The influence of agitation on nucleation of butyl paraben and m-hydroxybenzoic acid polymorphs has been investigated through 330 cooling crystallization experiments. The induction time has been measured at different supersaturation and temperature in three parallel jacketed vessels equipped with different overhead stirring agitators. In each case, the nucleating polymorph of mhydroxybenzoic acid has been identified by infrared spectroscopy. The influence of agitation rate, impeller type, impeller diameter, impeller to bottom clearance and the use of baffles have been investigated. A general trend in all the experiments is that the induction time decreases with increasing agitation rate. Across all experiments with different fluid mechanics for the butyl paraben system, the induction time is correlated to the average energy dissipation rate raised to the power -0.3. It is shown that this dependence is consistent with a turbulent flow enhanced cluster coalescence mechanism. In experiments with m-hydroxybenzoic acid, the metastable form II was always obtained at higher nucleation driving force while both polymorphs were obtained at lower driving force. In the latter case, form I was obtained in the majority of experiments at low agitation rate (100 rpm) while form II was obtained in all experiments at higher agitation rate (≥300 rpm).

Abstract. Conventional models of pumping tests in unconfined aquifers often neglect the unsaturated flow process. This study concerns the coupled unsaturated–saturated flow process induced by vertical, horizontal, and slant wells positioned in an unconfined aquifer. A mathematical model is established with special consideration of the coupled unsaturated–saturated flow process and the well orientation. Groundwater flow in the saturated zone is described by a three-dimensional governing equation and a linearized three-dimensional Richards' equation in the unsaturated zone. A solution in the Laplace domain is derived by the Laplace–finite-Fourier-transform and the method of separation of variables, and the semi-analytical solutions are obtained using a numerical inverse Laplace method. The solution is verified by a finite-element numerical model. It is found that the effects of the unsaturated zone on the drawdown of a pumping test exist at any angle of inclination of the pumping well, and this impact is more significant in the case of a horizontal well. The effects of the unsaturated zone on the drawdown are independent of the length of the horizontal well screen. The vertical well leads to the largest water volume drained from the unsaturated zone (W) during the early pumping time, and the effects of the well orientation on W values become insignificant at the later time. The screen length of the horizontal well does not affect W for the whole pumping period. The proposed solutions are useful for the parameter identification of pumping tests with a general well orientation (vertical, horizontal, and slant) in unconfined aquifers affected from above by the unsaturated flow process.

An analytical solution is presented for the slug tests conducted in a partially penetrating well in an unconfined aquifer affected from above by an unsaturated zone. The solution considers the effects of wellbore skin and oscillatory responses on underdamped slug tests. The flow in the saturated zone is described by a two‐dimensional, axially symmetric governing equation, and the flow in the unsaturated zone above the water table by a linearized one‐dimensional Richards' equation. The unsaturated medium properties are represented by the exponential constitutive relationships. A Laplace domain solution is derived using the Laplace and finite Fourier transform and the solution in the real‐time domain is evaluated using the numerical inverse Laplace transform method. The solution derived in this study is more general and reduces to the most commonly used solutions for slug tests in their specified conditions. It is found that the unsaturated flow has a significant impact on the slug test conducted in an unconfined aquifer. The impact of unsaturated flow on such a slug test is enhanced with a larger anisotropy ratio, a shorter well screen length, a shorter distance between the well screen and the water table, or a larger well screen radius. The impact of unsaturated flow on slug tests decreases as the degree of penetration (the length of well screen) increases. For a fixed well screen length, the impact of unsaturated flow on slug tests decreases as the distance between the centre of screen and the water table increases. A large dimensionless well screen radius (>0.01) leads to significant effects of unsaturated flow on slug tests. The unsaturated flow reduces the oscillatory responses to underdamped slug tests. The unsaturated zone has significant impact on slug test under high‐permeability wellbore skin.

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