LMTD â Log mean Temperature Difference. TTD â Terminal .... when calculation the value for multipass exchangers correction factors also must be applied to ...
MONITORING OF HEAT TRANSFER IN COOLING WATER SYSTEMS S. Banerjee1 Abstract: In this era, where coal availability is becoming a significant concern, sustainability requires monitoring systems and tools to reduce any loss of efficiency from any system in a power plant The thermal power plants are designed to generate power based on required conditions or designed conditions viz. coal quality, water quality, ambient conditions and good health of heat transfer surfaces and equipment), but in our Country, due to huge variations in coal mine seams, strata, ambient conditions and surface water quality actually, the conditions are often not as per the designed conditions. In practical situations, when power plants are installed there are lots of constraints. This tends to reduce or increase output power and heat rate of thermal power plants. Due to these conditions, the designed power and heat rate are never achieved. Variations in the power outputs from plant are always a matter of disputes. So the parameters for power and heat rate are generated for different conditions of condenser pressure, flow rate of water through the condenser, Temperature difference. On the basis of site measurement and design data collection performance of the Condenser unit can be evaluated. These evaluations indicate that if operating conditions vary, then power output and heat rate also vary. This paper deals with the factors or parameters which reduced the efficiency of the condenser and proposes a method for monitoring heat transfer surfaces, equipment and cooling tower. This paper focuses on the development of monitoring system for Cooling Water Systems (CWS). The purpose of monitoring is to draw the attention of operating personnel to energy efficiency and to reflect the magnitude of the potential for operational improvement. The challenges are to model the heat transfer rate from the condenser with reasonable accuracy and to ensure that the inferences are proactive or fast enough to be used.
Key words Water, Flow of water, saving energy, power plant, chemicals, hardness, fouling, scaling, Corrosion, Scale, condenser. List of Abbreviations: O&M – Operation and maintenance MUR = Total make-up rate BDR = Total blow-down rate NTU – Nephlometric Turbidity Unit
List of Symbols: CH - Hydraulic factor
CW – Cooling Water CT – Cooling Tower U = Overall heat transfer coefficient LMTD – Log mean Temperature Difference TTD – Terminal Temperature difference
VT - system volume BT - total water loss U - Overall Heat Transfer Coefficient µs/cm – micro siemens per cm - measurement of electrical conductivity INTRODUCTION: All heat transfer processes, involve the transfer of energy and obey the first as well as the second law of thermodynamics. The energy in transit cannot be measured or observed directly, but the effects it produces can be observed and measured. From our viewpoint, the determination of the rate of heat transfer needs special consideration. The transport of heat energy from one region to another occurs by any (or a combination) of similar methods. In literature such three methods of heat transmission are recognized by the terms conduction, convection and radiation respectively. If the flow of heat is a result of transfer of internal energy from one molecule to other, the process is called conduction. Through solids, this is the only possible mode of heat transmission. In liquid and gases, however, the molecules are no longer confined to a certain point but constantly change their positions even if the substance is at rest. The heat energy is transported along with the motion of these molecules from one region to another. This process is called convection. All solid bodies as well as liquids and gases have a tendency of radiating thermal energy in the form of electromagnetic waves and of absorbing similar energy emerging from the neighboring bodies. This type of heat transport is known as thermal radiation. In industrial processes, heat transfer may occur due to one or due to a combination of more than one of these three modes of transport. Basically, a condenser is a device where steam condenses and latent heat of evaporation released by the steam is absorbed by cooling water.
Combined Heat transfer process: In most of the engineering applications, however, heat is transferred in successive steps by similar or different mechanisms. For instance, let us consider the case of heating of water in a tube laid in a heat exchanger (or cooling of hot fluid in shell by CW). The water will receive heat from the products of combustion that emit and absorb radiation. The heat will flow by combination of different modes through successive steps as indicated below (fig 1). Steps 1 2 3 T1
t1 t3
t2 Hot fluid film fig. 1.0
t4 Water film Tube wall
It may be clarified here that the tube wall surface temperatures are different than the fluid temperatures on the respective sides. This can be explained by assuming that a thin layer of fluid adheres to the wall on both sides. The temperature gradient exits only within this thin layer. Considering the temperatures at each step and resistance to heat flow through each step (R) where R1, R2 and R3 are resistances through step 1, 2 & 3 respectively. Since the same quantity of heat is flowing through each step we obtain: q = t1-t2 = t2-t3 = t3-t4 R1 R2 R3
eq. 1.0
= (t1-t2)+(t2-t3)+(t3-t4) R1+R2+R3
eq. 1.1
q = t1 – t4 R1+R2+R3
eq. 1.2
= t1-t4 ∑R
If we designate the reciprocal of the resistance by UA, then: UA =
1 . R1+R2+R3
eq. 1.3
Or q = UA (t1 – t4)
eq. 1.4
This equation represents the heat flow from the hot fluid to water. Here U is known as the Overall unit conductance or the Overall coefficient of heat transfer.
