Abstract:
Scale deposition on a heat transfer surface in a liquid system such as a heat exchanger is estimated by directing of small portion of the liquid flow through a test cell, consisting of a sensor positioned on and projecting through a conduit wall. The sensor consists of a conductive block containing a heater and having a heated wetted test surface that is flush with the inside of the conduit wall and in contact with the flow through the conduit. Within the conductive block are two temperature sensors which are at different distances from the heated wetted test surface and the heater. The periphery of the apparatus is designed to reduce heat flow through the periphery and allow greater heat flow through the heated wetted test surface. By comparing the temperature differential between the two temperature sensors to the differential when no scale is present, the presence of and amount of scale can be determined, based on reduced heat transfer through the heated wetted surface caused by the accumulated scale. The change in the temperature differential is directly proportional to the scale thickness for a given type of scale. When the thickness of the scale is determined by another means, the nature of the scale can be implied. The sensitivity of the measurement can be adjusted to accommodate a very wide range of bulk liquid or ambient temperature via adjustment of the heat flux through the provided secondary heat flux path.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of and priority to U.S. Provisional Application Ser. No. 61/739,785, filed Dec. 20, 2013 and entitled “METHOD AND APPARATUS FOR ESTIMATING FOULING FACTOR AND/OR INVERSE SOLUBLE SCALE THICKNESS IN HEAT TRANSFER EQUIPMENT”, the disclosure of which is incorporated by reference herein in its entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     Industrial plants, such as power plants, steel mills, pulp or paper making plants, have relatively complex water/fluid systems. Organic and inorganic matter deposits on the inner walls of these systems forming an accumulation of fouling or scaling deposits which interfere with the proper operation of the system. This is particularly severe on heated surfaces such as heat exchanger surfaces. This is an unwanted occurrence that causes a number of operational problems such as inadequate heat exchange, plugging of equipment, inefficient usage of chemicals, increased utility costs, lost production due to downtime, corrosion, and downgraded products from increased dirt counts. 
     In principle, one can distinguish between fouling deposits on the one hand and scaling deposits on the other hand. Fouling deposits are organic deposits which often occur in the form of biofilms in aqueous systems. Such biofilms substantially consist of micro-organisms, e.g. bacteria, algae, fungi and protozoa. Scale is formed from inorganic matter such as complexes of calcium (carbonate, oxalate, sulfate, silicates), aluminum (silicates, hydroxides, phosphates), barium sulfate, radioactive radium sulfate, and silicates of magnesium. 
     In order to avoid the accumulation of fouling deposits and in particular the growth of biofilms, biocides are added into the fluid concerned as countermeasures. Scale deposits can be removed or prevented by adding chemical deposit control agents based on homopolymers, copolymers and terpolymers of acrylic acid, methacrylic acid, maleic acid and aspartic acid. Chemical deposit control agents include organic phosphonates and their derivatives, as well as polyphosphates. The dosage of these biocides and chemical deposit control agents should be controlled very carefully because they are very expensive. 
     In line sensors are particularly useful in detecting and quantifying scale for controlling the addition of scale treatment additives. High temperature scaling conditions present a significant challenge to developing an in line scale sensor. Such flows generally preclude the use of most non-metal materials for any surface that is in contact with the flow, and also can be challenging environments for proper operation of electronic components. In addition, the liquid comprising the flow may have other properties that make sensor development difficult; the flow can contain particulates, be toxic, be corrosive to some material, not have constant density, etc. For example, cooling water may have a significant content of dissolved salts, but it is still called water. In many industries, water with a high content of dissolved salts may be called brine, although that term is usually applied to solutions of highly soluble salts. In pulp producing mills, water with certain dissolved salts and dissolved lignin may be called black liquor. Even solutions of highly soluble salts can accumulate troublesome amounts of inverse soluble salts that accumulate in the water for various reasons. Since the most common scale type is inverse soluble scale, the sensor needs to have a surface exposed to the flow that is at a higher temperature than the bulk liquid flow. This requires some form of heating, to produce a heated wetted test surface that is predisposed for the accumulation of scale. The heating must be accomplished in a manner that allows the accumulation to be quantified. This quantification may be a measurement of the reduced heat transfer capabilities resulting from the accumulation, or of the thickness of the accumulation, or both. 
     SUMMARY OF THE INVENTION 
     The present invention is premised on the realization that fouling factor (reduced heat transfer effectiveness due to the buildup of inverse soluble scale on a heat transfer surfaces) can be estimated by diverting a small amount of working fluid through a flow cell, across a heated wetted test surface, in which the heated wetted test surface temperature and the flow conditions over it mimic the heat transfer surface of interest. The heated wetted test surface is either an integral part of a block of material capable of conducting heat (conductive block) or is in intimate contact with said block. Heat is supplied to the conductive block by a simple cartridge heater contained at least partially within the conductive block, or by other appropriate means. The conductive block is provided with insulation around it such that the primary heat conduction plate is toward the heated wetted test surface and such that there is at least one secondary heat conduction path away from the heated wetted test surface. As scale accumulates on the heated wetted test surface, the scale presents an added resistance to heat transfer towards the heated wetted test surface. The heat transfer resistance along the secondary heat conduction path is not affected by the accumulation of scale. Therefore, as scale accumulates there is reduced heat transfer toward the heat wetted test surface and increased heat transfer along the secondary heat conduction path. Measurement of the heat transfer resistance added by the scale on the heated wetted test surface is taken as an indication of the severity of scale on the heat transfer surface. 
