Article pubs.acs.org/IECR
Phase-Shift Method to Estimate Solids Circulation Rate in Circulating Fluidized Beds J. Christopher Ludlow, Rupen Panday, and Lawrence J. Shadle* National Energy Technology Laboratory, 3610 Collins Ferry Road, Morgantown, West Virginia 26507, United States ABSTRACT: While solids circulation rate is a critical design and control parameter in circulating fluidized bed (CFB) reactor systems, there are no available techniques to measure it directly at conditions of industrial interest. Cold flow tests have been conducted at NETL in an industrial scale CFB unit where the solids flow has been the topic of research in order to develop an independent method which could be applied to CFBs operating under the erosive and corrosive high temperatures and pressures of a coal fired boiler or gasifier. The dynamic responses of the CFB loop to modest modulated aeration flows in the return leg or standpipe were imposed to establish a periodic response in the unit without causing upset in the process performance. The resulting periodic behavior could then be analyzed with a dynamic model and the average solids circulation rate could be established. This method was applied to the CFB unit operated under a wide range of operating conditions including fast fluidization, core annular flow, dilute and dense transport, and dense suspension upflow. In addition, the system was operated in both low and high total solids inventories to explore the influence of inventory limiting cases on the estimated results. The technique was able to estimate the solids circulation rate for all transport circulating fluidized beds when operating above upper transport velocity, Utr2. For CFB operating in the fast fluidized bed regime (i.e., Ug < Utr2), the phase shift technique was not successful. The riser pressure drop becomes independent of the solids circulation rate and the mass flow rate out of the riser does not show modulated behavior even when the riser pressure drop does.
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INTRODUCTION Most advanced fossil energy conversion technologies under development involve the contacting of gaseous streams with solid streams. This contacting often occurs in circulating fluidized bed boilers or gasifiers, or in cleanup processes to remove unwanted contaminants such as H2S or CO2 from product gas streams. For such processes, the enhanced heat and mass transfer as well as the vigorous mixing associated with circulating fluidized bed (CFB) technology is very attractive. For CFB systems, it is widely recognized that the solids circulation rate (SCR) is one of the key operating parameters influencing mixing, heat transfer, and gas−solids residence times. Unfortunately, the SCR is quite a difficult process variable to measure in a CFB system. While various techniques have been proposed to make this measurement, most are best suited to the more benign conditions associated with a laboratory system. Many research groups worldwide are developing Computational Fluid Dynamic (CFD) models to improve the ability to optimize design and performance of reacting gas−solids flow systems;1,2 however, one of the most important parameters, the SCR, is often not even known. Techniques used to estimate the solids circulation rate can be characterized as being either intrusive mechanical devices or nonmechanical methods. Mechanical devices such as weigh bucket elevators are commonly used in advanced power systems. However, these are only feasible in processes such as the ambient silo filling operations. In a CFB loop, a twisted vane can be installed in the moving bed region of the solids return leg with some success, but care must be taken in the placement of the device and correcting the velocity and voidage for process operating conditions.3,4 Researchers have employed solids impact during freefall, diversion measurements, and coriolis meters.5 Unfortunately, none of these mechanical This article not subject to U.S. Copyright. Published 2013 by the American Chemical Society
devices have been designed to function at elevated temperatures and pressures commonly found in advanced power systems and gas cleanup devices. Nonmechanical methods to measure SCR include electrostatic methods,6 capacitance tomographic techniques,7 Doppler ultrasonic meter,8 mass flow gamma density meter,9 visually tracking particle flow in some transparent section of the system, calibrating the pressure drop across some characteristic section of the system (such as the crossover connecting the exit of the riser with the entrance of the primary cyclone),10 measuring process transient after halting the solids flow,3,11 or diverting the solids being circulated to an external receiver for a known period of time and then weighing the collected solids. In large hot pressurized units, where mechanical devices, imposing large process transients (including diverting solids), and visual tracking of solids is impractical, other indirect methods have been employed. These indirect methods include techniques such as energy balances across in-bed heat exchangers and calibration of the response. In virtually all cases, a relatively detailed knowledge of the bed material or the process operating regime is required to estimate the solids circulation rate. This paper suggests different methods to estimate the SCR where a minimum of process knowledge is required. Presently, there are no commercially available solids flow meters that can sustain high operating temperatures. Several manufacturers offer ″high temperature″ options, but these are unlikely to exceed 400 °C.12,13 Thus, there is a need for a way Received: Revised: Accepted: Published: 1958
May 15, 2012 December 19, 2012 January 7, 2013 January 7, 2013 dx.doi.org/10.1021/ie301275c | Ind. Eng. Chem. Res. 2013, 52, 1958−1969
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to measure solids mass flow rate under hot and pressurized conditions. In this study cold flow experiments were conducted in an industrial scale CFB (based upon the physical size, i.e. >15 m height) to validate a method that can be employed under many transport conditions. The method employs perturbing the steady state flow by modulating the aeration to the nonmechanical valve or standpipe and recording the time delay between resultant modulations in the total pressure drop measured across the riser and modulated aerations. In these cold flow tests this technique was verified using a twisted vane in the return leg to develop a method to measure the SCR, but it does not itself require an intrusive mechanical device so that it can be employed in a high temperature and high pressure CFB reactor system with standard process measuring equipment.
