An analysis of how measurement accuracies affect drilling parameters has been performed.
The presented case is a simplified drilling situation. The purpose is to investigate how inaccuracies in measurements of density, viscosity and flow rate affect the BHP, the asso-ciated ECD, and required pump pressure. The simulation has been performed using the MATLAB software.
11.1 Data
In lack of data from real measurements the presented data is synthetic, with the intention of resembling realistic data. A wellbore schematic of the well is presented inFig. 11.1.
The well is drilled vertically, such that MD equals TVD. After drilling a 17 1/2” hole, a 13 3/8” casing is landed and cemented. A 12 1/4” hole is then drilled and at the current situation, the drill bit is at 2600 m. It is assumed that the inner diameter of the 13 3/8”
casing is the same as the diameter of the 12 1/4” hole. The drillstring is made up of 5” drill pipe, and the BHA is represented by 200 m of drill collars and a drill bit with 5 nozzles.
Surface lines from the top of the drillstring to the mud pumps are represented by 100 m of 5” pipe. The annulus is open to atmospheric pressure of 14.696 psi. The data input used in the simulation is found inTable 11.1.
Fig. 11.1– Wellbore schematic of the well.
The accuracy of viscosity and density is found by looking up real instruments of differ-ent vendors online. The accuracy of the viscosity is the accuracy of the Fann Instrumdiffer-ent Model 35 viscometer [51]. The density accuracy is the accuracy of the Model RCMB Mud Balance [52]. The flow rate accuracy is presented as a typical accuracy of a Coriolis flow rate measurement for drilling applications [53]. The rest of the data are inspired by an exercise given in the courseTPG4215 - Drilling Engineering, Advanced Course 1 - High Deviation Drillingat the Norwegian University of Science and Technology.
Table 11.1– Data input of accuracy analysis.
Parameter MATLAB
Symbol Value
Surface pressure p surface 14.696 psi
Inner diameter of 12 1/4” hole and 13 3/8” casing OD 12.25 in
Drill pipe external diameter ID 1 5 in
Drill collar external diameter ID 2 6.25 in
Drill pipe internal diameter d 1 4.276 in
Drill collar internal diameter d 2 3.1 in
Surface lines internal diameter d 3 4.276 in
True vertical depth TVD 2600 m
Length of drill pipe L 1 2400 m
Length of drill collars L 2 200 m
Length of surface lines L 3 100 m
Dial reading of viscometer at 600 rpm theta 600 84 cP Dial reading of viscometer at 300 rpm theta 300 53 cP
Accuracy of dial readings theta a ±1.5cP
Mud density rho 12.8 ppg
Mud density measurement accuracy rho a ±0.01g/cm3
Flow rate q 850 GPM
Flow rate measurement accuracy q a ±2%
Discharge coefficient Cd 0.95
Nozzle diameter d n 15/32 in
Number of nozzles n n 5
11.2 Equations
The main equations utilized for pressure calculations in drilling hydraulics is presented in [54]. A selection of the most important equations follows. The constants in the equations require the input parameters in oil field units.
The hydrostatic pressure p in a liquid column is defined in Eq. 11.1.
p = 0.052ρD + p0 (11.1)
whereρis density, D is TVD and p0is the static surface pressure. For dynamic situations the drilling mud rheology is often described by the Bingham plastic model. The plastic viscosityµplis defined by Eq. 11.2.
µpl=θ600–θ300 (11.2)
whereθ600andθ300is the dial readings of the rotational viscometer with an outer cylinder speed of rotation of 600 and 300 rpm respectively. The dial reading at 300 and the plastic viscosity is used to calculate shear stressτy, as seen in Eq. 11.3.
τy=θ300–µpl (11.3)
Mean velocity¯v in an annulus can be calculated by Eq. 11.4, and mean velocity in a pipe can be calculated by Eq. 11.5.
where q is the flow rate, OD is the inner diameter of outer pipe or borehole, ID is the external diameter of inner pipe, and d is the internal diameter of the pipe.
To determine if the flow is laminar or turbulent, the Reynolds number NRefor flow in an-nulus can be calculated by Eq. 11.6, and by Eq. 11.7 for flow in pipe. Usually NRe<2100 means laminar flow, and NRe >2100 means turbulent flow.
NRe= 757ρ¯v(OD – ID)
µpl (11.6)
NRe= 928ρ¯vd
µpl (11.7)
For laminar flow the frictional pressure lossdp
dL
lamin the annulus can be calculated by Eq. 11.8, and in the pipe by Eq. 11.9.
