METHOD AND DEVICE FOR DETERMINING FIBRE POROSITY IN A FIBRE SUSPENSION, AND CONTROL SYSTEM

Abstract

Disclosed is a method for determining fibre porosity in a fibre suspension. A sample is taken from a fibre suspension and fibre porosity determination is performed by determining the ratio of fibre-internal water to fibre-external bound water as an online measurement using a NMR spectroscope in successive steps of: generating a magnetic field for exciting protons of water contained in the sample; exciting water molecules of fibre suspension contained in the sample with a frequency pulse provided by a coil; measuring a return signal of the frequency pulse that returns from water molecules to the coil; determining the proton relaxation time and the amplitude of the return signal from the return signal; and determining fibre porosity of the fibre suspension based on the amplitude and the relaxation time of the exponential return signal. Also disclosed is a device for determining fibre porosity of a fibre suspension and a control system connected to a fibre web machine.

Claims

1. A method for determining fibre porosity in a fibre suspension, comprising steps of: diverting a sample from the fibre suspension in a fibre suspension flow channel to a side flow channel; leading the sample in the side flow channel to an online NMR spectroscope; generating a magnetic field for exciting protons of water contained in the sample; providing radiofrequency pulses by a coil for exciting the water molecules of the sample; measuring return signals of the radiofrequency pulses returning from the water molecules to the coil; determining a proton's relaxation time and an amplitude of the return signal from each return signal; determining a ratio of fibre-internal water to fibre-external bound water based on the amplitudes and the relaxation times of an exponential of the return signals using a double exponential signal model Exp=A.sub.I*exp(R.sub.2I*t)+A.sub.E*exp(R.sub.2E*t)+D for determining the relaxation time, where A.sub.I is an amplitude representing an amount of fibre-internal water, R.sub.2I is a relaxation speed of fibre-internal bound water, A.sub.E is an amplitude representing an amount of fibre-external water, R.sub.2E is a relaxation speed of fibre-external bound water, and D is an empirical constant; and determining the fibre porosity as a Water Retention Value (WRV) in successive steps including: calculating, based on the amplitudes A.sub.I and A.sub.E, a relative amount of fibre-internal water A.sub.I_rel and a relative amount of fibre-external bound water A.sub.E_rel; calculating a proportion of fibre-internal bound water p.sub.IB based on a relaxation speed of completely free water R.sub.2F, a relaxation speed of completely bound water R.sub.2B and the relaxation speed of fibre-internal bound water R.sub.2I; calculating a proportion of fibre-external bound p.sub.EB based on the relaxation speed of completely free water R.sub.2F, the relaxation speed of completely bound water R.sub.2B and the relaxation speed of fibre-external bound water R.sub.2E; calculating an amount of fiber-internal bound water W.sub.IB based on the relative amount of fibre-internal water A.sub.I_rel, the proportion of fiber-internal bound water p.sub.IB and a consistency c of the fibre; calculating an amount of fibre-external bound water W.sub.EB based on the relative amount of fibre-external water A.sub.E_rel, the proportion of fiber-external bound water p.sub.EB and the consistency c of the sample; and calculating the WRV value as a sum of the amount of fibre-internal bound water W.sub.IB and the amount of fiber-external bound water W.sub.EB.

2. The method according to claim 1, wherein the value of the empirical constant D is between 0 and 1.

3. The method according to claim 1, further comprising further steps of: determining the fibre porosity using both a single exponential signal model and the double exponential signal model by steps including: forming a first porosity value based on a single exponential signal model Exp=A*exp(R.sub.2*t) for determining the relaxation time and a linear formula WRV.sub.NMR=kk*[R.sub.2−a*(c−c.sub.ref)]+C for determining fibre porosity as a WRV value, where kk is a slope of the linear formula, C is a second empirical constant, a is another empirical constant, and c.sub.ref is a reference consistency, and forming a second porosity value based on the double exponential signal model; and comparing the first porosity value and the second porosity value with each other for forming a comparison result.

4. The method according to claim 3, wherein the comparison result is calculated as a difference of the first porosity result and the second porosity result and by dividing the difference by the first porosity result and, if the comparison result is less than 5% of the first porosity result, the fibre porosity is calculated as an average of the first porosity result and the second porosity result.

