Abstract:
A system and process are provided for determining the concentration of a first component of a mixture wherein the first component includes at least 3 materials. The process includes directing 2 beams of x-rays into the mixture and receiving portions of the beams which are transmitted through the mixture. The concentration of the first component is determined based upon the beams transmitted through the mixture.

Description:
This is a continuation of 07/892,595 filed May 28, 1992 now abandoned which is a continuation of 07/552,338 filed Jul. 12, 1990 now abandoned which is a continuation of 07/274,645 filed Nov. 17, 1988 now abandoned which is a continuation of 06/541,622 filed Oct. 13, 1983 now abandoned. 
    
    
     BACKGROUND OF THE INVENTION 
     1. The Field of The Invention 
     The present invention relates to apparatus and process for measuring the percentage of ash in paper. 
     2. Description of the Prior Art 
     Paper and similar materials such as box board and corrugated board include wood material called fiber and other material called ash. Generally speaking, ash is defined as the residue remaining after complete combustion of paper. Ash can include various materials. Many paper manufacturers use clay, titanium dioxide or calcium carbonate; and in some cases barium sulfate and talc also comprise ash. In some cases only one of these materials will be used, whereas some manufacturers use mixtures of these materials, a common combination being clay and titanium dioxide or clay and calcium carbonate. During the manufacture of paper, it is important to control the ash content of the paper. The concentration of ash can affect the strength of the paper and also certain qualities such as printability. Furthermore, clay, which is often a component of ash, is generally far cheaper than wood fiber. Therefore, it is often important to maintain the ash content as high as reasonably possible while still maintaining other characteristics of the paper within specification. 
     The percentage of ash can be controlled manually by setting the rates of flow of clay and other ash stock as well as the flow of wood fiber to the paper making system and periodically sampling the paper to determine the value of ash in a laboratory. When the ash content is determined in the laboratory, the paper is burned under predetermined conditions and the resulting ash is weighed. This procedure of manual control suffers from the main disadvantage that it is time consuming and can result in the production of large quantities of paper which do not meet specifications. 
     An automated system to determine the percentage of ash relies upon the selective absorption of x-rays. The transmission of x-rays through paper can be characterized by Beer&#39;s Law: 
     
         R=I÷I(O)=e.sup.-μW 
    
     Where μ is the mass absorption coefficient and W is the weight of the paper. I is the intensity of the x-rays through the sample and I(O) is the intensity of the x-rays without the sample present. 
     The mass absorption coefficient, μ, can be viewed as the sum of the products of the individual mass absorption coefficients of each constituent and their respective weight fractions. ##EQU1## 
     The paper can be understood to consist of fiber and ash, and therefore: 
     
         μ=μ.sub.f W.sub.f +μ.sub.a W.sub.a 
    
     Thus, when μ f  and μ a  are known, the percentage of ash can be determined. 
     The system for accomplishing this includes a source of x-rays mounted on one side of a sheet of paper and an x-ray detector mounted on the other side of the paper to receive x-rays which are transmitted through the paper. The detector is coupled to an electronic system to measure the intensities I and I(o) and a computer is coupled to the electronics to carry out the necessary calculations. Such a system is generally satisfactory when the ash has one or two components. However, such a system generally will not achieve satisfactory results when the ash contains three components. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic illustration, partially in cross section, of a system according to the preferred embodiment of the present invention. 
     FIG. 2 is a graph showing the x-ray energy vs. the mass absorption coefficient, μ, for three constituents of ash. 
    