For turbulent flow the frictional pressure lossdp
dL
turbin the annulus can be calculated by Eq. 11.10, and in the pipe by Eq. 11.11.
Pressure drop through the bit∆pbitcan be calculated by Eq. 11.12.
∆pbit= 8.311∗10–5ρq2
C2dA2t (11.12)
where Cdis the discharge coefficient and Atis the total nozzle flow area.
Several assumptions lie behind the equations. This is to simplify the situation, making cal-culations more straightforward. Assumptions include incompressible fluids and isothermal flow. It is also assumed that the placement of the drillstring in the hole is concentric and that there is no rotation of the drillstring. Another assumption is that shape of the open hole sections is circular and the diameter is known [54].
11.3 Results
The simulation was carried out using the two MATLAB functionspressure ECD input plots.m andpressure ECD calculations.mthat can be found in Appendix A.1 and Ap-pendix A.2, respectively. 4 different simulations are run. Two plots are created for each simulation. The first one displays the pressure during circulation, plotted from the sur-face, down the annulus, through the bit, up the drillstring, and via surface lines to the mud pump. The second displays the ECD in the annulus and is plotted from 1000 m depth and down to TD. Three different cases are shown in each simulation. The ideal cases, where all measurements are fully accurate is represented by the green lines. The calculated re-sults for the ideal case are shown inTable 11.2. The purple lines represent the worst-case accuracies resulting in a decrease of pressure and ECD, while the red lines represent the worst-case accuracies resulting in an increase of pressure and ECD. In the pressure plots, the blue dotted lines are the static mud column plotted for reference to highlight the effect of the frictional pressure drop through pipes and annulus.
Table 11.2– Results for the ideal case.
Parameter Value
Annulus BHP 396.0 bar
Pump pressure 277.9 bar Annulus ECD at TD 12.949 ppg
11.3.1 Simulation 1
The first simulation is looking at the effect of viscosity accuracy on pressures and ECD. In [51] it was found that an accuracy of±1.5 cP could be expected. By looking at Eq. 11.2 it is clear that to create the worst-case accuracies, the dial readings need to be inaccurate with opposite signs. To create the purple case the 600 rpm dial reading needs to undershoot the true value, and the 300 rpm dial reading needs to overshoot. To create the red case the 600 rpm dial reading needs to overshoot the true value, and the 300 rpm dial reading needs to undershoot. The effect of viscosity accuracy on pressure is shown inFig. 11.2and the effect of viscosity accuracy on ECD is shown inFig. 11.3. The calculated results can be found inTable 11.3. For the annulus BHP, the resulting deviation is±0.1 bar, the pump pressure deviations are + 4.5 bar and - 4.8 bar, and the annulus ECD deviation at TD is± 0.003 ppg.
Fig. 11.2– The effect of viscosity accuracy on pressure.
Fig. 11.3– The effect of viscosity accuracy on ECD.
Table 11.3– Results for viscosity accuracy calculations.
Parameter Value
θ600– a,θ300+ a θ600+ a,θ300– a
Annulus BHP 395.9 bar 396.1 bar
Pump pressure 273.1 282.4 bar
Annulus ECD at TD 12.946 ppg 12.952 ppg
11.3.2 Simulation 2
The second simulation is looking at the effect of density accuracy on pressures and ECD.
In [52] it was found that accuracy of±0.01 g/cm3could be expected. To create the purple case the density measurement needs to undershoot the true value, and to create the red case the density measurement needs to overshoot the true value. The effect of density accuracy on pressure is shown inFig. 11.4and the effect of density accuracy on ECD is shown in Fig. 11.5. The calculated results can be found inTable 11.4. For the annulus BHP, the resulting deviations are + 2.6 bar and - 2.5 bar, the pump pressure deviations are + 1.4 bar and - 1.5 bar, and the annulus ECD deviation at TD is±0.084 ppg.
Fig. 11.4– The effect of density accuracy on pressure.
Fig. 11.5– The effect of density accuracy on ECD.
Table 11.4– Results for density accuracy calculations.
Parameter Value
density-a density+a
Annulus BHP 393.5 bar 398.6 bar
Pump pressure 276.4 bar 279.3 bar Annulus ECD at TD 12.865 ppg 13.033 ppg
11.3.3 Simulation 3
The third simulation is looking at the effect of flow rate accuracy on pressures and ECD.
