WO2012070947A1

WO2012070947A1 - Method for detection and localization of a fluid leak related to a piston machine

Info

Publication number: WO2012070947A1
Application number: PCT/NO2011/000322
Authority: WO
Inventors: Åge KYLLINGSTAD; Pål Jakob NESSJØEN
Original assignee: National Oilwell Varco Norway As
Priority date: 2010-11-22
Filing date: 2011-11-18
Publication date: 2012-05-31
Also published as: CA2816485C; EP2643673A1; US9476417B2; EP2643673A4; NO336024B1; EP2643673B1; CA2816485A1; BR112013012487A2; US20130280106A1; NO20101641A1

Abstract

A method for detecting and localizing a valve leak in a piston machine (1) having a shaft 24, where the method includes: - attaching at least one vibration sensor (16', 16", 16''') to a valve block (14', 14", 14'''), of the piston machine (1); - measuring the vibrations from all vibration sensors (16', 16", 16'''); - attaching a sensor (22) to the piston machine (1) where the sensor is designed to produce, directly or indirectly, an angular shaft position signal for the shaft (24), and where the method further includes: - determining, directly or indirectly, an angular shaft position signal for the shaft (24); - transforming the vibration signals from all vibration sensors (16', 16", 16''') into one envelope signal representing the instant vibration level; - using the window functions to find sector based averages of the vibration level, and - comparing said averages with a critical ambient vibration level to detect and localize leaks in one or two valves.

Description

METHOD FOR DETECTION AND LOCALIZATION OF A FLUID LEAK RELATED TO A PISTON MACHINE

This invention concerns detection and localization of a fluid leak in the valves of a reciprocating piston machine. More specifically the invention concerns a method for detection and localization of a fluid leak related to a piston machine, where the method includes:

- attaching at least one vibration sensor to a valve block of the piston machine;

- measuring the vibrations from all vibration sensors; and

- attaching a sensor to the piston machine where the sensor is designed to produce, directly or indirectly, an angular shaft position signal for the shaft.

Detection, localization and quantification of leaks related to piston machines (hereafter referred to as pumps, for simplicity) are important for minimizing costs and down time related to valve and piston failures. Today's practice provides no certain way to localize leaks. A leak in one or more valves or pistons will cause a drop in the volumetric efficiency. If a pump is running at a constant speed, this reduction in volumetric efficiency also causes the mean discharge pressure to drop. However, a pressure drop can result also from leaks outside the pump or even reductions in the flow resistance not related to leaks. Such reductions in flow resistance may arise from temperature and viscosity or they can come from a bypass of one or more flow restrictors. Therefore, a pressure drop cannot be used for localizing the leak.

Skilled operators can sometimes localize valve leaks by listening to the sound of the pump by a simple stethoscope, normally in the form of a screwdriver or a wooden stick held between the valve block and the human ear. There is however some disadvantages related to this method, such as:

- The localization is uncertain, even for a trained and experienced person.

- It is generally not possible to distinguish between a suction valve and a discharge valve.

- The person has to make the diagnosis in hazardous area because he/she must stay very close to the pump while it is running.

- The person will also be exposed to injuriously high sound pressure levels, often exceeding 100 dBA near the pump.

- The diagnosis is time consuming.

- The check will only be carried out at certain intervals.

A leak in a valve or piston manifests itself by several effects that can be picked up by various sensors. The most striking changes due to a growing leak are:

- The discharge pressure starts dropping, provided that the loss in pressure is not compensated by an increase in the total pump rate.

- The discharge pressure from a pump starts to vary cyclically with a period equal to the pump rotation period.

- The suction pressure to a pump also starts to vary cyclically with the same period.

- Low frequency and cyclic vibrations increase, especially on flexible hoses, both the high-pressure hose and the low-pressure hose.

- The high frequency vibration level of the pump near the leak source increases.

Prior art include several methods for leak detection that are utilizing the first four features listed above. According to US-patent 5720598 the pressure from at least one pump in combination with the rotational speed of the pump, measured in time, are utilized to determine and analyze the pump harmonics for the presence of a defect and the type of defect. The specific pump unit having the defect is then determined.

WO document 03/087754 describes a method using a combination of active speed variation tests and harmonic analysis to both quantify and localize a leakage.

Experience has shown that the prior art methods above do not work satisfactorily in in situ environments. It is particularly difficult to pinpoint the actual valve leaking.

