GB2270385A - Method for determining weight on bit - Google Patents

Abstract

A method of determining the weight applied to a drill bit during drilling a borehole comprising: a) determining for a given period of time t, values of hookload H and surface drilling string velocity Vs; b) from the determined values of H and Vs, calculating a quantity indicative of bit velocity Vb; and c) from the determined value of H and the quantity indicative of Vb, determining the effect w of drilling string weight and drill string interaction with the borehole on the determined value of H so as to determine the weight F applied to the bit. All the necessary measurements can thus be taken on the surface and the method allows for drill string compliance as well as friction with the borehole.

Description

METHOD FOR DETERMINING WEIGHT ON BIT The present invention relates to a method for determining the weight applied to a drill bit during drilling a borehole in subsurface formations. In particular, the invention relates to a method which uses information which can be obtained at the surface during drilling to provide a determination of a downhole parameter.

The determination of weight on bit (WOB) during drilling has long been recognised as important since with this information, important details of the drilling process can be obtained if other parameters such as rate of penetration or torque applied to the drill bit are known. A crude estimation of WOB can be obtained by monitoring the hook load during drilling and comparing this to the hook load when the bit is off bottom, ie the weight of the drill string. Simply subtracting the hook load measured during drilling from the off bottom hook load is then taken as the weight applied to the drill bit. While this might not be a bad estimation in very shallow, vertical boreholes, as the borehole becomes deeper and the direction deviates from vertical the inaccuracy in this approach increases.In an attempt to overcome this problem, attempts have been made to measure WOB with a sensor located near the drill bit and to transmit the information to the surface by means of MWD telemetry.

While this approach is generally accepted as giving good results, it does require the use of expensive MWD equipment and if this equipment fails or is not available (such as might be the case for small diameter boreholes, "slim holes", where the WOB MWD sub is too large to fit in the borehole) or if the well becomes too deep for the MWD signal to be reliable, the measurement of WOB becomes difficult.

To date, no system has existed which provides an accurate estimation of WOB from measurements made at the surface only. It is an object of the present invention to provide a method which allows this to be done.

In accordance with a first aspect of the present invention, there is provided a method of determining the weight applied to a drill bit during drilling a borehole comprising: a) determining, for a given period of time t, values of hookload H and surface drill string velocity V,; b) deriving a value of the drillstring compliance A from the values of H and V,; c) from the derived values of A and the determined values of H and V" determining a drill bit velocity V,; and d) from H and Vb determining the effect w of drill string weight and drill string interaction with the borehole on the determined value of H so as to determine the weight applied to the bit F.

This method has the advantage that it only relies on measurements of t, H and V which are all surface measurements rather than any downhole MWD measurements. It has been shown that rate of penetration (bit velocity) is roughly proportional to WOB all else being held constant and the present invention inverts this assumption to allow WOB to be obtained from an estimation of bit velocity.The drill bit velocity is typically derived from the relationship: Vb + A- = V, and the dt compliance A obtained according to the method described in US 4843875 (incorporated herein by reference). w can be derived from the relationship: H=w+Vb, wherein w = (weight of drill string -effective weight loss due to interaction with the borehole) and a is a constant, the values of W and a being obtained by fitting a relationship to the values of H and Vb such that w is obtained when Vb=O.

The method according to the present invention allows the use of dynamic data, i.e. data obtained while drilling is taking place. The measurement of H is commonly achieved by measuring the deadline anchor tension although measurement of motion compensator displacement is also possible on floating rigs. A convenient system for recording the useful data for the present invention is the MDS computerised drilling monitoring system available from Sedco Forex.

The present invention will now be described by way of example, with reference to the accompanying drawings, in which: - Figure 1 is a schematic view of a rotary drilling rig; - Figure 2 is a plot of deadline anchor tension (kN) versus bit velocity (m / s); - Figure 3 is a plot of hookload (kW) versus bit velocity (m / s); - Figure 4 is a corresponding plot to Figure 3 using averaged hookload data; - Figure 5 is a plot of WOB (klbft) versus well depth; - Figure 6 is a plot of drillstring weight (klbft) versus well depth; and - Figure 7 is a further plot of hookload (kin) versus bit velocity (m / s).