5. The method according to claim 1, comprising determining a ratio of bound water to free water both inside fibre and outside fibre.

6. A device for determining a fibre porosity of a fibre suspension, including: a time-domain NMR spectroscope for determining the fibre porosity based on a fibre sample of the fibre suspension as an online measurement; and connection equipment for connecting the time-domain NMR spectroscope to a refiner for refining a fiber suspension, either directly to a fibre suspension flow channel or to a side flow channel, which side flow channel is arranged to lead part of the fibre suspension flow arriving from the refiner to form a separate sample; wherein the time-domain NMR spectroscope comprises: a sample channel; at least one coil arranged around the sample channel to excite water protons of the fibre suspension contained in the sample by frequency pulses; a magnet arranged around the sample channel for generating a magnetic field in the sample channel; a power source with controllers connected to the coil for generating the frequency pulses; measuring equipment for measuring an intensity of current generated by the frequency pulses returning to the coil from protons for generating return signals; and a computer equipped for determining the fibre porosity of samples based on the return signals, by being arranged to: determine a proton's relaxation time and an amplitude of each return signal using a double exponential signal model Exp=A.sub.I*exp(R.sub.2I*t)+A.sub.E*exp(R.sub.2E*t)+D for determining the relaxation time, where A.sub.I is an amplitude representing an amount of fibre-internal water, R.sub.2I is a relaxation speed of fibre-internal bound water, A.sub.E is an amplitude representing an amount of fibre-external water, R.sub.2E is a relaxation speed of fibre-external bound water, and D is an empirical constant; determine the fibre porosity as a Water Retention Value (WRV); and calculate: a relative amount of fibre-internal water A.sub.I_rel and a relative amount of fibre-external water A.sub.E_rel, based on the amplitudes A.sub.I and A.sub.E; a proportion of fibre-internal bound water p.sub.IB based on a relaxation speed of completely free water R.sub.2F, the relaxation speed of completely bound water R.sub.2B and the relaxation speed of fibre-internal bound water R.sub.2I; a proportion of fibre-external bound water p.sub.EB based on the relaxation speed of completely free water R.sub.2F, the relaxation speed of completely bound water R.sub.2B and the relaxation speed of fibre-external bound water R.sub.2E; an amount of fiber-internal bound water W.sub.IB based on the relative amount of fibre-internal water A.sub.I_rel, the proportion of fibre-internal bound water p.sub.IB and a consistency c of the sample; an amount of fibre-external bound water W.sub.EB based on the relative amount of fibre-external water A.sub.E_rel, the proportion of fibre-external bound water p.sub.EB and the consistency c of the fibre sample; and the WRV value as a sum of the amount of fibre-internal bound water W.sub.IB and the amount of fibre-external bound water W.sub.EB.

7. The device according to claim 6, comprising a pump for aspirating the sample from the flow channel to the side flow channel and to the time-domain NMR spectroscope located in the side flow channel after the refiner.

8. A control system for a fibre web machine, the control system comprising: a device according to claim 6 for measuring a fibre porosity of a fibre suspension exiting a refiner; a computing unit for calculating control parameters based on the fibre porosity measured with the device and a selected target, wherein the computing unit is arranged to calculate fibre porosity and a related comparison value from the samples taken before and after the refiner and to control the refiner or the fibre web machine based on the comparison value; data transfer equipment for transferring control parameters from the computing unit to the refiner or the fibre web machine or both, and two side flow channels for taking a sample both before and after the refiner.

9. The control system according to claim 8, further comprising a first valve and a further valve arranged in the side flow channels for stopping the sample during measurement.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The invention is described below in detail with reference to the accompanying drawings that illustrate some of the embodiments of the invention, in which:

[0040] FIG. 1 is a basic view of the location and movements of water relative to fibre;

[0041] FIG. 2a depicts the process position according to a first embodiment of the system according to the invention;

[0042] FIG. 2b depicts the process position according to a second embodiment of the system according to the invention;

[0043] FIG. 3 is a basic overview of a system according to the invention;

[0044] FIG. 4 is a cross-sectional view of a device according to the invention;

[0045] FIG. 5 is a block diagram illustrating the steps of the method according to the invention;

[0046] FIG. 6 is a basic view of the design of a control system according to the invention; and

[0047] FIG. 7 is a graphic representation of the double exponential model.

