Batch Reactors Versus Continuous Reactors

The most common reactors in the chemical industry are tank reactors, which can be used as batch reactors or continuous reactors. Batch reactors process reactants one batch at a time, whereas continuous reactors carry reactants in a constant flow with continuous, steady-state production.

Batch reactors are used in a range of unit operations from mixing to crystallization, and are able to carry out a series of different reactions within the same container. Due to these abilities, they’re useful for testing new processes and manufacturing expensive products that are produced in relatively small volumes. For example, they are used in the fine chemicals industry, where the same reactor can be used for several processes (one at a time). Additionally, some chemicals aren’t suitable for continuous processes. Batch reactors are reliable options in, for example, fermentation processes and can even yield high conversion numbers for slow reactions, where you simply allow the process to run until completion.

An image of a batch reactor mixer modeled in the COMSOL® software.

Continuous reactors are usually part of a continuous process that runs at steady state and may do so for many months without interruption. They are the most commonly used option for the production of bulk chemicals and petrochemicals, where the volumes are several orders of magnitude larger than in the fine chemical, pharmaceutical, and food industries.

Plate Reactors

One type of reactor is used as an alternative to the tank reactor in the fine chemical industry: the plate reactor. While expensive, there are times when a plate reactor is the best option for ensuring high-quality products. Since this type of reactor is used for relatively slow reactions, it works like a very long tubular reactor with a relatively large residence time.

Plate reactors are seldom used in bulk processes, since they give pressure losses that require large pumping power for large volumes. They are an alternative to tank reactors when temperature- or composition-sensitive products are manufactured, regardless of the process being batch or continuous. Plate reactors are a good option in fine chemical, pharmaceutical, and food processing applications in which quality is highly important, such as the pasteurization of milk, beer, or juice.

A model of flow through a unit cell in a typical plate reactor.

Using the Chemical Reaction Engineering Module, an add-on to the COMSOL Multiphysics® software, we can analyze the reacting flow in a continuous plate reactor design.

Modeling Chemical Production in a Plate Reactor with COMSOL Multiphysics®

When modeling reactor plates and cooling/heating plates, we can treat the model setup as we would a heat exchanger model, in that the plates are stacked on top of one another. The 3D geometry of the model, below, shows the winding interior of the reactor plate. On the left side of the model, there are two inlet streams where reactants can enter the system:

1. Inlet I, A + B, at the top of the reactor
2. Inlet II, B, lower in the reactor

The heat exchange zones are also indicated, as they can affect the outer boundaries of the model.

In this example, there are two exothermic reactions that occur in an aqueous solution. The first reaction generates the desired product, D (A + B produces D). In the second reaction, the desired product reacts with B to produce the unwanted product, U (D + B produces U).

The design goal is to avoid generating an unwanted product in the plate reactor. Keeping in mind that the reactions are both exothermic and therefore prone to runaway temperatures, we need to find a way to dissipate the heat of the reaction so that the first reaction can proceed at a steady rate while inhibiting the second reaction. This outcome can be achieved via a cooling medium. The second half of the reactor exchanges heat with a cooling medium at a lower temperature than the first half.

Next, we account for the coupled momentum, energy, and mass transport within the plate reactor using the:

1. Laminar Flow interface, which models the momentum transport (fluid flow) described by the Navier-Stokes equations at steady state
2. Heat Transfer in Fluids interface, which models the energy balance
3. Transport of Diluted Species interface, which models the mass transfer in the reactor domain, accounting for convection and diffusion

For more information on the boundary conditions for these three interfaces, refer to the model documentation in the Fine Chemical Production in a Plate Reactor tutorial.

Simulation Results

Let’s take a look at the streamlines of the fluid flow in the reactor plate. As shown below on the left, the concentration of reactant A is indicated by the color scale. We can see that the concentration is much higher at reactant A’s point of entry (Inlet I) at the top of the plate and decreases as it flows to the bottom. The second study’s results, below on the right, show the isosurfaces for the concentration of reactant B. Notice how the injection stream at Inlet II mixes with the main stream, causing reactant B’s distribution to be more uniform in the lower part of the reactor. Overall, we can see that the chemical reactions consume the reactant along the entire reactor volume.

