**4.1 Heat transfer correlation**

We briefly explain the composition of the tube-side heat transfer correlation for a heat exchanger which also applies recirculation of the particles and the liquid.

Fig. 6 shows the significant liquid velocities influencing the wall-to-liquid heat transfer coefficient for an exchanger with a circulating fluidised bed, such as:

Us = superficial liquid velocity in the tubes relative to the tube wall,


Fig. 6. Significant liquid velocities in tube of exchanger with circulating fluidised bed.

Where the superficial liquid velocity refers to the tube liquid velocity in the empty tube. From the explanation above, it follows:

$$
\mathcal{U}\mathcal{U}\_s = \mathcal{U}\_{b,w} + \mathcal{U}\_{l,s} \tag{1}
$$

For Ub,w = 0, the circulating fluidised bed satisfies the conditions of a stationary fluidised bed, which then yields:

$$
\mathcal{U}\_s = \mathcal{U}\_{l,s} \tag{2}
$$

where Ul,s follows from the theory presented by Richardson and Zaki, Ref. [10].

The heat transfer coefficient αw,l between the wall and the liquid of a circulating fluidised bed exchanger, is composed as follows:

$$
\alpha\_{w,l} = \alpha\_l + \alpha\_c \tag{3}
$$

where:

558 Heat Exchangers – Basics Design Applications

The performance of a self-cleaning fluidised bed heat exchanger and its design

We briefly explain the composition of the tube-side heat transfer correlation for a heat

Fig. 6 shows the significant liquid velocities influencing the wall-to-liquid heat transfer

U

Fig. 6. Significant liquid velocities in tube of exchanger with circulating fluidised bed.

Where the superficial liquid velocity refers to the tube liquid velocity in the empty tube.

s

Boundary limits of the (moving) swarm of fluidised particles

Tube wall

U b,w

U l,s

Ub,w = velocity of (moving) swarm of fluidised particles relative to the tube wall, Ul,s = superficial liquid velocity relative to the boundary limits of the (moving) swarm.

**4. Performance of the self-cleaning fluidised bed heat exchanger** 

exchanger which also applies recirculation of the particles and the liquid.

Us = superficial liquid velocity in the tubes relative to the tube wall,

coefficient for an exchanger with a circulating fluidised bed, such as:

consequences have to be divided in the following subjects:

 Heat transfer correlation. Design consequences.

**4.1 Heat transfer correlation** 

Fouling removal.

Wear.

Pumping power requirements.

From the explanation above, it follows:

αl = wall-to-liquid heat transfer coefficient of a stationary fluidised bed with a superficial velocity Ul,s related to the porosity ε of the bed

αc = wall-to-liquid heat transfer coefficient for forced convection in a tube, taking into account a liquid velocity Ub,w, which actually corresponds with the velocity of the (stationary) fluidised bed moving along the tube wall

For the heat transfer coefficient αl one is referred to Ruckenstein, Ref. [11], as long as superficial liquid velocities are calculated from porosities (ε) lower than 0.9. For porosities in the range 0.9 < ε 1.0 , the following equation is suggested:

$$\|\alpha\|\_{l} = \alpha\|\_{\varepsilon=1.0} + \frac{(1-\varepsilon)}{(1-0.9)} \times \left\{ \left. \alpha\right|\_{\varepsilon=0.9} - \left. \alpha\right|\_{\varepsilon=1.0} \right\} \tag{4}$$

The heat transfer coefficient αl|<sup>ε</sup> <sup>=</sup> 1.0 is calculated using the equation of Dittus and Boelter taking into account the liquid velocity in the tube which corresponds with the terminal falling velocity on one single particle in the tube, i.e. ε = 1.0, as the liquid velocity used in the Reynolds number.

The heat transfer coefficient αc is also obtained using the equation of Dittus and Boelter with Ub,w as the liquid velocity used in the Reynolds number.

Fig. 7 shows the wall-to-liquid heat transfer coefficients in an exchanger with a circulating fluidised bed as a function of the various process parameters using 2.0 mm glass particles. It should be noticed that in Fig. 7 the curve Us = Ul,s shows the relation between heat transfer coefficient and relevant parameters for the stationary fluidised bed bed.