Heat Transfer in Cooling Tower: Two kind of heat transfer occur within the tower between warm water and air. a) Latent heat of vaporization: Some of the liquid changes to vapor with the absorption of heat. This energy, called the latent heat of vaporization, is that necessary to overcome the attractive forces between molecules in the liquid state. Absorption of latent heat accounts for 75-80 percent of the heat transferred in cooling towers. b) As long as the wet-bulb temperature, which is a measure of the heat content of the atmospheric air, is lower than the water temperature heat is transferred from the water to the air, raising its temperature and lowering that of the water. This is called sensible heat; it accounts for the remaining 20-25 percent of heat transferred. Variable affecting performance of CT Heat transfer: The rate at which heat is transferred in a cooling tower depends upon four factors: (1) the area of the water surface in contact with air; (2) the relative velocity of air and water; (3) the time of contact between air and water; (4) the difference between the wet bulb temperature of the inlet air, A, and the temperature of the returned water, R.
Item (1) depends upon the construction of the fill; (2) can be controlled by regulating speed of the fans; (3) is a function of (2) and the height of the tower; (4) is fixed by climate. Wet bulb temperature can be measured with a sling psychrometer. Under ideal conditions, when a stream of unsaturated air passes over a wetted surface water evaporates saturating the air and lowering the temperature of the remaining water. When the water becomes cooler than the air, sensible heat flows from the air to the water, eventually reaching equilibrium at the wet-bulb temperature, where the loss of heat from the water by evaporation is equal to the sensible heat. Thus, as water falls through a cooling tower, the latent heat of vaporization and the sensible heat approach each other so that in an infinitely high structure the temperature of the bulk water would be equal to the wet-bulb temperature of the entering air. In a finite tower, however, it is impossible to achieve zero approach (approach = Supply temperature – wet bulb temperature) because not all the water falling through the structure can contact fresh cool air. One measure of the efficiency of a cooling tower is its approach, which is the difference between the temperature of the cooled water in the basin of the tower and wet-bulb temperature of the atmosphere. The second measure of performance is the cooling range, which is the difference between the supply temperature and return temperature.
The amount o heat rejected by a cooling tower can be calculated from the cooling range and the recirculation rate. This is also known as heat duty. 1 BTU is the amount of heat required to raise the temperature of one pound of water one degree F. Therefore: Heat duty, BTU/hr = gpm (circulation rate) >< 8.34 lb/gal >< Delta T deg F Another important characteristic of a cooling towers performance is L/G, the liquidgas mass transfer ratio: L/G = (water, kg/hr)/(air, kg/hr)
Heat transfer within cooling system (heat exchanger):
Fig. 1.1 The process represented in the above figure (1.1) is one in which hot fluid is cooled by water, which itself heated without any loss of exchanged heat. Industrial heat exchangers consist of a number of tubes enclose in a shell. Exchangers with cooling water in the tubes, and hot product in the shell are the most satisfactory. Fouling often occurs if water is circulated through the shell, because the velocity of the water stream is lower in this design. Tubes are much easier to clean than the shell. Matters are also so arranged that the pressure of the product being cooled is higher than that of cooling water, so that the water cannot leak into the hot product, and damage the equipment. In the figure (t1) temperature of CW inlet; (t2) temperature of CW outlet; (T1) temperature of process inlet; (T2) Temperature of process outlet. Here we will consider CW as cooling water and Process as P.
