PEER-REVIEWED TECHNICAL ARTICLE
THE INDUSTRIAL REFINING PROCESS
A FIRST THEORETICAL APROACH
By Georges Joris, Matech-Europe
Introduction
The fundamental techniques to optimise a low consistency industrial refining unit still lie on mostly irrational empirical methods. One feels a bit disconcerted from the lack of rigor usually widespread. The conservatism is certainly a brake to the development of rigorous theories and clear strategies in complete agreement with the industrial requirements. Unfortunately, one must also take into consideration the marketing politics carried off by some manufacturers, from which completely false assertions are conveyed. Matech-Europe is in a position to ascertain such weak points as we have diagnosed more than 120 industrial refining units (that is a bit more than 500 refiners) over the last 10 years.
Nowadays, in spite of technique developments, the frequency of technical problems is speedily increasing throughout the world. Why such evolution? There are two main reasons. On one hand, most process engineers are no longer on duty in the papermills and, on the other hand, marketing strategies are forcinh higher and higher sales in the same time frame.
Nowadays, the energy consumption from the stock preparation is higher and the potential of the paper characteristics remains lower than it should be. The progress achieved in paper chemistry and the newinnovative techniques successfully applied on the paper machines highlycompensate the losses from the industrial refining process. In other words, papermaking is now much more efficient than it was in the past and consequentlythe papermakers do not care too much about their refining units. This outstandingsituation greatly affects the runnability of the low consistency refining process. Hugeamounts of energy consumption could often be saved. The cost of the cellulose couldbe sometimes reduced while using the bijective diagram techniques to optimize thepulp composition, depending on the target objectives.
But first, it is important to distinguish the set views, the completely wrong ideas, the ambiguous notions and, finally, the wrong techniques.
As far as the set views are concerned, let us quote as examples :
1. Higher the bar angles, lower the cutting of the fibres.
2. Higher the consistency, lower the cutting of the fibres.
3. Lower the specific edge load, lower the cutting of the fibres.
4. Higher the inlet pressure, stronger the cutting of the fibres.
5. Greater the bar height, longer the plate lifetime.
6. Higher the applied power, greater the slowness or lower the freeness development.
7. Higher the recirculation flow, lower the energy consumption.
Actually, these set views among many others are only true within a range of values, depending on further parameters - provided that the pulp circulation in the refiner should be correct (at industrial level this is not always the case).
The completely wrong ideas are implemented by some manufacturers. For example:
1. The energy consumption is lower with conical refiners.
2. The energy consumption is lower with double discs refiners.
3. Bigger the refiner, higher its efficiency.
4. With spiral plate configurations, the refining process is homogeneous and consequently more efficient.
5. The duo-flow double discs refiners with only one inlet are more efficient.
6. To face a production rise, bigger and/or more refiners are required to reach the same papermaking targets.
The ambiguous notions are mainly based on how refining powers are considered or measured, but also on the pumping characteristics of the refiners and on the interpretation of the many theories proposed in the literature that stems usually from laboratory refining trials. It is also extremely difficult to compare two industrial refining units even when they seem to be the same – resulting in many papermakers attempting to extrapolate from their own refining unit the positive results from another industrial refining unit, often without success.
Finally, the wrong techniques stem mainly from bad definitions that have never been reconsidered in keeping with the development of new refiners. This does not necessarily mean that the new concepts are more efficient. For example, it has been rigorously demonstrated that the classical specific edge load has no physical meaning for conical and disc refiners, and leads to wrong results. A rigorous formulation [1] [2] [3] has been established to avoid a lot of misunderstandings but unfortunately only a few papermakers use it. They prefer to get the results from their plate manufacturers to avoid doing a few calculations by themselves.
The purpose of this paper consists on stressing the in’s and out’s of ambiguous interpretations that always lead to wrong decisions at industrial level. To meet our target, a rigorous theory must be developed.
2. THE REFINING EFFECTIVE POWER
The effective power is obtained by subtracting the no-load power from the applied power. This form of calculation puts into evidence a lacun: how can the effective power be calculated when it is not possible to accurately measure the no-load power [4] [5] [6] [7]? The definition of the effective power must be reconsidered. In so doing, it seems evident to link the effective power to the reference specific edge load [3].
Actually, the effective power cannot be exclusively linked to the effective refiningprocess. Through the pulp circulation in the refiner from the pumping actions of therotor (no-load power), the rubbing actions of fibres/fibres and fibres/bars create somevery light refining actions that are often ignored. Furthermore, when a rotor barimpacts a floc from the tertiary flow, its velocity Vg along the relevant stator bar(parallel to the bar edges) produces compression actions whereas its tangentialvelocity Vt produces through the bar edges shearing actions.