Streamlines of fluid flow with the concentrations of reactant A indicated by color (left); concentration of reactant B (mol/m³) across the reactor volume (right).

Finally, we can examine the temperature distribution throughout the plates, represented below by horizontal and vertical cut planes. These results help us see how the heat expelled by the reactions quickly cools throughout the reactor because of the cooling medium we implemented in the model.

Temperature distribution in the reactor plate.

This example model can be used as a guide for setting up and solving the coupled flow, mass, and energy transport equations in a reactor system. With the chemical modeling capabilities of the COMSOL® software, you can further develop plate reactor designs to help predict fine chemical reactions and increase product quality.

Next Steps

Try modeling the plate reactor yourself: The button below takes you to the Application Gallery, where you can access the MPH-file and step-by-step modeling instructions (requires a COMSOL Access account and valid software license).

Further Reading

Learn more about modeling chemical reactions and processes in the following blog posts:

• Comparing Static and Dynamic Wall Heat Exchangers with Simulation
• Using Simulation to Optimize Biopharmaceutical Processes
• Analyzing the Dissociation Process in a Tubular Reactor

Pablo Rolandi Discusses Modeling and Simulation in the Biopharma Industry

Simulation Applications for Biological and Synthetic Drugs

Rolandi began his keynote talk by explaining that there is diversity in the biopharma industry when it comes to what Amgen is modeling. Their projects have both breadth and depth, which can require advanced modeling of biological systems. Rolandi said that one of his team’s goals is to move “beyond” simulation through the development and deployment of modeling apps.

Pablo Rolandi divided his keynote talk into Amgen’s biologic and synthetic medicine projects. The first synthetics application he discussed was an agitated dryer filter (ADF). This filter helps avoid bottlenecks in the drying stage of drug manufacturing by performing three key isolation steps (instead of five, like earlier methods). Amgen researchers used simulation to determine pressure, temperature, and agitation operating conditions at the manufacturing site. They also built a simulation app so that other team members could evaluate quantitatively the difference between an ADF with a heating plate only and an ADF with a heating plate and added agitation.

Next, Rolandi discussed an ethylene oxide sterilization simulation model, which, at Amgen, they call ETHOSS. The background of this model was that a novel container used for vial sterilization did not comply with standards, so the team built a simulation app to test parameters for the transport diffusion process of ethylene oxide. They found concentration and time profiles as well as numerical values for point concentrations, speeding up the development of ETHOSS by months due to the avoidance of uninformative experiments.

From the video: Pablo Rolandi discusses ETHOSS, a model used to study vial sterilization processes.

The third application featured in the presentation dealt with the purification of biologic via a polishing cation exchange chromatography step. This unit operation is used in the biopharma industry to separate drug substances from materials that cause side effects, but simulating this process requires estimating many material properties and transport/isotherm parameters. Amgen built, calibrated, and validated a chromatography model before turning it into an app that end users could use to test the various design parameters.

Rolandi shifted gears to talk about simulation for Amgen’s combination product (i.e., drug and device) applications. First, he showed the crowd a plunger position model, nicknamed PIT. By building a simulation app and deploying it, team members across the organization were able to estimate process capability metrics of plunger position manufacturing operations to meet quality requirements.

The final model Rolandi discussed was a component injection time model, nicknamed KIT. In the biopharma field, the injection time for a drug delivery system must be precise, but factors like the container, drug product, and injector device cause variance. Amgen ran a global sensitivity analysis, or “factor analysis”, on the system’s parameters; e.g., viscosity, equilibrium length, and needle radius. They found that only the parameters for the needle and spring affected the results, simplifying the problem. Amgen built a KIT simulation app for team members to run uncertainty and sensitivity analyses using their own combination product parameters.