seal was used when the experiments were carried out with cork.) Transport air is introduced at the bottom of the riser through a porous plate distributor located 0.43 m below the centerline of the L-valve. At the top, solids leave the riser from the same side as they entered and pass through a short pipe before entering the primary cyclone. Separated solids fall into the 0.254 m diameter standpipe where they are fed back into the riser. Approximately 3.5 m above the entrance of the Lvalve from the standpipe is located NETL’s solids circulation measurement instrument, the Spiral. This device is described in more detail elsewhere.4 The spiral generates a continuous measurement of the solids circulation rate allowing the operators to perform dynamic experiments in the CFB. The volumetric flow measurement from the spiral was converted to a mass circulation using the packed bed density for the given materials corrected for changes due to standpipe aeration and solids flow using a standpipe model.14 There are nine aeration feeds at different locations in the standpipe. The standpipe model not only predicts the standpipe solids void fraction but also the magnitude of flows going up the standpipe and down into the riser. The latter flow and the L-valve sparger gas flow are combined along with the flow through the riser gas distributor to calculate the riser superficial velocity (Ug) at standard condition. Riser velocities were then corrected for temperature (TE) and pressure (Pb) measured at the base of the riser. The operating conditions were varied by adjusting the riser flow or solids circulating rate while maintaining constant system outlet pressure at 1 atm. The air’s relative humidity (RH) was maintained between 40% and 60% to minimize effects of static charge building up on the solids. Pressure drops resulting solely from gas flow were negligible. In addition to being relatively large, most of the NETL standpipe is made of clear acrylic plastic and hence a direct observation of the standpipe height could be made. Operating data was acquired at 1 Hz for all the variables except the bed height which was manually recorded at the end of each steady state condition. Steady state conditions were defined as holding a constant set of flow conditions and maintaining a constant response in the riser pressure differential over a five-minute period. Bed Materials. The bed properties of three different materials are given in Table 1. These materials include cork and high density polyethylene (HDPE) that belong to Geldart Group B family and small glass beads which fall under Geldart Group A category. The nominal void fraction listed in the table represents a value intermediate between the fully packed granular bed and a fluffed bed which corresponded to a
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EXPERIMENTAL SECTION Facility. Experimental verification of the presented technique was pursued at the circulating fluidized bed facility located at the United States Department of Energy’s National Energy Technology Laboratory (NETL) Morgantown campus. A detailed description of the facility can be found elsewhere.10 To summarize, the CFB consists of a riser 15.4 m tall with an inside diameter of 0.305 m (see Figure 1). Solids enter the riser at the bottom from an L-valve located on one side. (The loop-
Table 1. Granular Material Properties properties test name dp (μm) ρP (kg/ m3) εnom Umf (m/s) Utr1 (m/s) Utr2 (m/s)
Figure 1. Schematic drawing of NETL CFB test facility. 1959
HDPE beads (Geldart group B)
glass beads (Geldart group A)
cork (Geldar group B)
PMD 802 863
modulate 60 2483
K 825 189
0.35 0.174
0.41 0.034
0.43 0.094
4.33
1.84
2.3
6.25
2.96
3.59
dx.doi.org/10.1021/ie301275c | Ind. Eng. Chem. Res. 2013, 52, 1958−1969
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Table 2. Experimental Test Matrix under Study material HDPE
test
Ug (m/s)
Usp (cm/s)
% modulation
High Inventory 1.5 20% 2.3 20% 4.6 20% 3.6 20% 10.1 20%
Ms ± 2σ (kg/s)
Hsp,min (m)
ΔPr ± 2σ (kPa)
± ± ± ± ±
0.2 0.4 1.8 1.2 1.4
10.5 10 9.3 9.2 9.1
1.9 5.0 12.5 1.5 9.6
12.6 ± 4.0
10.1
12.9 ± 2.6
± ± ± ± ±
0.3 1.4 1.8 1.1 3.0
5.2 5.2 5.3 5.1 5.2
1.7 10.8 11.9 1.6 7.9
4.6 4.5 4.6 10.7 10.4
60
10.4
PMD16 PMD33 PMD12 PMD2 PMD10
fast fluid dilute fast fluid S-profile fast fluid dense transport dilute transport core annulus
60 60 60 60 60
4.7 5.2 4.5 10.6 10.6
modulate 8
transport core annulus transport core annulus transport core annulus transport core annulus transport core annulus
24
5.2
1.3
65%
14.8 ± 6.4
5.9
28.2 ± 2.7
209.8 ± 20.4
72
5.2
1.2
65%
14.5 ± 6.2
5.8
28.3 ± 3.9
210.9 ± 29.3
96
5.1
1.2
65%
14.4 ± 5.2
5.9
28.0 ± 4.5
208.2 ± 33.2
150
5.3
1.2
65%
14.3 ± 5.0
5.8
28.4 ± 4.3
211.1 ± 32.0
192
5.2
1.2
65%
14.4 ± 4.6
5.7
28.2 ± 3.6
210.0 ± 26.8
± ± ± ± ± ±
modulate 10 modulate 4 modulate 19
K41 K31 K32 K36 K38 K34
transport transport transport transport transport transport
K40
transport core annulus transport core annulus transport core annulus transport core annulus transport core annulus transport core annulus
K39 K30 K37 K35 K33
dilute dilute dilute dilute dilute dilute
11.6
20%
Low Inventory 2.9 20% 5.3 20% 6.7 20% 4.0 20% 11.6 20%
0.3 0.5 1.1 1.2 6.8
0.3 1.3 1.0 1.3 5.9
± ± ± ± ±
Mr ± 2σ (kg)
60 60 60 60 60
modulate 5
cork
period in Fsp (s)
fast fluid dilute fast fluid S-profile fast fluid dense transport dilute transport core annulus transport dense upflow
PMD1 PMD4 PMD13 PMD7 PMD11 PMD3
glass beads
riser regime
± ± ± ± ±
0.4 1.2 3.0 1.2 2.1
0.5 1.5 2.2 1.2 2.0
14.2 36.9 92.8 10.9 71.7
± ± ± ± ±
2.7 8.9 22.4 9.2 15.9
96.1 ± 19.0
12.4 80.1 88.2 11.6 58.5
± ± ± ± ±
3.8 11.4 16.6 8.7 15.0
0.4 0.3 0.3 0.3 0.3 0.3
9.9 9.5 9.5 10.2 10.2 10.5
60
Low Solids Circulation Rate 5.2 5.7 60% 5.2 5.7 60% 5.2 5.8 60% 5.2 5.9 60% 5.2 5.7 60% 5.2 5.7 60% High Solids Circulation Rate 5.2 9.8 35%
1.1 ± 0.4
8.0
2.1 ± 0.6
15.4 ± 4.2
90
5.2
9.9
35%
1.0 ± 0.3
7.9
2.1 ± 0.6
15.4 ± 4.4
90
5.2
10.1
35%
1.0 ± 0.3
9.8
2.1 ± 0.5
15.8 ± 3.9
120
5.1
9.8
35%
1.0 ± 0.3
8.2
2.0 ± 0.6
15.1 ± 4.7
120
5.2
9.7
35%
1.1 ± 0.3
8.1
2.1 ± 0.6
15.5 ± 4.3
120
5.2
9.8
35%
1.1 ± 0.3
8.5
2.1 ± 0.6
15.9 ± 4.5
60 60 90 90 120 120