DETAILED DESCRIPTION OF THE INVENTION

[0048] FIG. 1 depicts a basic view of how water is located relative to fibre. It is known that fibre includes internally bound water p.sub.IB and fibre-internally free water p.sub.FI. Water molecules can change place fibre-internally binding to water bound from free water or releasing from bound water into free water quite quickly due to physical phenomena or chemical reactions. Correspondingly, outside fibre, water p.sub.BE as well as free water p.sub.FE has bound to the fibre surface. Outside fibre, the transfer from bound water to free water and vice versa can also take place quickly. Instead, the transfer from fibre-internal water to external water has been found to be slow, due to the secondary wall structure of fibre. The sum of the proportions of fibre-internal free and bound water p.sub.BI+p.sub.FI=1 and the total sum of the proportions of external free and bound water p.sub.BE+p.sub.FE=1. The basic calculation principles of water exchange are known from the publication of Zimmerman, J. & Brittin, W. (1957). “Nuclear Magnetic Resonance Studies in Multiple Phase Systems: Lifetime Of A Water Molecule In An Adsorbing Phase On Silica Gel.,” J. Phys. Chem., 61(10), 1328-1333. doi: 10.1021/j150556a015, see equations 48 and 50.

[0049] As shown in FIGS. 2a and 2b, a device 10 according to the invention is arranged to be used in context with a refiner 100. According to FIG. 1a, the device 10 can be located in such a way that a small side flow is deviated from the flow 101 of the fibre suspension flow channel 101 going to the refiner 100 into a side flow channel 102, which is positioned, as shown in FIG. 1a, after the refiner 100 and which leads part of the fibre suspension flow to the device 10 according to the invention. The device 10 is advantageously connected to the side flow channel 102, which can be an already existing flow channel associated with the refiner or a part of a system according to the invention installed for this purpose.

[0050] The side flow channel 102 advantageously has a first valve 16 for sampling, with which it is possible to adjust the volume and flow rate of fibre suspension entering the device 10, and a second valve 17, with which the sample can be stopped in the device 10 for the duration of the measurement. According to FIG. 2b, a fibre suspension flow can also be led to the device 10 via two side flow channels 102. One side flow channel 102 is preferably a flow channel, which is used to lead the fibre suspension flow before the refiner 100 through the one first valve 16 to the device 10. The other side flow channel 102 is advantageously a flow channel, which is used to lead the fibre suspension flow after the refiner 100 through the second valve 15 to the device 10. In this way, it is possible to perform comparative measurements on both the fibre suspension that enters the refiner and the fibre suspension, already refined, that exits the refiner. The size of the sample led from the fibre suspension to the device can be as small as 1-10 cm.sup.3, in which case the equipment is also relatively small-scale. Nevertheless, such a sample is sufficient for determining fibre porosity.

[0051] According to FIGS. 2a-4, in the method according to the invention, part of the fibre suspension flow can be led to a side route for an online measurement, wherein the measurement is performed using the device 10 according to the invention. The first valve 16 is used to control sampling from the fibre suspension flow 14. Arranged in context with the side flow channel 102, there is a device 10 according to the invention comprising connection means 13 and equipment 18 for determining fibre porosity of the fibre suspension based on a sample, which equipment 18 is a time-domain NMR spectroscope 20. The connection means 13 can consist of connections, with which the sample channel 12 of the NMR spectroscope 20 is connected to the side flow channel 102 so that the sample channel 12 and the side flow channel 102 form a continuous route for the fibre suspension up to and through the NMR spectroscope 20.