By creating simulation apps like the five examples featured in Rolandi’s keynote presentation and deploying them organization-wide via the COMSOL Server™ product, Amgen has been able to move “beyond” simulation. Rolandi even said that at Amgen, they think of the COMSOL® software as their “compute kernel” and aim to find a way for everyone there to access the wealth of the simulation data they are producing. By moving beyond simulation with apps, Rolandi sees both new challenges and new opportunities.

To learn more about how Pablo Rolandi and Amgen use multiphysics modeling and simulation apps in biopharma applications, watch the video at the top of this post.

Studying the Effect of Microgravity on Metastatic Cancer Cells

Microgravity is the condition of “free fall” experienced by, for example, objects like satellites that “fall” toward Earth but actually never reach its surface. In this condition, gravity and weight does exist, but is not measurable on a scale. Some people refer to this as zero gravity.

Applying conditions of microgravity to certain systems and processes enables scientists to study them without accounting for effects like hydrostatic pressure and sedimentation. By investigating biological processes exposed to microgravity conditions, we can advance technologies associated with tissue engineering, stem cell research, vaccine development, and more.

One area where microgravity is proving helpful is cancer research. From previous studies, we know that microgravity exposure suppresses immune cell activity and changes genomic and proteomic expressions. As such, scientists are investigating whether these changes also influence cancer development. The goal is to find novel therapeutic targets for metastatic cancer cells by influencing their migration, and therefore their activity.

A research team from SUNY Polytechnic Institute and SpacePharma, Inc. joined forces to develop a culturing system to test how microgravity affects metastatic cancer cell migration. This system isolates gravity as an experimental variable, thereby determining its contribution to cellular function in normal gravity on Earth. Considering the behavior of the culturing system in Earth’s gravity will initially provide insight into how microgravity conditions can be used for lab-scale experiments. The simulation technique will eventually be translated and used for space flight experiments within a low Earth orbit (LEO).

The setup for performing cell culture chips experiments on a chip (left) and a CAD representation (right). Images by A. Dhall, T. Masiello, L. Butt, M. Strohmayer, M. Hemachandra, N. Tokranova, and J. Castracane and taken from their COMSOL Conference 2016 Boston poster.

Running these microgravity experiments in the normal gravity of Earth can be difficult and requires a robust system design. CFD simulation is one way to help understand this problem, augment a good design, and optimize operating and flow conditions.

Designing a System to Analyze Cancer Cell Migration in Microgravity

First, let’s take a closer look at the cell culturing system, which exposes human cancer cells (contained in cell culture chambers) to microgravity conditions. To increase the number of cells during cell maintenance, the system supplies growth media via a media inlet. The system can also reduce the number of cells — and avoid overcrowding — by lifting the cells with trypsin and flushing them out. Another key element in this system is chemoattractants, which influence cell migration.

The initial design of the culturing system. Image by A. Dhall et al. and taken from their COMSOL Conference 2016 Boston poster.

To perform the preliminary analyses of the culturing system, the research team used two interfaces:

1. The Single-Phase Flow interface, to simulate the flow of cell growth media under laminar conditions
2. The Transport of Diluted Species interface, to study the transport (diffusion and advection) of the chemoattractant (EGF)

When using the Single-Phase Flow interface, the team tested for backflow into the cell culture chamber when the outer channel is flushed with cell growth media. From their results, the researchers found that using either valves or nozzle-diffuser flow can help avoid backflow.

The potential backflow in a cell culture system that occurs due to flushing media through the outer channels of a culture unit. Image by A. Dhall et al. and taken from their COMSOL Conference 2016 Boston presentation.

Simulation was also used to calculate the optimal flow rate range under the chosen operating conditions. In these studies, the researchers modified the culture chip system to contain three chambers, as shown below.

Modified culture chip system with three chambers. Image by A. Dhall et al. and taken from their COMSOL Conference 2016 Boston presentation.

