Geomechanical evaluation
3.4.4 Time dependency
In the previous example we only considered the stress state versus failure. From field experience we know, however, that borehole stability problems are clearly time-dependent. If a well can be drilled and cased off in a short time, we usually have no problems. If, on the other hand, the borehole is allowed to stay open for some time, problems like difficulties to land the casing string may arise.
Figure 3.25 demonstrates the time dependency on hole enlargement below 4420 m.
We will in the following compare four production wells.
Figure 3.27 shows four wells. The open hole exposure time is different for these wells mainly because the coring programs were different. Figure 3.28 shows the time curves for the various parts of the boreholes, which is the time from drilling to logging.
From Figure 3.28 we see that the bottom section of each well has stayed open approximately the same time, from 30 to 60 hours. This is consistent with the caliper logs of Figure 3.27 which shows similar, but little, collapse for all four wells. Further up, the open hole exposure times are quite different, since various coring programs have been implemented, and the wells have also been temporarily abandoned because of bad weather conditions, as indicated with waiting on weather (WOW) in Figure 3.27.
Well A has been open for 650 hrs with a maximum collapse of 4.5 in. Wells B and C have been open for 320–350 hrs giving a maximum collapse of more than 2 in., while well D has been open 100 hrs, with a collapse less than 2 in.
The above example illustrates the time dependency of borehole collapse.
2700
2800
2900
650 hrs
0 0 0 0
320 hrs 350 hrs 100 hrs
3000
Figure 3.27 Caliperlogs for four production wells.
G e o m e c h a n i c a l e v a l u a t i o n 85 Berland (1993), performed an analysis of time-dependent borehole collapse of a North Sea oil field. The following main elements were investigated:
• the anisotropic stress field
• the overburden stress
• the time of open hole exposure
• the depth
• the lithology
• the effects of KCl inhibition
• effective stresses of the elements above
Since 41 different analyses were performed we will not discuss all aspects of the modelling, only point out some of the observations, which can be given as:
• although the use of anisotropic horizontal stress for the field gave best results, a reasonable correlation was obtained using the overburden stress as external loading.
• the collapse is clearly lithology-dependent, with the following order from most collapse to less: paleosol, mudstone, siltstone and sandstone.
600
D
B C Depth from
bottom (m)
A 500
400
300
200
100
0
0 100 200 300
Hours open hole
400 500 600 700
Figure 3.28 Open hole exposure time for the four wells.
86 M o d e r n w e l l d e s i g n
8.5 10 12 in.
sandstone
sandstone
sandstone earth profile
earth profile/mudstone sandstone sandstone
sandstone
sandstone mudstone mudstone
siltstone siltstone
sand/siltstone
siltstone mudstone
Figure 3.29 Collapse versus lithology and thickness of lithological unit. From Berland(1993).
• a new parameter was found that dominated the extent of the collapse. The collapse extent seemed to be proportional to the thickness of each lithological group.
The last element requires some explanation. Figure 3.29 shows a portion of a caliper-log. Also shown are the lithological groups. We observe that the sandstone sections are basically in-gauge, while the clay sections are collapsed. Berland (1993) observed that the collapse was proportional to the thickness of the lithological unit. Or put another way, if sand stringers occur within a clay sequence, the effect is that the collapse is reduced. The mechanisms are not fully understood.
To resolve the problem with unit thickness, Berland introduced a depth dependent collapse model. The principle is shown in Figure 3.30. For a clay sequence, the upper and lower sandstone boundaries are marked out. The collapse in between is represented
G e o m e c h a n i c a l e v a l u a t i o n 87
Diameter
H
TVD
Figure 3.30 Model of the collapse within a lithological unit.
by an ellipse or some other function. In our example we have used two straight lines.
The collapse within this triangle can be calculated from the following equation:
X=Dh− Dh
H (3.31)
Using this model, Berland derived a time-dependent collapse model of the following form:
Dh
Dh = Xσv
a+ bDTVD
ln(t) (3.32)
where the following notations are used:
Dh= hole diameter, where Dh= Dh(t) Dh= bit diameter
DTVD= true vertical depth of well X= geometrical factor
t= time a, b= constants
Using this approach Berland managed to model the collapse quite well.
It must be pointed out that Berland (1993) performed both modelling and hypoth-esis testing. The data had possibly too little variations to develop a general model.
Future work will refine this.
We have now shown that borehole collapse or borehole enlargement is a com-plex issue. Although simple stress and material models describes how the borehole behaves with respect to varying borehole pressures, they are often inadequate to sim-ulate real borehole behavior. We have shown that the open hole exposure time may be a governing parameter, and that unit thickness of the rock may also be a governing parameter.
88 M o d e r n w e l l d e s i g n
However, we have demonstrated that simple correlations can be established between the caliper log and the mud weight used to establish critical mud weights.
These can be important tools for field applications. Furthermore, this analysis can be expanded when other data become available.
3.5 D R I L L A B I L I T Y E VA L U AT I O N
3.5.1 Introduction
The nomenclature used in this chapter is:
ROP= rate of penetration of the drill bit.
WOB= weight applied on the drill bit.
N= rotary speed.
de= drillability called the d-exponent.
Dl= linear drillability
Dln= normalised linear drillability Dh= diameter of the drill bit.
σv= overburden stress gradient D= well depth
t= time
In petroleum engineering we have relatively few data available compared to the vast coverage of our wells. Logging of the well is important to determine the petrophysical parameters for further evaluation. One drawback is that the logs are always delayed in time, even the measurement-while-drilling tool (MWD) is lagging 5–10 meters behind the drill bit. However, the drill bit is at the very bottom of the hole. If we can utilise the drillbit information we will instantly know changes as they occur. Also, the drilling information is an under-utilised source of information with a large potential for cor-relations. In the future a high-quality drillability log will be generated which is used with the electrical logs. At the present time improvements in drilling data are being made, which will give us a higher quality drillability log in the future. Kyllingstad et al (1993) addresses some of the recent improvements in drilling data.
The d-exponent is actually a drillability which is used for pore pressure estimation.
The interpretation techniques have not advanced significantly in the past 20 years. The common interpretation is to look for deviations from a straight line, which is often interpreted as an indicator for increasing pore pressure. The d-exponent is a logarithmic function, as illustrated below:
G e o m e c h a n i c a l e v a l u a t i o n 89 We know that the drilling rate depends on the loading and the rotary speed. The simplest drilling model can then be expressed as:
ROP= d1
WOB× N
Dh
Here we have used (dl) to define the drillability, which is actually a scaling factor for the coupling between the rock and the drill bit. From the drilling data all parameters are available except the drillability. This is expressed as:
d1= ROP Dh
WOB× N (3.34)
We see that both Equations (3.33) and (3.34) actually define drillabilities. The draw-back of the d-exponent is that the logarithmic scale is non-linear. There is also little evidence that this logarithmic dependence is related to the real physics of the drilling process. In the following examples we will use only Equation (3.34).