Referring now to Figure 1, a typical land drilling rig is shown which comprises a mast or derrick 10 from which a drill string 12 is supported by means of a hook 13 mounted on a travelling block 15, the altitude of which can be adjusted by means of a cable 14. The drill string is formed from a number of drill pipes or drill collars 16 connected end to end and extends into the well, a drill bit 18 being mounted at its lower end. Drilling fluid is circulated from a pit 20 to the top of the drill string 12 via a standpipe 22 and down through the inside of the pipes and collars to the bit 18 where it exits through nozzles and returns to the surface in the annulus formed between the drill string and the well wall. On leaving the well at the surface, the fluid is returned to the pit and is recirculated into the well.In use, pipes or collars are added to or removed from the drill string in order to change the overall length. In drilling ahead, the travelling block is lowered by slackening off the cable such that at least some of the weight of the drill string is borne by the bit and the string is rotated so as to allow the bit to drill into the formation. Sensors are provided on the rig to measure flow rate of fluid entering the string and/or leaving the annulus at the surface, the pressure of fluid in the stand pipe, the altitude of the travelling block, the load on the cable and the rate of rotation of the drill string. Signals from these sensors can be processed to provide, inter alia, an indication of string length, rate of drill bit penetration when drilling, occurrence of fluid influxes and other events when rig operations are taking place.

The basic premise underlying the present invention is that the rate of penetration (bit velocity) is proportional to WOB if rotation speed, lithology and bottom hole pressure are substantially constant or are not correlated with WOB. Under the general assumption that rate of penetration increases with WOB, the following approximation hold true:

Additionally, the force at the bit (WOB) is given by: F=H-W-f=H-w (2) wherein F is the force at the bit, W is the drill string weight andf is the weight loss due to the interaction of the drill string with the well bore. If the bit velocity is proportional to the force F then Vb = GF = a(H - w) (3) and hence:

If the loss in weight termfis independent of hook load H, a direct comparison of equations (1) and (4) allows comparison of measured hook load and velocity and the extraction of parameters such as A and a.

Iff contains a Coulomb friction component (as is commonly supposed during non-rotating drilling) then equation 4 may be rewritten

where f is the non-Coulomb component of f. It is convenient to define w as w = W + f. If the well is planar, and the coefficient of friction IL does not vary along the well then

where the drillstring is of length L, X is the compliance per unit length along the drillstring, and ss is given in terms of the deviation 8 and friction coefficient IL by

with the sign of the right hand side of equation 8 positive for the drillstring in compression (below the neutral point), and negative for the drillstring in tension (above the neutral point).

If the drillstring is building or dropping angle, and there is appreciable change in deviation below the normal neutral point then ss will change with changing hookload, for normal hookload and hole deviations however it should be relatively constant, in which case: αc = αexp(- (#+ - #-)) (9) where 8+ is the total deviation below the neutral point, and # is the total deviation above the neutral point.

The weight-on-bit is similarly given by F = (Hw)exp(- (#±#-)) (10) and the bit velocity by

It is clear from equations 5 and 11 that any estimation method to find A, a and w with Coulomb friction absent, will estimate AC, ac and w if Coulomb friction is present.

Rig friction will affect the accurate estimation of bit rate-of-penetration due to inaccuracies in the hookload measurement. The form of the friction that may be compensated for is velocity dependent friction, the velocity in question being either the velocity of the travelling block (sheave friction), or the velocity of the motion compensator (compensator friction) when present. Techniques for evaluating friction have been proposed previously but it may not be necessary to correct for friction directly, but to assume that fiction is present in deriving the bit velocity.

If the measured deadline-anchor tension is given by T = H + au, (12) where Vf is appropriate velocity, then equation 1 becomes

It is the product Aa that appears in equation 13, and an estimate of this is what is required to calculate Vb from V,.

In addition to velocity dependent friction the sheaves are subject to other nonlinear frictional problems. Both types of friction are forms of noise that may be ameliorated by using more than one hookload sensor, such that different sources of noise affect different sensors. On a floating rig the motion compensator displacement may be used as a measurement proportional to hookload. The appropriate equation that connects V: to Vb is

where there are N measurements Hj, each of which is nominally proportional to the hookload, and N constants aj which reflect the combination of measurements that minimizes noise.

