Procedure for measuring the relative quantities of pulp components in wood or paper pulp

A procedure for measuring the relative quantities of pulp components in wood or paper pulp, wherein PA0 for the pulp components (a,b) present in the pulp, for each one separately, is measured the distribution, or probability density, function (b.sub.a, b.sub.b) of a given fibre-specific characteristic thereof, PA0 from the distribution functions are by calculation formed distribution functions (b.sub.a/b) corresponding to the pulp mixture, PA0 the distribution function (b.sub.x/y) of the corresponding characteristic of the pulp is measured, and PA0 by calculation are determined the correlations of the distribution function (b.sub.x/y) of the pulp under examination with the distribution functions (b.sub.a/b) found by calculation, for determining the proportions of the different pulp components.

The present invention concerns a procedure for measuring the relative 
quantities of different components (e.g. softwood/hardwood, 
cellulose/groundwood) in wood or paper pulp. 
Wood or paper pulp consists of a plurality of pulp components, depending on 
the quality requirements imposed on the end product. The differences in 
characteristics between the different components are due not only to 
differences in raw material (e.g. hardwood/softwood) but also on the 
defibration method. In chemical defibration (digestion, or cooking) the 
fibres are dotached from each other intact, and the adaptability of the 
fibre increases. In mechanical defibration (grinding, hot grinding) in 
contrast, fibres are broken and fines are produced at the same time. 
It is important in view of optimating the properties of the end product, to 
know the relative contributions of different components to the mixture. 
Also associated herewith is the determination of the fibre proportions in 
each individual pulp component--for instance: how high is the content of 
short hardwood cellulose (which presents poorer strength characteristics) 
among the long-fibre softwood cellulose. Cellulose makers furthermore 
control the species exchange (pine.fwdarw.birch) by determining the 
hardwood percentage. If one is able to determine the softwood/hardwood 
fibre proportion accurately and rapidly, considerable savings are achieved 
because the share of mixed pulp becomes less and the amount of softwood 
fibre present among hardwood pulp can be minimized. 
The traditional procedure serving determination of pulp components is to 
make a count, with the aid of a microscope, of the different kinds of 
fibres in a stained fibre preparation. This procedure is cumbersome and 
time-consuming and requires a person versed in its use. 
The procedure of the present invention is based on using, in determining 
the pulp components, a characteristic measured fibre-specifically from the 
wood pulp, and certain density functions established by measurements. The 
quantity measured from the wood pulp is, most advantageously, the fibre 
length; it may however equally be the fibre-individually measured fibre 
thickness, wall thickness, lightness of colour, lignin content, or another 
property characteristic of each kind of pulp which is measurable from the 
different pulps with adequate accuracy. The relative quantities of the 
components are calculated, applying correlation techniques. 
In the procedure of the invention the distributions, or probability 
functions, of a given, selected characteristic of those pulp components of 
which the proportion in a given mixture has to be determined, are measured 
from equivalent, pure specimens, and the corresponding distribution 
functions are formed by calculation for the pulp mixture. A measurement is 
furthermore made of the distribution function of the respective 
characteristic in the pulp under examination, whereafter the proportions 
of different kinds of pulp in the pulp under examination containing said 
pulp components are determined by calculating the correlations of the 
distribution function of the pulp under examination with those established 
by calculation.

In calculating the correlations, one may use Rank's correlation formula: 
##EQU1## 
where r.sub.rank =Rank's coefficient of correlation 
D.sub.i =Difference between the distribution curves in the length class 
N.sub.i (I=1 . . . N) 
N=Total number of length classes. 
Maximum correlation is obtained with that value of the proportions of pure 
specimens which comes closest to the proportion that is being determined. 
In an embodiment of the invention, the distributions corresponding to 
different pulp mixtures are formed from the distribution functions of a 
given characteristic with a selected set of pulp proportions, e.g. in 5% 
steps (5/95, 10/90, 15/85, . . . , 95/5). It is thereafter possible to 
determine the proportions of different kinds of pulp in the unknown sample 
under measurement which contains the above pulp components, by calculating 
the correlations between the distribution function of the pulp under 
examination and the above distribution functions established by 
calculation in 5% steps. 
In a situation encountered in actual practice the above resolution of 5% 
does not give adequate accuracy of measurement: an accuracy about 1% is 
required. Of course, the measurement could be carried out by calculating 
P.sub.a/b functions in steps of 1% and performing a calculation of 
correlation with each one of the 100 functions. This is however a slow 
operation, owing to the great number (100) of correlations which must be 
calculated. Significantly higher speed of calculation can be achieved on 
the basis of the knowledge that the calculated correlation function 
r(p.sub.x/y) is parabolic. The correlation may then be calculated for only 
three values of a/b, e.g. the values 10/90, 50/50 and 90/10, and the 
equation of the parabola passing through these points r(p.sub.x1/y1, 
r(p.sub.x2/y2), r(p.sub.x3/y3) can be formed: 
EQU r(p.sub.x/y)=k.multidot.x.sup.2 +l.multidot.x+m (2) 
where k, l, m are the coefficients of the parabola. 
The coefficients are found by solving the following simultaneous equations: 
EQU r(p.sub.x1/y1)=k(x1).sup.2 +l.multidot.x1+m (3) 
EQU r(p.sub.x2/y2)=k(x2).sup.2 +l.multidot.x2+m (4) 
EQU r(p.sub.x3/y3)=k(x3).sup.2 +l.multidot.x3+m (5) 
The maximum of the correlation function is now readily found by determining 
the zero of the first derivate of the parabola, i.e., 
EQU r'(p.sub.x/y)=2kx+l=0 (6) 
EQU Thus, 
EQU x=-1/2k=-1/2.multidot.(l/k) (7) 
l and k can be solved from equations (3) to (5). y can be found in like 
manner, or since we know that the sum of components constitutes the total 
mass, we find: y(%)=100-x(%). 
The procedure of the invention can also be expanded to be applied in 
measurement of more than two components. The calculations proceed in that 
case in the manner that calculation of two of the components is performed 
with the method just described by comparing the unknown sample with a 
calculated mixture of two pure specimens and the ratio of these two 
unknown is thus obtained. By varying, in the calculation, these pure pulps 
under examination a sufficient number of mutual proportions is found from 
which the overall proportions can be derived. 
Taking for example the proportion x/y/z of three pulp components: 
Measurement made of 
EQU x/y=A/B 
EQU and 
EQU y/z=C/D 
EQU Hence 
EQU x/y/z=A/B/(B.multidot.D/C) 
The measurement may also be accomplished in that e.g. in the case of three 
components the unknown sample under measurement is compared with a group 
of distributions formed by calculation from three pure specimens, one of 
the specimens serving as a parameter and the other two being varied. Three 
changes of the parameter enable correlation graphs to be established with 
each parameter, and their intersection will now indicate the quantitative 
proportions of the different kinds of pulp. 
In the foregoing the invention has been described by referring to certain 
embodiments thereof. However, the procedure of the invention is not 
exclusively confined to these embodiments: it may vary within the scope of 
the inventive idea delimited by the claims following below.