     The surface temperature of the flow cell heated wetted test surface is estimated by the use of two highly accurate temperature sensors/transmitters, which are spaced at a known distance from each other and at different and known distances from the heated wetted test surface and the heat source, within a conductive block. A heat conduction coefficient (k) for the conductive material comprising the block is calculated from the temperature difference reported by the two temperature transmitters (T 1  and T 2 ) and the known distance between them. The surface temperature of the heated wetted test surface is then estimated from the conduction coefficient and the distance from either temperature transmitter to the heated wetted test surface. As inverse soluble scale accumulates on the heated wetted test surface, the scale provides an additional restriction to the heat flow path through the conductive block to the heated wetted test surface, thus raising the temperature within the block as measured by both temperature transmitters. With a higher internal temperature, more heat exits via the secondary heat conduction path. This results in a reduced temperature differential between the two temperature transmitters, because less heat energy is exiting through the heated wetted test surface. If the temperature at the end of the secondary heat conduction path is constant or nearly so, the temperature difference between the two temperature transmitters in the conductive block is linear with the fouling factor which results from the accumulated scale on the heated wetted test surface, and indicative of the likely degree of fouling or scaling on the commercial heat transfer surface it emulates. The temperature differential between the two temperature transmitters is also linear with the scale thickness for any particular type of scale, but the relationship constant between temperature differential between the two temperature transmitters and scale thickness is different for different types of scale (e.g. calcium carbonate vs. calcium sulfate or calcium phosphate). 
     In a further embodiment, scale thickness on the heated wetted test surface can be concurrently measured via a pulsed ultrasonic signal, on the principle of time of flight reduction due to reduced distance for the ultrasonic pulse to travel to the scale and then return to the ultrasonic probe, as scale accumulates. 
     The range of the temperature differential between the two temperature transmitters can be controlled by many means, including varying the distance between the temperature transmitters, the temperature of the heater, the thickness of the insulation along the secondary heat conduction path, the heat conduction properties of the material from which the secondary heat path is constructed, the existence of more than one secondary heat conduction path, the temperature at the end of or along the secondary heat conduction path, addition of a layer of material with a different heat transfer coefficient as the heated wetted metal surface, or even the addition of heat or cooling at the end of the secondary heat conduction path. 
     By adjusting these variables, a usefully accurate indication of fouling factor can be determined across a very wide range of bulk liquid temperatures, bulk liquid flow rates, heater temperatures, and ambient environment surrounding the apparatus. When combined with an optional ultrasonic or other scale thickness indication, useful insight into the nature of the deposit can be inferred. This allows the scale control treatment to be adjusted in a more appropriate manner, to optimize heat transfer and minimize cost for a specific commercial heat transfer installation. 
     The objects and advantages of the present invention will be further appreciated in light of the following detailed description and drawings in which: 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagrammatic depiction of the present invention with an indication of temperature sensor locations; 
         FIG. 2  is a diagrammatic view, partially in cross section, of an alternate embodiment of the present invention; 
         FIG. 3  is a diagrammatic view similar to  FIG. 1  of a second alternate embodiment of the present invention; 
         FIG. 4  is a cross sectional diagrammatic view of a third alternate embodiment of the present invention; 
         FIG. 5  is a diagrammatic cross sectional view of a fourth alternate embodiment of the present invention; 
         FIG. 6  is a diagrammatic cross sectional view of a fifth alternate embodiment of the present invention; 
         FIG. 7  is a diagrammatic cross sectional view of a sixth alternate embodiment of the present invention; 
         FIG. 8  is a diagrammatic cross sectional view of a seventh alternate embodiment of the present invention; 
         FIG. 9  is a graph showing a change in temperature differential as scale accumulates; 
         FIG. 10  is an exploded partial cutaway drawing of the particular embodiment of the device of the present invention used to produce the data found in the graph shown as  FIG. 9 ; 
         FIG. 11  is a diagrammatic cross section of an alternative embodiment of the heated conductive block component of the present invention; 
         FIG. 12  is a graph showing the effect of material  30  conductivity on temperature difference with a scale formation of 200 microns; 
         FIG. 13  is a graph showing the effect of material  30  thickness on temperature difference with 200 micron scale; 
         FIG. 14  is a graph showing the effect of material  16  thickness on temperature difference with 200 micron scale; 
         FIG. 15  is a graph showing the effect of material  16  conductivity on temperature difference with 200 micron scale; 
         FIG. 16  is a graph showing the temperature differential vs. scale thickness; 
         FIG. 17  is a graph showing the temperature differential vs. scale thickness wherein the temperature T 4  is varied; and 
         FIG. 18  is a graph showing the temperature differential with the same conditions as in  FIG. 17  except in the high T scale  cases the power to the heater is 500 watts instead of 200 watts. 
     