It should be emphasised that this heat transfer correlation is only an attempt to produce some approximate numbers for the overall heat transfer coefficients for any preliminary design. The real numbers which should be used in the performance guarantee of the heat exchanger follow from experimental operation of a representative pilot plant. Such a pilot plant is anyhow necessary to demonstrate the non-fouling operation.

Self-Cleaning Fluidised Bed Heat Exchangers

Lt = Tube length [m]

Do = Outer diameter of the tube [m] Di = Inner diameter of the tube [m] l = Density of the liquid [kg/m³] cl = Specific heat of the liquid [J/(kg·K)]

and temperatures, Equation (5) can be simplified:

Where:

[°C]

example:

for Severely Fouling Liquids and Their Impact on Process Design 561

log 4

(5)

(6)

2

*<sup>D</sup> c V <sup>T</sup> L D*

ΔT = Temperature difference of the liquid between tube inlet and tube outlet

For a comparison of the tube length between different types of exchangers for the same duty

1 *o l <sup>t</sup> D V L C <sup>k</sup>*

Or in words: The length of the tubes Lt is directly proportional to the diameter of the tube Do , the liquid velocity in the tubes Vl , but inversely proportional to the heat transfer coefficient k. It can be stated that the clean k-values for self-cleaning fluidised bed heat exchangers are always somewhat higher than for the conventional heat exchangers at their normally much higher liquid velocities, with the remark that the clean k-values for the selfcleaning fluidised bed heat exchangers correspond with the design values used for the fullsize self-cleaning fluidised bed heat exchanger with no need for cleaning, while for the conventional heat exchangers due to fouling the design k-value may be 2, 3, 4 or even 5 times lower than the clean k-value and frequent cleanings may be still necessary.

What the design consequences of excellent heat transfer at very low liquid velocities do mean for a self-cleaning fluidised bed heat exchanger in comparison with a conventional heat exchanger for the same application can be best explained with the following striking

A conventional Multi-Stage Flash (MSF) evaporator for seawater desalination with a seawater velocity of 1.8 m/s in the condenser tubes of 19.05 × 1.21 mm and an average heat transfer coefficient of 2 500 W/(m²·K) required a total length of the condenser tubes of 173 m. Depending on the design of this seawater evaporator, this tube length requires the installation of 8 evaporator vessels in series, each vessel with a length of 20 m or even more. The same MSF desalination plant equipped with stationary fluidised bed heat exchangers required a seawater velocity in the tubes of only 0.125 m/s to maintain a fluidised bed in all parallel operating tubes with a porosity of 75 % using glass particles with a density of

*D kT* 

*<sup>i</sup> ll l t o o*

Vl = Superficial liquid velocity in the tube [m/s] k = Overall heat transfer coefficient [W/(m²·K)]

Where C1 is a constant for a particular installation/application.

∆Tlog = Logarithmic mean temperature difference across tube [°C]

Fig. 7. Heat transfer coefficients in exchanger with circulating fluidised bed.

#### **4.2 Design consequences**

A fluidised bed exchanger offers the possibility to obtain heat transfer film coefficients at the tube-side of the same order of magnitude as normally achieved in conventional tubular exchangers, although at much lower liquid velocities. For example, a stationary fluidised bed heat exchanger using glass beads of only 2 mm with a porosity of the fluidised bed in the tubes of 75 % (i.e. the liquid volume fraction in the tube) can achieve heat transfer film coefficients of approx. 10 kW/(m²·K) at a superficial velocity of approx. 0.12 m/s, which can only be realised in a conventional tubular heat exchanger with a liquid velocity of approx. 1.8 m/s.

The design consequences of this unique behaviour for a fluidised bed heat exchanger can be best explained with the help of the equation below for a heat exchange tube, which has been derived from the conservation equations for mass and energy:

$$L\_t = D\_o \times \left(\frac{D\_i}{D\_o}\right)^2 \times \frac{\rho\_l \times c\_l \times V\_l}{4 \times k} \times \frac{\Delta T}{\Delta T\_{\log}}\tag{5}$$

Where:

560 Heat Exchangers – Basics Design Applications

**PARTICLE SIZE**

**TEMPERATURE**

**PARTICLE MATERIAL**

**LIQUID**

**a a**

**a**

**l l**

**w,l ; ;**

 *w l*, *l*

**m/s 0.5**

**m/s**

**m/s**

**m/s**

**XO0.9**

**0.9 MXO**

*<sup>l</sup>* 0.9<

=≤0.9

**=**

**=**

**Ul,s**

**0.4**

**0.6 m/s**

**0.3**

**0.2**

**=**

**Us =**

**Us =**

**Us =**

**Us**

**Us**

**Us**

**0.7 0.8**

derived from the conservation equations for mass and energy:

Fig. 7. Heat transfer coefficients in exchanger with circulating fluidised bed.

