ACS PRF | ACS
All e-Annual Reports
44526-AC9
Drop Size Distributions of Oil-in-Water Emulsions During High Pressure Production and Storage
Oil-in-water emulsions are used to improve the flow characteristics of heavy oils for pipeline transportation. The drop size distribution has a strong effect on the viscosity of pipeline emulsions and on the physical properties of other oil-in-water emulsions. Typically these properties are determined for each candidate emulsion through a series of time consuming and expensive experiments. The objective of this project is to utilize targeted experiments and population balance equation (PBE) modeling to achieve a priori prediction of drop size distributions for oil-in-water emulsions.
Our previous work completed prior to this project focused on the use of inverse PBE modeling for extracting drop breakage functions from transient volume distributions obtained from a turbulently agitated batch emulsification vessel. Through simulation studies, we found that the inverse method exhibited high sensitivity to measurement errors such as random noise, data skewed towards smaller or larger drops, skewed data due to the presence of large dust peaks, and reduced resolution caused by data binning. The type of measurement errors considered generally produced underprediction of the breakage rate and, consequently, to overprediction of the number of large drops. Furthermore, the inverse method requires that new breakage functions be identified for each emulsion formulation and process operating condition of interest, effectively eliminating predictive capability of the PBE model.
During the first year of PRF support, we have pursued an alternative modeling approach based on the a priori specification of drop breakage functions followed by the application of parameter estimations techniques to transient volume distribution measurements. Our accomplishments include: (i) development of experimental capabilities to investigate emulsion drop breakage mechanisms in turbulent flow environments; (ii) derivation of a PBE model that explicitly accounts for the effects of formulation variables (dispersed phase volume fraction, viscosity, surface tension) and processing variables (pressure, number of passes) on drop breakage; (iii) development of a parameter estimation method that allows adjustable parameters in the drop breakage functions to be determined from transient drop volume distribution measurements; (iv) development of a computational fluid dynamics (CFD) code to investigate flow regimes in our high pressure homogenizer; and (v) evaluation of the parameter estimation method using experimental data obtained over a wide range of formulation and processing variables. Additional details are provided below.
Experimental Procedure: A model emulsion system consisting of soybean oil (0.5 weight percent) in water with Pluronic F-68 surfactant (0.1 weight percent) was subjected to turbulent flow environments in a high pressure homogenizer to investigate the mechanisms of drop breakage. Dispersed phase volume fractions were maintained below 0.005 to minimize the possibility of drop coalescence. Coarse pre-emulsions prepared with a rotor-stator device typically exhibited bimodal drop volume distributions, as measured with Coulter particle size analyzer. Volume distributions measurements were obtained after each pass of the homogenizer to provide the transient data required for parameter estimation.
PBE Model Formulation: For the sake of simplicity, our current PBE models only account for binary drop breakage and neglect drop coalescence. Our first generation model included a physically-based kernel for drop breakage derived under the assumption that breakage results from drop collision with turbulent eddies and a truncated normal distribution for the daughter drop distribution kernel such that equal division of volume between the two daughter drops was most probable. A CFD code developed using Fluent indicated the presence of locally high shear regions in the homogenizer, motivating the derivation of a second breakage kernel accounting for turbulent shear. The two breakage kernels are functions of the formulation and processing variables, thereby allowing the PBE model to generate predictions for experiments not yet performed.
Parameter Estimation Method and Results: A nonlinear parameter estimation technique based on a discretized version of the PBE model was developed. The objective function was chosen as the least-squares difference between the measured and predicted volume distributions after each pass of the homogenizer. The objective was minimize subject to the PBE model equations, with volume discretized through finite difference approximation and time discretized using Radau collocation on finite elements. The optimization problem was formulated in AMPL and solved using the nonlinear programming code CONOPT. We found that poor drop volume distribution predictions were obtained when the PBE model incorporated a single breakage function. Substantially improved predictions were obtained when both breakage functions were incorporated in an additive manner, suggesting that multiple breakage mechanisms are present even with this simple emulsion system. Depending on the initial guess, the optimizer converged to two local optima that differed according to the volume region over which each breakage function was dominant. The best predictions were obtained when the shear breakage function dominated at large drop volumes and the turbulent eddy function dominated at small drop volumes, suggesting size dependent domains for the different breakage phenomenon. We are currently preparing a journal manuscript with these experimental and modeling results.