[0052] More specifically, the NMR spectroscope 20 of the device 10 according to the invention includes a sample channel 12, at least one coil 22 for exciting protons p contained in free and bound water of fibres in the fibre suspension flow, arranged around the sample channel 12 as shown in FIG. 3. The NMR spectroscope 20 also includes a magnet 24 arranged around the sample channel 12 for generating a magnetic field E in the sample channel 12. Advantageously, the magnet 24 is also arranged around the coil 22 in the radial direction relative to the sample channel 12 above the coil 22. The magnetic field E generated by the magnet 24 is advantageously a magnetic field as homogeneous and static as possible, through which the fibre suspension flow 14 passes inside the sample channel 12. The magnetic field E is depicted in the figure with lines in the transverse direction relative to the sample channel. The direction of the magnetic field is advantageously transverse relative to the longitudinal direction of the sample channel. The magnet is advantageously a permanent magnet, which can be implemented without separate driving power in order to operate. A permanent magnet generates a static permanent magnetic field in itself. Alternatively, the magnet can also be an electromagnet, the magnetic field of which is provided by electric current.

[0053] In addition, the NMR spectroscope 20 includes, as shown in FIGS. 3 and 4, a power source 26 connected to a coil 22 for generating frequency pulses, measuring equipment 28 for measuring the intensity of voltage generated by the frequency pulse returning to the coil 22 from protons p for generating a return signal, and programmable means 30 for determining fibre porosity of samples based on the return signal and for controlling a first valve 16 for taking samples. With the power source 26, a frequency pulse is delivered to the coil 22 to excite protons p contained in bound and free water travelling inside the coil 22 into a higher energy state (spin) as the protons absorb the frequency pulse. This energy state discharges rapidly (in milliseconds), the proton p thereby delivering or emitting energy to its surrounding, which again generates a voltage in the coil 22, i.e., a return signal, the amplitude of which can be measured with the measuring equipment 28.

[0054] The equipment 18 of the device 10 further includes a computer 25 equipped with programmable means for determining fibre porosity of samples based on the return signal by determining the proton relaxation time and the amplitude of the return signal from the return signal and fibre porosity of a fibre suspension based on the relaxation time and the amplitude.

[0055] Advantageously, the magnet 24, the coil 22 and the sample channel 12 are encased using a box construction 32 according to FIG. 3. Advantageously, the box construction is made of metal, thus preventing expansion of the magnetic field to the environment and, on the other hand, access of disturbances external to the device to the magnetic field. In this way, the device according to the invention can easily provide a closed magnetic field and is thus easily applicable in mill conditions. Basically, the aforementioned components of the NMR spectroscope 20 can be placed within the same box construction; however, there are preferably two box constructions. One box construction includes measuring equipment 28, a computer 25 and a power source 26, whereas the other box construction encloses a magnet 24 and a coil 22. In this way, damage to sensitive electronic components is avoided in cases of leaking of a water-containing fibre suspension.

[0056] The relaxation time correlates with the ratio of free water to bound water contained in fibres in the fibre suspension, which ratio will change during refining as fines detach on the surface of fibres and fibres fibrillate. With increasing fibrillation, the relaxation time T2 decreases. The so-called CPMG (Carr-Parcell-Meiboom-Gill) pulse sequence, which contains one 90° pulse and several 180° pulses, can be used to determine the spin-spin relaxation time T2. Amplitudes of echoes of the pulse sequence attenuate according to the following equation:

a(t)=a.sub.o exp(−t/T2),

where a.sub.0 is the amplitude at the time t=0s and T2=spin−spin relaxation time. Parameters a.sub.o and T2 can be defined by placing the equation in an experimental signal.

[0057] The diameter of the sample channel can be at least 10 mm, preferably 10-20 mm, to allow for the fibre suspension to flow in the sample channel without problems. The dry solids content of the fibre suspension can generally range between 0.5% and 4.0% by weight, at which it remains pumpable. Fibre suspensions at a higher dry content may require a higher pressure to move in the sample channel, but when placed after the refiner, the sample is taken from the fibre suspension flow where the pressure is generally sufficient. Advantageously, a separate pump is also used in the side flow channel for moving the fibre suspension forward. A small diameter of the sample channel proposed above also enables the use of a smaller coil. In this case, the centre hole of the magnet placed on the coil, advantageously above the sample channel, can have a smaller diameter, approximately as small as between 30 mm and 40 mm. The manufacturing costs of the magnet are generally the lower, the smaller is the hole that needs to be produced in the magnet.