Velocity dependent friction in the borehole may also need to be considered Parameter estimation for equations such as 4 is simple if the coefficients in the equation are constant in time, and if the data fits the model perfectly. However, there is some time variation in all the terms, but the different terms may be expected to behave in different ways.

The drilistring compliance A may vary slowly over a stand (as the sheaves lengthen, and also may appear to change slightly if Coulomb friction is present (equation 7).

The weight of the drillstring W will vary only very slowly as the mud density changes, and as a changing weight distribution is supported by hole deviation.

The additional weight lossf may change over minutes and hours, but probably not over seconds.

The function a will change as a function of depth, and even for apparently uniform rock may deviate appreciably about a mean value.

Although the function a may be of interest in interpreting the drilling data the two quantities that are of interest to the driller are the bit velocity (Vh) and the downhole weight-on-bit (n. In the absence of friction A alone may be estimated and used to calculate Vb from equation 1, in the manner proposed in US Patent number 4943875. Alternatively equation 14 or 13 may be used, requiring estimates of respectively, the N numbers aj, or A and Av.

Calculation of F requires (from equation 2) w. To obtain this either equation 3 may be used directly, having first estimated Vb, or it may be used implicitly in conjunction with either of the equations 1, 13, 5 or 14.

A may be estimated in many ways, all of which are based on equation 1, or its embellishments. In cases where equation 1 may not always be valid, in which case there is not normally any correlation between dW / dt and V1, most best fit techniques will give the conservative answer of A = 0, and the best estimate available of the bit velocity is then the surface velocity.

Some possible methods to achieve this are Using linear regression on equation 1 over a chosen time period, having first low-pass filtered the data. An enhancement to this is to only accept the value of 3 if the data shbws sufficient correlation. Another slight modification is not to minimise the variance of Vb (standard linear regression), but to choose some other minimization criterion (such as total least squares, or total least distance).

'The bit velocity may be expected to vary much less than the surface velocity at high frequencies. Equivalently, the bit acceleration will be very much less than the surface acceleration. Differentiating equation 1 gives the approximate equation

A may be obtained from equation 15, using similar time domain minimization as with equation 1.

o If the surface velocity changes appreciably due to changing weight-on-bit, an alternative is to use equation 4 in estimating A, again by fitting the equation to the data over some time interval. Although this technique will also produce values of a and aw these need not be used in estimated w.

Kalman filtering may be used with any of the equations 1, 15 or 4.

When estimating A in the presence of Coulomb friction in the borehole, the equations being used will estimate Ac, not A. Since only Ac is needed to calculate the bit velocity it is not necessary to estimate A. If however A is known (for instance if the last drilling segment involved rotation and A could be measured), then equation 7 can be used to give some indication as to the distribution of p along the borehole.

If the frictional contribution to the deadline anchor tension is estimated separately, then it is not necessary to estimate rig friction, otherwise the method to be used is to use equation 13 to estimate Aa, using a time domain equation fitting or filtering technique, and use this value in correcting the bit velocity.

If more than one hookload sensor is being used then it is not necessary to calculated A , just the quantities a, in equation 14. Estimation of these quantities may be done along the same lines as estimating A, ie 'Fitting to equation 14 using some form of regression Substituting equation 3 into 14, and line fitting. In such a line fit only one hookload measurement need be used.

Using Kalman filtering on equation 14.

Estimating w has complications that do not occur in estimating A and V and this must alter the estimation method used.

Rearranging equation 3 gives

Equation 16 has in it the desired w, and the coefficient a. If the bit velocity does not depend on the weight-on-bit then H and Vb will be uncorrelated, but the conservative zero estimate of 11 a, gives an estimate of w equal to the mean value of the hookload. However, any estimation of w must include a check on how well the model fits the data and, answers must be rejected if they do not make physical sense.

Furthermore, if the dynamic range of the hookload is too low, then the estimate of w will have a lot of random scatter. The function a can also be expected to change at times quite suddenly, and to show some scatter since equation 3 is based on empirical evidence.