Now U = ΔHp/ΔtmA 1.0) Where:
(eq-
U = net effective overall heat transfer coefficient (Kcal/0C-h-m2) ΔH = difference in enthalpy of P at T1 and T2 (Kcal/kg) P = flow rate of the product (m3/h) A = area of heat transfer surface (m2) Δtm = the average of the temperature differences at both ends of the exchanger (0C) Δtm = (T1-t2) +(T2-t1) 2
(eq – 1.5)
Here it is assumed that the temperature of the fluid is in the shell falls continuously and uniformly from T1 to T2, while that of the water inside the tubes rises similarly from t1 to t2. With this assumption it is permissible to use the average of the terminal differences for the mean temperature difference. In more complicated heat exchangers, however, it is necessary to use the log mean temperature difference, and when calculation the value for multipass exchangers correction factors also must be applied to (Δtm). (Δt)log e =
(Δt)max - (Δt)min log e [(Δt)max/(Δt)min]
= (T2-t1) – (T1 – t2) log e [(T2-t1)/(T1-t2)]
(eq – 1.6)
(see topic LMTD for detailed description) In a water-tube exchanger U is likely to decrease gradually because of accumulating deposits, or because of scale formation on the tubes. Referring to the figure, the effect of these events on the heat transfer coefficient can be predicted qualitatively. If a thin layer of insulating scale forms on either side of the tube T2 rises and t2 falls as less heat passes from P to CW through the insulating layer. Thus ΔH decreases, and as both t1 and T1 are unaffected by conditions within the heat exchanger, Δt m increases. The net result is that the heat transfer coefficient becomes smaller. If deposits slow the flow of water, t2 and T2 both rise. In this event, however, Δtm may increase and ΔH may decrease by such small amounts that the effect on U may not be significant. The reciprocal of the heat transfer coefficient is called the “fouling resistance,” this number multiplied by one thousand is the “fouling factor.” Except in unusual circumstances the effect of fouling resistances can never be exactly known, as fouling within an actual heat exchanger is seldom uniform, and also the net effect is a combination of conditions on both sides of the heat transfer surface. CONDENSER: In a condenser the condensing fluid (hot fluid) remains at constant temperature throughout the exchanger while the temperature of the colder fluid gradually increases from inlet to outlet. Similarly in an evaporator the boiling fluid (cold fluid) remains at constant temperature while the hot fluid temperature gradually decreases. The temperature distribution in condenser is shown below. Since the temperature of one of these fluids remains constant, it is immaterial whether the two fluids flow in the same direction of opposite direction.
Tsat
t1
fig. 1.4
t2o t2i
Area
BASIC CALCULATION: The general equation for heat transfer across a surface is: Q = UA Δtm
(eq – 1.7)
Where Q = heat transferred per unit time (W) U = the overall heat transfer coefficient (W/m2 oC) A –heat-transfer area, m2, Δtm = the mean temperature difference, the temperature driving force, oC. The overall coefficient is the reciprocal of the overall resistance to heat transfer, which is the sum of several individual resistances, is given by: 1 = 1 + 1 + (doIn(do/di)) + do >< 1 + do >< 1 Uo ho hod 2kw di hid di hi
(eq – 1.8)
Where Uo = the overall coefficient based on the outside area of the tube, W/m2 oC, ho = outside fluid film coefficient, W/m2 oC, hi = inside fluid film coefficent, W/m2 oC, hod = outside dirt coefficient (fouling factor), W/m2 oC, hid = inside dirt coefficient, W/m2 oC, kw = thermal conductivity of the tube wall material, W/m2 oC, di = tube inside diameter, m, do= tube outside diameter, m. The magnitude of the individual coefficients will depend on the nature of the transfer process (conduction, convection, condensation, boiling or radiation), on the physical properties of fluids, on the fluid flow-rates, and on the physical arrangement of the heat transfer surface. Log Mean Temperature difference (Temperature driving force): Before equation (eq – 1.7) can be used to determine the heat transfer area required for a given duty, an estimate of the mean temperature difference Δtm must be made. This will normally be calculated from the terminal temperature differences: the difference in the fluid temperatures at the inlet and outlet of the exchanger. Condensation of Steam: The mean temperature difference is given here: A pure, saturated, vapour will condense at a fixed temperature, at constant pressure. For an isothermal process such as this, the simple LMTD can be used in equation 1.3; no correction factor for multiple passes is needed. The LMTD will be given by: ΔT m =
(t2 – t1) (eq. 1.34) ln [(Tsat-t1)/(Tsat-t2)]
Where T sat = t1 = t2 =
saturation temperature of the vapour, inlet coolant temperature, outlet coolant temperature.