    
    
     DETAILED DESCRIPTION 
     As shown in  FIG. 1 , an apparatus or sensor  10  used to detect scale formation on surfaces of a water system is located in a side conduit  11  of a water system. This side channel  11  takes water from the water system and subsequently returns this to the water system. The water system (not shown) can be any industrial water treatment system, such as a power plant, oil refinery, paper mill, or steel mill. The sensor is designed to measure scale accumulation on a surface with a temperature higher than the temperature of the bulk water. 
     The sensor  10  includes a heater  14  positioned within a conductive block  16  which includes a first temperature sensor  18  located at a first position in the metal block and a second temperature sensor  20  positioned within the conductive block  16 . The first temperature sensor  18  is positioned near a heated wetted test surface at a first end  22  of the block, and the second temperature sensor  20 , as shown, is near the heater  14 . The apparatus further includes a second end  24  opposite the heated wetted test surface at the first end  22 , which is as shown is exposed to ambient conditions. Heater  14  is a cartridge heater, which is positioned within conductive block  16  and which allows heat flow toward and away from the heated wetted test surface  22 . Although it can be formed from any suitable material, it will generally be metal. As shown, the heated wetted test surface  22  is in contact with the bulk water flow and therefore serves as the test surface, specifically the heated wetted test surface. 
     The apparatus  10  has four peripheral sides  26  (two shown). The peripheral sides  26  include an insulation layer  28  and the second end  24  includes an insulation layer  30  which may have a different heat conductivity than the insulation layer  28 . 
     The apparatus  10  is fixed to conduit  11  having walls  32  and  34 , with the heated wetted test surface at the first end  22  of conductive block  16  attached to the wall  32 , by means of appropriate fasteners such as screws, bolts, or clamps (not shown), but insulated from direct contact with wall  32  by means of insulation  33  to avoid conductive heat transfer. Ideally no heat is transferred from block  16  to wall  32  of conduit  11 . If little or no heat is transferred from the conductive block  16  to wall  32  of conduit  11 , the temperature across the heated wetted test surface  22  will be relatively even, and so will produce a more representative indication of the much larger commercial heat transfer surface it is attempting to emulate. The heated wetted test surface is flush with the inside surface of the side  32  of conduit  11  to minimize the disruption of flowing bulk liquid  36  in conduit  11 . 
     As shown, the conduit  11  is rectangular in shape. The conduit  11  directs fluid from a water system (not shown), particularly one which has a heated surface, such as a heat exchanger. The conduit simply draws off bulk water which flows in the direction of arrow  36  through the conduit  11 , ideally at flow conditions comparable to those in the commercial heat transfer equipment it is intended to emulate. 
     In operation, the heater  14  generates heat flow or heat flux as shown by arrow  38  towards the heated wetted test surface  22 . Test surface  22  is heated to a temperature approximating the temperature of the section of the heat exchanger or other water system heat transfer surface it is to emulate. Thus, the heated wetted test surface  22  is heated by the heater and wetted by the flow of fluid through conduit  11 . As a result, there is a likelihood that a layer of scale  40  will form on the heated wetted surface  22 . Temperature sensor  18  will record the temperature T 1  near the heated wetted surface  22 . The second temperature sensor  20  will report the temperature T 2  of block  16  adjacent the heater  14 . Since the heater  14  is located within the conductive block  16 , heat can flow outwardly from the second end  24  of the apparatus  10  as shown by arrow  42 . This is the secondary heat conduction path. 
     When the heater  14  is activated, initially heat flow will be in the direction of arrow  38  and T 2  will be recorded, and subsequently T 1 , which should be less than T 2 . As heat passes through the wetted surface  22  into the bulk flow as represented by arrow  36 , in other words, the heated wetted test surface is being cooled down, in turn making T 1  less than T 2 . 
     As scale  40  builds up on heated wetted test surface  22 , less heat will flow through the end  22  of the block  16 . The scale  40  acts as an insulator; heat transfer resistance is increased. Because the heat can travel rearwardly in the direction of arrow  42 , the temperature T 1  and T 2  will both increase because of reduced heat flow through the heated wetted test surface  22  due to the insulation effect of the scale  40 . However, since the temperature of block  16  is now higher, more heat energy will escape through the partially insulated second end  24  of block  16 , the secondary heat conduction path. This will reduce the temperature differential between T 1  and T 2  and provide an indication of scale formation, and the magnitude of the change in the temperature differential is an indication of the amount of scale, and, in particular, the negative impact of the scale on the heat transfer through the heated wetted test surface  22  of block  16 . 
     The heat transfer is governed by the following equations 
     
       
         
           
             
               
                 
                   q 
                   scale 
                 
                 A 
               
               = 
               
                 K 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         T 
                         2 
                       
                       - 
                       
                         T 
                         1 
                       
                     
                     
                       δ 
                       b 
                     
                   
                   ) 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   q 
                   total 
                 
                 A 
               
               = 
               
                 K 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         T 
                         3 
                       
                       - 
                       
                         T 
                         4 
                       
                     
                     
                       δ 
                       ⁢ 
                     
                   
                   ) 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   q 
                   total 
                 
                 A 
               
               = 
               
                 
                   
                     q 
                     scale 
                   
                   A 
                 
                 + 
                 
                   
                     q 
                     insul 
                   
                   A 
                 
               
             
           
         
       
     
