A new digital twin for enzymatic hydrolysis processes applied to model-based process design

Renewable raw materials containing starch and proteins are split into their main components using enzymatic hydrolysis processes. However, even small changes in temperature, pH or pressure may strongly affect the enzyme activity and stability. At the same time, natural fluctuations may lead to changes in the substrate composition. These mutually influencing factors place enormous demands on the design and control of enzymatic hydrolysis processes. Individual enzymatic hydrolysis processes have already been modelled, but models for the hydrolysis of potato starch by α-amylase and glucoamylase and the proteolysis of organic sunflower seed meal by endopeptidase and exopeptidase in a stirred tank reactor, or even digital twins, are unavailable. Therefore, a new mechanistic model for the combined starch hydrolysis and proteolysis was developed. Sigmoidal and double sigmoidal functions were implemented to map the temperature and pH-dependent enzyme activity. The model can simulate the enzymatic hydrolysis processes with an agreement of more than 90%. The new model was integrated into an existing digital twin of a 20 L stirred tank reactor to create a new stand-alone digital twin for enzymatic hydrolysis processes. Applying the new digital twin core model, a model-based process design strategy based on the open-loop-feedback-optimal and model-based design of experiment strategies was established. By applying the new strategy, the amount of α-amylase and glucoamylase required for starch hydrolysis could be reduced by more than 30%. In addition, the required amount of endopeptidase and exopeptidase for proteolysis could be reduced by more than 50%. Compared to the classic design of experiments approach, the number of experiments required for process optimisation could be reduced by more than 50%. The strategies resulting from this work can soon be used for the optimisation of the industrial organic nutrient media production from regenerative substrates for the cultivation of microorganisms such as Saccharomyces cerevisiae

Acceleration and collimation of relativistic MHD disk winds

We perform axisymmetric relativistic magnetohydrodynamic (MHD) simulations to investigate the acceleration and collimation of jets and outflows from disks around compact objects. The fiducial disk surface (respectively a slow disk wind) is prescribed as boundary condition for the outflow. We apply this technique for the first time in the context of relativistic jets. The strength of this approach is that it allows us to run a parameter study in order to investigate how the accretion disk conditions govern the outflow formation. Our simulations using the PLUTO code run for 500 inner disk rotations and on a physical grid size of 100x200 inner disk radii. In general, we obtain collimated beams of mildly relativistic speed and mass-weighted half-opening angles of 3-7 degrees. When we increase the outflow Poynting flux by injecting an additional disk toroidal field into the inlet, Lorentz factors up to 6 are reached. These flows gain super-magnetosonic speed and remain Poynting flux dominated. The light surface of the outflow magnetosphere tends to align vertically - implying three relativistically distinct regimes in the flow - an inner sub-relativistic domain close to the jet axis, a (rather narrow) relativistic jet and a surrounding subrelativistic outflow launched from the outer disk surface - similar to the spine-sheath structure currently discussed for asymptotic jet propagation and stability. The outer subrelativistic disk wind is a promising candidate for the X-ray absorption winds that are observed in many radio-quiet AGN.Comment: 22 pages, 15 figures; accepted for publication in ApJ; incorporates changes according to refere

Ultra-Relativistic Magneto-Hydro-Dynamic Jets in the context of Gamma Ray Bursts

We present a detailed numerical study of the dynamics and evolution of ultrarelativistic magnetohydrodynamic jets in the black hole-disk system under extreme magnetization conditions. We find that Lorentz factors of up to 3000 are achieved and derived a modifiedMichel scaling (Gamma ~ sigma) which allows for a wide variation in the flow Lorentz factor. Pending contamination induced by mass-entrainment, the linear Michel scaling links modulations in the ultrarelativistic wind to variations in mass accretion in the disk for a given magnetization. The jet is asymptotically dominated by the toroidal magnetic field allowing for efficient collimation. We discuss our solutions (jets) in the context of Gamma ray bursts and describe the relevant features such as the high variability in the Lorentz factor and how high collimation angles (~ 0-5 degrees), or cylindrical jets, can be achieved. We isolate a jet instability mechanism we refer to as the "bottle-neck" instability which essentially relies on a high magnetization and a recollimation of the magnetic flux surfaces. The instability occurs at large radii where any dissipation of the magnetic energy into radiation would in principle result in an optically thin emission.Comment: 31 pages, 6 figures. Submitted to ApJ. Higher Quality figures at http://www.capca.ucalgary.ca/paper

Development of a Digital Twin for Enzymatic Hydrolysis Processes

Enzymatic hydrolysis processes can be used to produce organic nutrient media from renewable raw materials. However, many of these processes are not optimally designed, so expensive enzymes and substrates are wasted. Mathematical models and Digital Twins (DTs) are powerful tools, which can be used to optimize bioprocesses and, thus, increase the yield of the desired products. Individual enzymatic hydrolysis processes have already been modeled, but models for the combined starch hydrolysis and proteolysis, or DTs, are not available yet. Therefore, an easily adaptable, dynamic, and mechanistic mathematical model representing the kinetics of the enzymatic hydrolysis process of the combined starch hydrolysis and proteolysis was developed and parameterized using experimental data. The model can simulate the starch hydrolysis process with an agreement of over 90% and the proteolysis process with an agreement of over 85%. Subsequently, this model was implemented into an existing DT of a 20 L stirred tank reactor (STR). Since the DT cannot only map the kinetics of the enzymatic process, but also the STR with the associated periphery (pumps, heating jacket, etc.), it is ideally suited for future process control strategy development and thus for the optimization of enzymatic hydrolysis processes