When the condensation process is not exactly isothermal but the temperature change is small; such as where here is a significant change in pressure; the LMTD can still be used but the temperature correction factor will be needed for multipass condensers. The appropriate terminal temperatures should be used in the calculation. Overall heat transfer coefficient: An important parameter in the design and monitoring of heat exchangers is the overall heat transfer coefficient, U, between the two fluids. A value for U can be easily obtained by knowing the followings: 1. Mass flow of the fluid, 2. Specific heat of the fluid, 3. Difference in temperature of the fluid across the heat exchanger, 4. Inlet and outlet temperature of both the fluids involved in heat exchanger and 5. Area of the heat transfer surface. From the equation Q = m.cp. Δt Calculating Q in watts: Where m = mass flow in kg/hr of kg/sec Cp= specific heat or heat content in KJ/Kg K Δt= Temperature difference across the heat exchanger. Calculating LMTD from the following equation with the inlet and outlet temperatures of the hot and cold fluid across the heat exchanger and with the knowledge of type of heat exchanger using: (For multipass heat exchangers) ΔT m = (∆T max) – (∆T min) ln [(∆T max)/(∆T min)] Where ΔT m = log mean temperature difference, T1 = inlet shell side fluid temperature, T2 = outlet shell side fluid temperature, t1 = inlet tube side temperature, t2 = outlet tube-side temperature, OR (for single pass heat exchanger) Δtm = (T1-t2) +(T2-t1) 2 We can calculate U from the equation Q = UA Δtm Where Q = heat transferred per unit time (W) U = the overall heat transfer coefficient (W/m2 oC) A –heat-transfer area, m2, Δtm = the mean temperature difference, the temperature driving force, oC.
U=
. Q . A Δtm
(eq. 1.14)
Elaborated method for calculating overall heat transfer coefficient: A general expression for U can be easily obtained as follows. Consider a double pipe heat exchanger in which one fluid through the inner pipe and the other fluid through the annular space between space between the two pipes. Let
L ri ro Ai Ao hi
= length of heat exchanger, m = inside radius of inner pipe, m = outside radius of inner pipe, m = inside surface area of inner pipe (2πriL), m2. = outside surface area of inner pipe (2πroL), m2. = film coefficient of heat transfer at inside surface of inner pipe, W/m2
ho W/m2 C kw ti to
= film coefficient of heat transfer at outside surface of inner pipe,
C
Ri Ro Rw (i)
Where Since
= thermal conductivity of inner pipe wall, W/m C. = temperature of fluid flowing through the inner pipe, C = temperature of fluid flowing through the annular space between the two pipes, C = thermal resistance of fluid film at the inside surface of inner pipe, m2 C/W = thermal resistance of fluid film at the outside surface of inner pipe, m2 C/W = thermal resistance of inner pipe, m2 C/W
The rate of heat transfer between the two fluids is given by: q = ti - to ΣR
(eq 1.15)
ΣR Ri Rw
= Ri + Ro +Rw = 1/Aihi = ln (ro/ri) 2πLKw
(eq. 1.16) (eq. 1.17) (eq. 1.19)
Ro
= 1/Aoho
(eq. 1.20)
q
=.
Hence (ti - to)
.
(eq. 1.21)
1/Aihi + ln (ro/ri) + 1/Aoho 2πLKw (ii) If Ui and Uo denote respectively the overall heat transfer coefficient based on unit area of the inside and outside surfaces of the inner pipe, then
q
= AiUi (ti - to) = AoUo (ti - to)
from eq. 1.21 and 1.22 Ui
Uo
=.
(eq. 1.22)
1 1/hi + Ai ln (ro/ri) + [Ai/Ao]. 1/ho 2πLKw
=.
1
(eq. 1.23)
(eq. 1.24)
[Ao/Ai].1/hi + [Ao/2πL].ln (ro/ri) + 1/ho Kw (iii) Since Ai = 2πriL and Ao = 2πroL, eq. c and d can also be written as: Ui
=.