     K is the conduction heat transfer coefficient for the respective materials, scale, insulation and metal. A is area, and q is the heat flux of heat energy. The heat transfer is two directional, in the direction of arrow  38  (toward the heated wetted surface) and in the direction of arrow  42  (the opposite direction, through end  24 , the partially insulated path to the ambient environment). As scale builds up on the heated wetted test surface  22 , the “resistance” to heat transfer in the direction of the heated wetted test surface increases. The “resistance” to heat transfer in the opposite direction is unchanged, thus q scale  decreases and q insul  increases with the associated ΔTs (both T 2 −T 1  and T 3 −T 4 ) changing accordingly and linearly with scale thickness. Either T 2 −T 1  or T 3 −T 4  could be used to estimate the accumulation of scale and its resulting heat transfer reduction. 
     Note that T 4  the temperature of the second end  24  will change with environmental conditions which will change the heat flux. Also the insulation along the peripheral surfaces  26  is assumed “perfect” which is not attainable in actual installations. There will be some radial heat flux in actual implementations and this heat flux will also be impacted by environmental conditions. In a non-quantitative sense, if the insulation of the peripheral surfaces  26  are assumed to be partially insulated also, as they would be in an actual installation, the combined area of end  24  and sides  26  can be conceptually thought of as the secondary heat conduction path. 
       FIG. 2  shows an alternate embodiment of the present invention. The scale sensor  10  is incorporated on conduit  11 , as shown in  FIG. 1 . In addition, a scale thickness measuring unit  50  is incorporated in wall  34  of conduit  11  directed at wall  32 . The scale thickness measuring unit  50  is mounted in an opening in wall  34  of conduit  11  such that the surface of measuring unit  50  is flush with the inside surface of wall  34  of conduit  11  to minimize disruption of the flow  36 . Any known means of attachment, such as screws or bolts, clamps, or threads (not shown) may be used. Since the thickness measuring unit  50  does not use a heater and is not involved in heat transfer, it is not necessary to insulate it from contact with the wall  34  of conduit  11 . 
     The measuring unit  50  comprises an ultrasonic transducer  52  and a detector. The ultrasonic transducer is but one of several methods to detect the thickness of the deposit on surface  32 . Any known apparatus can be employed in the present invention. With unit  50 , an ultrasonic signal  54  is emitted by the transducer  52  towards wall  32 . In order to detect and analyze fouling and/or scaling deposits  40  accumulated on the heated wetted test surface  22  of block  16 , an ultrasonic reflection signal  56  which occurs through a reflection of the ultrasonic emission signal  54  is measured. If no deposits  40  are accumulated, heated wetted test surface  22  mainly serves as a reflecting surface for the ultrasonic signal. The measuring unit will measure the time required for the signal to travel to heated wetted test surface  22  and back. If scaling and/or fouling deposits  40  cover the reflecting heated wetted test surface  22 , the ultrasonic signal is reflected at least partially at the surface of the deposits  40 . 
     If scale is present, the reflected signal requires less time to return, due to the shorter distance it travels after reflecting off the scale surface than earlier, when no scale was present. The thickness of the scale can be calculated based on the difference between the current “time of flight” measurement and a previous reference measurement when no scale was present, and the speed at which sound travels through water. 
     There are many different types of compounds that can form scale, such as carbonates, oxylates, sulfates, silicates, of calcium, aluminum compounds such as silicates, hydroxides, phosphates, as well as others. The different types of scale have different densities and different heat transfer resistance coefficients per unit of scale thickness. By measuring the q scale  and the thickness of the deposited scale, one can estimate the type of scale that is forming based on this empirical data. This will in turn allow the operator to apply appropriate remedial chemicals to the water system to remove or control that particular type of scale, or, in the event of a biofilm, the appropriate chemicals to treat the biofilm. 
     If only a biofilm is present, the reflected wave  56  will actually comprise a first small peak from reflection of the surface of the biofilm and a second higher peak from the reflection of the inner wall  32 . The amplitudes of the two signals are different because the acoustic impedance of the biofilm is lower than the acoustic impedance of the wall material  32 . The time difference between the two signals will indicate the thickness of the biofilm. 
     Scaling Tests 
     The apparatus of  FIG. 2  is shown in more detail in a cross sectional view shown at  FIG. 10 . In this embodiment, thickness measuring unit  50  is mounted in an opening  51  in wall  34  of conduit  11 , separated from the wall by a gasket  53 . Opposite the thickness measuring unit  50  is the sensor  10 . As shown, it is mounted in an opening  55  of conduit wall  32 , separated from the wall by a plastic insulater  33  which, in turn, is separated from the block  16  and the wall  32  by gaskets  57 . The block  16  includes a mounting flange  59 . Although the heat sensors are not shown, these would be located in channels  61  and  62  respectively, with the cartridge heater  14  located in enlarged channel  63 . All of this is encased by a PEEK insulator  64 . 
     The apparatus shown in  FIG. 10  (which included a 200 watt cartridge heater, a CuNi heated wetted test surface, two RTD temperature transmitters, PEEK (Polyether ether ketone) insulation, and a pulsed ultrasonic transducer for measuring distance to the heated wetted test surface via “time of flight” difference) attached to a cooling tower was tested using water as the bulk liquid. Block  16  was constructed of CuNiFeMg alloy. The test surface was about 14 mm from the center line of the cartridge heater. RTD temperature transmitters T 1  and T 2  were about 3.5 mm centerline to centerline and were offset along the direction of the heat flux from the heater toward the test surface to avoid interference of one transmitter from the another. Salts were added to deionized water to simulate 4 times concentration of our standard makeup water (e.g., the water was formulated to simulate standard makeup water that had been “precycled” to 4 cycles of concentration) and the water was circulated through the tower system, and allowed to cycle up to a target 6 cycles of concentration. The composition of the “precycled” water, the tower makeup water, and the 6 cycles of concentration water are listed in Table 1. 
     
       
         
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Cooling tower water data for the scaling trials, starting 20 Aug. 2012 
               
             
          
           
               
                   
                   
                   
                 Total 
                   
                   
                   
               
               
                   
                 Ca ++   
                 Mg ++   
                 Alkalinity 
                 Cl −   
                 SO 4   =   
                 Drew 2235 
               
               
                   
                 (as ppm 
                 (as ppm 
                 (as ppm 
                 (as ppm 
                 (as ppm 
                 (ppm 
               
               
                 Water type 
                 CaCO 3 ) 
                 CaCO 3 ) 
                 CaCO 3 ) 
                 Cl) 
                 SO 4 ) 
                 product) 
               
               
                   
               
             
          
           
               
                 Pre-cycled water 
                 400 
                 200 
                 400 
                 2856 
                 192 
                 110 
               
               
                 (simulates 4 cycles of 
                   
                   
                   
                   
                   
                   
               
               
                 concentration) 
                   
                   
                   
                   
                   
                   
               
               
                 System makeup water 
                 100 
                 50 
                 100 
                 714 
                 48 
                 27.5 
               
               
                 Target water 
                 600 
                 300 
                 600 
                 4284 
                 288 
                 165 
               
               
                 (simulates 6 cycles of 
                   
                   
                   
                   
                   
                   
               
               
                 concentration) 
               
               
                   
               
             
          
         
       
     