[0058] The device according to the invention can be realised using one coil or with two coils. When one coil is used, the same coil both delivers and receives the frequency pulse. When two coils are used, one coil can deliver the frequency pulse and the other one receives it. The use of one coil is possible, if the sample flows so slowly that the same protons that are exposed to the frequency pulse will also have time to deliver the return signal in the coil area. Alternatively, the device may include two valves, which are used to stop the sample for a moment at the coil and the magnet. In turn, the use of two coils enables the determination of porosity from a moving flow when correctly adjusted. The coil, also called a bobbin, used in the device is electrically dimensioned in such a way that, with a selected power source, it can produce the desired frequency pulse, or excitation pulse, in a selected magnetic field. For example, when the strength of the magnetic field E is 0.5 T, the frequency pulse applied is in the frequency range of 25 MHz-26 MHz. Generally, the frequency pulse used is in the range of 50 kHz-150 MHz. When one coil is used for the measurement, the length of the coil used may be approximately 10-20 cm, whereby protons in the fibre suspension flow will have time to get excited and deliver energy across the coil. The coil may have 100-200 turns.

[0059] Energy released by the proton p excited according to FIG. 3 provides a return frequency in the coil 22, which can be measured as a return signal. The return signal to be measured can be measured with extremely sensitive measuring equipment 28, for example, with a receiver whose measuring accuracy can be in the class of 1 μV. The return signal to be measured is only an average signal; that is, momentary values are measured for the return signal in a certain period and, based on these values, an average is calculated for this period. In other words, the entire spectrum is not measured, as is usually the case in spectroscopy. For example, the duration of the period may be between 0.5 s and 2.0 s. Based on the strength of the return signal, the relaxation times T1 and T2 of the proton can be calculated. The relaxation time can be calculated with the following formula: T2=−t/{ln[a(t)/a.sub.o}

[0060] Programmable means 30 have been implemented in a computer 25, which can be used for presenting results as well as for controlling the device. The computer can be a normal PC or equivalent. The material of the flow channel is preferably glass, Teflon or other equivalent non-magnetic material, which does not disturb the generation of the magnetic field within the flow channel. In turn, the power source is an AC power source, in relation to which a frequency converter can be used to achieve the correct frequency.

[0061] The control of device operations can take place with the same computer, provided with programmable means for determining fibre porosity using an empirical formula based on measured relaxation times. To control the device, it is possible to use separate control software that provides electric controls via a field bus, for example, for valve actuators, which open the valve of the flow channel for taking the sample either periodically or continuously.

[0062] FIG. 5 shows steps 40-62 of an embodiment of the method according to the invention in a block diagram. The method according to the invention starts from taking of a sample, either after the refiner 100 according to FIG. 1a, or both before and after the refiner 100 according to FIG. 1b. Advantageously, the sample is taken, according to FIG. 1b, both before the refiner 100 and after the refiner 100 by leading the fibre suspension to a separate side flow channel 102 as a sample, according to step 40, which allows determination of the fibre porosity of the sample. Connected to the flow channel 101 that enters the refiner 100 or exits the refiner 100, there is a side flow channel 102 having a first valve 16 and a second valve 17. By opening the first valve 16, part of the fibre suspension is led to the side flow channel 102 as a sample either periodically or continuously. Advantageously, the flow is led to the side flow channel 102 periodically, since then the sample flow can be stopped within the magnet of the device 10 for the duration of the measurement by means of the first valve 16 and the second valve 17. Periodically repeated, sampling can be repeated at intervals of 1 to 2 minutes, for example.

[0063] The first valve 16 and the second valve 17 are controlled preferably with a computer 25 and computer-operated programmable means 30, in which the sampling interval or the necessary volumetric flow per period has been defined. Based on the control software, the computer 25 sends a control command via a field bus, for example, advantageously to a relay 36 of FIG. 2, via which the power supply is connected to the actuators of the first valve 16 and the second valve 17. Advantageously, the first valve 16 and the second valve 17 are solenoid valves, since solenoid valves are not as sensitive to environmental disturbances as other valve types. When the power supply to the actuators of the valves 16 and 17 is disconnected with the relay 36, the valves 16 and 17 will close, while when under voltage, the valves 16 ja 17 are in their open positions enabling the fibre suspension flow in the side flow channel 102.