1
(eq. 1.25)
1/hi + [ri/kw] ln (ro/ri) + [ri/ro]. 1/ho Uo
=.
1
(eq. 1.26)
[ro/ri].1/hi + [ro/ Kw].ln (ro/ri) + 1/ho
Effect of scale formation: In most heat exchangers some scale formation will take place on both sides of the heat transfer surface after the heat exchanger has been in use for some time (unless scale inhibition mechanism is in place). This introduces two additional resistances in the heat flow path. Thus the total thermal resistance becomes: ΣR
= Ri + Rsi +Rw + Rso + Ro
(eq. 1.27)
Where Rsi = thermal resistance due to scale formation on inside surface of inner pipe, m2 C/W Rso = thermal resistance due to scale formation on outside surface of inner pipe, m2 C/W (We can here consider no scaling on outside surface of inner pipe) Since it is difficult to ascertain accurately the thickness and thermal conductivity of the scale formed, the effect of scale deposit on heat flow is generally taken into account by specifying an equivalent scale heat transfer coefficient, hs. The reciprocal of the scale heat transfer coefficient is called the fouling factor. If h si and hso denote the heat transfer coefficient for the scale formed on the inside and outside surface of he inner pipe, then: Rsi
= 1/Aihsi
(eq. 1.29)
Rso
= 1/Aohso
(eq. 1.30)
And q = .
(ti - to)
(eq. 1.31)
1/Aihi + 1/Aihsi + ln (ro/ri) +1/Aohso + 1/Aoho 2πLKw Ui
=.
1
(eq. 1.32)
1/hi + 1/hsi + Ai ln (ro/ri) + [Ai/Ao]. 1/hso + [Ai/Ao]. 1/ho 2πLKw or Ui
=
1
(eq.
1.33)
1/hi + 1/hsi + [ri/kw] ln (ro/ri) + [ri/ro]. 1/hso + [ri/ro]. 1/ho The fouling factor (1/hs) for some representative applications are listed in following table: Fluid Distilled water Sea water Well water Treated boiler feed water Fuel oil and crude oil Steam, non-oil bearing
Fouling factor (1/hs) (m2/K/W) 0.000086 0.000172 0.000344 0.000172 0.00086 0.00009
Condenser, where the hot fluid temperature varies: In some type of heat exchanger, the temperature of both the fluids is varying and there fore logarithmic mean temperature will have to be calculated. The temperature changes of water and hot fluid may be represented graphically by the following figure. During the process the hot fluid will reject heat in the following manner: (a) (b) (c)
To cool down to saturation temperature, (process DC) To liquefy (process CB) To subcool the liquid (process BA)
At the same time the water will receive heat and will get heated from tc1 to tc2.
This type of condenser may be assumed to consist of three sections i.e. (i) desuperheater (ii) liquefier (iii) subcooler. Subcooling
Condensation
Desuperheating th1
th3
th2
th4
tc2
tc1 A B Heat transfer in a condenser
C
D
Here if th1, 2, 3 & 4 is known then LMTD of each section can be calculated and average mean temperature difference is approximately given by: ΔT m =
total heat rejection (HR) (kJ/min) (eq. 1.35) (HRD-C/ ΔT m (D-C)) + (HRC-B/ ΔT m (C-B)) + (HRB-A/ ΔT m (B-A))
And then with this LMTD values for Q and/or U can be calculated. Significance of pressure: The cold and hot fluid inlet and outlet temperature and ΔP of the fluids across the heat exchangers are very significant in determination of the health of that heat exchanger. In condensers, the steam/condensate ΔP is shown as vacuum. Any increase in cooling waterside ΔP or decrease in steam/condensate vacuum is an indication of fouling or decrease in flow rate of the fluids. Increase in ΔP for hot fluid when the inlet hot fluid P remains same, across a heat exchanger could be due to fouling on the heat-exchanging surface exposed to the hot fluid. The same applies to CW side. An increase of ΔP with an increase in inlet P is very much possible. In condensers the decrease in vacuum could be due to fouling on heat-exchanging surface on both or either side. Most probably it will be due to fouling of heatexchanger surface on CW side. In condensers the decrease in vacuum could also be due to leakage from the heat-exchanging surface or from the surface exposed to atmosphere. Change in ΔP Increase, in hot fluid
Decrease, in hot fluid Increase, in cold fluid
Indication Increase in flow-rate of hot fluid Fouling on HE surface on hot-fluid side Decrease in flow-rate of hot fluid Leakage on hot fluid path. Increase in flow-rate of cold fluid
Fouling on HE surface on cold-fluid side Decrease in flow-rate of cold fluid Leakage on cold fluid path.