Consequently, therefining effective power involves the interconnected actions from its tangentialcomponent (rotor bar edge actions on the flocs from the tertiary flow within the bar crossingpoints) on one hand and its sliding component on the other. The component Vgproduces rubbing and compression actions and the component Vt produces shearingactions followed by light compression actions. From the former, brushing andfibrillating effects are mainly produced and from the latter, cutting effects areessentially generated.
According to Goncharov [8] and then confirmed by Ouellet andal. [9], the bar edge shearing actions are followed by light compression actions.Depending on their intensities, the compression actions can also produce somecutting effects of the fibres. The consideration of the tangential component calledshearing effective power and the sliding component called compression effectivepower will bring a better understanding of many industrial mysterious facts never before so rigorously explained.
Now, these components must be determined. Let usexamine the following figure in which a rotor bar crossing a stator one isconsidered successively at the instants t and t+dt.
Let ds and dr respectively be the elementary distances covered by the crossing point along the stator and the rotor bars. We have:
Then:
And consequently,
Thus:
Similarly,
From the sine law:
That is: then
And finally: with ≠ 0
Similarly, from:
we obtain: with ≠ 0
The sliding velocity of a rotor bar along a stator one depends on the polar position of the relevant crossing point, on the angle (t) and on the angle delimited by the rotor bar and the radius from its upper extremity. When the first rotor bar is taken into consideration, the angle is simply the grinding angle. Such development shows that the role played by the rotor pattern is particular and consequently must be distinguished from the stator one.
One can denote that from the figure aside the angle between the first rotor bar and the radius from its upper extremity ranges from to +in sectorial configuration. It is very similar in the case of a pseudo-sectorial configuration. The formulas described here above could be extended to other configurations. Then comes the question: What are the ranges of the sliding and tangential velocities in the case of an industrial refiner? Let us consider an example:
Let a DD 42’’ refiner, 480 RPM whose plates pattern are defined by a sector angle of
20°, grinding angles of 10° under a grinding code 3 -3-4. The inner and outer radius are respectively 533,5 mm and 320 mm. The peripherical rotation speed amounts to 26,8 m/sec what is suitable with regard to the refiner size. We calculate easily =
26,8/0.5335 = 50,2 rad/sec.
Depending on the relative position of the rotor against the stator, the bar crossing angle (t) ranges from 2= 20° to 2( ) = 60°. Depending on the rotor selected bar, the angle with the radius to its upper extremity ranges from = 10° to = 30°. The sliding velocity will be maximal at the periphery under min = 20° for the first rotor bar characterized by and an angle = 10°.
From the formula (9) we obtain v = 71,2 m/sec. This speed will be minimal on the inner diameter under max = 60° for the last bar of each segment characteriz ed by an angle = 30°. We have under these conditions v = 13,1 m/s ec. The energy transfer to the fibre flocs involves evidently the crossing point kinetic. As a consequence, a wide dispersion of energy distribution can be anticipated. The refining process is very heterogeneous. All crossing points are different, even when they have the same shape and surface. The reference specific edge load is thus only a global picture on the impacts on the fibre flocs. The refining process should be considered as the summation of micro-processes intensities, and whose number depends on the relative position of the rotor against the stator. This proves that the classical specific edge load is quite obsolete. The low consistency refining process is really very complex from its heterogeneity as it is depicted by the following graphic.
Even under relatively small sector angles to reduce the range of variation of the angles (t) (configurations insectorial) and under relatively wide grinding angles (maximum 30°), the polar position of any crossing point involve s a big variation of the sliding velocity from about 14 to 22 m/sec. This means that in this case, the heterogeneity is still wide with in addition big risks of compacting or plugging problems.
We should expect the same refining results. Actually the sliding velocity ranges this time from 290 m/sec (this working point is not represented on the graphic for 0 ) to 13,1m/sec. The variance of the energy transfer distribution is thus much wider.
Subsequently, we will see how much this variance affects the results on the refining process that will also be confirmed at industrial level. Every plate manufacturer has their own specific sector angle without caring about the effects on the refining process. Only the average crossing bar angle is considered whereas under the sameaverage bar angle and the same grinding code the results can be very different.
As far as the tangential velocity is concerned, as depicted in the next graphic,the velocity dispersion as function of the crossing point polar position is narrower.The tangential speeds are generally higher than the sliding ones.