[0064] Advantageously, the side flow channel 102 also includes a pump 34, with which a fibre suspension that is difficult to move can be reliably transferred along the side flow channel 102 to the equipment 18 for determining fibre porosity. For example, the pump can be a hose pump. Advantageously, power is supplied to the pump 34 via the same relay 36 so that the entire sampling process can be managed by controlling one relay 36. The sample is aspirated to the side flow channel 102, until the sample is conveyed into the magnet 24, at which time the power supply to the first valve 16 and the second valve 17 is disconnected with the relay 36, at which time these will close. At the same time, the power supply to the pump 34 is disconnected. The control of the relay 36 can be implemented by time control, for example.

[0065] At the same time, a magnetic field has been generated in the device preferably using a permanent magnet applied as the magnet 24 in the device, according to step 42 of FIG. 4. The purpose of the magnetic field is to enable excitation of protons with frequency pulses generated by the coil 22. When generated by a permanent magnet, the magnetic field is permanent and does not require any specific control. The computer can also be associated with an electronic control unit controlled by the control means, while the control unit, in turn, controls the power source of the device to generate frequency pulses for the coil, according to step 44 of FIG. 4. Frequency pulses are preferably generated at the frequency indicated above while the sample is in the magnetic field. Advantageously, the frequency pulse used is the so-called CPMG frequency pulse, which includes one 90° pulse and several 180° pulses. Pulses are delivered one after the other and they excite the protons in the magnetic field, according to step 46 of FIG. 4. The excitation is very rapidly discharged and the energy delivered by the proton arrives at the coil providing a low voltage in the coil, which is measured with the measuring equipment according to step 48. From the measuring equipment, the voltage data can be transferred in the analog form to an A/D converter or as a digital signal directly to the computer 25, where it will be stored in a memory 35 with the programmable means 30 for further processing.

[0066] The amplitude of voltage is advantageously measured continuously, and momentary measuring results of voltage are stored in the memory. Advantageously, the sample in the magnetic field is exposed to four different frequency pulses generated with the coil generating thereby four different attenuating signals, the amplitudes of which are measured with the measuring equipment. Based on the amplitudes measured, an average value can be calculated with the programmable means. In addition, an average value can be calculated over successive samples, since variations between individual samples are notably greater than variations between the successive signals of the same sample.

[0067] The proton relaxation time T1 or T2 calculated based on the measured amplitude of the return signal is used together with an empirically defined calculation model to determine fibre porosity with the programmable means 30 in step 50 of FIG. 5. The general form of the calculation model is as follows:

[00003]$\text{?}$$\text{?}\text{indicates text missing or illegible when filed}$

[0068] The model uses a relaxation speed or R.sub.x, the ratio of which to the relaxation time T is T=1/R.

[0069] The number of summable exponential factors used in the model can be between one and four, preferably one or two, most preferably two. The value of the exponential signal is directly obtained in the NMR measurement by the measuring equipment, measured at the coil and, based on it, it is possible to calculate the relaxation time and the amplitude using general calculation methods.

[0070] Example values for both spruce and birch pulps are given below:

TABLE-US-00001 Spruce Birch A.sub.I 1.482173 2.316276 A.sub.E 23.29918 20.00418 R.sub.2I 3.31536 3.007642 R.sub.2E 0.765683 0.985788

[0071] In the simplified single exponential factor model, the calculation is based on an empirical assumption that the experimental signal consists of one exponential signal as follows:

Exp=A*exp(R.sub.2*t),

where, based on the strength of the exponential signal determined by NMR spectroscopy, the relaxation speed R.sub.2 calculated in step 52 of FIG. 5 gives the average movement state of water molecules. The form of the exponential signal in the case of the double exponential model is shown in FIG. 7, but it should be understood that the single exponential model also follows quite well the shape of the exp curve of FIG. 7. With R.sub.2, it is possible to calculate the WRV value representing filtration of water in step 54 utilising the linear formula and calibration:

WRV.sub.NMR=kk*R.sub.2cor+constant,

where R.sub.2corr=R.sub.2−a*(c−c.sub.ref) and kk is the slope of the linear formula, a is an empirical constant, c is the sample consistency, c.sub.ref is the reference consistency and R.sub.2corr is the relaxation speed R.sub.2 corrected relative to consistency. This value corresponds to the WRV value measured in laboratory (unit g/g). In the calculation, in addition to the relaxation time, the NMR measurement provides the signal amplitude A, which is utilised in the calculation. The slope kk can be determined utilising calibration samples, for which the WRV values are known. As reference consistency, it is possible to use a selected value, relative to which all values are corrected computationally. Advantageously, the reference consistency can be 0.5%-4.0%, preferably 1.0-2.0%, most preferably 1.6%.

[0072] Particularly good accuracy has been achieved with an empirical constant value of 0.186 l/(%*s). Below is a description of parameters used in the NMR spectroscope, the use of which has provided particularly good accuracy with the empirical constant value. A resonance frequency of 21.73 MHz was used and the echo time in the CPMG pulse sequence is 2 ms. The time between the CPMG pulse sequences (same sample) is 6000 ms, when more than one pulse sequence is summed up, after which the sample is changed in the NMR spectroscope with a pump. If the number of samples is one, then the time between pulse sequences is 100 ms (sample changed in-between). The width of a 90 degrees pulse is 16 or 35 microseconds, while the width of a 180 degrees pulse is 36 or 70 microseconds depending on the magnet and the sample unit. With the aforementioned parameters, the value of the empirical constant can range between 0.1859 and 0.276.

[0073] Alternatively, for the single exponential factor model, it is possible to use the double exponential factor or the so-called physical model in the calculation, where the experimental signal Exp consists, as shown in FIG. 7, of two exponential parts, of which part 66 is from fibre-internal water and part 68 is from fibre-external water. This is because the exchange between fibre-external and fibre-internal water is slow. The experimental signal can be represented by the following formula:

Exp=A.sub.I*exp(R.sub.2I*t)+A.sub.E*exp(R.sub.2E*t)+C,

where amplitudes A.sub.I and A.sub.E indicate how much there is water in fibre and outside of it. Relaxation speeds calculated from the strength of the exponential signal in step 56, R.sub.2I=P.sub.IB*R.sub.IB+p.sub.IF*R.sub.IF and R.sub.2E=p.sub.EB*R.sub.EB+p.sub.EF*R.sub.EF, indicate the average movement state of water molecules inside and outside fibre. Water internal and external to fibre takes two different states: bound (p.sub.B) and free (p.sub.F). In addition, it is known that p.sub.IB+p.sub.IF=1 and p.sub.EB+p.sub.EF=1. The relative amplitude A.sub.I_rel indicates the proportion of water inside fibre and can be determined in step 58 with the following formula:

A.sub.I_rel=100%*A.sub.I/(A.sub.I+A.sub.E),

whereas the relative amplitude A.sub.E_rel indicates the proportion of water outside fibre and can be determined with the following formula:

A.sub.E_rel=100%*A.sub.E/(A.sub.I+A.sub.E).

[0074] Both portions include both bound and free water.

[0075] The proportions of bound water p in fibre and outside fibre can be calculated in step 60 as follows:

p.sub.IB=(R.sub.2I−R.sub.2F)/(R.sub.2B−R.sub.2F) and

p.sub.EB=(R.sub.2E−R.sub.2F)/(R.sub.2B−R.sub.2F),
where R.sub.2F is the relaxation time of completely free water, which can be measured, and R.sub.2B is the relaxation time of completely bound water, which can be assessed. The assessment can be done using a calibration constant; i.e., by defining an experimental WRV value for the sample, based on which the correct value is calculated for the relaxation speed of completely bound water R.sub.2B. Alternatively, R.sub.2B can be defined experimentally with the NMR equipment from a sample from which free water has been removed by centrifugation, for example, before the NMR measurement.

[0076] The product A.sub.I_rel*p.sub.IB indicates how large a portion from the total water amount is bound inside fibre and the product A.sub.E_rel*p.sub.EB indicates how large a portion of the total water amount is bound outside fibre.