Examining the Simulation Results in COMSOL Multiphysics®

The results, shown below, indicate that when the flow from the inner chamber is less than or equal to the flow from the outer chambers, the cell growth media do not leak into the outer chambers. However, as the flow into the inner chamber increases, the media within the inner chamber spread outward, eventually leaking into the outer chambers via the third channel.

The optimal flow rate range for a three-chamber chip. In these plots, the researchers varied the ratio of the input velocity in the inner chambers (V_IC) to input velocity in the outer chambers (V_OC) and visualized the resulting flow. Images by A. Dhall et al. and taken from their COMSOL Conference 2016 Boston presentation.

In the image below, the flow in the outer chambers runs opposite to the flow in the inner chamber. The result is that the cell growth media leak through all of the channels. Using the information they learned about the leakage, the team can improve the design of the cell culture chip.

Leakage in the cell culture chip system when the flow of the cell growth media has equal and antiparallel input velocities. Image by A. Dhall et al. and taken from their COMSOL Conference 2016 Boston paper.

The final simulations are of the diffusion of the chemoattractant along a gradient. The chemoattractant has an initial concentration of 0.04 mM and travels through a 0.6-mm migration channel. Simulating this migration shows that the researchers can establish a gradient at a practical timescale for cell migration experiments.

Diffusion of the chemoattractant over time. Image by A. Dhall et al. and taken from their COMSOL Conference 2016 Boston presentation.

Next Steps for Analyzing Cancer Cell Migration

Designing a functional culturing system is the key to successfully studying cancer cell migration in microgravity conditions, thus identifying new therapeutic targets for cell mestatatic behavior. In the future, the research team plans to enhance their study by looking into how the cell growth media and chemoattractant interact.

Read More About Medical Uses of Simulation

• Take a look at the researchers’ original work: “Simulating Fluid Flow through a Culture Chip for Cell Migration Studies in Microgravity“
• Check out these blog posts:
  • Preventing Airborne Infection with CFD Modeling
  • Study Radiofrequency Tissue Ablation Using Simulation
  • Evaluating an Insulin Micropump Design for Treating Diabetes
  • Finding an Accurate Model to Study Blood Flow Around a Stent

Modeling Heat and Moisture Transport in Building Materials

Building physics engineers aim to improve the energy performance and sustainability of building envelopes. Although their practices are based on past experience, new materials and building techniques are constantly being developed that offer a wide set of options in building design and thermal management. Let’s see how to model heat and moisture transport in building materials to help reduce energy costs and preserve buildings.

Building envelopes can be analyzed by modeling heat and moisture transport.

Controlling moisture is necessary to optimize the thermal performance of building envelopes and reduce energy costs. The thermal properties of insulation or isolation materials usually depend on both temperature and moisture content. Therefore, a coupled heat and moisture model helps us fully analyze the thermal performance of a building component. One example is the dependence of a lime silica brick’s thermal conductivity on relative humidity.

The moisture dependence of thermal conductivity for lime silica brick.

The figure above shows that lime silica brick becomes two times less thermally isolating for high relative humidity values.

In addition, we must consider moisture control in the building design process to choose building components that can reduce the risk of condensation. The coupled modeling of heat and moisture transport enables us to analyze different moisture variations and phenomena in building components, such as:

• Drying of moisture resulting from the initial construction
• Condensation due to the migration of moisture from outside to inside during warmer periods
• Moisture accumulation by interstitial condensation due to vapor diffusion during colder periods

Let’s consider a wood-frame wall between a warm indoor environment and a cold outdoor environment. Vapor diffuses through the wall from the high-moisture environment inside to the low-moisture environment outside. This creates high relative humidity values associated with low temperature values close to the exterior panel, with the risk of condensation as a direct consequence.

The relative humidity distribution in a wood-frame wall.