0.4 0.4 0.4 0.4 0.4 0.4
0.7 0.6 0.6 0.7 0.7 0.7
± ± ± ± ± ±
0.6 0.5 0.5 0.6 0.6 0.6
5.0 4.7 4.2 5.1 4.9 5.3
± ± ± ± ± ±
4.1 3.7 3.6 4.2 4.4 4.3
material. The objective of the tests was to investigate the phase relation between standpipe aerations and many primary response variables like solids circulation rate, total riser pressure drop, and pressure drops across other components of the CFB as a function of different riser regimes, standpipe inventories, and period of standpipe aerations. Each modulated experiment was conducted first by attaining steady state for the desired operating condition. The steady condition was maintained for five minutes and the five minute running average was recorded (Table 2). The modulation was then accomplished by sinusoidally perturbing the aeration 20% above and below the steady state value in the case of HDPE experiments. The aerations were perturbed by 35, 60 and 65% of their steady state for cork and glass beads. Glass beads and
practical voidage in the standpipe initially used for the spiral calculation. The particle density was measured using a standard pycnometer with water as the displacement fluid. A drop of methanol wetting agent was required when measuring the particle density for cork to overcome its hydrophobic nature. The particle size was estimated by a sieve analysis using the ASTM C-136-06 Standard as well as QICPIC Particle Size Analyzer (Sympatec GmbH, model QP0104). The minimum fluidization velocity was determined in a 5 cm diameter cylindrical fluid bed. The values of the transition velocities were determined in the 30 cm diameter circulating fluidized bed.15 Experimental Conditions. The data was collected at NETL circulating bed facility with three different materials including cork, HDPE beads, and glass beads as the bed 1960
dx.doi.org/10.1021/ie301275c | Ind. Eng. Chem. Res. 2013, 52, 1958−1969
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the same frequency but the riser mass should have a π/2 phase angle lag. As an example, if the sinusoidal mass flow into the riser had a period of 60 s then the angular frequency would be approximately 0.105 rad/s and the peak in the riser mass would occur 15 s after the peak in the mass flow into the riser occurred. While under typical operating conditions, the mass flow out of the riser is not a constant, there may be special circumstances where such an assumption is not unreasonable. Operating the riser in the fast fluidized regime at the saturation carrying capacity would be such a condition. A more general model for the riser assumes the mass flow out of the riser is a linear function of the total mass contained within the riser. When this assumption is applied, the overall mass balance can be written.
cork modulations were performed at different frequencies while the period was maintained at 60 s for HDPE material. The test conditions are provided in Table 2. Different riser operating regimes were realized with HDPE materials at both high and low solids inventory in the standpipe. The standpipe inventory was an independent parameter in addition to riser superficial gas velocity and solids circulation rate. Fast fluidized conditions were achieved between upper and lower transport velocities, Utr1 and Utr2 while homogeneous transport conditions were obtained above Utr2. (Homogeneous transport regime and transport regime are used interchangeably.) For 60 μm glass beads experiments, the period used to modulate the standpipe aeration was varied in each of the conditions while maintaining the same solids circulation rate, Ug and standpipe inventory. For cork, tests were conducted with fixed superficial gas velocity (Ug) at the riser bottom, while the modulation period for standpipe aerations and the standpipe inventory were used as the independent parameters at both low and high solids circulation rate. Both cork and glass beads experiments were conducted at homogeneous transport conditions.
d(M r) = [a sin(ωt ) + b] − cM r dt
where c is the proportionality constant between the riser mass and the mass flow out of the riser. Integrating this equation yields the solution
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THEORY The change in mass with respect to time within the riser of a CFB can easily be written as the following: dM r = Ms,in − Ms,out dt
(2)
(3)
φ = 2π
where d is the constant of integration. Note that if the mass in the riser is not allowed to change without bound, then (b − γ) = 0. The cosine function can also be replaced with the sine function to yield: ⎛ π⎞ a sin⎜ωt − ⎟ + d ⎝ ω 2⎠
2
Focusing on the trigonometric time varying term, again we see that the mass flow into the riser and the mass contained within the riser vary with the same frequency but that time lag between the solids flow into the riser and riser mass occurs as a function of the frequency as well as the constant c. Note that the constant c also represents the inverse time constant for the riser as indicated by the exponential term in the above equation. The occurrence of the constant c in the timedependent riser mass equation suggests indirect methods to determine the solids circulation rate in an industrial CFB. To perform this determination, two additional assumptions are needed. The first is that the total solids mass contained within the riser is equal to the product of the total pressure drop across the riser and the cross sectional area of the riser, Mr = ΔPrAr/g. This assumes that the solids were completely supported by the fluid and that gas−wall and solids−wall and solids−solids friction terms were negligible. The second assumption was that the solids circulation rate was a linear function of standpipe aerations. The first assumption is known to be imprecise yet still can be used to estimate the relative fluid bed inventory, but the second assumption is less common and will be considered in more detail later. Given these assumptions, the first step in estimating the solids circulation rate is to measure the time delay (Δt) between the aeration flow and the riser pressure drop which is then converted into a phase angle, φ, measured in radians.