     The tower was maintained at 24.5 C bulk water temperature, and with conductivity-initiated blow down/and level-controlled makeup water addition to control conductivity at about 3500 μmho (6 cycles of concentration which was reached about 60 hours after the start of scale Trial 1). The flow velocity in the conduit  11  was 0.75 meters per second, pH was 9.0, and the heater power was set to produce a temperature of 60.5° C. on the heated wetted test surface. Trial 1 was conducted for a total of 96 hours (3.5 days). At the end of that time, the accumulated scale on the heated wetted test surface was cleaned off, and the test was restarted as Trial 2, with the same conditions, except the heater power was increased to produce a surface temperature of 70° C. on the heated wetted surface. The water in the cooling tower sump was already at 6 cycles of concentration at the start of Trial 2, and was maintained as such. Trial 2 was allowed to run for 168 hours (7 days), but after 121 hours (5 days) the amount of Drew 2235 antiscalant was increase by 50%. 
       FIG. 9  shows the temperature differential between T 2  and T 1  plotted against scale build up thickness as measured with an ultrasonic transmitter and receiver. The response of the temperature differential is linear with scale thickness in the “prescale” buildup range of 0 to 45 μm, and also linear, but with a different slope, in the “steady state” range of 45-160 μm of scale thickness. During Trial 2, the response of temperature differential is linear with scale thickness across the entire range, but the absolute value of the temperature differential and the relationship coefficient (slope of the temperature differential vs. scale thickness plot) is different, because the insulating effect of the scale layer produces higher temperatures throughout the conducting block  16  and also higher temperature differentials between the two temperature measurements at higher heater power. A change in the addition rate of the antiscalant (Drew 2235) changes the rate of scale thickness accumulation vs. time (not shown) but not the relationship between temperature differential and scale thickness. 
     There were periods within both scaling trials where data was not available, due to data logging problems or other issues. 
     The temperature differential (T 2 −T 1 ) plotted against the scale thickness (as measured ultrasonically) is highly linear. In addition, the temperature difference (T 2 −T 1 ) is also highly linear when plotted against fouling factor, as determined with an Ashland OnGuard 2-Plus scale analyzer (plot not shown) which is widely used for monitoring fouling factor in commercial installations. In all cases, linearity is demonstrated by a linear correlation coefficient (R 2 ) of between about 0.91 and 0.99 (1.0 indicates perfect correlation and 0 indicates no correlation). 
     Thus, the embodiments shown in  FIGS. 1, 2, and 10  adequately measure the scale formation along the heated wetted metal test surface. The concept can be further enhanced by modifying sensor  10  to compensate for variables, in particular ambient conditions surrounding sensor  10 .  FIGS. 3 through 8  show various modified temperature measuring units. All of these are attached to and protruding through wall  32  of conduit  11 , with their heated wetted test surface  22  flush with the inside wall  32  of conduit  11  which directs fluid from the water system to the heated wetted test surface where scale is being measured. All must have an insulating element  33  to reduce the flow of heat from the conductive block to wall  32  of conduit  11 . In these embodiments in  FIGS. 3 to 8 , like elements will retain like numerals from  FIGS. 1 and 2 . All of the depictions shown schematically in  FIGS. 3-8  are intended to reduce the impact of variations of the ambient conditions surrounding the sensor  10 , or increase the sensitivity of the scale quantification measurement through manipulation of heat transfer along the secondary heat conduction path(s), or both. They are most applicable when the device is installed outside of a climate-controlled room, or when the temperature of the flow  36  is much higher than that of the ambient temperature, or both. It is emphasized that in some cases the bulk flow might be other than industrial cooling water, e.g., black liquor in a pulp mill, brine, or other bulk flow fluids. In some cases, the temperature may be too high or the fluid may be otherwise unsuitable for measurement of the scale thickness via pulsed ultrasonic signal. In such cases, the invention may be used with a different scale thickness measuring means suitable for the environment, or without a means of measuring scale thickness. In cases where there is no suitable scale thickness measurement means available, only heat transfer resistance information will be obtained, and it will not be readily possible to infer the chemical composition of the scale. 
     The embodiment shown in  FIG. 3  is a modified version of the embodiment shown in  FIG. 1 . The modification is the addition of a back heater  60  on the second end  24  opposite the wetted surface  32 . The heat flux is governed by the similar equations 
     
       
         
           
             
               
                 
                   
                     q 
                     
                       material 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   ⁢ 
                 
                 A 
               
               = 
               
                 K 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         T 
                         2 
                       
                       - 
                       
                         T 
                         1 
                       
                     
                     
                       δ 
                       b 
                     
                   
                   ) 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   
                     q 
                     
                       material 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   ⁢ 
                 
                 A 
               
               = 
               
                 K 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         T 
                         3 
                       
                       - 
                       
                         T 
                         4 
                       
                     
                     
                       δ 
                       d 
                     
                   
                   ) 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   q 
                   total 
                 
                 A 
               
               = 
               
                 
                   
                     
                       q 
                       
                         material 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     ⁢ 
                   
                   A 
                 
                 + 
                 
                   
                     
                       q 
                       
                         material 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     ⁢ 
                   
                   A 
                 
               
             
           
         
       
     
     Since T 4  is controlled there is the capability to actively control heat flux through insulation layer  30 . The heat flux control along the secondary heat conduction path is accomplished by controlling temperature T 4 . 
     Note the insulation  28  along the longitudinal surfaces is assumed “perfect” for this example, which is not attainable in actual installations. There will be some radial heat flux in actual implementations and this heat flux will be impacted by ambient conditions. The heat flux control depicted schematically in  FIG. 3  can be called active heat flux control, because it is supplied with a controlled amount of external energy. As such, the power supplied by the back heater  60  may be adjusted or controlled based on the temperature T 4 , which becomes a point of adjustment that can be used to optimize operation of the device when it must operate at more extreme conditions. A potential limitation of the device as depicted in  FIG. 3  is the inability to cool surfaces  26  and  24  of sensor  10 . 
     The following description is provided as an example of how to optimize the sensor design of  FIG. 3  to maximize its utility for a given implementation. For purposes of this analysis, T 2  and T 3  are positioned immediately adjacent either side of heater  14 . Since T 2  and T 3  are not in contact with the heater, it is assumed that T 2 =T 3 =T h . (T h  is temperature of the heater.) In addition, material  30  is extended from the surface of the heater  14  (the new location for sensor T 3 ) to the location of sensor T 4  (the interface between material  30  and heater  60 ); δ 2  is now the distance between heater  14  and heater  60 . 
     In any given implementation for this particular embodiment, the following will be known, bulk fluid temperature (which allows an estimate of temperature at the exposed surface of the scale. T scale ), and maximum available heater output. The optimization problem is to select material  16 , material  30 , distance δ 1 , δ 2  and the temperature maintained by the backside heater  60  (which is equal to T 4 ) so that over the anticipated operating range of the sensor, the temperature differences T 1  and T 3 −T 4  are maximized, thus providing the highest possible resolution for the scale accumulation measurement. 
     The heat flux balance for the sensor is given by 
                 q   T     A     =         q   16     A     +       q   30     A             
where g T  is the heater output, q 16  is the heat flux through material  16 , q 30  is the heat flux through material  30  and A is the area. The equation can be restated using the resistance analogy
 
                 q   30     A     =         T   h     -     T   4         R   4                       q   16     A     =         T   h     -     T   scale         R     16   -   scale               
to substitute for elements on the right hand side of the equation, yielding
 
                 q   T     A     =           T   h     -     T   scale         R     16   +   scale         +         T   h     -     T   4         R   30               
where R 16+scale  is the combined thermal resistance for material  16  and the scale and R 30  is the thermal resistance for material  30 . The equation can be rearranged to provide an expression for T h 
 
