H. Nasr-El-Din

Local solids concentration measurement in a slurry mixing tank

Abstract The local solids concentration in a mixing tank was measured using both sample withdrawal and a new conductivity probe. The conductivity probe was used to assess the errors associated with various sample withdrawa! techniques and to measure solids concentration profiles in the mixing tank. The effects of sampling tube design (tip shape, face angle and inside diameter), sampling position, bulk solids concentration and particle size on the sampling errors were examined in detail. Solids concentration profiles were also measured as a function of particle size, bulk solids concentration and mixer rotational speed. The experimental results indicated that on the impeller plane, the sample withdrawal techniques (tapered sample tube) gave a lower solids concentration than that in the tank at a sampling velocity ratio of unity. These results suggest that the flow at the impeller plane was three-dimensional. The errors associated with sampling techniques depended on the sample tube shape and location in tank, and were significant for the coarse sand particles of 1000 μm. When sampling at right angle to the flow, sampling errors increased with particle size, especially when a small diameter sample tube was used. The data provided in the present study can be employed to correct for the errors associated with the sampling withdrawal techniques over a wide range of parameters. Solids concentration profiles in the mixing tank were found to be a function of the particle size, bulk solids concentration and mixer rotational speed. Solids concentration varied with the radial position, except when fine sand particles of 82 μm were used. A strong variation in solids concentration with the axial position was observed at the impeller plane for the sand particles examined in the present study. This variation increased with the particle mean size and the mixer rotational speed.

Modelling dynamic adsorption of an anionic surfactant on Berea sandstone with radial flow

Abstract A study of the dynamic adsorption of an anionic surfactant, Neodol® 25-3S, on Berea sandstone is presented. Cylindrical cores with axisymmetric radial flow are used in order to simulate the flow pattern near an oilfield injection wellbore, and also to allow greater sensitivity in testing various transport and adsorption mechanism. Mathematical models based on the advective-dispersive transport equation of mass coupled with an adsorption model were applied. Numerical solutions of the coupled transport and adsorption equations were obtained using the Galerkin finite element method. Equilibrium and kinetic Langmuir, two-site, and bilayer adsorption models were evaluated. Linear (Henrys law) and non-linear (Langmuir) equilibrium adsorption models were found to be unsuitable for modelling the surfactant effluent profiles. Improved fits to the experimental data were obtained using a kinetic Langmuir model, but the total amount of adsorption was over-estimated by a factor of three. It was found that the two-site or bilayer model was required to produce consistent model parameters for the experimental conditions employed. The effect of salinity on the adsorption of surfactant was examined using the two-site model. A small decrease in the rate constant for the first type of adsorption kinetics and an increase for the second type were observed. At high salinity, the axisymmetric radial transport equation was not able to predict the tracer and surfactant profiles during the brine flood. At such conditions, the mobility ratio was not favourable and, as the result, the displacement front was not stable. The flow pattern became two-dimensional and could not be described by the one-dimensional model used. An increase in the rate of adsorption was observed with increasing injection flow rate. It is proposed that the adsorption kinetics depend strongly on the concentration of surfactant monomers in the bulk solution. The results from this study can be used to estimate surfactant loss due to adsorption during many surfactant-based EOR processes. The surfactant loss in the wellbore region is a very important parameter for determining surfactant propagation in the reservoir.

Continuous gravity separation of a bidisperse suspension in a vertical column

Abstract Continuous separation of bidisperse suspensions containing particle species lighter and heavier than the suspending fluid in a vertical settler has been studied. Polystyrene (light) and polymethyl methacrylate (heavy) beads of respective uniform size and density suspended in a salt solution were used. The purity and recovery of both species in the overflow and underflow streams were evaluated as a function of the feed flow rate [up to 1(cm 3 /s)/(cm 2 )], feed total solids concentration (up to 18 vol.%) and the fraction of feed in the underflow (i.e. split ratios of 0.1 to 0.9). A theoretical model, based on mass balances and slip velocities, has been developed. The model predicts all the observed trends and agrees fairly well with the quantitative measurements. The degree of differential settling achieved in the column decreases with increasing feed flow rate or increasing feed total solids concentration. At a fixed feed flow rate, there is a threshold split ratio, beyond which the recovery drops linearly with increasing split ratio. The threshold split ratio itself decreases with increasing feed flow rate as well as increasing feed total solids concentration. Increasing feed flow rate or total solids concentration also results in increased impurities in the product streams (i.e. light in underflow and heavy in overflow).