(1)
where γ is the constant solids flow out of the riser. Integrating the above equation yields the particular solution a M r = − cos(ωt ) + (b − γ )t + d (4) ω
Mr =
2
(7)
where a is the amplitude of the sinusoidal variation in solids circulation rate (kg/s), b is the average steady state value of the solids circulation rate (kg/s), and ω is the frequency of the solids circulation rate variation (rad/s). The mass flow out of the riser can be modeled in various ways, but perhaps the simplest is to assume that the solids flow out is constant. Under this condition, the overall riser mass balance can be written as follows: dM r = [a sin(ωt ) + b] − γ dt
⎛ ⎛ ω ⎞⎞ b sin⎜ωt − tan−1⎜ ⎟⎟ + + d e−ct ⎝ c ⎠⎠ ⎝ c c +ω a
Mr =
where Mr is the total mass of circulating solids contained within the CFB riser (kg), Ms,in is the mass flow of solids into the riser (kg/s), and Ms,out is the mass flow of solids out of the riser (kg/ s). The transient analysis involves the modulation of the solids flow into the riser by making the standpipe aeration a sinusoidal function of time. Under this condition, the solids mass flow into the riser can be modeled as the following: Ms,in = a sin(ωt ) + b
(6)
Δt T
(8)
The variable c is then calculated from the phase angle in eqs 7 and 8. ω c= −tan(φ) (9) Substituting eqs 8 and 9 into eq 6 yields
(5)
Comparing the time dependent riser mass to the mass flow into the riser shows that the two variables should change with
Ms,out = 1961
ω 1 −tan(φ) T
∫0
T
ΔPA r r dt g
(10)
dx.doi.org/10.1021/ie301275c | Ind. Eng. Chem. Res. 2013, 52, 1958−1969
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The term (1/T)∫ T0 (Δ(PrAr/g)) dt is needed to obtain the time average riser solids mass from the varying riser pressure drop data. Interestingly there is no need in this theory to specify the bed material properties. In other words, the methodology does not distinguish between particles of different size, shape, or size distribution, and can be applied equally irrespective of bed materials. This can be a great advantage when considering that the feed material is sometimes difficult to control or becomes off the desired specifications or bed material changes as a result of process upsets or other transients. It should also be noted that this theory was developed for an open loop system in which the solids flow into the riser are independent of the riser conditions. However, it is recognized that CFBs may exhibit characteristics of closed loop systems due to the fixed inventory of solids. In other words, over the short-term, the solids inventory in a CFB shifts from riser to standpipe depending on the operating conditions. When the solids inventory and gas flow in the riser are relatively high, and the SCR are low, then the CFB will behave with more open loop character. Conversely, low solids inventory and riser flows and high SCR results in a CFB which has more closed loop character. For this reason it was necessary to experimentally explore the impact of solids inventory on the application.
aeration as the input to the riser and the solids inventory Mr developed within the riser as the output. (In econometric time series analysis or systems theory, the term ARX stands for Auto Regressive Model with Exogenous Input.) Detrending was performed to remove means, offsets, and linear trends from time domain input−output data before applying them to the ARX method. This data processing helps the estimation of more accurate linear responses from data because linear empirical fits may not capture arbitrary differences between the input and output signal levels physically built in.16 The parameter estimates were based on the comparison of ARX fit with different delays and terms: M r(t ) + κ1M r(t − 1) + ··· + κnκM r(t − nκ ) = λ1Fsp(t − Δt ) + ··· + λnλFsp(t − nλ − Δt + 1)
or Κ(q) M r(t ) = Λ(q)Fsp(t − Δt )
(11)
where Κ(q) = 1 + κ1q−1 + ··· + κnκq−nκ
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and Λ(q) = λ1 + λ 2q−1 + ··· + λnλq−nλ − 1
RESULTS AND DISCUSSIONS Phase Shift in CFB Responses to Changes in Standpipe Aeration. Typical time series data for the modulated solids flow into the riser and the total pressure drop across the riser is shown in Figure 2. In this experiment the riser was
The integers, nκ and nλ, are the orders of polynomials K and Λ, respectively. The parameter Δt represents the time delay between the input (Fsp) and the output (Mr), and q is the time shift operator. During estimation, the ranges of both delay parameter and ARX terms were set between 1 and 20. Akaike Information Criteria (AIC) was used to select the best combination of nκ, nλ, and Δt to give ARX(nκ, nλ, Δt). Evaluation of Assumptions. The development of the theory considers that the CFB riser acts like an open system. The extent that this is true was tested by varying the solids inventory and by operating the riser in different operating regimes. Effect of System Inventory on Response Variables. The solids inventory influences whether the solids circulation rate follow the change in standpipe aeration during a modulated experiment or if the there is an apparent anomalous reversal in the response such that the SCR appeared to lead the changes in standpipe aeration. At low inventory transport conditions (PMD2 and PMD10) and the fast fluidized regimes (PMD12, PMD33, and PMD43), changes in the solids circulation rate led the standpipe aeration changes. As an illustration, the measured solids circulation rate (PMD10) was fitted to a sinusoidal curve at different delays (Δt = 1:150 s). Based on the maximum fit between the sine curve and the experimental data of solids circulation rate, the best curve represented by Ms,fit was chosen (Figure 3a). The model fit was defined as
Figure 2. Riser pressure drop (solid blue line) and solids flow into the riser (solid black line) as a function of time when operating the riser in the homogeneous transport regime (PMD7). Also shown is the pressure drop across the crossover (thin gray line) connecting the top of the riser and the primary cyclone. Data used: HDPE.
operated at transport dilute regime (PMD7). The solids flow varied in concert with the modulated standpipe aeration. The pressure drops in the riser and in the crossover also varied sinusoidally; however, these pressures exhibited a measurable time delay compared to the input aeration. On the basis of the presented theory, it is only required to determine the time delay between the riser inventory (or the riser ΔPr) and the modulated standpipe aeration (Fsp) to predict solids circulation rate out of the riser. The autoregressive (ARX) method was utilized to determine the time delay between the standpipe aeration and the riser pressure drop, considering standpipe
⎛ ⎜ Modelfit = 100⎜1 − ⎝
⎞ ∑tN= 1(xexp(t ) − xmodel(t ))2 ⎟ ⎟ ∑tN= 1(xexp(t ) − xexp(t ))2 ⎠ (12)
Then, the time delay between the standpipe aerations and Ms,fit was calculated. Figure 3a showed that the solids circulation rate led the standpipe aeration by 3 s in the inventory limiting PMD10 case. This observation seems impossible in the sense that the output is leading the input or the dependent variable is 1962
dx.doi.org/10.1021/ie301275c | Ind. Eng. Chem. Res. 2013, 52, 1958−1969
