. Results from eq 4 are compared against experimental circulation rate results, obtained with the spiral, and presented in Figure 2. The points plotted represent a very wide range of operating conditions; including the dense, core-annulus, and dilute regimes. Here the mean square error is 0.27 kg/s and the mean relative error is 30%. Figure 3 presents a wire frame 3-dimentional plot of the operating regime of the data in Figure 2. Crossover. Pressure drop across the crossover is thought to mostly be influenced by the acceleration required as the air and solids transition from the larger diameter riser to the smaller diameter crossover. The Bernoulli equation,20 generally used to calculate pressure drop of a single phase through an “ideal” restriction, was adapted for flow through the crossover piping components. Here, the crossover pressure drop was assumed to be a function of the density and the velocity of the bulk fluid moving through the piping. The void fractions for the gas and solids were determined from a ratio of the volumetric flow rate of solids to the total volumetric flow. The equations are ΔPxo =

1 KLρUxo 2 2

Figure 3. Three-dimensional wire frame surface of the predicted mass circulation rate over the experimentally used range of solids inventory and gas velocity.

where ρ = ερg + (1 − ε)ρs

and 1−ε=

Ṁ s ρs Ṁ s ρs

+ UgA r

KL was an empirically fit head loss coefficient and found to be 9.7, ρ the density (kg/m3), and Uxo the superficial gas velocity entering the crossover. The superficial gas velocity in the crossover was determined from the riser superficial gas velocity with a correction for the change in pressure. Other variables are the volume fraction, ε, and the steady state mass circulation rate, Ṁ s (kg/s). The equation was fit with the same data set of 321 steady state measurements ranging from 3 to 10 m/s and 0 to 1.75 kg/s, yielding a mean square error of 0.050 kPa and mean relative error of 11%. It is assumed that (1) there was no slip between the gas and solids and (2) the density of the bulk fluid was an average of the gas and solids density. A comparison of the measured and

(5) 291


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Industrial & Engineering Chemistry Research predicted values of the crossover pressure drop is shown in Figure 4. A three-dimensional surface of the predicted pressure drop is shown in Figure 5. This figure revealed that, over the

Figure 6. Measured and predicted values for the cyclone pressuredrop. The experimental values are from 176 experiments with the cork bed material.

Figure 4. Measured and predicted values for the crossover pressuredrop. The experimental values are from 455 experiments with the cork bed material.

surface for predicted cyclone pressure drop as a function of gas velocity and circulation rate is also illustrated in Figure 7. As expected, strong dependence of cyclone pressure drop on gas velocity was observed.

Figure 5. Pressure drop through the crossover predicted using eq 5.

Figure 7. Example of the predicted cyclone pressure drop and its indirect dependence on mass circulation rate and riser gas velocity.

current range of operating conditions, the cross over pressure drop was strongly a function of both mass circulation rate and riser gas velocity. Primary Cyclone. The pressure drop for the cyclone was experimentally measured across two regions: between the inlet and the solids outlet, and between the inlet and the gas outlet. The first, which is basically the pressure drop within the body of the cyclone, was neglected because the values were relatively small and difficult to correlate. The second accounts for the pressure drop as the gas enters and leaves through the exit piping. The following correlation21 was developed for predicting cyclone pressure drop as a function of the inlet gas velocity and concentration of solids. 1 ΔPc = KL ρg Uxo 2[1 + Bcm] (6) 2 where KL is the cyclone loss coefficient (found to be equal to 12.4), ρg is the gas density (kg/m3), Uxo is the gas velocity leaving the crossover and entering the cyclone, and cm is the mass ratio of solids to gas entering the cyclone. The equation was fit using pressure drop data from 176 experiments in which the riser gas velocity was varied from 3 to 10 m/s and the mass circulation rate varied from 0 to 1.75 kg/s. The mean square error was 0.034 kPa and the mean relative error was 14%. Figure 6 shows the predicted values from eq 6 versus the measured values of the cyclone pressure drop. The response