An Experimental Study of Pressure Drop in Helical Pipes

Pressure drops of fully-developed incompressible laminar newtonian flows in helical pipes of constant circular cross-section having a finite pitch are experimentally investigated. For the case of loosely coiled pipes of 0 < η/λ < 41.22, f Re (f is the Fanning friction factor and Re is the Reynolds number) is found to be proportional to the square root of the flow Dean number, Dn = Re λ½. Here λ and η are the normalized curvature ratio and torsion which incorporate both the coil radius and its pitch. In all cases studied, the experimental results for f Re are in excellent agreement with the theoretical prediction of Liu & Masliyah.

Continuous gravity separation of concentrated bidisperse suspensions in a vertical column

Abstract An experimental study for continuous separation of concentrated bidisperse suspensions in a vertical settler has been conducted. The bidisperse suspension examined consisted of light polystyrene beads and heavy polyvinyl chloride beads in a salt solution. The effects of the feed total solids concentration, feed flow rate and split ratio (defined as the ratio of either the underflow or the overflow to the feed flow rate) on the performance of the settler were examined. A zone having strong lateral nonhomogeneities in the form of instabilities (fingers) was observed in the settler for a feed having high total solids concentration. The size of the instability zone was found to be a strong function of the split ratio and feed flow rate. The presence of these instabilities significantly improved the performance of the settler, especially at low feed flow rates. For low feed total solids concentration, a previously developed kinematic model which assumes a uniform lateral concentration profile, i.e., in the absence of local instabilities, was found to predict the experimental measurements well. For high feed total solids concentration where strong local instabilities occur, the model is used to assess the effect of the local instabilities on the performance of the settler.

Solids segregation in slurry flow through a T-junction with a horizontal approach

Abstract Particle segregation in slurry flow through a T-junction with a horizontal approach has been examined. Water-sand slurries were used with T-junctions of various orientations: upward and downward in a vertical plane and side orientation in a horizontal plane. The effects of particle size, upstream solids concentration, upstream bulk velocity and flow ratio (defined as branch flow rate to upstream flow rate) on the branch and run solids concentration were studied. For given upstream conditions, the experimental results showed that for all branch orientations the concentration ratios of the branch and run (defined as the ratio of the branch or run solids concentration to the upstream solids concentration) are strong functions of the flow ratio. For the vertical upward and side orientations, the concentration ratio was round to be less than unity and approaches one as the flow ratio approaches unity. For the vertical downward orientation, it was found that the concentration ratio was mainly greater than unity and approached unity as the flow ratio approached one. For all orientations, the branch concentration ratio was round to be a function of the upstream bulk velocity, solids concentration and particle size. For the vertical upward orientation, the concentration ratio increased as the upstream velocity or solids concentration increased, but decreased as the particle size increase. The opposite trends occurred for the vertical downward orientation. For the side orientation, the branch concentration ratio decreased as the upstream velocity, particle size increased, whereas the effect of upstream solids concentration on the branch concentration ratio was found to be insignificant.

Continuous separation of bidisperse suspensions in inclined channels

Abstract An experimental study was conducted to evaluate the enhancement for the continuous separation of light and heavy particles in an inclined column. A bidisperse suspension consisting of polystyrene (light) and polymethyl methacrylate (heavy) beads of respective uniform size and density, suspended in a salt solution, was used. The total solids volume fraction did not exceed 0.18 to insure uniform lateral concentration profile. The effects of feed flow rate, feed total solids concentration, feed composition, angle of inclination and split ratio on the recovery and on the purity of both species in the overflow and underflow streams were examined. The split ratio is defined as the ratio of the underflow volumetric flow rate to that of the feed. At a fixed feed flow rate, there is a threshold split ratio, beyond which the recovery drops linearly with increasing the split ratio. The threshold split ratio was found to be a function of the operating conditions. At a fixed set of operating conditions, increasing the angle of inclination results in a greater degree of separation. At a given split ratio, there is an optimum feed flow rate beyond which the enhancement decreases as the feed flow rate increases. A mathematical model based on the continuity equations and the PNK concept has been developed that predicts adequately the experimental measurements.

Dispersion in consolidated sandstone with radial flow

AbstractThis paper presents some experimental and theoretical results for dispersion processes occurring in consolidated Berea sandstone with radial flow geometry. A comprehensive review of the derivation and application of several analytical solutions is also presented. The Galerkin finite element method is applied to solve the advection-dispersion equation for unidimensional radial flow.Individual and combined effects of mechanical dispersion and molecular diffusion are examined using velocity-dependent dispersion models. Comparison of simulated results with experimental data is made. The effect of flow rates is examined. The results suggest that a linear dispersion model,D=αu, whereD is the dispersion coefficient,u the velocity andα a constant, is not a good approximation despite its wide acceptance in the literature. The most suitable mathematical formulation is given by an empirical form of

WALL SAMPLING FROM HORIZONTAL SLURRY PIPELINES

D = D_0 + \mathop \alpha \limits^` u^m