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*Data from Beeson and Wright.21

*Data from Beeson and Wright.21

Effect per mud type particles whose median diameter was about one-third the median pore size of a 5 darcy sand pack would bridge that pack. In order to form an effective base for a filter cake, a mud must therefore contain primary bridging particlcs ranging in size from slightly less than the largest pore opening in the formation about to be drilled, down to about one-third that size. In addition, there must be smaller particles ranging down to colloidal size, to bridge the smaller formation pores and the interstices between the coarser bridging particles.

The best way to determine primary bridging sizes is to make trial and error tests on cores of the formation of interest. When this is not possible, some guidance may be obtained from published datau> 18< 10 which relates bridging size to permeability. To summarize, it was found that particles less than 2 microns in diameter will bridge rocks of permeability less than 100 md: 10-micron particles will bridge consolidated rocks of permeability between i 00 and 1000 md; and 74-micron (200-mesh) particles will bridge sands up 10 darcies. A mud containing a suite of particle sizes up to a maximum of 74 microns should bridge and form a filter cake on all formations except those with macro-openings, such as gravel beds and formations with open fractures, which are discussed in the section on loss of circulation, in Chapter 9

The greater the concentration of bridging particles, the quicker bridging will occur, and the less will be the mud spurt. On consolidated rocks with permeabilities in the range of 100 to 1000 md,about 1 lb/bbl (2.8 kg/m;i)ofthe required size range is sufficient to prevent the mud spurt from invading further than an inch into the rock.16 On unconsolidated sands about 5 10 lb bbl (14-28kg/m3) may be required.

Bridging particles in the size ranges and amounts specified above will normally be present in any mud that has been used to drill more than a few feet, except that there will be a shortage of coarse particles if extensive use is made of desanders and desilters when drilling unconsolidated sands. Bridging particles must, however, be added to muds that are formulated for production repair jobs when no drilling is involved (see Chapter 10).

Dynamic Filtration

Under the condition of dynamic filtration, the growth of the filter cake is limited by the erosive action of the mud stream. When the surface of the rock is first exposed, the rate of filtration is very high, and the cake grows rapidly. However, the growth rate decreases as time passes, until eventually it is equal to the erosion rate; thereafter the thickness of the cake is constant. Under equilibrium dynamic conditions, therefore, the rate of filtration depends on the thickness and permeability of the cake, and is governed by Darcy's law (Equation 6-3), whereas under static conditions cake thickness increases ad infinitum, and the rate of filtration is governed by Equation 6-6. Dynamic filter cakes differ from static cakes in that the soft surface layers of

Figure 6-12. Relative static and dynamic filtration in the bore hole. (From Outmans. Courtesy Soc. Petrol. Eng. J. Copyright 1963 by SPE-AIME.)

layer (see Chapter 9 for definition of this parameter), 3 is the thickness of the cake subject to erosion, and ( — v+1) is a function of the cake compressibility.

Prokop23 measured dynamic filtration rates in a laboratory tester, in which mud flowed through a concentric hole in a cylindrical artificial core Table 6 4 shows the equilibrium cake thickness thus obtained with a huge number of laboratory muds.

Ferguson and Klotz24 obtained some excellent data on dynamic filtration rates in a model well which duplicated field geometry. Holes were drilled in artificial sandstone blocks with 5|;inch and 5$inch bits. Figures 6 13 through 6 16 show the change in dynamic filtration rates with time for four muds at various circulating velocities. Note that the dynamic rates were considerably greater than the static rates as extrapolated from the API filter loss tests. Note also that the time to reach constant dynamic filter rates varied from 2 hours to over 25 hours, depending on the type of mud and on the flow velocity. Figure 6-17 shows the increase in filtration rate with increase in flow velocity. The API filter losses have been marked on the curves of their respective muds to show the lack of correlation with the dynamic rate.

A marked increase in filtration rates under dynamic conditions was also observed by Vaussard et al24b in the cell shown in Figure 6-17a (note: for filtration

Table 6-4

Equilibrium Cake Thickness under Dynamic Filtration^

Mud base (all muds treated with lime, caustic soda and quebracho)

API filter loss (cc in 30 min)

Equilibrium cake Thickness

Mud velocit\ Equilibrium

Mud base (all muds treated with lime, caustic soda and quebracho)

Bentonite

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