A leak flow in the reverse direction through a defective valve will generate high frequency vibrations in the valve block. The vibrations may be picked up by an accelerometer placed close to the leak source, for instance on the outside surface of a valve block.

US-patent 5650943 describes a method utilizing portable equipment where

transducers are applied to appropriate locations in the valve system to obtain sound signals. The signals are fast Fourier transformed into valve signatures. The differential signature method is used to make determinations of valve leaks. The method is designed to evaluate whether a valve is leaking or not. It is not designed to distinguish between leaks in the suction valve and the discharge valve in a valve block. Thus, the method includes comparing obtained signals with stored signals from the actual valve, where the stored signal is obtained from a previously made database. The method will not distinguish between valves in the same valve block.

Norwegian document 20072230 discloses a method that utilizes the fact that a leak in a closed valve of a piston machine will generate high frequency vibrations in the valve block containing the leaky valve. By picking up these vibrations by accelerometers (one per valve block), process the vibration data together with a timing signal it is possible by use of the method to detect a leak and localize the leak source.

In suit tests has shown that the described method applies for Hex pumps where the valve blocks are widely separated so that a leak induced vibration transferred from the leaky valve block to another valve block, is small. However, field experience has also shown that said method does not work with pumps, such as quintuplex pumps, having one integrated valve block instead of split valve blocks. The reason is that the damping of the vibration within the block is relatively low. In other words, leak induced vibration can be picked up almost anywhere on the valve block and accelerometer placement will not help to localize the leak like it does in a Hex pump.

In situ measurements also indicate that said method does not work satisfactorily on triplex pumps, although a triplex pump have separated valve blocks. A possible reason for an observed relatively strong vibration transfer between valve blocks in a triplex pump, may be the suction manifold. The suction manifold is often a relatively large pipe having flanges and it acts as an effective bridge for transfer of vibration between the three suction valve blocks.

The object of the invention is to overcome or reduce at least one of the drawbacks of the prior art.

The object is achieved according to the invention by the features as disclosed in the description below and the following patent claims.

There is provided a method for detecting and localization of a valve leak in a piston machine having a shaft , where the method includes:

- attaching at least one vibration sensor to a valve block, of the piston machine;

- measuring the vibrations from the at least one vibration sensor;

- attaching a sensor to the piston machine where the sensor is designed to produce, directly or indirectly, an angular shaft position signal for the shaft, wherein the method further including:

- determining, directly or indirectly, an angular shaft position signal for the shaft; - transforming the vibration signals from all vibration sensors into one envelope signal reflecting the instant vibration level;

- using the angular position signal for constructing window functions that pick up the envelope signal in selected angular shaft sectors;

- using the window functions to find sector based averages of the vibration level; and

- compare said averages with a critical ambient vibration level to detect and localize leaks in one or two valves.

The proposed method may be described by two slightly different algorithms. A first algorithm is a simpler one that is well suited for detecting and localizing a single leak. A second algorithm is more advanced and capable of localizing double leaks.

Both algorithms require a shaft angle Θ that may be measured directly from a sensor or calculated for instance as explained below:

A timer signal originates from a sensor that is designed to give a digital timer signal with one pulse per revolution that is used for finding the pump shaft angle at all times. The following sub-algorithm may be used for this timer to angle transformation. The timing signal, which is typically the digital, two levels, signal from a proximity sensor, is essential in this method. The sensor must give only one pulse per revolution but it may be installed at different places, such as the main gear, the crank shaft or one of the piston rods. The following algorithm may be applied to transform the timing signal to the pump shaft angle, Θ . This method applies even if the pump speed is not constant but changes slowly during the analysis period. i. Determine all timer events {t_uP(i} when the timing signal turns from a low value to a high value. ii. Find the corresponding revolution periods T_j from the difference between

successive times. iii. Find corresponding average pump speeds = 2n/T_j and centre times

t_j = (t_up,i₊i +t_uP(l)/2. It should be noted that the number of averages is one less than the number of timer events. iv. Apply a suitable ID interpolation/extrapolation method to find the angular

pump speed for all time samples: Ω = interpl(t_j, Q_if t). v. Time integrate said speed to obtain an accumulated pump shaft angle:

Gacc = Σ Ω-At where∑ denotes where accumulated summation and At denotes sample time interval. vi. Calculate the difference between said accumulated angle and the real angular shaft position at the first timer event by interpolation,

e_acc,_uP = interpl(t, e_acc,t_up,i) . vii. Finally find the pump shaft position as the accumulated pump angle minus said difference: Θ = 9_acc-0_acc,up+6up where θ_υρ represents the true pump shaft angle when the timer signal goes high.