Decrease, in cold fluid
It is important to know the design pressure on both sides (hot & cold). The highpressure fluid may ingress in low-pressure fluid. Normally the hot fluid pressure is higher than cold fluid pressure.
Significance of flow-rates: Flow-rates and any change in flow-rates have different effects on Q and U values. Following are the effects: Changes If hot fluid flow rate is increased
Effects The ΔP of hot fluid across the heat exchanger will increase. The inlet P of hot fluid will increase The ΔT of hot fluid will decrease The ΔT of cold fluid will increase The Q value will increase is Vice-versa of the above effects
If hot fluid flow rate decreased If cold fluid flow rate is The ΔP of cold fluid across the heat exchanger increased will increase. The inlet P of cold fluid will increase The ΔT of cold fluid will decrease The ΔT of hot fluid will increase The Q value will increase The fouling/scaling propensity of Cold fluid will decrease The flow induced corrosion/erosion may increase If cold fluid flow rate is The ΔP of cold fluid across the heat decreased exchanger will decrease. The inlet P of cold fluid will decrease The ΔT of cold fluid will increase The Q value will decrease The fouling/scaling propensity of Cold fluid will increase – Avoid such situations
Methods of checking steam condenser performance: It is desirable to get a rated load or some agreed-upon load on the turbine which will be the same for each successive check and read the load, air leakage, inlet water temperature, outlet water temperature and the absolute pressure in the condenser, and convert the absolute pressure into the corresponding saturated steam temperature; also, calculate the temperature rise, initial temperature difference and terminal difference. The terminal difference is the difference between the steam temperature and the outlet water temperature; the temperature rise is the increase in the CW temperature. The initial temperature difference is the difference between the inlet water temperature and the steam temperature (or the saturation temperature corresponding to the absolute pressure). If this data is recorded periodically and checked, any deviation will give the operator the best indication of what has been happening to his condenser. During a period of high air leakage, when air blankets tube surfaces, the absolute pressure, air leakage, steam temperature and terminal difference will rise and again upon correcting the leakage, will return to normal. Also, during a period of dirty condenser tubes, the absolute pressure, steam temperature and terminal difference increases and after cleaning will return to normal. This holds true with non-condenser type heat exchanger. Other factors: Other factors, which would affect the condenser trend, are the change in water inlet temperatures and change in loads. These changes do not affect the condenser performance although they change most of the condenser temperature values and do change the condenser backpressure. As a guide to condenser performance the terminal difference gives the operator the alarm and should be watched carefully. Data taken at a different lad may be compared to that at the desired load by the following device. Load to the condenser, either in terms of BTU per hour or kw load plotted against rise and initial temperature difference. “Rise” will be a straight line from zero at no load to maximum rise at full load. Disregarding the effects of air leakage and vacuum pump capacity and some of these matters in the very low load range, the initial temperature difference will also be a straight line. Operators should watch pump discharge pressures and pump horsepower for clues as to tube sheets plugged by rubbish accumulation. These indications can also be obtained from delta P of CW across the condenser. Poor heat transfer due to tube fouling will affect vacuum performance at all loads but will be most noticeable at high loads. Circulating water pump data to approximate water flow, which with rise in circulating water temperature gives another approximation of heat load. The condenser performance is evaluated, expressed as percentage: % = U actual >< 100 U designed
U actual can be calculated as: U = Q/A∆Tlmtd U actual = actual heat transfer rate, btu/hr/sq ft/deg F Lmtd Q = duty, Btu/hr References: 1. Engineering Heat Transfer by Shri. C. P. Gupta & Shri. Rajendra Prakash 2. The Nalco Water handbook by NALCO company 3. Engineering Chemistry by Shri. P. C. Jain and Ms. Monika Jain 4. Outline of Chemical Technology by Shri. M Gopal Rao and Marshall Sittig