“Bigger the grinding angle, lower the shearing energy transmitted to the fibre flocs and thus lower the cutting effect under some conditions.” This statement which seems evident had never been rigorously quantified or even proven before.
From the fundamental formula described in [10], we have:
in which Pm is the normal component of the average mechanical pressure transmitted to the bar crossing points and Ph is the normal component of the average hydraulic pressure. stands for half the cone angle in case of a conical refiner. With disc refiner we have sin() = 1.
By definition:
When the refiner is unloaded, it is evident to write:
and consequently:
With f(t) as the friction factor, we have finally:
The friction factor depends on the fibre morphology, on the metal grade and on the wearing state of the bar edges. Thus, it is impossible to determine an analytic expression of the friction factor. Actually, at industrial level, the state of wearing of the plates is usually heterogeneous. The relative position of the rotor against the stator does not greatly affect the friction factor, so within the frame of this paper we will consider that .
Furthermore, the function Ph() increases and it depends on the flow and on the plate patterns. Within the range of this paper, only the average value of the hydraulic pressure is considered. This is acceptable in the case of industrial refiners for which the efficiency is usually correct.
We have the trivial expressionin which the function is periodic. Its period is 2
Let us consider its development into Fourier series:
We can calculate its root means square 2eff through Parseval equation
Finally:
This later expression shows how complex the determination of the friction forces is that depends on the polar and relative position of the relevant crossing points.
Let us first consider the compression forces on the bars, disregarding the light periodical fluctuations of the energy transfer fromabout its average value
. The compression effective power is the scalar product of by that gives:
This elementary power along the radius depends on the relative position of the rotor against the stator expressed by sin() but also on the relevant rotor bar expressed by sin().
3. ENERGY DISTRIBUTION
Let us determine the distribution of the compression effective powers within a refiner. We have:
The total effective power is given by
with , expression empirically developed by BANKS [11] in 1967 and then formally demonstrated by Roux [10] in which stands for the outer radius of the fillings (radius of the big base for conical refiners) and where i stands for the inner radius.
When the periodic fluctuations are disregarded, it can be written
The cumulative function of the compression effective power can be determined from the equation (16) that is :
As depicted by the figure below, whatever is the relative position of the rotor against the stator, it always exists in two different configurations - the first one defined by the angle (t) and the other one by the angle (t+).
Consequently, along any circle of radius the power transfer under the angles (t) and (t+) must be simultaneously taken into consideration. Considering again our industrial example, the 20° characteristic must be linked to the 40° characteristic. Nevertheless, the power transfers along any circle of radius must be pondered by the instantaneous number of crossing points that consequently must be determined. Then, in an elementary corona d:
to obtain finally by double integration [12]:
in which * stands for the star angle of the bar crossing points [1].
Let us consider the following graphic that represents the instantaneous variations of the number of bar crossing points within a given sector .
The number of bar crossing points has been calculated for sector angles of 10°, 15°, 20° and 30°. When this number vanishes to zero, it means that the rotor bar leaves the relevant sector of the stator. The total number of crossing points along a radius is obtained by adding the functions N(t) for every sectors of the stator. Thus, we have:
and
For one complete revolution of the rotor we have:
From this simplified expression one can calculate the compression effective powers per bar crossing point under the condition Peff =0 for i. Let us bear in mind that any angle 1 must square with another angle 2 = + 1 that is
Whatever the pattern under consideration is, the compression effective power depends on , and which means that the fibrillation effects are different is in relation to the polar position of the relevant crossing point but also in relation to the relative position of the rotor against the stator. The shearing effective power is determined by the same developments and we have
This expression is not integrable for and consequently between 0 and i where the power is null. As a result,
We remind you that from this expression, the shearing effective powers per bar crossing point can be calculated under the condition: Peff =0 for i .
Nevertheless, the expression shows that the shearing effective power per bar crossing point mainly depends on the angle (see following graph). The determination of the limit conditions is beyond the frame of this paper.
The cos() is determined from integration of the expressions (18) and (20) while considering the trivial equation . The angle is independent of as a first approximation, so we have:
The expression can be integrated with the help of the value intermediary theorem taking into consideration that the cosine function is positive in the interval [-/2 ;+/2] and all functions are continuous within the integration limits. Let be this intermediary value. It can be written
From (23) and (24) we finally obtain:
under the evident bounding condition : k > sin().
In the particular case for which = 0, the later expression can be simplified to