**WALL-TO-LIQUID HEAT TRANSFER COEFFICIENTS**

**[kW/(m²·K)]**

**,**

*αw,l,αl*

**w,l a**

**2**

**4**

**6**

**8**

**10**

**12 l a**

**14**

**16**

**0**

**4.2 Design consequences** 

approx. 1.8 m/s.

**POROSITY** 

A fluidised bed exchanger offers the possibility to obtain heat transfer film coefficients at the tube-side of the same order of magnitude as normally achieved in conventional tubular exchangers, although at much lower liquid velocities. For example, a stationary fluidised bed heat exchanger using glass beads of only 2 mm with a porosity of the fluidised bed in the tubes of 75 % (i.e. the liquid volume fraction in the tube) can achieve heat transfer film coefficients of approx. 10 kW/(m²·K) at a superficial velocity of approx. 0.12 m/s, which can only be realised in a conventional tubular heat exchanger with a liquid velocity of

The design consequences of this unique behaviour for a fluidised bed heat exchanger can be best explained with the help of the equation below for a heat exchange tube, which has been

**1.0**

≤1.0

**<sup>X</sup> 0.9 1.0**

**: GLASS : 80 °C**

**: WATER**

**: 2.0 mm**


For a comparison of the tube length between different types of exchangers for the same duty and temperatures, Equation (5) can be simplified:

$$L\_t = C\_1 \times \frac{D\_o \times V\_l}{k} \tag{6}$$

Where C1 is a constant for a particular installation/application.

Or in words: The length of the tubes Lt is directly proportional to the diameter of the tube Do , the liquid velocity in the tubes Vl , but inversely proportional to the heat transfer coefficient k. It can be stated that the clean k-values for self-cleaning fluidised bed heat exchangers are always somewhat higher than for the conventional heat exchangers at their normally much higher liquid velocities, with the remark that the clean k-values for the selfcleaning fluidised bed heat exchangers correspond with the design values used for the fullsize self-cleaning fluidised bed heat exchanger with no need for cleaning, while for the conventional heat exchangers due to fouling the design k-value may be 2, 3, 4 or even 5 times lower than the clean k-value and frequent cleanings may be still necessary.

What the design consequences of excellent heat transfer at very low liquid velocities do mean for a self-cleaning fluidised bed heat exchanger in comparison with a conventional heat exchanger for the same application can be best explained with the following striking example:

A conventional Multi-Stage Flash (MSF) evaporator for seawater desalination with a seawater velocity of 1.8 m/s in the condenser tubes of 19.05 × 1.21 mm and an average heat transfer coefficient of 2 500 W/(m²·K) required a total length of the condenser tubes of 173 m. Depending on the design of this seawater evaporator, this tube length requires the installation of 8 evaporator vessels in series, each vessel with a length of 20 m or even more.

The same MSF desalination plant equipped with stationary fluidised bed heat exchangers required a seawater velocity in the tubes of only 0.125 m/s to maintain a fluidised bed in all parallel operating tubes with a porosity of 75 % using glass particles with a density of

Self-Cleaning Fluidised Bed Heat Exchangers

**4.4 Fouling removal** 

always two causes:

evaporators:

fouling liquids.

process of heat transfer.

for Severely Fouling Liquids and Their Impact on Process Design 563

Fouling of heat exchangers is experienced by a gradual and steady reduction in the value of the overall heat transfer coefficient. A closer look into this phenomenon shows that there are

1. Fouling of the actual heat transfer surface by the forming of an insulating layer of

2. Clogging of flow distribution system in the inlet channel and / or the inlets of the heat exchanger tubes by large pieces of dirt or deposits broken loose from the wall of vessel and piping upstream the exchanger and present in the feed flow of the exchanger. Clogging of tubes removes heat exchanger tubes from participation in the actual

The first cause can be solved by the mild scouring action of the fluidised solid particles in the tubes. The second cause, at least of the same importance as the first cause but often neglected, can only be solved by the installation of a strainer upstream the self-cleaning fluidised bed heat exchanger. To minimise the cost for such a strainer and the ground area for the heat exchanger and its accessories, we have developed a proprietary self-cleaning