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ARX method (eq 11) was chosen to predict the delay between the standpipe aeration Fsp and the riser inventory Mr. The influence of CFB inventory on the CFB dynamics depends upon the fluidization regime. In general, the process dynamics and SCR in the fast fluid bed regime where Ug < Utr2 depends upon the inventory and the riser gas velocity. When the inventory was low more standpipe aeration was required to achieve a given circulation rate than the higher inventory cases. This was found comparing cases PMD1 and 16, PMD4 and 33, PMD13 and 12. The SCR in the FFB cases where the dense bed was formed (PMD4 and 33) was dependent upon only the gas velocity and is defined as the gas saturation carrying capacity. It is in this regime where the fluctuations in the SCR were dependent on the inventory. At low inventory the variability in the SCR was ±1.4 kg/s which decreased to ±0.4 kg/s at high inventory. This was not accompanied by a change in the pressure fluctuations. In the transport fluid bed cases the where Ug > Utr2 inventory did not influence the CFB performance with respect to the standpipe aeration required to achieve SCR. However, when operating in a core annular regime, as defined by a C-shaped axial pressure profile, the fluctuations in the SCR also displayed dependence on solids inventory. The low inventory case exhibited greater variability PMD10 ± 3 kg/s as compared to PMD11 ± 1.4 kg/s. As with the fast fluid regime there was no apparent inventory dependence on the pressure fluctuations. Thus, the fluidization regimes did under certain cases exhibit various influences on the process dynamics as manifested in the variations in the SCR more so than the pressure. Validation of Ms,out = cMr at Various Fluidization Regimes. The primary factor which influences the relationship between the SCR and the riser inventory was the fluidization regime as defined here by Ug relative to Utr2. Fast Fluidized Regime. The second plot in Figure 3 shows the slugs (represented by high peaks in the signals) in fast fluidized dense regime (PMD13). They were generated in the riser when the riser was operated closer to the lower transport velocity, Utr1. Near Utr1, the solids circulation rate in the riser reaches the saturation carrying capacity, leading to a collapse of a dilute gas−solids suspension to a relatively dense suspension.17 At the choking condition the dense suspension is usually characterized by the presence of the slugs18 yielding considerable pressure fluctuations. The slugs in the riser immediately affected ΔPco and influenced the spiral measurement after 1 s. When the phase shift technique was applied to these fast fluidized regimes, the solids circulation rate was not modeled well except in fast fluid dilute case (PMD1) and its duplicate (PMD31 not shown in Table 2). The minimum percent error was found to be 190% and it increased up to 944%. At fast fluidization, the pressure drop across the riser was independent of mass flowing into the riser. The theory was derived under the assumption that the mass flow out of the riser is a linear function of mass inventory within the riser. This assumption did not hold true when the system was operating under fast fluidized conditions. This is best illustrated in a time series comparison depicted in Figure 4a. From eq 1, the mass flow rate out of the riser was calculated by taking the difference between the solids circulation rate measured by the spiral and the rate of change of mass within the riser. The mass flow out of the riser was plotted as a dependent variable against the natural log of riser inventory calculated from the total pressure drop across the riser (ΔPrAr/g). Typically, the fast fluidization regime is characterized by a dense region at the bottom of the
Figure 3. Dependent variables leading the independent variables at different operating regimes of the riser. Data used: HDPE. (Top) PMD10: Time delay between the standpipe aerations, Fsp, (solid red line) and sinusoidal fit to Ms,fit (solid light blue line) of measured solids circulation rate, Ms (solid black line) when operating the CFB riser in the homogeneous transport regime. Ms led Fsp by 4, 4, 8, and 3 s in PMD12, PMD33, PMD43, and PMD2 conditions, respectively, (not shown). (Bottom) PMD13: Time delay between the riser pressure drop, ΔPr (solid blue line) and measured solids circulation rate, Ms (solid black line) during slugging. Slugs are also visible in the pressure drop across the crossover, ΔPco (thin gray line).
anticipating future changes before aeration has actually changed. On the other hand, the time delay between the measured solids circulation rate and the standpipe aerations was zero at higher inventory PMD11 condition. In CFB operation, it is the aeration in the standpipe which induces the solids to start moving from the initially loaded standpipe to the riser. At higher standpipe bed height, the standpipe aeration effectively produces a given solids circulation rate. In other words, a high solids level in the standpipe requires less aeration to generate a given Ms. As the aeration approaches its maximum value (and the standpipe inventory approaches its minimum value), the amplitude of the modulated solids circulation rate decreases. This represents classic closed loop CFB system. While the solids flow into the riser decreases from the drop of standpipe inventory, the flow out of the riser is still at the higher level. The higher flow out of the riser coupled with the low solids flow out of the standpipe causing the standpipe to rebuild. This dependence of Ms on the standpipe bed height for a given aeration and the resulting shift of solids inventory from the standpipe to the riser and back again are the fundamental reasons for solids circulation rate leading the standpipe aerations at these conditions. To capture the feedback due to the riser that is critical to this behavior, the 1963
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Figure 5. Relationship between the mass flowing out of the riser and mass within the riser operating in the homogeneous transport regimes. Data used: HDPE.
and eq 1 gives Ms,in = Ms,out. If the spiral Ms is substituted for Ms,in then Ms,out = Ms.
Figure 4. Response of CFB process variables at fast fluidized conditions. Data used: HDPE. (Top) Mass flowing out of the riser is not a function of the mass within the riser operating in the fast fluidization regime. (Bottom) Pressure drop across the crossover do not show modulation in fast fluidization regimes.
riser and a dilute region above it.19 The axial voidage across the riser shows an S-shaped pressure profile when the solids exit at the top is either smooth or abrupt. The pressure drop across the crossover may not show any modulation as it does for the transport condition of Figure 2 (see Figure 4(b)). This implies that the mass flow out of the riser is not sinusoidal with respect to time even though the riser is. Under these conditions, the fundamental assumption (eq 6) of the analysis did not hold true, and therefore poor results are expected. Homogeneous Transport Regime. The transport regime is characterized as having a uniform axial pressure profile or constant voidage along the height except for a denser region due to acceleration and mixing at the bottom, The abrupt exit, on the other hand, can complicate the axial profiles further. Such exits can change the axial voidage profile significantly and give a voidage profile of C-shape with high voidage in the middle and lower voidage at both ends of the bed.20,21 In transport conditions above Utr2, the mass flowing out of the riser appeared to be linearly related to the mass contained within the riser. As can be seen from the time series comparison shown in Figure 5, there was a linear change in solids accumulating in the riser (solids flow in minus solids flow out, Ms − dMr/dt) with the apparent solids holdup in the riser (ΔPrAr/g). The slope of the line is close to 1 indicating a direct relationship between these two parameters. To cross-validate the linearity assumption between Mr and Ms,out, the steady state data of Ms was used to calibrate mass flow out of the riser (Figure 6). At steady state, the time derivative becomes zero
Figure 6. Calibration of Ms,out in terms of solids circulation rate Ms measured by the spiral. Data used: HDPE.