The expression

W.sub.IB=A.sub.I_rel*p.sub.IB*(100−c)/c

indicates how many grams of water is bound per each gram of fibre inside fibre and

W.sub.EB=A.sub.E_rel*p.sub.EB*(100−c)/c

outside fibre (the unit is g/g), with c being the sample consistency (%).
Finally, it is possible to calculate, in step 62, the WRV value determined with the NMR technique using the following formula:

WRW_NMR=W.sub.IB+W.sub.EB

[0077] This value corresponds to the WRV value measured in laboratory (unit g/g).

[0078] According to an advantageous embodiment, the fibre porosity WRV value calculated in step 54 using the single exponential signal model and the fibre porosity WRV value calculated in step 62 using the double exponential signal model are compared to each other 64 for evaluating the reliability of calculation. A reliability metric can be, for example, the percent deviation of these two calculated WRV values relative to each other or relative to the previously calculated value. The final porosity measurement result can be an average of these WRV values or a filtered average.

[0079] FIG. 6 shows an example of a control system 11 according to the invention. The control system 11 includes, in all of the embodiments, a device 10 according to the invention for measuring the porosity of fibres of a fibre suspension exiting the refiner 100, a computing unit 112 for calculating control parameters based on fibre porosity measured with the device 10 and a selected target, and data transfer equipment 114 for transferring control parameters from the computing unit 112 to the refiner 100 or the fibre web machine 110 or both. Information on fibre porosity can be utilised to control refining or improve the runnability of a fibre web machine 110 or both. Fibre porosity is measured at least from the fibre suspension that exits the refiner 100, but the measurement can be preferably performed both before and after the refiners 100 as in FIG. 6. In this way, it is possible to obtain accurate information about the effect of refining on the properties of fibres of the fibre suspension.

[0080] In the control system, the computing unit 112 receives the fibre porosity information relating to the sample, calculated in near real time by the device 10, using the data transfer equipment 114, along a field bus, for example. A target value, which is the desired fibre porosity value, has preferably been entered in the computing unit 112. The remainder between the measured value and the target is calculated and, based on the remainder, the refiner is controlled, for example, by changing the specific energy consumption of refining or the blade angles of the refiner. The control performed based on the porosity value can also consist of controlling the fibre web machine, for example, by changing the ratio of fibre suspension to fillers in paper production, steam use in the dryer section of a fibre web machine or press pressures in the press section.

[0081] The computing unit of the control system can be a separate computer, but the computing unit of the control system is preferably integrated into the computer of the device according to the invention. Advantageously, the control system 11 includes, according to FIG. 6, two side flow channels 102 for taking a sample both before and after the refiner 100. In addition, the control system preferably also includes a first valve 16 and a third valve 15, with which the sample can be stopped at the device 10. If the sample is taken before the refiner 100, the sample is stopped by using a second valve 17 and the third valve 15. If the sample is taken after the refiner 100, the sample is stopped by using the second valve 17 and the first valve 16. The computing unit 112 is arranged to calculate fibre porosity from the samples taken before and after the refiner 100 and the related comparison value and to control the refiner 100 or the fibre web machine 110 based on the comparison value. The control of the refiner can be feedback control and it is possible to use prior art PID controllers associated with the control for accelerating the control.

[0082] According to an embodiment, programmable means of the device are arranged to use previous memorised porosity measurement values for calculating the control in such a way that two or more last porosity measurement values are used to calculate an average or other statistical value, with which the significance of an individual measurement deviation on the control is reduced and the control is stabilised.

[0083] As a part not included in the invention, it can be contemplated that the NMR spectroscope is only used for determining the amount of fibre-internal and fibre-external water. The amount of fibre-internal water correlates to how refining has provided fibre-internal fibrillation, whereas the amount of external bound water correlates to how refining has provided fibre-external fibrillation. In this way, based only on the amounts of fibre-external and fibre-internal water, it is possible to conclude facts about the performance of refining without determining fibre porosity as a whole.

[0084] It will be understood that the above description of the present invention is susceptible to various modifications, changes, and adaptations, and that the same are intended to be comprehended within the meaning and range of equivalents of the appended claims.