     
       
         
           
             
               
                 
                   [ 
                   
                     
                       
                         q 
                         T 
                       
                       A 
                     
                     + 
                     
                       
                         T 
                         scale 
                       
                       
                         R 
                         
                           16 
                           + 
                           scale 
                         
                       
                     
                     + 
                     
                       
                         T 
                         4 
                       
                       
                         R 
                         30 
                       
                     
                   
                   ] 
                 
                 ⁡ 
                 
                   [ 
                   
                     
                       1 
                       
                         R 
                         
                           1 
                           + 
                           scale 
                         
                       
                     
                     + 
                     
                       1 
                       
                         R 
                         30 
                       
                     
                   
                   ] 
                 
               
               
                 - 
                 1 
               
             
             = 
             
               T 
               h 
             
           
         
       
     
     For a given material  16 , material  30 , and scale type the above equation can be used to calculate T h . Once T h  is calculated the two heat fluxes can be calculated as follows 
     
       
         
           
             
               q 
               16 
             
             = 
             
               
                 
                   
                     T 
                     h 
                   
                   - 
                   
                     T 
                     scale 
                   
                 
                 
                   R 
                   
                     16 
                     - 
                     scale 
                   
                 
               
               ⁢ 
               A 
             
           
         
       
       
         
           where 
         
       
       
         
           
             
               R 
               
                 16 
                 - 
                 scale 
               
             
             = 
             
               
                 
                   δ 
                   1 
                 
                 
                   k 
                   16 
                 
               
               + 
               
                 
                   δ 
                   scale 
                 
                 
                   k 
                   scale 
                 
               
             
           
         
       
       
         
           and 
         
       
       
         
           
             
               q 
               30 
             
             = 
             
               
                 
                   
                     T 
                     h 
                   
                   - 
                   
                     T 
                     4 
                   
                 
                 
                   R 
                   4 
                 
               
               ⁢ 
               A 
             
           
         
       
       
         
           where 
         
       
       
         
           
             
               R 
               30 
             
             = 
             
               
                 δ 
                 2 
               
               
                 k 
                 30 
               
             
           
         
       
     
     Once the heat fluxes are calculated the remaining parameters can be calculated. 
     In optimizing the design, the primary factors to consider are the thermal conductivity and thickness of material  16  and material  30 , the temperature T 4 , the temperature at the scale surface T scale  and the power to the main heater. The goal is to maximize the temperature differential along the lengths of material  16  and material  30  as scale builds up on the surface exposed to the bulk fluid flow. 
     As an example it is assumed the available heater has an output of 200 W and the conductive block has a cross section measuring 10 mm×50 mm. Using the above equations it is possible to investigate the effects of changing T 4 . T scale , material  16 , material  30 , δ 1 ,δ 2  and then to ascertain the device configuration that best meets the design goal of maximizing the temperature differentials in the sensor. 
       FIG. 12  shows the effect of varying the thermal conductivity of material  30 . The design could be optimized for maximizing the temperature differential in material  30 , while ignoring the temperature differential in material  16 . In this case, the thermal conductivity of material  30  would be as low as possible. The drawback is that the temperature difference in material  16  would not change significantly as scale developed. The figure shows that there is an optimum thermal conductivity for material  30 , one that maximizes the temperature differential in material  16 , i.e. K 30 =˜20 W/m-° K. For the purposes of this example the thermal conductivity of material  30  is set at 20 W/m-° K. The rationale is that it would be better to have two different temperature differences indicating scale growth rather than only one. 
     In  FIG. 13  the effects of varying the thickness of Material  30  are examined. As the thickness of material  30  (δ 2 ) is increased the effective thermal resistance increases, causing it to appear more like an insulator. Thus, the results are similar to those shown in  FIG. 12 . Again, there is an optimum thickness of material  30  (δ 2 ) for maximizing the temperature difference in material  16 . For maximizing the temperature difference in material  16 , the thickness of material  30  is set at 10 mm. 
     The thickness of material  16  is addressed in  FIG. 14 . The effect of increasing material  16  thickness plateaus at around δ 1 =˜10 mm. At this thickness there is still a reasonable temperature difference across material  30 , the thickness of material  16  is therefore set at 10 mm for the purposes of this example. 
     In  FIG. 15  the thermal conductivity of material  16  is considered. Since changing thickness has the effect of changing the thermal resistance, the results are similar to what occurred with material  30 . The effect of increasing the thermal conductivity plateaus. The sensor used in the previously described scaling test had a thermal conductivity of ˜42 W/m° K, which also provides a reasonable temperature difference across material  30 , the thermal conductivity of material  16  is set to 42 W/m° K for the purposes of this example. 
       FIG. 16  shows the temperature difference across both material  16  and material  30  for several different conditions and a range of scale thicknesses. The cases with T scale  of 40 and 70 C are lower temperature applications, more common to what would be found in standard industrial heat exchanger applications. The temperature differences in both material  16  and material  30  are adequate for monitoring scale development. The results for the cases with T scale  of 130 and 170 C are not as satisfactory. These cases are more representative of paper mill pulping and black liquor applications. 
       FIG. 17  shows that utility of adjusting T 4  for a specific application. In all the previous graphs T 4  was set at 50 C. In  FIG. 18 , T 4  is set for the particular case
 
 T   scale =40 C→ T   4 =80 C  1.
 
 T   scale =70 C→ T   4 =100 C  2.
 
 T   scale =130 C→ T   4 =100 C  3.
 
 T   scale =170 C→ T   4 =130 C  4.
 