In general, the mass flow out, Ms,out, can be expressed in terms of the mass contained within the riser as Ms,out = cM rn
(13)
The constant c and the exponent n were determined from calibration data collected at two different riser superficial gas velocities, Ug = 9 m/s and 7 m/s. Note that the calibration data set (HDPE) is different from the PMD series used to validate the phase shift technique. The exponent and slope were obtained by taking the natural log of Mr and Ms and then by fitting a straight line through the steady state data (Figure 6). The values obtained from the least-squares fit were: n = 0.82 and c = 0.43 indicating a nonlinear relationship between the riser inventory and the solids flow rate out of the riser. However, there was an apparent lack of fit as evidenced by the curvature even though the relationship yielded an R2 of 94%. Moreover this nonlinear expression gave a slope of 2.5 when Ms,out was plotted against Ms (Figure 7) violating the relation that Ms,in = Ms,out at the steady state. 1964
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Figure 7. Best fit slope and exponent from the steady state data. Data used: HDPE. Calibration data tests at Ug = 7 and 9 m/s. This plot shows that the solids circulation rate out of the riser that is a linear function of riser inventory is almost equal to the solids circulation rate into the riser at the steady state.
Figure 8. Linearity between time series data for Ms and Fsp for three different materials at homogeneous transport condition. Solid blue lines represent the linear least-squares regression line for each material.
Linear and square root relationships were tested to determine which best represented the calibration data. The square root relationship is common in tank systems where the effluent flow rate is expressed as a square root of the liquid level at turbulent flow conditions.22 In Figure 7 the slope, c, was calculated as c=
∑ (M r − M̅ r )(Ms − M̅ s) ∑ (M r − M̅ r )2
estimated from the phase shift technique from the low inventory cases had smaller deviation than the high inventory cases. Both estimated values were within the variability associated with the measured SCR using the spiral device. There are two main factors that affect the uncertainty in the SCR estimation using the phase shift technique. It should be recognized that the present technique uses time series data to estimate solids circulation rate. The measurement of the solids circulation rate is continuous at the NETL facility and to the authors’ knowledge such time series data are not available in the literature. On the basis of this experience it is believed that in any gas−solids application, the variability in solids circulation rate measurement is quite large on a second-by-second basis. Assuming the distribution of CFB parameters follows the Gaussian curve, the rough estimate of ±95% confidence interval of the solids circulation rate and riser inventory were calculated as 2 standard deviations (Table 2). The solids circulation rate varies on a second-by-second basis over a wide range. At some test conditions the range of measured solids circulation rates varied more than 100% from its mean value. This is depicted in Figure 9 in which the difference between the minimum and maximum solids flow rates, of 0.8 and 1.8 kg/s, was nearly the same as average solids flow rate of 1.2 kg/s. The process variability in the solids circulation rate on a second-by-second basis was larger than that in the pressure drops. This is reasonable since the pressure drop reflects the accumulation of solids and therefore averages out perturbations in the solids flow in and out of the riser. The phase lag between the standpipe aeration and the riser pressure drop were estimated using ARX method. At the transport dilute condition (PMD7), the riser inventory lagged the standpipe aeration by 7 s which corresponds to a phase lag of around 0.73 radians when the modulation had a 60 s period (eq 8). The time averaged mass within the riser was 10.93 kg and the calculated solids circulation rate based on the offset of 7 s was 1.27 kg/s. This compares favorably to the time averaged mass circulation rate measured by the spiral of 1.25 kg/s resulting in error of only about 1%. However, majority of estimation results (Table 3) for different transport conditions are not as perfect as PMD7 case. The ±1 s uncertainty in the estimated lag results in significant difference in percent error between measured and estimated solids circulation rate. For instance, the estimated lag for modulate 8 test condition was found to be 4 s. At this lag, the percent error was 115%. Taking
(14)
where, M̅ r and M̅ s are the sample means. The correlation represented by diamonds was extracted which had a pure linear dependence, n = 1 and constant c = 0.07 with a variance explained, R2, of 95% and slope of 0.97. For the square root dependence, n = 0.5 with constant c = 0.97, the slope was 1.2 and it explained only 72% of the variance in the data exhibiting lack of fit. Thus, a linear relationship was observed between Mr and Ms,out. Linearity between Fsp and Ms. The aeration at the bottom of the standpipe has a strong influence on the solids circulation rate and the standpipe bed height. At different operating conditions and different standpipe bed heights, if the steady state values of the solids circulation rate are plotted as a function of standpipe aeration, one might expect nonlinear relationships between each. However, for each test point taken in the homogeneous transport regime, the solids circulation rate was found to be linearly related to the standpipe aeration as can be seen from the time series data plotted in Figure 8. The plot consists of solids circulation rate (5 s moving average) and the raw standpipe aeration data for each of the three bed materials tested. Only 1% improvement in the variance explained, R2, was achieved with the quadratic fit as compared against the linear fit. The slope of these plots are different for different materials; however, it is not necessary to know the slope between Fsp and Ms to utilize the present method. Analysis of SCR Estimation. The phase shift technique was applied to every test condition in Table 2 conducted in the transport regime. The results are summarized in Table 3 which also includes duplicates of HDPE test conditions presented in Table 2. The experimental uncertainty can be evaluated by comparing the duplicates both conducted in the core annulus regime. The PMD11 and 15 represent a high inventory cases and PMD10 and 26 represent duplicates taken both with low inventory. The duplicate measurements were close providing evidence for process repeatability. Surprisingly, the SCR 1965