Standpipe. The standpipe has two distinct regions of solids flow: the dilute freeboard and the dense moving or packed bed. The freeboard is recognized as the region above the packed bed where solids freefall through air after leaving the cyclone. The packed bed is characterized as having a constant void fraction equivalent to the bulk void fraction of the solids material. Under extreme conditions, excess aeration air to the standpipe can fluidize the packed bed and thereby increase the void fraction. However, in this work, total standpipe aeration was maintained below the fluidization velocity. Considering the Freeboard section, the experimental pressure drop was measured across the top 5.2-m of the standpipe when the bed was not in the top region. In Figure 8, a linear correlation is illustrated between this pressure drop in the freeboard and the measured solids circulation rate. The slope of the line was used to determine the dependence of pressure drop on the mass circulation rate through the freeboard. Dividing the slope of the line by 5.2-m yielded the equation used for determining the pressure drop through the freeboard for any observed bed height. ΔPfreeboard = 0.0445(hsp − hobs)Ṁ s (7) where hsp and hobs are the total height of the standpipe and the observed height of the solids in the standpipe, respectively. In the model, the observed height of solids in the standpipe was 292


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Figure 8. Experimentally measured pressure difference in the top 17.1 feet of the standpipe when the pack bed is below the region.

calculated from the mass inventory of solids in the standpipe, assuming that the bulk density was constant in the packed bed:

hobs =

Msp ρb A sp

(8)

While prediction of the pressure gradient in the freeboard was important, the pressure gradient within the packed bed of the standpipe was much greater importance. The packed bed creates a significant resistance to air flow, which results in a larger pressure gradient. From the Move Air location to the cyclone, the gas inventory, pressure, and flux were calculated for each of the standpipe sections. Changes in the operating pressure of the system propagate from the center of the standpipe packed bed outward. To capture this dynamic, multiple standpipe sections are required. Since the standpipe is not fluidized, the bulk air-flow through the standpipe is understood to be a function of the pressure gradient and the void fraction of the bed. This is captured with the conservation of mass, the ideal gas law, and the Ergun equations. Under general operating conditions, the pressure at the location of the Move Air inlet is higher than anywhere else in the unit. Therefore, the air entering the process at this location will flow in all directions (see Figure 9). This means that some air will flow toward the loopseal and some will flow opposite the flow direction of the solids. It is important to clarify that the air flows with respect to the solids and not the equipment. If the solids flux is high enough, air can be flowing up with respect to the solids but down with respect to the equipment. The present model can be used to predict the relative Move Air split and superficial velocity of the gas at any point in the unit. In order to capture the dynamics in the packed bed, the pressure drop and air flux equations are discretized, and are applied to a total of eight segments used to represent the pack bed region in the standpipe. The segments are identified from top to bottom, using numerals 1 through 8. Since the experimenters can chose to add aeration at various locations in the standpipe packed bed, modeling the standpipe in sections allows staged aeration to be accounted for. The mass of gas in a section, Mg, is calculated from initial conditions and the conservation of mass.

Figure 9. Representation of how the move aeration splits.

Mg = Mg,i +

∫i

f

(Ṁ g,i − Ṁ g,o) dt

(9)

The flow of gas into the section, Ṁ g,i, is the sum of air entering from the section located below and the amount of staged aeration entering at that location. Once Mg is known, the ideal gas law is used to determine the absolute pressure in the section.

P=

MgRT V

(10)

where R is the gas constant for air and V is the volume available for air (the volume of the section multiplied by the void fraction of the bed). Using the absolute pressure of the segment above, the pressure gradient is calculated and then used to determine the flux of gas leaving through the top of the section. 293


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are most responsible for determining the rate of solids flux from the standpipe. The pressure imbalance between the riser and standpipe is minimized by the transfer of solids from the standpipe to the riser. The mathematical mechanism for this phenomenon is based on air flow as a function of pressure drop and circulation rate as a function of air flow. The equations look like:

A reduced form of the Ergun equation is then used to calculate the flux (a similar result can be found from Darcy’s law):

̇ = K sp Vg,o

ΔP Δh

(11)

where Ksp is the permeability of the bed, and is approximately 0.0139

mair 3 / s . kPa / m

The volumetric flow of air is then used to

calculate the mass flux of air entering the next section by rearranging eq 10 by replacing the mass and volume terms with their rate equivalents. Loopseal. Combined with the move air, the loopseal serves as a control valve for solids circulation rate. The loopseal can be subdivided into a bubbling fluidized bed and a sliding board. Solids that bubble over the top of the fluidized bed are moved down the sliding board by the force of gravity. Pressure drop in the loopseal is determined as a function of the bed material, the bed height, and the mass circulation rate while gas volume is currently neglected. The pressure drop is calculated by ΔPls =

