Dynamic filtration drilling fluids

Dynamic Filtration. Dynamic (or cross-flow) filtration is a considerably more complex separation process than static filtration as the rate of filtration is a strong function of the flow of the drilling fluid. A number of studies (see reference 128 and the references cited therein) have demonstrated the various factors that control dynamic filtration rates. 

The elaborate nature of the equipment needed to study realistic dynamic filtration on representative rock samples has largely precluded routine measurements of the dynamic fluid loss of drilling fluid samples at the rig site during drilling operations. Figure 36, for example, shows the equipment used by Fordham and co-workers (129, 135) to measure dynamic filtration rates of water-based drilling fluids. Similarly large and complex equipment has been used recently by Jiao and Sharma... 

Figure 37 shows a schematic of the dynamic filtration of a drilling fluid. The drilling fluid is filtered across the filter medium at the pressure difference APfd while being subjected to flow (assumed laminar in the following discussion), which gives rise to a shear stress rc at the cake-fluid interface where the shear rate is yc. 

Figure 37. Schematic of dynamic filtration of drilling fluid against a filter medium.

Figure 42. Dependence of (a) limiting dynamic filtration rate (Q/d) and (b) inverse of filter cake thickness (l/hc) on shear rate of drilling fluid. (Muds 2 and 3 from reference 139 with Fordham and Ladva s data from reference 135.) Lines show least squares fit to data from muds 2 and 3.

The dynamic filtration theory of Outmans (127) requires experimental terms such as particle-particle stresses, particle friction factors, and thickness of a shear zone within the filter cake that would be difficult to determine. However, the qualitative picture of dynamic filtration presented by Outmans, namely, irreversible adhesion of solid particles up to a certain thickness that is determined by the shear stress (or shear rate) at the surface of the cake, accords with the experiments of Fordham and co-workers (129,135). Once a filter cake has formed under dynamic conditions, it is difficult to remove it by subsequent changes in yc or vm. Figure 44 shows the effect of changes in the flow rate on cumulative filtrate volume. The limiting filtration rate obtained when the initial flow rate of the drilling fluid was 1.8 m3/h remained unaltered when the flow rate of the drilling fluid was increased to 7.0 m3/h in a step-... 

Figure 44. Effect of changes inflow rate of drilling fluid on rate of dynamic filtration. (Reproduced with permission from reference 135. Copyright 1989 Advance Publications Ltd.)...

Effect of Composition on Fluid Loss. There have been many studies and tests of the effects of various additives (usually polymeric) on the static fluid loss of drilling fluids. There have been many fewer studies on the effect of these additives on dynamic filtration rates and very few that compare their effect on both dynamic and static rates. 

Figure 48. Comparison of rates offiltration of an invert emulsion oil-based drilling fluid under static and various dynamic conditions. 1. vm = 0 (extrapolated static filtration rate) 2. vm = 0.6 m/s 3. vm = 1.5 m/s 4. vm = 2.9 m/s. (Reproduced with permission from reference 142. Copyright 1954 American Institute of Mechanical Engineers.)...

Figure 53. Time dependence of normalized permeability of water-saturated sandstone samples during dynamic filtration of various water-based drilling fluids and injection of filtrate. (A) 20 gjL bentonite suspension (B) 40 gjL bentonite suspension (C) injection of fresh-water filtrate (D) 40 g/L bentonite in 0.51 M NaCl. (Reproduced with permission from reference 150. Copyright 1992 Society of Petroleum Engineers.)...

Dynamic filtration in Newtonian fluids. While borehole annular flows are rarely Newtonian (e.g., fluids such as water or air, where viscous stress is linearly proportional to the rate of strain), many drilling fluids are thin and briny, and at times, simply water. Thus, for analysis purposes, the study of Newtonian flows is more than academic. Furthermore, the mathematical simplicity that it offers sheds some insight into the parameters that influence the value of equilibrium cake thickness in the presence of erosive annular flow. Whether our annular flow is Newtonian or power law, concentric or eccentric, it is important to consider two underlying asymptotic fluid-dynamical models. The first applies during small times when borehole fluid enters the formation radially as filtrate, decelerating with time, while the second deals with large times, when invasion rates are so slow that we essentially have classical no-slip velocity boundary conditions. We will first eonsider the small time limit, assuming that the drill pipe does not rotate. 

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