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Table 3. Solids Circulation Rate Estimation from the Time Delay between ΔPr and Fsp for Homogeneous Transport Conditionsa results test HDPE PMD7 PMD2 PMD11 PMD15 PMD10 PMD26 PMD3 PMD27 glass beads modulate 8 modulate 5 modulate 10 modulate 4 modulate 19
riser regime transport dilute transport dilute transport core annulus transport core annulus transport dense upflow transport core annulus transport core annulus transport core annulus transport core annulus transport core annulus transport core annulus
period in Fsp (s)
Δt between ΔPr and Fsp (s)
φ (rad)
c = −ω/tan(φ) (1/s)
τc = 1/c (s)
Ms,out (kg/s)
Ms (kg/s)
percent error
60 60 60 60 60 60 60 60 60
−7 −9 −9 −9 −8 −7 −6 −7
−0.73 −0.94 −0.94 −0.94 −0.84 −0.73 −0.63 −0.73
0.12 0.08 0.08 0.08 0.09 0.12 0.14 0.12
9 13 13 13 11 9 7 9
1.3 0.9 5.4 4.7 5.5 6.5 13.8 11.0
1.3 1.3 6.8 6.2 5.9 6.1 12.6 12.8
1% −31% −21% −24% −7% 6% 10% −14%
24
−5
−1.31
0.07
14
14.7
14.8
0%
72
−8
−0.70
0.10
10
21.9
14.5
51%
96
−10
−0.65
0.09
12
17.8
14.4
23%
150
−11
−0.46
0.08
12
17.8
14.3
25%
192
−14
−0.46
0.07
15
13.9
14.4
−3%
Low Solids Circulation Rate cork K41 K31 K32 K36 K38 K34 K40 K39 K30 K37 K35 K33
transport transport transport transport transport transport
dilute dilute dilute dilute dilute dilute
transport core annulus transport core annulus transport core annulus transport core annulus transport core annulus transport core annulus
60 60 90 90 120 120
−7 −7 −13 −11 −18 −14
0.09 0.09 0.09 0.07 0.07 0.05 Rate 0.08
11 11 11 15 14 21
0.5 0.4 0.4 0.3 0.4 0.3
0.4 0.4 0.4 0.4 0.4 0.4
22% 14% 3% −21% −14% −39%
−6
−0.73 −0.71 −0.91 −0.77 −0.94 −0.73 High Solids Circulation −0.63
60
13
1.2
1.1
11%
90
−8
−0.56
0.04
23
0.7
1.0
−33%
90
−10
−0.70
0.06
17
0.9
1.0
−11%
120
−16
−0.84
0.06
17
0.9
1.0
−16%
120
−15
−0.79
0.05
19
0.8
1.1
−25%
120
−16
−0.84
0.06
17
0.9
1.1
−15%
Percent error was optimized at ±l second from the time delay originally estimated from the ARX method. Low inventory conditions are italicized for HDPE material. Minus (−) sign in φ represents phase lag, i.e., ΔPr lags Fsp by −φ radians. a
the ±1 s uncertainty into account, the error increased to 272% for 3 s, but decreased to nearly 0% for 5 s. Using this approach the lag listed in Table 3 was the minimum percent error resulting from ±1 s uncertainty in the estimated lag. Figure 10 shows the overall improvement of solids circulation rate estimation for all the data sets under consideration. A large variation can be seen in glass beads at Ms > 14 kg/s where only 5 conditions were tested. The overall comparison between M s measured by spiral and Ms, out estimated by phase shift technique was quite good with relatively low bias of about 11% and 94% variance explained. The percent error was always found to be within the variability of the measured time series solids circulation rate.
Considerations for Industrial Scale Applications. It is common industrial practice to calibrate the circulation rate using some variation of eq 13. Thus, for illustrative purposes it was decided to compare the responses using the best parameters from the calibration data to the phase shift technique. The best calibrated values for the inventory−solids flow relationship, eq 13, were applied to the data taken during the PMD tests. The predicted mass flows out were compared against the measured solids circulation rate (Figure 11). Using n = 1 and c = 0.07, the percentage error between measured solids circulation rate and predicted Ms,out was between 42 and 152% and the overall fit is shown in Figure 11 with a 60% bias high and R2 of 91%. The phase shift technique, where Ms,out was 1966
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Figure 11. Comparison of measured solids circulation rate and mass flow out of the riser using the calibration curve from eq 13 and using the phase shift optimized for best lag ±1 s for three different regimes. TD, transport dilute regime (solid symbols); TCA, transport core annulus regime (shaded symbols); and TDU, transport dense upflow regime (open symbols). Solid trend line is for Ms,out calculated from the phase shift technique while the dotted trend line is for Ms,out calculated from the calibrated data. Predictions from phase shift were represented by circles and those from calibrated data by diamonds. Data used: HDPE PMD data series.
Figure 9. Steady state condition for PMD7 case before modulation started. Modulated data set for this condition was shown in Figure 2. Dependent variables include riser pressure drop (solid blue line) and solids flow into the riser (solid black line) and independent variables are volumetric gas flow rate at riser (dark blue solid line) and standpipe (dotted solid black line) bottom.
to be consistent with the ratio of riser and standpipe aeration flows in industrial applications such FCC operations, though it is recognized that more aeration is required for Group B particles than for Group A particles such as FCC. Certainly if the perturbation of the system affects the gas-make or conversion process then the mass balance expression (eq 1) used to extract the circulation rates will also be affected in a complex manner. Experiments where riser solids flow were converted into gas flow, as in the case of a catalytic cracker were not conducted. The operating policy in some commercialized conversion processes is to run at the maximum solids circulation rate possible. With this in mind, there may not be a possibility for the proposed sinusoidal variation in standpipe aeration. While this may be true, if estimation of the solids circulation rate is of critical interest, and if it is feasible, then reducing the aeration into the nonmechanical valve could establish an observable periodic response in the riser pressure drop. In the hot industrial process, it is expected that the effluent solids rate would be tied to the level of gas−solids contacting that occurs within the riser. It also seems reasonable that a higher variation in standpipe aeration along with the attendant variation in solids circulation rate could affect this contacting thereby creating an unquantifiable shift in the solids circulation rate that is sought. The method does not require variation such as 20%, 35%, or 65% in the standpipe aeration from its steady state values as was done in the experiments under study, but only a variation necessary to result in an observable periodic response in the riser pressure drop. Recently, it has been found that the necessary response in the total riser pressure drop were observed in tests with variations in the standpipe aeration as small as 5−10%. If the perturbation alters the conversion process then the technique will be compromised. However, if a process parameter which moderates any effects can also be varied in sync with the standpipe aeration it may be possible to avoid these complications. This method could be readily applied to the pneumatic conveying of solids without these potential complications.