Condensation leads to mold growth, which directly affects human health and building sustainability. The rate of mold growth is key data for the preservation of historical buildings, for example. To prevent the risk of interstitial condensation, it is common practice to add a vapor barrier between the interior gypsum panel and the cellulose isolation board. This reduces the moisture values where they are at a maximum. The figure below shows the relative humidity distribution across the wood-frame wall through a wood stud (red lines) and a cellulose board (blue lines), with and without the vapor barrier (dashed lines and solid lines, respectively).

Effect of a vapor barrier on relative humidity distribution across the wood-frame wall in a wood stud and cellulose board.

For this model, we consider the building materials to be specific unsaturated porous media in which the moisture exists in both liquid and vapor phases and only some transport processes are relevant. The norm EN 15026 standard addresses the transport moisture phenomena that is taken into account in building materials, following the theory expressed in Ref. 1.

The transport equation established as a standard by the norm accounts for liquid transport by capillary forces, vapor diffusion due to a vapor pressure gradient, and moisture storage.

We model the latent heat effect due to vapor condensation by adding the following flux in the heat transfer equation:

In addition, the moisture dependence of the thermal properties is assessed.

Find details about the moisture transport equation in building materials in the Heat Transfer Module User’s Guide.

When using the Heat Transfer Module, the Heat and Moisture Transport interface adds a:

1. Heat and Moisture coupling node
2. Heat Transfer in Building Materials interface
3. Moisture Transport in Building Materials interface
4. Building Material feature for heat transfer
5. Building Material feature for moisture transport
6. Thin Moisture Barrier feature for modeling the vapor barrier

Finally, the latent heat source due to evaporation is added to the heat transfer equation by the Building Material feature of the Heat Transfer interface.

The model tree and subsequent subnodes when choosing the Heat Transfer in Building Materials interface, along with the Settings window of the Building Material feature.

Coupled Modeling of Heat and Moisture Transport in Unsaturated Porous Media

Modeling heat and moisture transport in an unsaturated porous medium is important for analyzing polymer materials for the pharmaceutical industry, protective layers on electrical cables, and food-drying processes, to name a few examples.

For these applications, phenomenological models, such as the one presented above for building materials, may not be available. However, by considering the conservation of heat and moisture in each phase (solid, liquid, and gas), and volume averaging over the different phases, we can derive a mechanistic model.

To compute the moisture distribution, we solve a two-phase flow problem in the porous medium. Two equations of transport are solved: one for the vapor and one for the liquid water. The coupling between the vapor and liquid water operates through the definition of saturation variables, S_vapor + S_liquid = 1. The changing water saturation is taken into consideration for the definition of the effective vapor diffusivity and liquid permeability.

For quick processes, with a time scale comparable to the time it takes to reach equilibrium between the liquid and gas phases inside the pores of the medium, a nonequilibrium formulation can be defined through the following evaporation flux:

In this definition, the equilibrium vapor concentration, defined as the product of the saturation concentration c_sat and the water activity a_w, is used to account for the porous medium structure. Indeed, due to capillary forces, equilibrium is reached for concentrations that are lower than in a free medium.

By letting the evaporation rate K go to infinity, an equilibrium formulation is obtained with the vapor concentration equal to the equilibrium concentration.

Let’s consider a food-drying process. A piece of potato, initially saturated with liquid water, is placed in an airflow to be dried. Inside the potato, the vapor is transported by binary diffusion in air. We use a Brinkman formulation to model the flow induced by the moist air pressure gradient in the pores. As the liquid phase velocity is small compared to the moist air velocity, Darcy’s law is used for the liquid water flow due to the pressure gradient. The capillary flow, due to the difference between the relative attraction of the water molecules for each other and the potato, is also considered in the liquid water transport.

The vapor and liquid water distributions over time for this model are shown in the following two animations. Note that water can leave the potato as vapor only.

The liquid water concentration over time.

The vapor is transported away by the airflow, as shown in this animation:

The water vapor concentration over time.

The evaporation causes a reduction of the temperature in the potato. The temperature distribution over time is shown below.

Temperature distribution over time.