Appropriate methods are time based linear regression, or averaging: Fit filtered data to equation 16 over a given time period. As well as equation 16, equation 3 may be used to give an estimate of w, obtained by dividing the estimate of aw by the estimate of a. As the correlation between Vb and H decreases, these two answers will diverge, similarly as the dynamic range of H decreases they will diverge. The value of w obtained can be used if the fit to equation 16 exceeds a threshold correlation. For the A calculation it is possible to use a fixed time period for the fit.For this calculation the fit must take place over a time period long enough for the bit velocity to change significantly due to changes in weight-on-bit which should be significantly longer than Al a. This time has the physical interpretation as the distance the bit would drill if the brake were locked, divided by the rate-ofpenetration at the mean weight-on-bit. The time period may be set as the time taken to drill a set distance.

o An alternative approach is hookload based averaging. The procedure is to take the time series of hookload and bit velocity over a set distance (or time), and then to average the data points according to hookload. The hookload is split up into intervals, and the hookloads and velocities of all the points in each interval are averaged. An example of this is shown by figures 3 and 4. Figure 3 shows hookload plotted against bit velocity for 25 feet of drilling. As in figure 2 the data has been low-pass filtered and resampled at 0.25Hz. The two lines show the two linear fits obtained using equations 16 and 3. There is no evidence from this graph of a strong relation between weight-on-bit and bit velocity. Figure 4 shows the result after averaging in hookload intervals 2kN wide.The two lines come from a weighted linear fit to equations 3 and 16, and the data clearly supports a linear relationship between hookload and bit velocity. Having averaged the data it can then be fitted to both equations 16 and 3, as before. In performing the fit there is the question of how to weight the points. Since a data point obtained by averaging over 100 samples is more trustworthy than one obtained by averaging over 5 samples. If the samples were chosen from a random distribution then one measure of the accuracy of the data point is the variance of the sample mean of the bit velocity. This is given by the variance of the samples that make up the data point, divided by the number of samples.In order to apply this the points composed of the average of insufficient samples would have to be discarded, and then a weight function used that is proportional to the inverse sample-mean variance. A cruder but more robust weight function is given by some function of the number of samples composing the data point, again with a cut-off number of data points per sample. In figure 4 the weight used is the square root of the number of samples, with at least 3 samples (12 seconds of data) per data point. In figure 5 this procedure has been used on recorded data, where MWD measurements of downhole weight-on-bit (DWOB) were also being made. The dynamic weight-on-bit determined according to this method is shown by the solid line, and the dashed lines show DWOB and conventional surface WOB. The drilling was at about 50 degrees deviation, mostly without rotation.No account has been taken of Coulomb friction effects on the dynamic WOB which was calculated over 8 feet intervals. Between 6780 ft and 6860 ft the dynamic and DWOB measurements agree well and decrease while SWOB increases. This can be seen more clearly comparing the drillstring weight (w) estimated dynamically with the direct measurement (the sum of the hookload and DWOB). The solid line in figure 6 shows w, the dashed line shows the MWD measurement. There is clear agreement about about the loss of 8 klbf in weight between 6780 and 6860 feet. Instead of using points equally based in time for the hookload averaging it is possible to convert to a depth scale. Equivalently, the time based points could be weighted according the depth drilled.This is theoretically better, because if a has a scatter due to the fluctuations in lithology that scatter is depth based, not time based. Sometimes the best estimate of the bit velocity is positive (i.e. the bit is moving upwards), and hence a negative distance is drilled.

Since in a weighted average all weights must be positive averaging could not be performed. Positive estimate of bit velocities are common only on floating rigs, so depth based averaging may be possible on fixed rigs. The hookload averaging technique may also be applied directly to the surface velocity, V,, instead of the bit velocity Vb. Over a sufficiently large depth interval the rate of change of hookload will be uncorrelated with the hookload, thus the average value of V, for such hookload will be the same as the average value of V. As the surface velocity generally has greater variance than the bit velocity the averaged data points will also have greater scatter, and a less reliable answer for the drillstring weight will be produced If no Coulomb friction is suspected (for instance, while rotating), then F may be directly calculated from w.In the presence of Coulomb friction the estimation method used in the previous section will produce w. With Coulomb friction present F may be calculated from w using equation 10. 8+ and 8 are known from the well geometry, and ij can be estimated from the difference between the non-rotating and rotating hookloads, assuming that all the difference comes from Coulomb friction. Another possibility comes from monitoring the slope of the bit velocitylhookload graph. With no Coulomb friction this is the coefficient a, with Coulomb friction it is aC. The ratio of the two, for the same lithology and drilling conditions is the factor required to extract F from H and w. If the same rock is being drilled in rotating and non-rotating segments then the ratio of the slopes may be this factor, however the difference in drilling conditions may make it unusable. In any case although (H - w) is not the weight-on-bit, the bit velocity is proportional to this quantity.