Figure 10. Comparison between measured and estimated solids circulation rate from the phase shift technique using the best lag ±1 s for three different materials (cork, circles; HDPE, diamonds; and glass beads, triangles) at different operating conditions.
assumed to be equal to cMr, showed significant improvement in overall prediction (slope = 0.9424, R2 = 94%) of solids circulation rate. Thus, the phase shift technique for predicting SCR was better than the predictions obtained by utilizing the calibration technique on the PMD data series. The characterization of the present unit as an industrial scale is based upon the physical size or height of the facility as well as the fact that this unit is the smallest CFB riser diameter in which the wall effects as reported by Knowlton et al.23 are negligible. The phase lag or time constant of the CFB riser response to solids circulation will be unaffected by scale as long as the measurement accuracy does not suffer and the fluidization is in the transport regime. However, the relationship between pressure drop and solids circulation can be affected by scale. The effect of wall friction due to solids becomes negligible as the fluid bed diameter increases. Also, small diameter risers have a tendency to entrain the solids clusters sloughing off the wall producing more dilute risers than found in larger diameter units operated under the same conditions. As a result this method will be more accurate and can be successfully applied in larger diameter risers. In these experiments, the standpipe aeration was considerably smaller than the riser gas flow (Table 2). This is thought 1967
dx.doi.org/10.1021/ie301275c | Ind. Eng. Chem. Res. 2013, 52, 1958−1969
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Article
CONCLUSIONS AND FUTURE WORK A simple approach was presented to estimate a solids circulation rate from a dynamic time series in the circulating fluidized bed. This critical operating parameter was determined from the easily measurable pressure drop and aerations information with minimal knowledge of material properties. The time delay between modulated process parameters such as the mass contained within the riser and the standpipe aeration was determined using the autoregressive method. This delay gave a satisfactory prediction of the solids circulation rate in transport regimes even in the inventory limiting case where changes in the solids circulation rate actually led the standpipe aeration changes. At fast fluidized regimes, the lack of dependency of mass flow rate out of the riser on the riser inventory (Figure 4a) resulted in higher percentage error between measured and estimated solids circulation rate. In summary, the phase shift method was able to predict the solids circulation rate in all homogeneous transport regimes for Group A and Group B particles within the variability imposed by second-by-second measurement of solids circulation rate and ±1 s uncertainty in the lag estimation. The percent error between measured and estimated SCR depends on the time lag, and unless the true time constant (or c) of the riser is known for each operating condition, this dependency cannot be avoided in the absence of solids circulation rate measurement. According to eqs 7 and 8, the amplitude ratio and phase shift are dependent on frequency. That functional form can be described in a Bode plot in which the inflection point in the plot of phase lag (∠Mr(ω)/Fsp(ω)) against frequency represents the time constant, or c, in the riser. In a plot of the frequency against the amplitude ratio, or | Mr(ω)/Fsp(ω)|, the amplitude ratio decreases from its maximum at this time constant. The practical solution might be modulating the standpipe aeration with different frequencies for each condition and to identify the frequency where the phase lag between Fsp and ΔPr appears to be 45 degrees when operating under transport conditions where the SCR is linearly related to ΔPr. The 45 degrees lag corresponds to the frequency where the time constant of the first order system (eq 6 in the present case) becomes equal to its inverse. The specific frequency responses and the implications to dynamics and control of the CFB systems deserve further study than was possible here.
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AUTHOR INFORMATION
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Corresponding Author
*E-mail:
[email protected]. Notes
g = acceleration due to gravity (m/s2) Mr = total mass of circulating solids contained with the CFB riser (kg) M̅ r = sample mean of riser inventory in the calibration data set (kg) Ms = measured solids circulation rate by the spiral (kg/s) M̅ s = sample mean of measured solids circulation rate in the calibration data set (kg/s) Ms,in = mass flow of solids into the riser (kg/s) Ms,out = mass flow of solids out of the riser (kg/s) n = exponent of Mr in order to relate to the mass flow out of the riser Pb = pressure at the base of the riser, (Pa,g) q = time shift operator in AR method R = correlation coefficient RH = relative humidity (%) t = time (s) Δt = time delay between Fsp and ΔPr (not dead time) (s) T = period of modulation (s) TE = temperature at the base of the riser (°C) u = general input(s) to the ARX analysis Ug = total superficial riser gas velocity, (m/s) Usp = superficial gas velocity at the bottom of the standpipe, (cm/s) Umf = minimum fluidization velocity (m/s) Utr1 = lower transport velocity in the riser (m/s) Utr2 = upper transport velocity in the riser (m/s) xexpt = experimental data xmodel = model prediction y = general output(s) of the ARX method ΔPr = pressure drop across the riser (Pa) ΔPco = pressure drop across the crossover (Pa) εnom = nominal voidage used for solids circulation rate calculation in the spiral K(q) = polynomial of output in time shift operator q used in AR method Λ(q) = polynomial of input in time shift operator q used in AR method nκ = polynomial order of K(q) nλ = polynomial order of Λ(q) γ = constant solids flow out of the riser (kg/s) ω = angular frequency of the solids circulation rate variation (rad/s) φ = phase angle between different parameters (rad) ρp = particle density (kg/m3) τc = time constant of the riser (s)
REFERENCES
(1) Syamlal, M.; Guenther, C.; Cugini, A.; Ge, W.; Wang, W.; Yang, N.; Li, J. Computational Science: Enabling Technology Development. Chem. Eng. Progress 2011, 7, 23. (2) Wang, W.; Lu, B.; Zhang, N.; Shi, Z.; Li, J. A Review of Multiscale CFD for Gas−Solid CFB Modeling. Int. J. Multiphase Flow 2010, 36 (2), 109. (3) Ludlow, J. C.; Monazam, E. R.; Shadle, L. J. Improvement of Continuous Solid Circulation Rate Measurement in Cold Flow Circulating Fluidized Bed. Powder Technol. 2008, 182, 379. (4) Ludlow, J. C.; Shadle, L. J.; Syamlal, M. Method to Continuously Monitor Solids Circulation Rate. In Circulating Fluidized Bed Technology VII; Grace, J.R., de Lasa, H., Eds.; Canadian Society of Chemical Engineering: Ottawa, Canada, 2002; pp 513−520. (5) Eastern Instruments, K-tron, SchneckAccuRate, CentriFlow, S-EG Instrument, www.easterninstruments.com.
The authors declare no competing financial interest.
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NOTATIONS AND SYMBOLS a = amplitude of the sinusoidal variation in solids circulation rate (kg/s) Ar = cross-sectional area of the riser (m2) b = average steady-state value of the solids circulation rate (kg/s) c = proportionality constant between Mr and Ms,out d = constant of integration dp = particle diameter (micrometers) Fr = volumetric gas flow rate at the bottom of the riser (m3/ s) Fsp = aeration given near the bottom of the standpipe (m3/s) 1968
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1969
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