You can implement the equations in the Heat Transfer in Porous Media interface within the Heat Transfer Module and the Transport of Diluted Species interface within the Chemical Reaction Engineering Module. This process requires some steps in order to couple the multiphase flow in a porous medium together with the evaporation process.

Read the article “Engineering Perfect Puffed Snacks” on pages 7–9 of COMSOL News 2017 to see how Cornell University researchers used COMSOL Multiphysics to model rice puffing. In this numerically challenging process, the rapid evaporation of liquid water results in a large gas pressure buildup and phase transformation in the grain.

Closing Remarks on Modeling Heat and Moisture Transport in Porous Media

In this blog post, we discussed COMSOL® software features for modeling heat and moisture transport in porous media. COMSOL Multiphysics (along with the Chemical Reaction Engineering Module and Heat Transfer Module) provides you with tools to define the corresponding phenomenological and mechanistic models for a large range of applications. Depending on the dominant transport processes, you can use predefined interfaces or define your own model.

Reference

Künzel, H. 1995. Simultaneous Heat and Moisture Transport in Building Components. One and two-dimensional calculation using simple parameters. PhD Thesis. Fraunhofer Institute of Building Physics.

Try It Yourself

• Check out the tutorial models featured in this blog post:
  • Condensation in a Wood-Frame Wall
  • Evaporation in Porous Media with Large Evaporation Rate

Treating Renal Failure with Hemodialysis

Renal failure, also known as kidney failure, occurs when a patient’s kidneys fail to properly remove excess waste and fluid from their blood, causing it to build up within the body. To help patients with failed kidneys, doctors use dialysis to replicate the kidneys’ blood-cleaning function.

Dialysis is a diffusion-driven process that transports only certain components through a membrane. Diffusion occurs due to the different concentrations of the dialysate and permeate located on either side of the membrane. During this process, chemical species are separated by variations in solubility and diffusivity, resulting in different transport rates for different species across the membrane.

One type of dialysis, hemodialysis, uses membranes as artificial kidneys. They serve some of the same functions as a healthy kidney and alleviate issues associated with kidney failure. For the hemodialysis process to work, the membrane dialysis device must be able to successfully remove contaminants from the bloodstream.

A look inside a machine used for hemodialysis. Image by luke130. Licensed under CC BY-SA 3.0, via Wikimedia Commons.

While modeling experts like you can find optimal dialysis device parameters by analyzing different materials and operating conditions with simulation, you can provide an easier way for colleagues and customers to run these analyses by building a COMSOL® app. Apps, an example of which we’ll discuss in the next section, help users more efficiently test different inputs and visualize how they affect the contaminant concentration in a membrane dialysis device.

Analyzing Contaminant Concentration in a Membrane Dialysis Device

Our demo app models a membrane dialysis device with a bloodstream flowing through it and calculates the bloodstream’s resulting contaminant concentration. The device featured in this app is made of a hollow-fiber module with walls that function as a membrane to remove contaminants. The following schematic shows the hollow-fiber assembly, a part in the dialysis device.

A schematic of the hollow-fiber assembly used in a membrane dialysis device.

In the membrane dialysis device, the dialysate and permeate flow inside and outside the fibers, respectively. Contaminants are transported via diffusion and convection within these liquids. However, in the model below, when contaminants pass through the membrane and move through the fiber walls to the permeate side, diffusion is the sole form of transport. Species with a higher weight and a lower solubility and diffusivity remain on the dialysate side. When simulating ultrafiltration, a process often used in hemodialysis, we can apply a pressure gradient across the membrane wall, which enables advective transport across the membrane for the species with lower weights. This transport mechanism can also be easily added to the model described below.

The setup of the hollow fiber, dialysate, and permeate (left) and the model domain (right).

Let’s take a closer look at this underlying model, which uses the Transport of Diluted Species interface to model mass transport and the Laminar Flow interface to model convective flux, under the assumption that there is a laminar flow.