ρs,b hlsg N 1000 kN

⎛ kPa ⎞ ̇ + ⎜0.2766 ⎟M s kg/s ⎠ ⎝

⎛ m 3/s ⎞ Vġ = ⎜0.683 ⎟ΔP kPa ⎠ ⎝

(13)

⎛ kg/s ⎞ ̇ ) Ṁ s = ⎜0.144 3 ⎟ × (Vġ + Vbase ⎝ m /s ⎠

(14)

The constants in eqs 13 and 14, along with the permeability constants for the other eight sections of the standpipe, are selected such that the pressure drop across each section matches the experimental pressure gradient over a wide range of operating conditions. These constants are the last parameters of the model to be determined. Equation 14 includes both the aeration coming down at the Move Air split and any aeration added at the base of the standpipe. These equations predict a linear relationship between pressure drop and solids flux as is seen in Figure 10. Other researchers10 have reported solids flow as being proportional to the square root of pressure drop. This is expected for designs where the aeration flows through a uniform bed with near constant void fraction. For the present work, the relationship between pressure drop and circulation rate was found to be simply proportional. The difference is attributed to the possible restructuring of the solids as the aeration increases. Response of the system indicates that the solids move through only part of the cross sectional area of the connecting pipe and that aeration through the stagnant solids is not productive. At higher aeration, the cross sectional area of moving solids is speculated to increase.

(12)

where ρ is the solid bulk density and is 99 kg/m3 and h is the height of the bed in the loopseal and is 1.17 m. The functional dependency on mass circulation rate is not well understood. Two possible explanations have been considered: (1) Increasing mass circulation rate can support a higher bed height before the particles fall down the sliding board. The taller bed causes there to be an increased resistance to air flow. (2) The work required to lift the mass of the solids to the top of the fluid bed is significant. For increasing circulation rate, the pressure drop associated with moving the bed becomes significant compared to the pressure drop required to support the bed. During the recent experimental series involving cork material, the loopseal fluidization air was set to 0.13 m/s. There exists one last section of the system, which consists of the piping that connects the standpipe to the loopseal riser. The geometry resembles a U-bend. The section is the smallest of the unit; however, the process variables around this section

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MODEL DESCRIPTION The dynamic model was developed in the commercial software ProTrax. This software is used by various power generation industries because it is robust and intuitive to use. ProTrax requires object oriented programming and includes standard

Figure 10. Experimentally measured pressure drop data for the loopseal with a least-squares fit correlation line. 294


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Figure 11. Flow sheet for the CFB model.

the variable “i”, which ranges from 1 to 6). The seventh segment is significant because it is where the Move Air enters the unit. The eighth segment is below the move air inlet and has negligible contribution to the operation of the unit. Other notes of interest are that P0 = Pfb, and Ṁ g,out is calculated in ProTrax based on POUT, ambient pressure and the position of the Back Pressure Valve. The summation blocks in the diagram are used to indicate both addition and subtraction, depending on whether the calculation is for total pressure or pressure differential.

blocks for valves, controllers, and boundary conditions, as well as components such as cyclones, turbines, and boilers. However, commercial support of circulating fluidized bed technology from advanced commercial software is limited and there is not currently a circulating fluidized bed available in the ProTrax component library. Taking up the challenge, we have written our own component coding for the CFB, a schematic of which is presented in Figure 11. A substantial benefit of using a simulation package like ProTrax is the capability to impose changes to the process during run time. That is, the input signal for a transient does not have to be programmed into the model prior to initiating the simulation. The ProTrax graphical user interface allows real time process simulation and results trending. One aspect of ProTrax that makes it less acceptable by peer review is that the equations are simulated, not solved. Due to the multi gas-path nature of the circulating fluidized bed process, solving the nonlinear hydrodynamic equations would be computationally prohibitive to reaching real time operations. Therefore, the individual equations are solved for each time step assuming that the rest of the process is in equilibrium. The source code file, which encompasses all the CFB components where solids are located, is written in ACSL (Advanced Continuous Simulation Language). The source code file is used to model components that are not available in the ProTrax library. Integration in the code is handled with the first order Runga-Kutta algorithm (ACSL ref. Man. pp 4−5).22 A diagram of the source code file is shown in Figure 12. From the overall flow sheet in Figure 11, there are two input streams and one output stream connected to the source code block. The streams are the riser gas flow rate, Ug,r; the Move Air, Ṁ g,7,staged; and the flow of air out of the unit, Ṁ g,out. The diagram was simplified to include the seventh segment of the standpipe and one generalized segment (denoted with