There are two equations that form the basis of this method. Equation 1 and equation 3. It is unlikely for equation 3 to hold and equation 1 to fail, however there are circumstances where equation 1 holds and equation 3 does not, and circumstances in which they both fail. Equation 1 can only be derived as a limit of the full elastic equations for the drillstring with certain conditions on the relation between bit rate-ofpenetration and weight-on-bit These are, that on the average, increasing weight does not lead to decreasing rate-of-penetration. In some circumstances this is not the case, and drilling data supports the observation that if increasing weight-on-bit leads to decreasing rate-of-penetration then often there is no correlation at all between the hookload derivative and the surface velocity.Indeed often there is no relationship at all between the surface velocity and the hookload. The ways that equation 3 may fail are various, e The lithology is insufficiently consistent. This is not 'fail' strictly, however equation 3 is unusable. In these circumstances a bad fit to the hookload averaged data will be obtained, and no new estimate made of w.

If the lithology is less consistent than the weight-on-bit, then equation 3 will also be unusable. The use of equation 3 requires that the predominant cause for the bit velocity to change is that the weight-on-bit has changed. If the weight-on-bit barely changes at all then all the variation in vb comes from the lithology. For instance if the lithology is consistent within 3%, but the weight-on-bit varies only by 1% then equation 3 will not worE If the relation between vb and F is non-linear, or non-existent (v6 is independent of F), then no true value of w can be deprived. This commonly happens when drilling at too high a weight on bit. This is useful information for the driller, but can interfere with the calculation of w.For instance, consider a relation between hookload and bit velocity as shown in figure 7. In this theoretical example w = 750.

In the hookload interval between 650 and 750 kN a good estimate of w may be obtained. If however the hookload is varying between 580 and 670 kN then a good straight line fit may be obtained, but the indicated w will be too high. Once the hookload reaches between 550 and 600 kN then any calculated value for w can be eliminated because of the negative gradient of the fit. If the data on which w is based is displayed at the same time as the value of w then the driller can use his judgement as to whether the indicated w is real or an artefact.

Another 'failure' is if there is a threshold effect, that is, a fixed amount of the weight-on-bit is not involved in drilling, so that Vb = CG(F F,) (17) In the estimation process F0 will be included within w, so instead of the actual weight-on-bit F, the result of the estimation is the weight actively involved in drilling (F-F0).

The estimation of dynamic weight-on-bit depends on a good estimate of bit velocity. The estimation of bit velocity requires a good measurement of rate of change of hookload. At present hookload is measured indirectly at a location remote from the hook. This location is adequate if the hookload alone is required, but leads to considerable added noise if the hookload rate of change is needed Some of this added noise can be compensated for, but the single best way to enhance this technique would be to measure hookload (or its rate of change) at the hook.

Claims (7)

1A method of determining the weight applied to a drill bit during drilling a borehole comprising: a) determining for a given period of time t, values of hookload H and surface drilling string velocity V,; b) from the determined values of H and V,, calculating a quantity indicative of bit velocity Vb; and

c) from the determined value of H and the quantity indicative of Vb, determining the effect w of drilling string weight and drill string interaction with the borehole on the determined value of H so as to determine the weight F applied to the bit.

2 A method as claimed in claim 1, wherein a value of drill string compliance A is determined from the values of H and V, and the drill bit velocity Vb is calculated from H, V and A.

3 A method as claimed in claim 2, wherein the drill bit velocity is derived from the relationship

4 A method as claimed in claim 2 or 3, wherein w is derived from the relationship H=w+ V, a wherein w = (weight of drill string - effective weight loss due to interaction with the borehole) and a is a constant, the values of W and a being obtained by fitting a relationship to the values of H and Vb such that w is obtained when Vb=O.

5 A method as claimed in claim 1, wherein the quantity indicative of bit velocity Vb comprises the average V, for given values of H, the quantity V1 corresponding to the average bit velocity Vb.

6 A method as claimed in any preceding claim, wherein the determined parameters include components due to friction.

7 A method as claimed in claim 6, wherein the friction components are evaluated with respect to deviation of the borehole from vertical.