In [53] it was found that an accuracy of ±2 % could be expected. To create the pur-ple case the flow rate measurement needs to undershoot the true value, and to create the red case the flow rate measurement needs to overshoot the true value. The effect of flow rate accuracy on pressure is shown inFig. 11.6and the effect of flow rate accuracy on ECD is shown inFig. 11.7. The calculated results can be found inTable 11.5. For the annulus BHP, the resulting deviations are + 0.2 bar and - 0.1 bar, the pump pressure de-viations are + 10.1 bar and - 10 bar, and the annulus ECD deviation at TD is±0.0004 ppg.
Fig. 11.6– The effect of flow rate accuracy on pressure.
Fig. 11.7– The effect of flow rate accuracy on ECD.
Table 11.5– Results for flow rate accuracy calculations.
Parameter Value
flow rate-a flow rate+a
Annulus BHP 395.9 bar 396.2 bar
Pump pressure 267.9 bar 288.0 bar Annulus ECD at TD 12.945 ppg 12.953 ppg
11.3.4 Simulation 4
The fourth simulation is looking at the combined effect of viscosity, density, and flow rate accuracy on pressures and ECD. The overshooting and undershooting cases are de-signed as worst-case scenarios, by respectively combining all the accuracies that resulted in overshooting and undershooting the results. The effect of viscosity, density, and flow rate accuracy on pressure is shown inFig. 11.8and the effect of viscosity, density, and flow rate accuracy on ECD is shown inFig. 11.9. The calculated results can be found in Table 11.6. For the annulus BHP, the resulting deviations are + 2.8 bar and - 2.7 bar, the pump pressure deviations are + 16.3 bar and - 16.1 bar, and the annulus ECD deviation at TD are + 0.091 ppg and - 0.09 ppg.
Fig. 11.8– The effect of viscosity, density, and flow rate accuracy on pressure.
Fig. 11.9– The effect of viscosity, density, and flow rate accuracy on ECD.
Table 11.6– Results for viscosity, density, and flow rate accuracy calculations.
Annulus ECD at TD 12.859 ppg 13.040 ppg
11.4 Discussion
By looking at the four pressure plots it clear that the effects of the frictional pressure drop and the measurement accuracies are much larger within the drillstring than in the annu-lus. This can be seen by the large difference between the circulating pressure lines within the drillstring and the static mud pressure column plotted for reference. This is reason-able as the inner diameter of the drillstring is much smaller than the diameter difference in the annulus between the exterior of the drillstring and the open/cased hole. The clear line deflection when changing between drill collars and drill pipe within the drillstring is caused by the same reason. This line deflection is less apparent on the annulus side, but when looking at the ECD plots the line deflection can also be seen on the annulus side. By zooming in, or adjusting the scales of the axes, the line deflection would also be visible on the annulus side of the pressure plot.
To evaluate the results the calculated deviations are compared to acceptable MPD devi-ations discussed by Bjørkevoll et al. [48] and Rodriguez et al. [49] in chapter 10. For the automated MPD case presented in [48], the constant BHP had an acceptable deviation of ±2.5 bar, and the automated MPD case presented in [49] had a mud weight window narrower than 0.09 g/cm3, which in oil field units is 0.751 ppg.
For simulation 1 the changes to annulus BHP and ECD at TD caused by the accuracy of the viscometer are so small that they are barely identifiable. The changes in pump pressure are above the 2.5 bar deviation, so in a narrow MPD operation, such a deviation could be challenging. However, for conventional drilling, where pressure windows are wider, the deviation should not be problematic.
For simulation 2 the changes in ECD at TD are also very small. Here the pump pressure deviation is below the 2.5 bar deviation. The changes of annulus BHP is approximately equal to the 2.5 bar deviation and is at the edge of being acceptable in the narrow MPD operation described in chapter 10.
For simulation 3 the situation with annulus BHP and ECD at TD is the same as for sim-ulation 1. The pump pressure changes are more than doubled compared to simsim-ulation 1,
and in the MPD operation described in [48] it would be a challenge.
In simulation 4, when all accuracies are added, the changes in ECD at TD are still very small, and far below what was described as a very narrow window of 0.751 ppg in [49].
The changes in annulus BHP are just above what was acceptable in [48], but still so small that it could work in other MPD operations that are less strict. The changes in pump pres-sure are quite large and would be challenging in the described operation.