Now, let us pay attention to some of our fouling removal experiences in a fluidised bed heat exchanger and, therefore, we once more should pay attention to our MSF seawater

It is known that natural seawater cannot be heated to temperatures above 40 to 50 °C because of the formation of calcium carbonate scale. Conventional MSF evaporators often operate at maximum seawater temperatures of 100 °C, but only after chemical treatment of the seawater feed which removes the bicarbonates from the seawater and prevents the forming of scale. Of course, this is a complication in the process and does cost money. The MSF evaporator equipped with the stationary fluidised bed condensers, using 2 mm glass beads, has convincingly demonstrated that it can operate at even much higher temperatures than 100 °C without scale forming on the tube walls. Although, the scale crystals are precipitating from the seawater on the tube walls these crystals are knocked off by the glass beads at an early stage, so that it never comes to the formation of an insulating scale layer and the tube walls remain clean and shiny. Here we have clearly demonstrated the fouling removal, self-cleaning or non-fouling behaviour of a fluidised bed heat exchanger operating under harsh conditions as the result of the scouring action of the fluidised particles. No doubt that this feature is of extreme importance for heat exchangers operating on severely

Meanwhile, with many self-cleaning fluidised bed heat exchangers already installed in different industries, commercial operating experiences have shown that the self-cleaning fluidised bed heat exchanger, which can remain clean indefinitely, is a cost-effective alternative to the conventional heat exchanger which suffers from severe fouling in a couple of hours, days or weeks and even months. Any type of fouling deposit, whether hard or soft; biological or chemical; fibrous, protein, or other organic types; or a combination of the above can be handled by the self-cleaning fluidised bed heat exchanger. Moreover, later in this chapter it will be shown that the unique characteristics of this heat exchange technology allow for the introduction of major design changes of installations in traditional processes

deposits, which reduces the heat transfer through the tube wall.

strainer which forms an integral part with the inlet channel of the exchanger.

2 750 kg/m³ and a diameter of 2 mm. In spite of this low seawater velocity, an overall heat transfer coefficient of 2 500 W/(m²·K) was achieved. From the equations above, it can be concluded that this desalination plant required only 0.125/1.8 × 173 = 12 m condenser tube length in series, which can be installed in only one vessel with an overall height of less than 15 m.

#### **4.3 Pumping power requirements**

Pumping power is influenced by the pressure drop across the heat exchanger and the pressure drop to support a stationary fluidised bed, which is determined by the following equation:

$$AP\_t = L\_t \times \left(\rho\_s - \rho\_l\right) \times \left(1 - \varepsilon\_t\right) \times g \tag{7}$$

Where:


For the MSF desalination plant with stationary fluidised bed condensers specified above, the pressure drop to support the bed weight amounts to 47 000 N/m². On top of this pressure drop we have to add a pressure drop caused by the flow distribution system of 4 000 N/m² for stabilisation of the flow through all tubes. Pressure drop due to wall friction has not to be taken into account because of the very low liquid velocities in the tubes of only 0.125 m/s. However, for this particular application, we have to add the lifting height for the liquid which requires an additional pressure drop of 120 000 N/m² resulting in a total pressure drop of 47 000 + 4 000 + 120 000 = 171 000 N/m².

For the conventional MSF desalination plant we calculate a pressure drop of approx. 400 000 N/m² required by the wall friction in these very long condenser tubes with much higher liquid velocities, and when we take into account the losses in water boxes we end up with a total pressure drop of approx. 450 000 N/m².

It should be emphasised that for this particular application the pressure drop influencing the heat transfer coefficient and required by the condenser bundle installed in the conventional MSF is a factor 400 000 / 51 000 = 7.9 (!!) higher than this pressure drop for the MSF equipped with stationary fluidised bed condensers. These differences in pressure drop directly influence the pumping power requirements for both installations. In general, when also considering 'circulating' fluidised bed heat exchangers operating at somewhat higher liquid velocities and using higher density solid particles, the differences in pumping power requirements will not be that much as presented above, although, for all applications, the differences in pumping power remain easily a factor 2 to 3 times lower for the fluidised bed heat exchanger compared to the conventional shell and tube heat exchanger.
