Compute Advective and Diffusive Transport

The AddiDict module simulates and predicts the transport of particles or molecules by advection and diffusion. The flow field that advectively transports particles is driven by an external pressure drop or prescribed mean velocity and computed using the solvers available in FlowDict. Advective and diffusive transport phenomena are modeled using direct particle dynamics or solving the field-based advection equation in combination with Laplace diffusion.

Both methods allow to analyze time-dependent distribution of mass, outlet or layered concentrations, residence time, breakthrough curves, and other statistics.

It is also possible to perform adsorption simulations using Langmuir and Toth adsorption isotherms.

AddiDict is applicable to studies on the transport of particles in suspensions and emulsions in porous media in industrial and natural processes:

• Treatment of wastewater 
• Sub-surface propagation of pollutants 
• Fouling of membranes 
• Seawater injection in oil reservoirs
• Particle-adsorbed organic contaminants in groundwater
• Adsorption for filtration and capture processes of gases, contaminants, vapors, and carbon capture & storage (CCS)
• Modelling of exhaust treatment in catalysts

AddiDict traces the movement of particles by advection and diffusion. In a 3D digital structure model, such a tracer experiment begins with the initial placement of particles, followed by tracking their movement until they either exit the computational domain or reach a structure surface that collects them.

The flow field inducing advection is determined by an external pressure drop or prescribed mean velocity and is computed using the solvers available in FlowDict. Diffusion is modeled by a random walk algorithm, which can represent either the Brownian motion of large particles in a surrounding fluid or the diffusive motion of individual molecules.

Particle interactions with solid or porous components can be modeled in various ways, causing the particles to become immobile upon impact or to bounce off and continue their transport through the structure.

In post-processing, breakthrough curves, time-dependent particle concentrations, and simple first-order chemical reactions are computed.

Unlike Track Particles & Molecules, Transport Concentration Field employs a continuum-mechanical approach, focusing on the concentration field as the primary variable rather than tracking individual particles. This enhancement allows users to model the molar concentration of solutes within a solvent, capturing both the transport due to solvent motion (advection) and the diffusion-driven movement from high to low concentration regions.

The solution algorithm is integrated into the LIR solver, and the flow field required for advection can be computed using LIR, EJ, or SimpleFFT solvers. Users have the flexibility to apply either or both transport mechanisms as needed.

The solver accommodates the full range of Péclet numbers, from pure diffusion (Pe = 0) to pure advection (Pe = ∞), thus enabling all transport regimes. Additionally, the transport algorithm is fully compatible with adaptive grids that stem from the flow computation with the LIR solver.

In post-processing, breakthrough curves and the intrinsically-averaged concentration per slice perpendicular to the through direction is plotted.

Adsorption-based processes are widely used to remove contaminants and odors in various everyday applications. These processes often rely on materials with large internal sub-micron surfaces, such as activated carbon or zeolites. For instance, in agriculture, these materials help protect against exposure to fertilizers and pesticides, while they are also vital for ensuring the safety of drinking water and the treatment of wastewater.

Use AddiDict - Adsorption to model those processes by simulating tracer particles moving through the structure and interacting with porous voxels. Within the porous active zone, the governing adsorption equations are solved based on the transported concentration and the equilibrium concentration. The results include breakthrough behavior of given species as well as the locally adsorbed load inside the porous active zones over time.