The angle conversion method above applies equally well if the positive timer signal edge is substituted by the negative timer edge, provided that the pump angle for the negative edge is known. The method requires at least two complete revolutions to able to provide the angle with a variable speed. Otherwise a constant speed is assumed. If an additional timer signal is used, for instance a proximity sensor sensing all gear teeth of the main gear, a more detailed speed profile can be calculated, without requiring more than two revolutions.

The relatively simple version of the new leak detection algorithm includes the following steps, and it allows one or more acceleration signals to be used.

a) Capture high rate data on acceleration(s), a,, and proximity sensor over a time interval covering at least one pump revolution.

b) Optionally, apply a signal conditioning filter to the raw acceleration signals. c) Analyze the timing signal to find the shaft angle Θ as a function of time, as described above.

d) Construct an envelope function, for instance a_env= V(∑a,²), representing the instantaneous vibration level

e) Calculate the 1^st harmonic complex Fourier component of the envelop signal by Ci= 2(a_en_Vexp(j9)), where j is the imaginary unit (-l) and the brackets < ) denote averaging over an integer number of revolutions.

f) Determine the potential leak angle by Q\_eak = angle(ci), representing the

sector centre of enhanced vibrations.

g) Construct angle based window function, Wi, picking the envelope function in a sector centered on the leak angle 0|_eai<, and another window, w₀, picking the envelope function in a sector centered on the complementary angle (Q\_eak±n) . h) Find the corresponding vibration levels

i) Set a leak alarm if the highest vibration level exceeds a critical level, for instance s_cr=2s₀ and determine that the leaky valve being the one having its closing phase nearest to the observed leak phase 9i_eak-

The sampling frequency from the accelerometer should be high enough, typically 25 kHz, to include the dominating leak noise vibration frequencies. The conditioning filter in the second step may include firstly a de-spiking or clipping to minimize the effect of valve closing spikes and secondly a band-pass filter for maximize the contrast between leak noise and normal, ambient noise. The envelope function can

alternatively include a multiplicative factor or, if only one accelerometer signal is used, be constructed by applying Hilbert transform : a_env= | Hilbert(a) | .

Also the envelope function may optionally, for presentation purposes, be smoothed by a low pass filter having no phase shifts. A possible choice for the windows Wi and w₀, which represent the sectors of respective maximum and minimum vibrations, is

Wi= H(cos(e-eieak)) and w₀= H(-cos(9-9|_eak))_/ H being the Heaviside step function defined as 1 for positive arguments and 0 otherwise. The suggested windows can alternatively be substituted by smaller sectors (180°-2ΔΘ) by using the more general formulas H(cos(9-9|_eak)-sin(A9)) and w₀= H(-cos(9-9|_eak)+sin(A9)), or by

continuously varying window functions, such as

· H(cos(9-9|_eak)) and

· H(-cos(9-9iea_k))- An alternative to using the current low vibration level, s₀, as a reference for the critical vibration level, is to use normal ambient vibration levels based on past measurements all valves were healthy.

Concerning the last step on localizing the leak, it should be realized that each valve has a unique phase representing the centre of the leak phase. As an example, if the "firing" order of a quintuplex pump is {1,5,2,4,3} (the numbers representing the linear position order), then the corresponding suction valves have the following centre phases {9_Si, 9_S2, 9_S3,9_S4, 9_Ss}= {90°, 162°, -126°, -54°, 18°}, and the discharge valves have the following phases {9_Di, 9_D2, 9_D3,9_D4, 9_D5} = {-90°, -18°, 54°,126°,-162°}. Here the subscript _Si, say, refers the closing phase and the potential leak phase of suction valve 1. The above phase angles are theoretical and based on the assumptions of perfect valves and no fluid compressibility.

In reality inertia and fluid compressibility cause a phase lag. This phase lag can be modelled and corrected for, either by shifting the above valve phases to higher values or by shifting the observed leak phase to a lower value. A suitable model for the lag shift is 9i_ag = Ω·τ + Δθ_ρ where Ω is the pump rotation speed (in rad/s), τ is the valve closing delay time (typically 0.02 s) and Δθ_ρ is a pressure lag function. It is a nonlinear and complicated function dependent on many factors, such as discharge pressure, fluid compressibility and the so-called clearance volume. The clearance volume is the residual fluid volume between the suction and discharge valves when the piston is fully extended.