     Adjusting T 4  up or down can expand or contract the range of the temperature differential as scale builds up. By adjusting T 4 , control is being exerted over the heat transfer through the secondary heat flow path. The utility of the device depends on manipulating the temperatures inside the device to maximize the temperature differentials. In the high T scale  cases the task can be made easier by providing more power to the heater, thus making it possible to increase T h  for a given set of conditions.  FIG. 18  shows the same conditions as  FIG. 17 , except in the high T scale  cases the power to the heater is 500 W instead of 200 W. 
     The embodiment shown in  FIG. 4  is a modification of the embodiment shown in  FIG. 1 . The modification is intended to eliminate the impact of ambient condition changes and provide known conditions along the secondary heat conduction path by providing a nominally isothermal boundary condition. It also compensates for velocity and temperature changes in bulk fluid flow. 
     This is accomplished by enclosing the device and circulating the fluid from the water system around the entirety of the sensor device. The sensor  10  is surrounded by the fluid from the water system by running conduit  11  around the sensor  10 , back to a return conduit  66 . Conduit  11  enlarges at area  68  to allow working fluid to surround all sides of the sensor  10 , except the portion of sensor  10  that comprises the heated wetted test surface  22  where scale accumulates, which is already in contact with the flow passing through conduit  11 . The environment surrounding sensor  10  is thus at the same temperature as the fluid, and is maintained constant to the extent that the temperature of the fluid id maintained constant. While heat is lost to the bulk flow  36  as before through the heated wetted test surface  22 , and from all exposed sides  26  and from the second end  24 , the loss of heat through sides  26  and end  24  is now nearly constant, since the temperature of the bulk water flow  36  is generally nearly constant. 
     Because the bulk flow  36  is utilized for temperature control, but no external energy is added, this device can be considered to make use of semi active heat flux control. 
     The heat flux is governed by the equations 
     
       
         
           
             
               
                 
                   
                     q 
                     
                       material 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   ⁢ 
                 
                 A 
               
               = 
               
                 K 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         T 
                         2 
                       
                       - 
                       
                         T 
                         1 
                       
                     
                     
                       δ 
                       b 
                     
                   
                   ) 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   
                     q 
                     
                       material 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   ⁢ 
                 
                 A 
               
               = 
               
                 K 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         T 
                         3 
                       
                       - 
                       
                         T 
                         4 
                       
                     
                     
                       δ 
                       d 
                     
                   
                   ) 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   q 
                   total 
                 
                 A 
               
               = 
               
                 
                   
                     
                       q 
                       
                         material 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     ⁢ 
                   
                   A 
                 
                 + 
                 
                   
                     
                       q 
                       
                         material 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     ⁢ 
                   
                   A 
                 
               
             
           
         
       
     
       FIG. 5  shows a modified version of  FIG. 1 . It is intended to eliminate the impact of environmental changes by providing an isothermal boundary condition. In this case the device is surrounded by a second heater  68 . Therefore, in a manner similar to the device shown in  FIG. 4  there is heat flux control along the secondary heat conduction path. The heat flux control depicted schematically in  FIG. 5  can be called active heat flux control, because it is supplied with a controlled amount of external energy. As such, the power supplied by secondary heater  68  may be adjusted or controlled by the temperature signal of T 4 , which becomes a point of adjustment that can be used to optimize operation of the device when it must operate at more extreme conditions. A potential limitation of the device as depicted in  FIG. 5  is the inability to cool surfaces  26  and  24  of sensor  10 . 
     The heat flux is governed by the equations 
     
       
         
           
             
               
                 
                   
                     q 
                     
                       material 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   ⁢ 
                 
                 A 
               
               = 
               
                 K 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         T 
                         2 
                       
                       - 
                       
                         T 
                         1 
                       
                     
                     
                       δ 
                       b 
                     
                   
                   ) 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   
                     q 
                     
                       material 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   ⁢ 
                 
                 A 
               
               = 
               
                 K 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         T 
                         3 
                       
                       - 
                       
                         T 
                         4 
                       
                     
                     
                       δ 
                       d 
                     
                   
                   ) 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   q 
                   total 
                 
                 A 
               
               = 
               
                 
                   
                     
                       q 
                       
                         material 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     ⁢ 
                   
                   A 
                 
                 + 
                 
                   
                     
                       q 
                       
                         material 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     ⁢ 
                   
                   A 
                 
               
             
           
         
       
     
       FIG. 6  shows a refinement of the embodiment shown in  FIG. 5  in that there are now separate heaters  70  for the peripheral surfaces  26  of the sensor  10  and a separate heater  72  for second end  24 . This embodiment has two distinct secondary heat conduction paths. This provides an enhanced capability for controlling heat flux both along the longitudinal axis and perpendicular to the longitudinal axis by controlling the temperatures along those surfaces. The heat flux control depicted schematically in  FIG. 6  can be called active heat flux control along the secondary heat conduction paths, because it is supplied with a controlled amount of external energy. As such, the power supplied by the secondary heaters  70  and  72  are independently and collectively adjustable to maintain a constant temperature at T 4  or other potential temperature measurement locations, and can be used for further optimize operation of the device when it must operate at more extreme conditions. A potential limitation of the device as depicted in  FIG. 6  is the inability to cool surfaces  26  and  24 . 
     The heat flux is governed by the equations 
     
       
         
           
             
               
                 
                   
                     q 
                     
                       material 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   ⁢ 
                 
                 A 
               
               = 
               
                 K 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         T 
                         2 
                       
                       - 
                       
                         T 
                         1 
                       
                     
                     
                       δ 
                       b 
                     
                   
                   ) 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   
                     q 
                     
                       material 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   ⁢ 
                 
                 A 
               
               = 
               
                 K 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         T 
                         3 
                       
                       - 
                       
                         T 
                         4 
                       
                     
                     
                       δ 
                       d 
                     
                   
                   ) 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   q 
                   total 
                 
                 A 
               
               = 
               
                 
                   
                     
                       q 
                       
                         material 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     ⁢ 
                   
                   A 
                 
                 + 
                 
                   
                     
                       q 
                       
                         material 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     ⁢ 
                   
                   A 
                 
               
             
           
         
       
     