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RESULTS AND DISCUSSION Model Validation. Step changes and modulations around a base case with Ug and Fm are not expected to be normal operating conditions for CFBs. However, building a model that can demonstrate the quantitative nature and the time dependence of primary variables gives confidence in the controls for normal operations. This section highlights the special features of the model; most notably the segmented standpipe, move air circulation rate dependence, and riser transient response. Also identified are the limitations of the current model, such as not using a segmented riser and being limited to homogeneous transport riser cases. Step Ug. A step change in the riser gas velocity was imposed to demonstrate the dynamic response of key process variables and to evaluate the ability of the model to simulate the process. The set point for flow control valve FY431 was stepped up then back down approximately enough to change the flow by 10%. The data in Figure 13−15 are for this step change increase in the riser gas velocity at a time of about 60s from a value of about 4.9 m/s to a value of 5.5 m/s and a step change decrease in the riser gas velocity at a time of about 110s from a value of about 5.4 m/s to a value of 4.7 m/s. Even though the actual 295


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Figure 12. Diagram of the ACSL source code.

actual riser flow response to use as input to the model. A step increase in gas flow resulted in an initial drop in the circulation rate into the riser due to a sharp increase in the ΔP across the cyclone and crossover piping, and the absolute pressure at the base of the riser increased quickly. The result of the step increase was a rapid shift in the move air split up the standpipe, temporarily slowing the solids flow into the riser. This is observed in both the experiment and the simulation. Higher gas rates increase the solids velocity. According to mass continuity this decreases solids inventory in riser and subsequently decreases the pressure drop as shown in Figure 3. This functionality is not linear and depends upon the regime.

valve position responded more slowly than desired, the experiment still met the criteria of imparting a transient on riser aeration. In addition, the controller for the Back pressure valve was set to manual to remove unwanted dynamics caused by the controller on the valve. Other process conditions for this experiment are listed Table 2. The gas velocity during the experiment exhibits first order response toward the new steady state. The trends for the gas velocity and circulation rate are shown in Figure 13. It should be noted that the solids flow rate was controlled by a separate control loop. The solids flow responded to the change in the riser gas velocity and the controller brought it back to the set point. The simulation was conducted by piecewise fitting the 296


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were distributed uniformly throughout the riser. It should be noted that the gas velocity did not return to the initial value but to a value slightly lower when stepped back down. Therefore, the pressure drop was slightly higher after the return to the initial conditions. In Figure 15 the pressure drop in the middle and top of the standpipe are displayed through the step change in the

Figure 13. Circulation rate charge as a transient in gas velocity is imposed.

Table 2. Operating Conditions for the Experiments

ambient temperature (°C) system inventory (kg) staged aeration at SP base (cm/s) staged aeration at 2.3 m (cm/s) staged aeration at 4.7 m (cm/s) staged aeration at 6.3 m (cm/s)

riser velocity step change

move air modulation

−4 66 0

16 53 1.6

0.4 0.4 0.4

0.8 1.6 0

Figure 15. Change in pressure drop in the standpipe at two locations.

riser flow. The top section of the model standpipe responded initially to this loss in pressure across the riser with an equivalent decrease in pressure (Figure 15). The inventory then began to shift more slowly to the standpipe as it was carried out of the riser. This shift in inventory produced a more gradual increase in the ΔP at the top of the standpipe. The size and rate of these changes were simulated very accurately by the model. The ΔP response in the middle of the standpipe was different than at the top and in the opposite direction. Initially, there was little change to the experimentally observed ΔP/dL in the middle of the standpipe, but then it gradually decreased as the standpipe height increased. The model ΔP/dL in this midstandpipe section increased initially due to a surging of the move air upward through the standpipe. The initial surge predicted by the model was not observed experimentally and may be a result of the coarse number of sections used in the dynamic model being unable to dissipate the initial pressure surge through the bed. In reality, the bed is a compressible fluid with local velocity gradients able to vary dramatically in order to absorb large surges. However, the model uses fixed bed voidage and thus was incompressible, causing surges to propagate through the standpipe with little or no attenuation. The surge was followed by a more gradual loss in pressure drop with increasing bed height similar in both magnitude and time rate as the test data, which the model captured very closely in both size and magnitude. The overall magnitude of the bed ΔP/dL was overpredicted for the midstandpipe location. This may be due to the lack of incorporation of the solids shear and wall friction contributions along the length of the standpipe (which were assumed to be negligible). With these experiments we also showed that there is negligible delay in the time to reach new steady state conditions for the gas velocity between the various components of the system, suggesting that our assumption of negligible gas transport time out of the unit was satisfactory. Extrapolated from this, solids transport time between the standpipe and riser and back again was also assumed negligible; but as reported