The density accuracy has the largest effect on the BHP, while the flow rate accuracy has the largest effect on the pump pressure. The ECD at TD is not significantly affected by the accuracies. Choosing the flow rate accuracy from a different method than Coriolis could have resulted in larger changes, as the Coriolis is known for accurate measurements.
Another factor to consider is that in a MPD operation, the back pressure pump would be located closer to the well than the mud pumps, and the effect of the frictional pressure drop in the surface lines would be reduced.
It is important to point out that the simulations were run with worst-case scenarios and especially the last simulation is very pessimistic as the probability of all measurements co-inciding to overshooting or undershooting the pressures and ECD. For the viscometer, it is less probable that the dial readings at 300 and 600 rpm would have the largest deviation in opposite directions at the same time. When the two deviations are on the same side of the true value the applied changes will decrease. It is also important to remember that the two automated MPD operations described were very challenging with small acceptable devi-ations, and many other MPD and conventional drilling operations have a larger operating window.
In reality, the wellbore situation is much more complicated. There are several other sim-plifications than the assumptions behind the equations. Utilizing a real drillstring with tool joints and numerous BHA tools would add complexity. The mud column in the well is also much more complex. The presence of gas, cuttings, and cavings complicates the situation.
The mud column might not be uniform and can not be represented by one density from top to bottom. There are also many additional uncertainties that are not included or discussed here.
Chapter 12
Discussion
The discussion on chapters 2-6 is taken directly from the TPG4560 project report by Stein-sheim [1]. The discussion is included to provide an important foundation for the extended literature study conducted in Part I and for the flow loop project in Part II.
12.1 Chapters 2-6
Several flow measurements are performed as a part of the drilling procedure. There are many possible methods to obtain the desired information. Advantages and disadvantages of the many methods have been described.
There exist numerous methods for measuring flow rate. The venturi meter is not com-monly used during drilling. It is an intrusive method with high associated pressure drop.
The restriction in the meter poses a risk for accumulation of cuttings and cavings during drilling. The gamma-ray multiphase flow meter is suitable for production pipes but is lim-ited by the large diameter of the flow line between the wellbore and the shale shakers.
For measuring the flow into the well the pump stroke counter is found to be the primary method despite the gradual wear and tear of the components leading to inaccuracy. The PVT system and the flow paddle meter are old methods that are still used for measuring the return flow. The three methods are based on simple principles, but the reliability of methods has led to the methods still being in use decades after they were implemented, despite the low sensitivity and accuracy. Many of the challenges of these methods could be solved by flow meters. Flow meters can measure the reduced flow rate due to decreased pump performance caused by wear and tear of the components in the pump. Comparing the PVT system and a flow meter, the flow meter can detect considerably smaller changes than the PVT system. When a kick occurs the quick detection of increased volume influx can be crucial for handling the situation before it develops. The flow paddle gives
qualita-tive results, while a flow meter can give quantitaqualita-tive results that contain more information.
The Coriolis meter is a flow meter that has many of the advantages described above. How-ever, the high sensitivity of the meter also makes it sensitive to parameters not intended to measure, such as vibrations at the rig, wellbore ballooning, and heave caused by waves. In some cases, the Coriolis meter can become too sensitive, which can also be a disadvantage.
If alarms go off regularly in the dog house it leads to stress and an increased workload for the driller. It can also cause reduced focus on the tasks at drill floor and a tendency to cate-gorize alarms as false too quickly. The consequences can be dangerous. Disadvantages of the Coriolis meter compared to pump stroke counter, PVT, and flow paddle are the large occupied rig space and additional cost of implementation, as the first three systems are already in use at most rigs. The Coriolis meter definitely has potential for becoming the leading method for flow measurements during drilling operations.
Acoustic measurements during drilling have many challenges. Many of the methods are limited by the sensitivity to background noise which is present at high levels dur-ing drilldur-ing. Cuttdur-ings or gas bubbles in the flow can lead to signal dampdur-ing. The results are also affected by the temperature, viscosity, and density of the fluids. Getting quantita-tive measurements is difficult as conducting absolute measurements of acoustic signals is not possible. The non-intrusive mounting which applies for many of the acoustic methods would be a benefit for implementation.
The density and viscosity measurements described are found to be the main methods uti-lized offshore. The manual work associated with the measurements has many disadvan-tages, such as the occupational hazards connected to working in the shale shaker room.
Getting true measurements relies on the methods being conducted in the correct way. As
Getting true measurements relies on the methods being conducted in the correct way. As