Dynamic Pore Pressure Ahead of the Bit
- Bertrand Peltier (Schlumberger Cambridge Research) | Colin Atkinson (Imperial C.)
- Document ID
- Society of Petroleum Engineers
- SPE Drilling Engineering
- Publication Date
- December 1987
- Document Type
- Journal Paper
- 351 - 358
- 1987. Society of Petroleum Engineers
- 4.1.2 Separation and Treating, 1.6 Drilling Operations, 1.2.3 Rock properties, 1.11 Drilling Fluids and Materials, 4.1.5 Processing Equipment, 1.11.2 Drilling Fluid Selection and Formulation (Chemistry, Properties), 4.3.4 Scale, 5.1 Reservoir Characterisation
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Summary. An analytic approach is presented in an attempt to improve the understanding of the mechanism of pore-pressure invasion ahead of the bit during drilling. An axisymmetric model accounts for a zone of damaged permeability (skin) on the work front. The effect of rate of penetration (ROP) and rotation speed on the pore pressure at the depth of cut is significant in the lower range of permeabilities, while for the high permeabilities, the skin has an overwhelming control on the pressure invasion.
During drilling, the mud density is usually selected to ensure a bot-tomhole mud pressure higher than the formation pore pressure to avoid any influx of formation fluid into the well. Conversely. this condition of overbalance results in a filtration of the mud into the formation, which modifies the pore pressure of the rock in the vicinity of the wellbore.
The filtration of the mud-i.e., the formation of a mudcake and the invasion of the rock by the mud filtrate-into the bore wall is considered an influential factor in terms of the stability of the hole. Much research has been devoted to this subject in the oil industry. On the other hand, the filtration that takes place beneath the bit at the bottom of the hole has been the subject of a more limited number of papers, the bulk of which were published between 1953 and 1961. This last aspect of the filtration is nonetheless known to have a great influence on the drilling rate insofar as it controls what is called work-front pore pressure drop, delta p, rock effective stress, sigma e, or chip holddown.
An analytic approach is presented here in an attempt to improve the understanding of the mechanism of pore-pressure invasion ahead of the bit during drilling. This is tackled in three steps: the planar geometry, as a first approximation, then the axisymmetric geometry, and finally the implementation of a skin effect at the mud/rock interface.
The planar geometry is used to analyze the transient state induced by a change of ROP and the spurt-invasion pulse existing between two consecutive cutter actions, while the axisymmetric model accounts for the effect of a damaged-permeability zone on the work front. The question of- the effect of this pore pressure on the ROP is not addressed here.
The differential equation governing dynamic pore pressure ahead of a drilling bit the axisymmetric case expressed in cylindrical coordinates is
------ + -- --- r--- +R ---- = ---- ...............(1)
Planar Geometry With No Skin Effect
Steady State. In the absence of a complete solution of the differential equation (Eq. 1), it is interesting to see whether any practical information can be determined from the more trivial planar case. This planar solution corresponds to a plane wave of pressure. This approximation may be acceptable for those points on the axis of the bit that are close enough to the work front that the influence of the lateral boundaries of the work front is negligible. Typically, for a 21.6-cm [8 1/2 -in.] bit at a depth 10mm [0.4 in.] ahead of the bit, the ratio L/rb is 0.1. We will consider first the steady state.
----- + --- ----- = 0,.................................(2a)
= ---- = -----------,................................(2b)
P = Pf +(Pm -Pf)e ..................................(2c)
The indentation of the bit's cutters takes place on the first few millimeters of rock, and only the pressure difference across this first slice of rock is responsible for the rock effective stress that affects the cutters' action. Assuming that the pore-fluid characteristics are close to those of water in normal temperature-and-pressure conditons, one can consider the following numerical values of interest: mu = 1 mPa.s [1 cp] and c=0.5 nPa-1 [3.45 x 10 -9 psi-1]. Ranges of reasonable field values are phi=0.2, KE 1x10-6 to 1.10 (3) md, and RE3.6 to 36 m/h [11.8 to 118 ft/hr].
Fig. 1 presents the normalized pore pressure at a dept 10 mm 10.4 in.] ahead of the bit vs. the rock permeability for two ROP'S. It can be seen that, with the planar model and for permeability above 0.1 to 1 md, the drilling-fluid invasion is so important that virtually no pressure drop is encountered across the first millimeters of the work front, whatever the pressure difference between the mud and the formation pore fluid may be. At the other extreme, for those rocks with a permeability of less than 0.1 X 10-3 md, no fluid invasion can take place on the time scale of drilling, and therefore the full differential pressure is applied to the indented zone. Even-tually, for those rocks where the permeability is in the middle range (0.5 to 0.5 x 10 -3 md), the differential pressure, and therefore the effective stress, applied on the indentation zone is dynamically dependent on the ROP.
These conclusions imply several things of practical importance. In the middle range of permeability, the rock effective stress on the work front increases with the ROP-i.e. . the higher the ROP, the harder the rock looks to the bit.
The second aspect of this same phenomenon is that, in these intermediate-permeability rocks, it is impossible to isolate the effect of a given parameter from the dynamic-pore-pressure effect unless the differential pressure between the mud and the formation is zero. Results from drilling tests performed with 98-mm [3 7/8-in.] three-cone bits tend to support this view. Fig. 2 presents the effect of mud pressure, rotation speed, and weight on bit (WOB). The holddown is the ratio of the ROP obtained with mud pressure to me ROP obtained in the same conditions but without mud pressure. The three curves look sufficiently similar to confirm the interpretation of dynamic pore pressure.SPEDE
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