No comprehensive mathematical models are available that can predict solids conveyance and shaker fluid handling capacity for arbitrary predict solids conveyance and shaker fluid handling capacity for arbitrary solids in a specified drilling fluid. This paper addresses the solids loading problem and presents an analytical approach to the design of shale shakers, based on a dynamic model for solids conveyance off the screen and fluid flow through the screen. First, the solids loading is derived as a function of shaker geometry, solids-conveying speed, bit penetration rate, hole size, drilling fluid flow rate, particle size distribution of drilled solids, and screen opening size. Second, the solids-conveyance model is developed, based on the physics of the problem, accounting for the adhesive forces resulting from wet solids. The effect of various parameters, such as vibration pattern and normal acceleration on solids conveyance, is discussed. The solids-conveyance model can give the optimum set of shaker design parameters for efficient solids conveyance off the screen. For a given shaker, the solids conveying speed predicted by the model can also be used to obtain the flow capacity of the shaker in the presence of solids. Experimental and field results relevant to this study are also discussed.
A shale shaker is a vibrating screen used for solid/liquid separation and is the first of several serially connected solids-control devices to process the drilling fluid returning from a well. It is an important device in the solids-control system because efficient operation of other surface solids-separation equipment is critically de-pendent on proper functioning of the shale shaker. Because nanalytical design methods are currently available, shakers with widely varying design parameters are on the market-namely, with deck angles varying from 5 deg. parameters are on the market-namely, with deck angles varying from 5 deg. uphill to 30 deg. downhill, normal acceleration from 1.1 to 8.3 g, screen vibration patterns varying among linear, elliptical, and circular, and vibrator rotary speeds varying from 900 to 3,600 rev/min.
The results of vibratory screening technology, developed for such industries as mining and parts manufacturing, unfortunately are not applicable to drilling fluids screening because, unlike other industries, the main material processed by shale shakers is drilling fluid rather than solids. Analytical work relevant to drilling fluids screening was first reported by Hoberock, who presented an analytical model for determining the screen fluid flow rate in the absence of solids in drilling fluids. From this model, the fluid-only flow capacity (no solids) Qf, which establishes the upper limit for flow capacity, can be predicted from the drilling fluid properties, screen characteristics, and vibration dynamics. Curves such as those shown in Fig. 1 can be obtained from the model in Ref. 1 to determine these capacity limits for conventional shaker screens for different fluid characteristics and for specified vibration dynamics. This capacity usually increases with decreasing plastic viscosity (PV), increasing screening area, increasing normal acceleration, and increasing uphill deck angle.
Obviously, the fluid handling-capacity limit for a shaker is determined by both liquid and solid portions of the returning drilling fluid. In fact, the actual flow capacity of shakers is considerably less than the fluid-only flow capacity because of the presence of solids. When a drilling fluid with drilled solids flows through a screen, three effects reduce the flow capacity.
First, those particles considerably larger than the screen pores tend to cover the opening, thus reducing the effective screening area for the fluid and smaller particles to pass. This effect usually can be reduced if such solids are conveyed off the screen with a high conveying velocity. However, it is possible that changing a particular parameter may increase the solids-conveying speed, but particular parameter may increase the solids-conveying speed, but decrease the fluid flow through the screen. For example, an increase in downhill screen tilt improves solids conveyance, but also causes more fluid and wetter solids to run off the screen.
Second, the so-called "blinding" effect occurs when particles slightly larger than the pores wedge permanently in the openings.
Third, particles slightly smaller than the screen pores pass through the screen openings with difficulty because of poor orientation or speed with respect to a given screen aperture.
In this paper, we are concerned with the study of solids loading and solids-conveyance dynamics. A mathematical model for solids conveyance will not only enable us to predict the average solids-conveying velocity, required for determining a solids loading factor and actual fluid handling capacity of a given shaker, but also help us to design shakers for efficient solids removal. The vibratory-conveying literature contains numerous studies on the subject of vibratory conveyors and feeders. Redford and Boothroyd's work on vibratory feeding on a track, used widely in the feeding of components to automatic assembly machines and automatic machine tools, is the most complete and useful for our purposes. Most of the work on vibratory conveyors and feeders, however, is not directly applicable to vibratory screening and conveying of wet deified solids. Some of the factors that make this problem unique are the filtering of fluids through a screen vibrating at high normal acceleration, the nature of the drilled solids, and the role played by adhesive forces resulting from surface tension in forming wet solid patties of certain shapes and sizes and in their conveyance during flight and sliding modes. In our development, we build on the vibratory-feeding work and follow an analytical approach similar to that of Redford and Boothroyd.
The actual fluid flow capacity qs can be related to qf in terms of the solids loading factor r, representing the effect of large-sized solids, and the solids/screen interference factor rI, representing the effect of critical or near-sized particles, defined by Taggert as particles ranging in size from 25 % smaller to 50 % larger than the pore particles ranging in size from 25 % smaller to 50 % larger than the pore openings in the screen. The expression relating qs to qf is obtained as (see Appendix A)
r, derived in Appendix A, is given by