     The embodiment shown by  FIG. 7  uses active control of heat flux along the secondary heat conduction paths. In this case the device is surrounded by a variable heat sink  78 , here represented by cooling fins  74  and a means of forcing air over the variable heat sink (not shown) which forces air in the direction of arrow  76 . Heat removal is altered by increasing or decreasing the rate of air flow over the fins. It is also conceivable that a hot air flow could be used to reduce heat flux from the device. A more refined version would have separate heat flux control for the longitudinal surfaces of the device. A yet more refined version would have a water mist of adjustable magnitude sprayed on the variable heat sink surface to control the temperature of the exterior surfaces of sensor  10  even more effectively under even more extreme environmental conditions. The heat flux control depicted schematically in  FIG. 7  can be called active heat flux control along the secondary heat conduction paths, because it is supplied with a controlled amount of external energy. As such, the set point of the air flow temperature or volume or run duration and/or water mist flow and/or duration are independently and collectively adjustable to further optimize operation of the device when it must operate at more extreme conditions, by providing means to further reduce the effect of changing ambient conditions. 
     The heat flux is governed by the equations 
     
       
         
           
             
               
                 
                   
                     q 
                     
                       material 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   ⁢ 
                 
                 A 
               
               = 
               
                 K 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         T 
                         2 
                       
                       - 
                       
                         T 
                         1 
                       
                     
                     
                       δ 
                       b 
                     
                   
                   ) 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   
                     q 
                     
                       material 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   ⁢ 
                 
                 A 
               
               = 
               
                 K 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         T 
                         3 
                       
                       - 
                       
                         T 
                         4 
                       
                     
                     
                       δ 
                       d 
                     
                   
                   ) 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   q 
                   total 
                 
                 A 
               
               = 
               
                 
                   
                     
                       q 
                       
                         material 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     ⁢ 
                   
                   A 
                 
                 + 
                 
                   
                     
                       q 
                       
                         material 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     ⁢ 
                   
                   A 
                 
               
             
           
         
       
     
     The embodiment shown in  FIG. 8  is similar to the embodiment shown in  FIG. 4 . It uses a separate fluid flow to actively heat or cool the device. Therefore, this implementation provides the capability to control heat flux through temperature control, i.e., using a fluid at a specific temperature and to control heat flux directly, i.e., by changing the rate of fluid flow and thus the heat removed from or added to the device. The heat flux control depicted schematically in  FIG. 8  can be called active heat flux control along the secondary heat conduction path, because it is supplied with a controlled amount of external energy. As such, the temperature set point and/or the flow rate of the separate working fluid are independently and collectively adjustable to further optimize operation of the device when it must operate at more extreme conditions, by providing means to further reduce the effect of changing ambient conditions. 
     The heat flux is governed by the equations 
     
       
         
           
             
               
                 
                   
                     q 
                     
                       material 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       1 
                     
                   
                   ⁢ 
                 
                 A 
               
               = 
               
                 K 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         T 
                         2 
                       
                       - 
                       
                         T 
                         1 
                       
                     
                     
                       δ 
                       b 
                     
                   
                   ) 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   
                     q 
                     
                       material 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       2 
                     
                   
                   ⁢ 
                 
                 A 
               
               = 
               
                 K 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         T 
                         3 
                       
                       - 
                       
                         T 
                         4 
                       
                     
                     
                       δ 
                       d 
                     
                   
                   ) 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               
                 
                   q 
                   total 
                 
                 A 
               
               = 
               
                 
                   
                     
                       q 
                       
                         material 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     ⁢ 
                   
                   A 
                 
                 + 
                 
                   
                     
                       q 
                       
                         material 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     ⁢ 
                   
                   A 
                 
               
             
           
         
       
     
       FIG. 11  shows a diagrammatic cross section of an alternative embodiment of a component of the invention, conductive block  16 . In  FIG. 11 , the conductive block  16  is comprised of a highly conductive material surrounding or partially surrounding the heating means  14 , a second material  80  attached to the first material as the heated wetted test surface  22 , and a third material  82  attached to the opposite end  24 . The first material is chosen for its high heat conductivity, and could be copper, gold, silver, CuNi alloy, brass, aluminum, or any other highly conductive material. The use of a highly conductive material in this position facilitates good heat transfer in the direction indicated by arrow  38 , to minimize the power required for heater  14  to produce the target temperature at the heated wetted test surface  22 . Such a highly conductive material may not be appropriately corrosion resistant for exposure to the fluid in conduit  11  in some applications. The second material layer  80  is thin and is chosen for corrosion resistance, biofilm resistance, or to match the heat transfer surface of the heat transfer surface to be emulated. Since it is thin, its heat transfer characteristics are less critical. The third material  82  is chosen for its lower heat conductivity and adequate structural properties, and could be mild steel, stainless steel, or any plastic with sufficient structural strength to serve its mechanical needs at the anticipated temperature. It is chosen to resist the flow of heat in the direction of the secondary heat conduction path. 
     The materials may be bonded together by any appropriate mechanical means such as screws or bolts, clamps, or the like, by welding, brazing, or other appropriate techniques for the particular metals. Of particular interest is a foil brazing technique, which can bond a variety of metal types well. 
     In each of the embodiments shown in  FIGS. 3 through 8 and 11 , an apparatus, as shown in  FIG. 2  used to measure the thickness of the deposited scale, can be incorporated in the same manner as in  FIG. 2 . In each of these embodiments, the scale measuring sensor  10  would determine the fouling factor of deposited scale. In each of these, as inverse soluble scale accumulates on the heated wetted test surface  22 , the scale  40  provides an additional restriction to heat flow path through the metal block  16  through the heated wetted test surface  22  to the bulk flow. The rising the temperature in the block is registered by both temperature sensors. With a higher internal temperature, more heat exits via the provided partially insulated heat flow path to the atmosphere. This results in a reduced temperature differential between the two temperature sensors because less heat is exiting through the heated wetted test surface  22 . The fouling factor, or reduction in heat flow through the heated wetted metal surface indicates the accumulated scale. The temperature differential between the two temperature sensors is linear with respect to scale thickness for any particular type of scale. The temperature differential between the two temperature sensors is different for different types of scale. By measuring the scale thickness, such as by pulsed ultrasonic signal, one can ascertain the type of scale deposited and, in turn, provide the most effective treatment. 
     This has been a description of the present invention along with the preferred method of practicing the present invention. However, the invention itself should only be defined by the appended claims,