Solid-free fluids

The compressive strength of a formation rock provides a measure of its solids-producing tendency. Formations with a compressive strength exceeding about 6900 kPa (1000 psi) will generally produce solid-free fluid, if good completion and production practices are observed. In moderately consolidated formations, the compressive strength is only about 690 kPa (100 psi) and solids production can be expected (4). 

Whenever possible, the column should be started up on total reflux, using a solid-free fluid. 

For solid-free fluids where corrosion is not anticipated, or when corrosion is controlled by inhibition, or by employing corrosion-resistant alloys, values of c from 183 to 244 may be used for continuous flow, and values up to 305 can be used for intermittent service. 

An injectivity test is performed using clean, solids-free water or brine. If a low fluid loss completion fluid is in the hole, it must be displaced from the perforations before starting the injecting. This test will give an idea of the permeability of the formation to the cement filtrate. 

Viswanathan et al. (V6) measured gas holdup in fluidized beds of quartz particles of 0.649- and 0.928-mm mean diameter and glass beads of 4-mm diameter. The fluid media were air and water. Holdup measurements were also carried out for air-water systems free of solids in order to evaluate the influence of the solid particles. It was found that the gas holdup of a bed of 4-mm particles was higher than that of a solids-free system, whereas the gas holdup in a bed of 0.649- or 0.928-mm particles was lower than that of a solids-free system. An attempt was made to correlate the gas holdup data for gas-liquid fluidized beds using a mathematical model for two-phase gas-liquid systems proposed by Bankoff (B4). 

McDaniel, R.R. Houx, M.R. Barringer, D.K. "A New Generation of Solid-Free Fracturing Fluids", SPE paper 5641, 1975 SPE Annual Meeting, Dallas, September 28-October 1. 

Resistance functions have been evaluated in numerical compu-tations15831 for low Reynolds number flows past spherical particles, droplets and bubbles in cylindrical tubes. The undisturbed fluid may be at rest or subject to a pressure-driven flow. A spectral boundary element method was employed to calculate the resistance force for torque-free bodies in three cases (a) rigid solids, (b) fluid droplets with viscosity ratio of unity, and (c) bubbles with viscosity ratio of zero. A lubrication theory was developed to predict the limiting resistance of bodies near contact with the cylinder walls. Compact algebraic expressions were derived to accurately represent the numerical data over the entire range of particle positions in a tube for all particle diameters ranging from nearly zero up to almost the tube diameter. The resistance functions formulated are consistent with known analytical results and are presented in a form suitable for further studies of particle migration in cylindrical vessels. 

The 13C nuclear resonance studies in my report provide some informations on lipid membrane fluctuations in binary mixtures. Totally unsolved problems include an appropriate two-dimensional Debye-Huckel theory for membranes, and theoretical treatments of boundary free energies (between proteins and lipids, and between solid and fluid phase lipids). 

Proceeding from a binary mixture consisting of solid and fluid constituents denoted by a = S, F, the solid phase is extended by incorporating the volume free fixed charges Furthermore, the interstitial fluid fF is assumed to be composed of three components, namely the liquid solvent, the cations and the anions, in the following indicated by (3 = L, +, —. By introducing the volume fractions na = dtA/dv, the saturation constraint yields... 

Consider a bubble rising in a fluidized bed. It is assumed that the bubble is solids-free, is spherical, and has a constant internal pressure. Moreover, the emulsion phase is assumed to be a pseudocontinuum, incompressible, and inviscid single fluid with an apparent density of pp(l — amf) + pamf. It should be noted that the assumption of incompressibility of the mixture is not strictly valid as voidage in the vicinity of the bubble is higher than that in the emulsion phase [Jackson, 1963 Yates et al., 1994]. With these assumptions, the velocity and pressure distributions of the fluid in a uniform potential flow field around a bubble, as portrayed by Fig. 9.10, can be given as [Davidson and Harrison, 1963]... 

The reaction is accomplished by spraying UNH into a bed of fluidized UOg particles at a temperature of about 300°C. The UNH is deposited on the UO particles and decomposed. Fluidized-bed reactors are well suited for this process because high rates of heat and mass transfer are required between the solid and fluid. Under normal operating conditions, UO produced in a fluidized-bed is granular, free flowing material with a particle size distribution suitable for subsequent fluidized-bed operations (4). The UO is a chemically stable, mildly hygroscopic solid with a crystal density of 7.3 g/cm3. 

Fig. 1 The Gibbs free energy as a function of temperature for solid and fluid phases.

It is generally immaterial which phase, solid or fluid, is assumed to be at rest, and it is the relative velocity between the two that is important. An exception to this is met in some situations when the fluid stream has been previously influenced by solid walls and is in turbulent flow. The scale and intensity of turbulence then may be important parameters in the process. In wind tunnels, for example, where the solid shape is at rest and the stream of air is in motion, turbulence may give different forces on the solid than if the solid were moving at the same relative velocity through a quiescent and turbulence-free mass of air. Objects in free fall through a continuous medium may move in spiral patterns or rotate about their axis or both again the forces acting on them are not the same as when they are held stationary and the fluid is passed over them. 

Particulate and Aggregative Fluidization. When the fluid phase is liquid, the difference in the densities of fluid and solid is not very large, and the particle size is small, the bed is fluidized homogeneously with an apparent uniform bed structure as the fluid velocity exceeds the minimum fluidization velocity. The fluid passes through the interstitial spaces between the fluidizing particles without forming solids-free bubbles or voids. This state of fluidization characterizes particulate fluidization. In particulate fluidization, the bed voidage can be related to the superficial fluid velocity by the Richardson-Zaki equation. The particulate fluidization occurs when the Froude number at the minimum fluidization is less than 0.13 [9],... 

When the solids-free bubbles or voids are present in the bed as in bubbling or turbulent fluidization, the bed of solid particles is fluidized nonhomogeneously. This state of fluidization characterizes aggregative fluidization. The distinct properties of aggregative fluidization are intense mixing of particles, bypassing of fluid through bubbles, and solids entrainment above the bed surface. 

Specially designed equipment and techniques are required for the surface handling of high solids cut fluids. Separation, cleaning, and disposal of produced solids can be costly, especially if the solids must be oil-free to satisfy environmental regulations. 

Fig. 6. Equation of state in the high density region. The solid line represents the data for the 32 hard sphere system in the solid" and fluid" branches. The dashed line is calculated by the free-volume theory, Eq. (23).

Many researches adopted one of the aforanentioned approaches and modified it to include various aspects of the pneumatic drying process. Andrieu and Bressat [16] presented a simple model for pneumatic drying of polyvinyl chloride (PVC), particles. Their model was based on elementary momentum, heat and mass transfer between the fluid and the particles. In order to simplify their model, they assumed that the flow is unidirectional, the relative velocity is a function of the buoyancy and drag forces, solid temperature is uniform and equal to the evaporation temperature, and that evaporation of free water occurs in a constant rate period. Based on their simplifying assumptions, six balance equations were written for six unknowns, namely, relative velocity, air humidity, solid moisture content, equilibrium humidity, and both solid and fluid temperatures. The model was then solved numerically, and satisfactory agreanent with their experimental results was obtained. A similar model was presented by Tanthapanichakoon and Srivotanai [24]. Their model was solved numerically and compared with their experimental data. Their comparison between the experimental data and their model predictions showed large scattering for the gas temperature and absolute humidity. However, their comparisons for the solid temperature and the water content were failed. 

We first seek the values of that minimize the free energy of the system for constant intensive properties and constant volumes of the solid and fluid phases. We have... 

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