The riser ΔP drops rapidly with this increase in gas flow (Figure 14). The magnitude and general trend in these responses were captured by the dynamic model. The standpipe height matches well within experimental variability for this measurement.

Figure 14. Change in riser pressure drop and Standpipe Height during a step change in riser gas velocity. Data points are from experiments; the lines are simulated.

However, the initial ΔP response to this step change was slightly faster for the experimental riser ΔP than the simulated ΔP. Though this difference is not large it may be due to the use of a lumped parameter model for the riser that does not include the end effect. A step change in the riser flow might be expected to initially sweep out much of the dense bed present at the top of the riser that is present when using a cushion Tee design. The model on the other hand does not account for this dense bed near the outlet. In the model we assumed that the solids 297


Article


The solids circulation into and out of the riser is presented in Figure 17. Again, both variables clearly modulate with the varying standpipe aeration. The solids flow out of the standpipe into the riser exhibited no delay relative to the move aeration, both experimentally and using the dynamic model. The predicted solids flow out of the riser, however, did demonstrate a time lag of about 10 s relative to the flow in. The lag amounts to about 1/4 of the 45 s period of the modulation on Move Air. It can be shown that for a stiff riser, where the solids flow out is linearly related to the inventory, solids flow out is delayed from flow in by just such a 1/4 of the period. The response of the standpipe pressure drop to the modulated standpipe aeration is presented in Figure 18. The response at the top of the standpipe differs from that deeper in the bed. The top of the standpipe was fully expanded and the pressure gradient is in phase with the pressure drop across the riser, while the response deeper in the standpipe is confined and the pressure gradient responds to the move air. The slightly higher pressure gradient at the top of the bed is a result of staged aeration. Located directly below the measurement location for the deep bed gradient at a bed height of 4.7 m, a total of 1.6 cm/s of aeration is staged into the bed (Table 1). A less obvious difference between the pressure gradient for the two locations is the magnitude of variation. The response deep in the standpipe bed is smoothed out with approximately half the amplitude. The model results and experimental pressure drop measurements for the lower standpipe interval match well in both magnitude and phase. At the higher interval, the phase is matched well but an offset of about 0.9 kPa/m exists.

later, this assumption may be less valid than initially assumed. The analysis did not include transport time through the standpipe freeboard, which has fairly stagnant air flow. For operations around the conditions tested in this experiment, it is concluded that the gain for riser velocity and circulation rate is

kg/s ΔṀ s = 0.038 ΔUg m/s

(15)

In summary, consider the case where the gas velocity is increased through a step change. The increased flow of air through the riser, crossover, cyclone and rest of the exhaust piping, causes the absolute pressure at the base of the riser to increase. This is followed by an interesting transient as the circulation rate plummets because the quickest gas path for increasing the pressure at the base of the standpipe is backward of what is considered normal flow, going from the base of the riser through the loopseal. The decrease in the flow of solids from the standpipe, combined with the increased flow of riser aeration, acts to deplete the riser of inventory. This loss of inventory in the riser translates into a gain in standpipe bed height. As discussed earlier, for constant Move Aeration, an increased bed height shifts the move air split down and increase circulation rate. Modulate Fm. The aeration at the base of the standpipe was modulated in a sinusoidal manner to impart a continuous oscillation to the circulation rate into the riser. The independent variation of the move aeration is depicted in Figure 16.

