#### Numerical analysis of multiphase flows

Similarly to the single-phase case, even a multiphase flow can be subject of numerical analysis in order to find an approximate solution of some transiet problems. Starting from the Navier -Stokes equations and using appropriate models and closure equations, we can get systems of equations then numerically solved by calculator.

Among these models we remember the homogeneous model, the drift-flux model and the two-fluid model. There are also many methods for the numerical discretization of such models, in order to obtain stable codes for the simulation of different scenarios (for example, given a horizontal tube, i.e. a pipeline, which transports oil and gas and given some initial and boundary conditions, we can obtain the real-time profiles of some characteristic variables of the system, as the volumetric fraction of liquid) .

Finally, through numerical analysis, it is possible to make simulations of production or flow assurance system.

##### Inverse problem

A research field of multiphase flows currently in fast development, based on numerical codes, is represented by the search for a solution to the inverse problem, i.e. the possibility to estimate real-time values and trends of some variables of the problem (the volumetric flow rates in entrance to the pipes, some parameters, etc.) knowing only the values of some variables by measurements (especially in the industrial field, for example, in a wellbore, only the outlet variables or pressure profiles are easily measured) . To achieve this we can use the usual methods of numerical analysis for direct problems in combination with mathematical recursive filters (sequential methods), such as the Kalman filter, which at each time step adjust the values of the unknowns of the problem, comparing them with real time measurements (soft- sensing and data assimilation problems). The solution of this kind of problems (i.e. the estimation of the trends of the characteristic values of a system knowning only some measurements) will allows us, especially in the oil industry, to optimize the management of mining and flow assurance of hydrocarbons.

#### Multiphase flow with non-Newtonian fluids

The research aim is to study multiphase flows in pipes with the presence of a non-Newtonian fluid. A non-Newtonian fluid is a fluid which relationship between shear stress and rate of strain is not linear but is described by a model: power-law model or the Herschel- Bulkley model can be used to describe the rheological behavior of a given fluid.

Gas/non-Newtonian fluid systems are often encountered in many engineering applications, especially related to oil extraction and transportation in pipes. For example, it is a common practice to inject gas to reduce the pressure drop during the transport of non-Newtonian fluids (like slurries).

The research is carried out both experimentally and theorically.

The stratified flow regime, when the gas and the liquid phase flows separately in a pipe (the lightest at the top and the other at the bottom), was studied developing a new model (PTF model: the pre- integrated model) to predict hold-up and pressure drop. The existing theory on the transition from the stratified flow regime was extended for the case of a non-Newtonian fluid.

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#### High-viscous oils

Many gas-liquid flows show properties and behaviours very far from air/water flows (e.g. high viscous oil/air flows in pipelines or magmas rising in volcanoes conduits) but research has been carried out mainly with air/water mixtures.

Thus, theories and models have been developed starting from that particular system and, probably, this has affected the results, which do not always take into account mechanisms and parameters that would be relevant for other systems.

The aim of the investigations in the field of highly viscous oils is to experimentally investigate heavy oil/air two-phase flows in order to better comprehend the influence of viscosity. This will help to develop new theoretical correlations useful for predicting operative conditions in pipelines and wells.

#### Air micro bubble generators

Air micro bubbles are widely used in many industrial processes. Some examples include wine industry, waste water treatment and growth enhancement of aerobic organisms. The wide applicability of micro bubbles results from their large gas-liquid surface area, increased gas hold up and slower rise velocity compared with bubbles of larger size.

In our laboratory we are conducting research in conjunction with Biokavitus with the aim to improve the design of currently produced air bubble generators. In order to achieve this aim we are studying the size distribution of micro bubbles using custom designed optical method. This allows us to identify aspects of design which influence the size of air bubbles thus enabling us to come up with ways of improving it.