    
     OBJECTS OF THE INVENTION 
     An object of the present invention is to provide a system and process for determining the percentage of ash in paper when the ash comprises three components. 
     Further objects and advantages of the invention can be ascertained by reference to the specification and drawings herein which are by way of example only and not in limitation of the invention which is defined by the claims and equivalents thereto. 
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     With reference to FIG. 1, the preferred embodiment includes a source housing 10 located to one side of a moving sheet of paper 12. A detector housing 14 is located on the side of the paper 12 opposite the source housing 10, and both housings 10 and 14 are constructed and arranged to be movable in synchronized fashion across the sheet of paper 12 so that measurements of ash can be made across the sheet of paper. Various types of conventional scanning systems are available to move the housings 10 and 14. 
     The source housing 10 contains two x-ray sources, the first source including an x-ray tube 16 coupled to a power supply 18 and a second x-ray tube 20 coupled to a second power supply 22. The first and second x-ray tubes 16 and 20 generate first and second x-ray beams 24 and 26, respectively. The portion of the first x-ray beam 24 which passes through the paper is designated as beam 30, and the portion of the second x-ray beam 26 which passes through the paper 12 is designated as 32. 
     The detector housing 14 contains a first x-ray detector 34 which is mounted to receive the beam 30, and a second x-ray detector 36 mounted to receive the beam 32. In practice the detectors 34 and 36 can be krypton-filled ion chambers with beryllium windows so that the x-rays received by the detectors generate small currents in the ion chamber. The current is proportional to the strength of the x-ray beam entering the chamber. The two detectors 34 and 36 are electrically coupled to amplifiers 40 and 42 which generate analog type electrical signals proportional to the signals from the detector. The amplifiers 40 and 42 are electrically coupled to voltage-to-frequency converters 44 and 46 which convert the analog signals from the amplifiers into digital signals to be transmitted over lines 50 and 52 to a computer 60. 
     The computer 60 is coupled to receive signals representing the basis weight of the paper 62 and the moisture of the paper 64. The basis weight and moisture signals can be generated by conventional devices. 
     In FIG. 2 there is shown a plot of x-ray energy vs. mass absorption coefficient, μ, for three constituents of ash, namely clay indicated by line 70, titanium dioxide (TiO 2 ), indicated by line 72 and calcium carbonate (CaCO 3 )) indicated by line 74. The x-ray energy is normally measured in thousands of electron volts, KeV, and the mass absorption coefficient, μ, is normally measured in units of square centimeters per gram, Cm 2  /g. It should be understood that the graph in FIG. 2 is not intended to be to any particular scale, nor is it intended to be completely accurate. However, the important feature of the graph which is intended to be illustrated is the relative locations of the curves for the three components and the locations of the discontinuities in the graphs 72 and 74. The discontinuities in the two graphs are located at the so called K edges, and the K edge for graph 72 is at about 5 KeV; whereas the K-edge for the curve 74 is located at about 4 KeV. 
     In operation of the present system, the first x-ray tube 16 is constructed to generate x-rays having an evergy above the K-edges for both titanium dioxide and calcium carbonate. A preferred energy is about 7 KeV. The second x-ray tube 20 is constructed to generate x-rays having an energy below the K-edge for both titanium dioxide and calcium carbonate. A preferred energy is about 3.9 KeV. We have found that a satisfactory method of generating x-rays in these ranges is to construct the first x-ray tube with a tungsten target and to set the anode voltage to 7 KeV. This produces a Brenstrahlung spectrum of x-rays with a maximum energy determined by the anode voltage. The low energy x-rays are removed by placing a suitable &#34;filter&#34; consisting of a steel or aluminum sheet of calculated thickness in front of the source. This allows tuning the x-ray energy to the proper range. Alternatively, a cobalt target x-ray tube could be used to produce mono-energetic x-rays of about 8 KeV. This would eliminate the need for filtering. 
     The second x-ray tube 20 preferably uses a tungsten target with the anode voltage set below the K-edge energy, preferably about 3.9 KeV. No filtering is required with respect to this tube since all the x-rays have energies below the K-edge. 
     The equations required to determine the ash content are as follows: 
     For the signal from the first detector 34: ##EQU2## where R1=ratio of signal in the presence of the paper to signal in the absence of the paper. 
     μ 1  =mass absorption coefficient of ash component 1 (TiO 2 ) 
     w 1  =weight per unit area of ash component 1 
     μ 2  =mass absorption coefficient of ash component 2 (CaCO 3 ) 
     w 2  =weight per unit area of ash component 2 
     μ 3  =mass absorption coefficient of ash component 3 (Clay) 
     w 3  =weight per unit area of ash component 3 
     μ f  =mass absorption coefficient of paper fiber 
     w f  =weight per unit area of paper fiber 
     μ w  =mass abosorption coefficient of water 
     w w  =weight per unit area of water (Moisture or MOI) 
     The x-ray energy on the first x-ray tube 16 is chosen such that: 
     μ1≅μ2&gt;&gt;μ3 
     For the signal from the second detector 36: ##EQU3## where the variables are defined as for Eq. 1 except that the mass absorption coefficients μ have values different from μ because the x-ray energy is different. The x-ray energy of the second tube is chosen such that: 
     μ&#39; 1  ≅μ&#39; 2  &lt;&lt;μ&#39; 3   
     Furthermore, the following equations are known: 
     