The algorithm for leak detection described is not capable of detecting and localizing two leaky valves simultaneously, unless the leaks have very different strength. The reason is that two leaks will interfere with each other and the resulting envelope function will have a centre that may not correspond to any of the leaky valves.

However, a skilled operator may probably localize multiple leaks by comparing the vibration signal with the different valve closing phases.

The method may further include:

- letting the windows represent 2p non-overlapping sectors where p is the number of pistons in the piston machine;

- setting a leak alarm if a group of p or more adjacent sectors have a vibration level exceeding a critical level; and

- determining, if the leak alarm is a set, the leaky valves as those valves having closing sectors that match either the first p sectors or the last p sectors of said group.

The method may further include:

- determining the centre angle of the envelope vibration signal by Fourier analysis;

- using said centre angle to construct two wide and complementary window functions representing shaft sectors for respective the highest and the lowest vibration level; and

- using these window functions and the envelope function to find the average signal level in said sectors; and

- setting a leak alarm if the highest vibration level exceeds the critical value; and

- determining, if the leak alarm is set, the leaky valve as the valve having its closing sector nearest to the window sector of highest vibration level.

The method may further include:

- setting a critical vibration level that triggers a leak alarm equal to a multiplicative factor times the minimum value of sector based vibration levels.

The method may further include:

- setting a critical vibration level that triggers a leak alarm to a value that is either calculated from an empirical formula as a function of pump speed and discharge pressure, or picked from a look-up table, and where in both cases past measurements of normal ambient vibrations are built-in. The following alternative algorithm may be used for automatically detect single and double leaks. This applies for pumps with p pistons and when using one or more accelerometers.

A. Capture a relatively high rate data on accelerations and proximity sensor signal over a time covering at least one pump revolution.

B. Optionally, apply a signal conditioning filter to the raw acceleration signals.

C. Construct an envelope vibration function, based on all accelerometer signals, for instance by a_env= V(∑aj²), representing the instantaneous vibration level.

D. Analyze the timing signal to find the shaft angle Θ as a function of time, as described above.

E. Construct 2p non-overlapping window functions, w_k, that selectively pick the envelope function in corresponding shaft sectors, such that each valve closing phase consists of p adjacent sectors.

F. Calculate the noise level in all 2p shaft sectors by

G. If p or more adjacent sectors have a noise level exceeding a critical noise level, then set a leak alarm.

H. Determine the potential leaky valves as those valves having opening or closing sectors that match either the first p sectors or the last p sectors of enhanced noise.

A suitable choice for window functions in step E is w_k= H(cos(6-(2k-l)7i/(2p)- 0|_ag)- cos(w7t/p)) where k is an integer that runs from 1 to 2p, 9|_ag is the estimated lag phase and w is a window width factor equal to or less than unity. A reason for using a reduced window width (w< l) in step E is to exclude the vibration spikes occurring when the valves hit the valve seats. These vibrations are not related to leaks and tend to blur the contrast between leaking phases and the non-leaking phases. An alternative to using reduced window width is to use continuously weighted windows representing low weights at the transition sectors, similar to those mentioned as an option in the simple algorithm above. The formula in step F applies for any window option and averages do not require integer revolutions.

By using the minimum sector based vibration level as a reference for the critical level, the method above is able to localize up to two simultaneous leaks of comparable strength, unless both the suction valve and the discharge valve for the same piston are leaking. These valves are perfectly complementary without overlapping closing phases, implying that all sectors could have enhanced vibration levels.

A possible way around this problem is, instead of using the minimum vibration level as a reference, to determine the critical vibration level as a function of pump speed and discharge pressure. The level could either be calculated from an empirical formula or picked from a look-up table. Such a table should incorporate past experience with healthy valves and with different pump speeds and discharge pressures.

The last step in the above algorithm excludes the possibility of triple leaks. This is because when p+2 or more adjacent sectors have enhance vibrations there is a theoretical possibility that also the valves not covering the end sectors could have a leak. However, the probability for a triple leak of comparable size is so low that flagging them as possible leaky valves makes little sense.