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SUMMARY A dynamic model of the Cold Flow Circulating Fluidized Bed at NETL in Morgantown, WV was created to predict the steady state and transient responses of gas and solids flows throughout the unit. Experiments were conducted to determine response curves for the system components, and data from the response curves was used to determine the coefficients for equations derived from fundamental and literature theories. The model is described as a pressure balance between the riser and standpipe, with prediction of circulation rate and solids inventory for the riser and standpipe. Component pressure drops are also predicted for the cyclone, crossover piping and nonmechanical valve. A new equation is reported for the mass flux out of a riser as a function of solids inventory and gas velocity. The empirical relation was determined with data from dense, core-annulus, and dilute riser regimes. This response curve was determined to be continuous over the entire range of operating conditions tested. The correlations presented in the paper are strictly empirical for the particular geometry, flow rates and particle type used. Even though the correlations are empirical they have value as they represent data from a large unit (16 m in height and 0.3 m in diameter), whereas the bulk of the data in the literature come from experimental units less than 0.15 m in diameter and significantly shorter. The objective of the paper is the dynamic aspect of the model methodology. Important general features of the model include quick riser response, effect of absolute pressure on gas velocities, inventory shift and move air split. Dynamics experiments, designed to highlight these features, were performed to compare the model with experimental results. The model predictions were used to gain insight into the mechanisms that

Figure 16. Modulated Move Air and Riser Pressure Drop. Amplitude of Move Air modulations was 0.73 cm/s. Data points are from experiments; the lines are simulated.

The simulation was driven in the same sinusoidal pattern of modulating the move aeration 0.73 cm/s from the average value with a 45 s period. Both the experimental and model responses to this modulated flow in the riser and standpipe are shown in Figures 16−18. The riser pressure drop follows the move air modulation with about a 9 s lag due to the transit of solids through the Loopseal and the delay in time required to build the bed in the standpipe. The model captures the variation in riser pressure remarkably well (Figure 16). The standpipe height was not monitored continuously but the observed changes were relatively small and the average height matched that predicted by the model. In the simulation, the height varied from 8.26 to 8.44 m and during the experiment the variation went from 8.38 to 8.60 m. The model predicted that the standpipe height was 180° out of phase with the circulation rate (Figure 18). 298


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Figure 17. Circulation rate at various locations during modulation experiment.

apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the Department of Energy for funding the research through the Fossil Energy’s Integrated Gasification Combined Cycle program. Operations of the unit were made possible with support from Jim Devault, Todd Worstell, and Angela Sarra. Additionally, this research was supported in part by an appointment to the National Energy Technology Laboratory Research Participation Program, sponsored by the U.S. Department of Energy and administered by the Oak Ridge Institute for Science and Education.

Figure 18. Standpipe height and pressure gradient during modulation experiment. Data points are from experiments; the lines are simulated.

create some dynamics. The correlations presented in the paper are not expected to be universal; however, it is expected that the methodology is transferable. With the present dynamic model, components that exhibit nonlinear responses are no more difficult to implement than simple linear models. Experimental and simulation results are compared for a step change in riser gas velocity and a modulation of the move air velocity.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Ronald W. Breault: 0000-0002-5552-4050 Notes

The U.S. Department of Energy, NETL, and REM contributions to this report were prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, 299

NOTATION A = cross sectional area (m2) B = coefficient in eq 6 cm = mass ratio of solids to gas d = diameter (m) Fm = gas flow to standpipe (m3/s) g = acceleration by gravity (m/s2) h = height (m) KL = head loss coefficient (various) 3 Ksp = permeability ( mair / s ) kPa / m M = mass (kg) Ṁ s = mass flow rate (kg/s) N = Number of experiments P = pressure (kPa) R = gas constant T = temperature (K) Ug = superficial gas velocity (m/s) V = volume (m3) V̇ = Volumetric flow (m3/s) DOI: 10.1021/acs.iecr.6b03536 Ind. Eng. Chem. Res. 2017, 56, 288−300