         BW=w.sub.1 +w.sub.2 +w.sub.3 +w.sub.f +w.sub.w             (Eq. 3) 
    
     where BW is the basis weight or weight per unit area of the sheet of paper 12, i.e.: 
     
         w.sub.f= BW-w.sub.1 -w.sub.2 -w.sub.3 -w.sub.w             (Eq. 4) 
    
     Calculations: 
     Take the log of both sides of Eqs. 1 and 2 and substitute Eq. 4 for w f   
     
         -1nR1=(μ.sub.1 -μ.sub.f)w.sub.1 +(μ.sub.2 -μ.sub.f)w.sub.2 +(μ.sub.3 -μ.sub.f)w.sub.3 +μ.sub.f BW+(μ.sub.w -μ.sub.f)w.sub.w                                       (Eq. 5) 
    
     
         -1nR2=(μ&#39;.sub.1 -μ&#39;.sub.f)w.sub.1 +(μ&#39;.sub.2 -μ.sub.f)w.sub.2 +(μ.sub.3 -μ.sub.f)w.sub.3 +μ.sub.f BW+(μ&#39;.sub.w -μ&#39;.sub.f)w.sub.w                                      (Eq. 6) 
    
     The values of BW and w w  are provided by a basis weight sensor and a moisture sensor which are standard components of a paper measurement system. 
     By taking advantage of the μ values provided by the energy selection criteria we can define the following constants: 
     A=μ 1  -μ f  ≅μ 2  -μ f   
     B=μ 3  -μ f   
     C=μ w  -μ f   
     D=μ f   
     and 
     A&#39;=μ&#39; 1  -μ&#39; f  =μ&#39; 2  -μ&#39; f   
     B&#39;=μ&#39; 3  -μ&#39; f   
     C&#39;=μ&#39; w  -μ&#39; f   
     D&#39;=μ&#39; f   
     also it is usual to use the fractional ash content 
     f 1  =w 1  /BW 
     f 2  =w 2  /BW 
     f 3  -w 3  /BW 
     MOI=w w  /BW 
     Thus, ##EQU4## From Eqs. 7 and 8 the values of f 1  +f 2  and f 3  can be determined. ##EQU5## The total fractional ash content is ##EQU6## At this point it is convenient to regroup the constants into a set of linear coefficients. ##EQU7## Thus total percent ash is ##EQU8## 
     In practice the coefficients C0, C1, C2 and C3 are determined by first analyzing samples of paper containing various amounts of the ash to determine a plurality of values of R1 and R2. Standard laboratory methods are used to determine BW, MOI and percent ash. Then the coefficients are determined using multiple linear regression. 
     It should be understood that although FIG. 2 concerns an ash having three components, the present process can be applied to an ash having more than three components. For example, if the ash contains a fourth component, talc, the graph of x-ray energy versus mass absorption coefficient for the talc would be almost the same as the graph for clay, and the present process would be applicable. Thus, the present process is applicable to a mixture containing at least three materials. In such a case the first beam must have an energy above K-edges of at least two of the materials and the second beam must have an energy below the K-edges of the same at least two materials.