The method may further include presenting the actual leaking valve or valves to a human with an indicator panel or user interface with indicators and historical trending.

A preferred way to present the valve conditions to a human is to use a computer interface screen showing a generic view of the pump with its p suction valves and p discharge valves. Leaky valves could for example be highlighted by red indicators and the healthy ones by green indicators.

In cases when the leak alarm is triggered, it will be useful for an operator to view recorded acceleration signals together with the various closing windows on the computer screen. A trained operator could use this information to confirm and check the computer based diagnosis, especially in the case of possible multiple leaks.

A comparative trend plot of the various vibration levels, preferably after normalizing by the critical level, will also help an operator to make a manual evaluation of the valve conditions. Such a plot could reveal a starting leak even before the leak alarm is triggered, and before a second leak has started to develop. Another advantage by storing old time records and processed data is that erratic leak alarms could be ruled out. Such alarms could be triggered by debris of particles temporarily blocking the seal function of an otherwise healthy valve. Erratic alarms could preferably be avoided by advanced logics requiring that a leak must be detected over some specified time interval before the leak alarm is set.

The vibration signals are, when emitted for instance by a loudspeaker, surprisingly well suited for the human ear to identify a leak. When the signals are processed as described above and disturbing noises to a large extent are filtered away, the ear also easily identifies the severity of a leak, in relative terms.

The operator may listen in real time, if there is more than one valve block, to the different valve blocks. This can be done remotely by use of an earphone or a loudspeaker system, and a switch selecting one vibration sensor (valve block) at a time, in the case when multiple accelerometers are used. An operator will even without much training, quickly determine at which valve block the leak is developing. Volume and equalizer filter adjustments can optionally be included to make the leak sound more pronounced.

The method according the invention discloses a relatively simple and reliable way of detecting and localizing a valve fluid leak in a piston machine, even if the valves are positioned in the same valve block.

In the following there is described an example of use of the method illustrated in the accompanying drawings, in which:

Fig. 1 schematically shows a triplex pump with vibration sensors attaches to each valve block of the pump as well as a rotary angle transmitter positioned at the pump shaft;

Fig. 2 shows the same as in fig. 1 of a quintuplex pump where only one vibration sensor is attached to a common valve block; and

Fig. 3 shows a graph illustrating a raw vibration signal as a function of time, as well as a signal that is processed by used of a method according to the invention as a function of shaft angle.

On the drawings the reference numeral 1 denotes a so-called triplex pump, below termed pump, provided with three individually acting pistons 2, extending through their respective cylinders 4. Only the first piston 2 and corresponding cylinder 4 is shown. The cylinders 4 communicate with an inlet manifold 6 through their respective suction valves SI, S2 and S3, and an outlet manifold 10 through their respective discharge valves Dl, D2 and D3, see fig. 1.

The first suction valve SI and the first discharge valve Dl are built into a first valve block 14' that communicates with the first cylinder 4. In the same way the second suction valve S2 and the second discharge valve D2 are built into a second valve block 14", and the third suction valve S3 and the third discharge valve D3 are built into a third valve block 14"'.

On smaller triplex pumps, the valve blocks 14', 14" and 14"' may be parts of a common piece of metal. A first vibration sensor 16' that communicates with a computer 18 through a first cable 20', is attached to the first valve block 14'. A second vibration sensor 16" that communicates with the computer 18 through a second cable 20", is attached to the second valve block 14", while a third vibration sensor 16"' that communicates with the computer 18 through a third cable 20"', is attached to the third valve block 14"'.

A rotary angle transmitter 22 that communicates with the computer 18 through a fourth cable 20"", is arranged to give one pulse signal pr revolution of the crankshaft 24 of the pump 1.

The computer 18 is equipped with a screen 26 and a loudspeaker 28.

The sensors 16', 16" and 16"', the transmitter 22 and the computer 18 are of types that are known per se, and the computer 18 is programmed to carry out the calculations in question.

Vibrations sensed from the valve blocks 14', 14" and 14"' are picked up by the vibration sensors 16', 16" and 16"' respectively, and transmitted as signals to the computer 18.

The signals are prepared as described in the general part of the description and displayed on the screen 26. Alarms may be given trough the loud speaker 28.

When a leak is developing, a distinctive "hizzing" noise that appears at regular intervals, may be transmitted through the loud speaker 28. The loudness of the hizzing noise increases as the leak develops.