Article

Industrial & Engineering Chemistry Research Greek

ρ Δ ε ξ Ω

(14) Reed, M. E.; White, J. S. Dynamic modeling of power systems. Adv. Coal-Fired Power Systems ’95 Review Meeting, Conf-950616246, 1995; p 109. (15) Ludlow, J. C.; Lawson, L.; Shadle, L. J.; Syamlal, M. Circulating Fluidized Bed Technology VII; Grace, J. R., Zhu, J., de Lasa, H., Eds.; Ottawa, Canada, 2002; p 513. (16) Ludlow, J. C.; Monazam, E. R.; Shadle, L. J. Improvement of continuous solid circulation rate measurement in a cold flow circulating fluidized bed. Powder Technol. 2008, 182, 379. (17) Kunii, D.; Levenspiel, O. The K-L reactor model for circulating fluidized beds. Chem. Eng. Sci. 2000, 55, 4563. (18) Sarra, A.; Miller, A. L.; Shadle, L. J. Experimentally measured shear stress in the standpipe of a circulating fluidized bed. AIChE J. 2005, 51, 1131. (19) Monazam, E. R.; Shadle, L. J.; Lawson, L. A transient method for determination of saturation carrying capacity. Powder Technol. 2001, 121, 205. (20) Munson, B. R.; Young, D. F.; Okiishi, T. H. Fundamentals of Fluid Mechanics, 2nd ed.; Wiley: New York, 1994. (21) Comas, M.; Comas, J.; Chetrit, C.; Casal, J. Cyclone pressure drop and efficiency with and without an inlet vane. Powder Technol. 1991, 66, 143. (22) Advanced Continuous Simulation Language (ACSL) Reference Manual, version 11; MGA Software: Concord, Massachusetts, 1995.

density (kg/m3) differential voidage mean square error mean relative error

Subscripts

air b base c calc exp g i f FB ls o, out obs r s sp xo 1−7

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air bulk base of the standpipe cyclone calculated experimental gas property in/initial final Freeboard loopseal out observed riser solids property standpipe crossover height segments in standpipe

REFERENCES

(1) Davis, B.; Vimalchand, P.; Liu, G.; Smith, P.; Longanbach, J. Operation of the PSDF Transport Gasifier. Nineteenth Annual Pittsburgh Coal Conference September 23-27, 2002, Pittsburgh, Pennsylvania, USA. (2) Breault, R. W.; Mathur, V. K. High-Velocity Fluidized Bed Hydrodynamic Modeling. 2. Circulating Bed Pressure Drop Modeling. Ind. Eng. Chem. Res. 1989, 28, 688−693. (3) Chen, H.; Yang, D.; Li, H.; Tan, S. Study on the overall pressure balance of a downflow circulating fluidized bed system. China Particuol. 2006, 4, 153. (4) Lei, H.; Horio, M. A Comprehensive Pressure Balance Model of Circulating Fluidized Beds. J. Chem. Eng. Jpn. 1998, 31, 83. (5) Grieco, E.; Marmo, L. A model for the pressure balance of a low density circulating fluidized bed. Chem. Eng. J. 2008, 140, 414. (6) Hyppanen, T.; Lee, Y. Y.; Kettunen, A.; Riiali, J. Dynamic simulation of a CFB based utility power plant. Proc. Int. Fluidized Bed Conf.; ASME, 1993; Vol. 2, p 1121. (7) Alves, J. J. N.; Mori, M. Fluid dynamic modelling and simulation of circulating fluidized bed reactors: analyses of particle phase stress models. Comput. Chem. Eng. 1998, 22, S763. (8) Park, C. K.; Basu, P. A model for the prediction of transient response to the change of fuel feed rate to a circulating fluidized bed boiler furnace. Chem. Eng. Sci. 1997, 52, 3499. (9) Muir, J. R.; Brereton, C.; Grace, J. R.; Lim, C. J. Dynamic modeling for simulation and control of circulation fluidized-bed combustor. AIChE J. 1997, 43, 1141. (10) Zhang, L.; Li, T. D.; Zheng, Q. Y.; Lu, C. D. A General Dynamic Model for Circulating Fluidized Bed Combustion Systems with Wide Particle Size Distributions. Proc. Int. Fluidized Bed Conf.; ASME, 1991; p 1289. (11) Mori, S.; Narukawa, K.; Yamada, I.; Takebayashi, T.; Tanii; Tomoyasu, Y.; Mii, T. Dynamic model of a circulating fluidized bed coal fired boiler. Proc. Int. Fluidized Bed Conf.; ASME, 1991; p 1269. (12) Shadle, L. J.; Monazam, E. R.; Mei, J. S. Circulating fluidized bed operation. Circulating Fluidized Bed Technology VII 2002, 255. (13) Monazam, E. R.; Shadle, L. A transient method for characterizing flow regimes in a circulating fluidized bed. Powder Technol. 2004, 139, 89. 300


Development and Validation of a Dynamic Response Model for a Cold

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