In fig . 2 a quintuplex pump 28 is shown having only one vibration sensor 16 attached to a valve block 14. A first suction valve SI and a first discharge valve Dl of the pump 28 are shown.

In fig . 3, upper subplot, the raw signal a from the sensor 16 from a test is shown as a function of time. The upper subplot thus shows the raw accelerometer signal a, scaled in g, during a 2 s period . The window function w_Si, which represent the theoretical closing interval of the suction valve SI, is included for easy interpretation. This window function is calculated from a timer signal, not shown here, by the method described in the general part of the description. The pump speed varied slightly from about 135 spm at start of record to 127 spm at the end and the discharge pressure was about 70 bar. The upper subplot clearly shows that the discharge valve Dl is leaking because of the enhanced vibration level during the closing phase of Dl (complementary phase to the shown SI).

The lower subplot that is plotted against shaft angle in revolutions, shows the envelope acceleration a_env after smoothing it with a 200 Hz low pass filter. The window function Wi in the lower subplot is the leak window found by Fourier analysis as described by the steps e-g in the algorithm in the general part of the description. The center point, illustrated by a circle in the lower subplot, of this window represents a pump shaft angle of -84°. This value matches almost perfectly with the theoretic value of -90°, taking into account that no lag shift corrections are applied. The vibration level ratio in leaking and non-leaking phases is determined to be 8.6, far exceeding a leak detection threshold typically set to 1.5.

Claims

C l a i m s

1. A method for detecting and localizing a valve leak in a piston machine (1) having a shaft 24 , where the method includes:

- attaching at least one vibration sensor (16', 16", 16"') to a valve block (14', 14", 14"'), of the piston machine (1);

- measuring the vibrations from all vibration sensors (16', 16", 16"');

- attaching a sensor (22) to the piston machine (1) where the sensor is designed to produce, directly or indirectly, an angular shaft position signal for the shaft (24), c h a r a c t e r i z e d i n that the method further includes:

- determining, directly or indirectly, an angular shaft position signal for the shaft (24);

- transforming the vibration signals from all vibration sensors (16', 16", 16"') into one envelope signal representing the instant vibration level;

- using the angular position signal for constructing window functions that pick the envelope signal in selected angular shaft sectors;

- using the window functions to find sector based averages of the vibration level, and

- comparing said averages with a critical ambient vibration level to detect and localize leaks in one or two valves.

2. A method according to claim 1, c h a r a c t e r i z e d i n that the method further includes:

- letting the windows represent 2p non-overlapping sectors, where p is the number of pistons in the piston machine (1);

- setting a leak alarm if a group of p or more adjacent sectors having a vibration level exceeding a critical level; and

3. A method according to claim 1, c h a r a c t e r i z e d i n that the method further includes:

- using said centre angle to construct two wide and complementary window functions representing shaft sectors for respective the highest and the lowest vibration level; - using these window functions and the envelope function to find the average signal level in said sectors; and

- setting a leak alarm if the highest vibration level exceeds a critical value; and

4. A method according to claim l to3, c h a r a c t e r i z e d i n that the method further includes:

- setting a critical vibration level that triggers a leak alarm equal to a

multiplicative factor times the minimum value of sector based vibration levels.

5. A method according to claim l to 3, c h a r a c t e r i z e d i n that the method further includes:

- setting a critical vibration level that triggers a leak alarm to a value that is either calculated from an empirical formula as a function of pump speed and discharge pressure, or picked from a look-up table, and where in both cases past measurements of normal ambient vibrations are incorporated.

6. A method according to claim l to 5, c h a r a c t e r i z e d i n that the method further includes:

- presenting the actual leaking valve or valves for a human.

7. A method according to claim 1, c h a r a c t e r i z e d i n that the method further includes:

- attaching a sensor (22) to the piston machine (1) where the sensor is designed to produce a digital timer signal with one pulse per revolution;

- determining all timer events when the timing signal turns from a low value to a high value or from high value to low value;

- finding the corresponding revolution periods from the difference between successive timer events;

- finding corresponding average pump speeds and centre times;

- applying a suitable ID interpolation/extrapolation method to find the angular pump speed for all time samples;

- time integrating said speed to obtain an accumulated pump shaft angle;

- calculating the difference between said accumulated angle and the real angular shaft position at the first timer event; and

- finding the pump shaft position as the accumulated pump angle minus said difference.