When creating the underlying model, we paid special attention to defining the appropriate boundary conditions. The model deals with discontinuous concentration fields and requires boundary conditions to be set at each liquid interface on both sides of the membrane. You can see the boundaries that need to be considered in the image below.

All of the boundaries used in the underlying model.

Further, the underlying model uses an axisymmetrical approximation because the angular gradients are considered negligible. In the axisymmetrical geometry, symmetry applies to the leftmost boundary.

Since the advective term runs parallel with the right edge and the concentration gradients are eliminated by advection, a no-flux boundary condition is set at the right vertical boundary. Additionally, because the membrane is attached to the frame at the upper and lower edges, we can also set no-flux boundary conditions at these boundaries.

Note that while this demo app uses the model described above, you can easily modify the underlying geometry to fit your specific needs. You can also add a pressure-driven term to model ultrafiltration.

All of this complexity and more is hidden from the app user in an easy-to-use interface. With this app, people with little to no simulation knowledge can analyze membrane dialysis devices.

Optimizing a Membrane Dialysis Device with a Numerical Modeling App

The goal of this demo app is to maximize contaminant removal within a membrane dialysis device. This can be done in the app by testing different input parameters, including:

• The inlet’s contaminant concentration within the dialysate
• Diffusion coefficients within the dialysate and permeate
• The diffusion coefficient in the membrane
• The partition coefficient at the liquid-membrane interfaces
• The model domain geometry

As we can see in the following annotated screenshot, users are able to modify these values in the Input & Results section on the left side of the app. Once the user has entered their desired inputs, they can click Compute at the top of the app to run a study and generate results.

The user interface for our Calculating the Contaminant Concentration in Membrane Dialysis app.

After running a study with the desired inputs, users receive values for both the contaminant concentration in dialyzed blood as well as the contaminant removal in the Input & Results section. Further results are found in the Graphics & Results section, which contains three tabs: Geometry, Concentration, and Concentration Profiles.

The Concentration tab provides a detailed 3D view of the contaminant-concentration distribution within the three model domains. When listed from the center of the model outward, these domains include:

• Dialysate within the hollow fiber
• Membrane
• Permeate surrounding the hollow fiber

Results from the Concentration tab, showing contaminant concentrations in three domains.

The results plotted above show that as fluid flows from the inlet over a distance of 10 mm, the concentration within the hollow fiber experiences a marked decrease, indicating a successful contaminant removal. Meanwhile, the concentration in the permeate is highest closest to the outlet. The risk of a high filtered species concentration causing a deposition on the outer surface of the fiber is largest at this location. In this graph, we also see diffusion layers developing on the sides of the fiber wall.

Moving on to the Concentration Profiles tab, we see that the demo app enables users to generate a plot detailing the contaminant concentrations in all three domains for both the middle of the fiber and the outlet. The plot shows the discontinuity of the concentration field at the boundaries located between domains, which is caused by the relatively low porosity of the membrane. However, the flux is continuous over the boundaries of the membrane.

The concentration profiles at half of the fiber’s length and at the outlet, which are plotted along the model geometry’s radius.

With intuitive apps, users can easily test different input parameters to analyze dialysis devices. Results generated by the app discussed here enable users to find the device’s optimal operating conditions, membrane materials, and fiber dimensions for removing contaminants within the membrane dialysis device — helping to improve the dialysis process for renal patients.

Explore More Medical-Related Applications of Multiphysics Modeling

• Read more about biomedical uses of simulation on the COMSOL Blog:
  • Improving Vascular Access for the Treatment of ESRD Patients
  • Designing Effective Transdermal Drug Delivery Patches with Simulation
  • Preventing Airborne Infection with CFD Modeling

Design Considerations for Transdermal Drug Delivery Patches

After a TDD patch is applied to the skin, it continuously delivers a low-level drug dose. This is beneficial when dealing with drugs with a rapid onset and short duration, like the pain medication fentanyl, because the patch releases the drug gradually over time. TDD patches are also more effective and convenient than traditional drug delivery methods.

Transdermal drug delivery patch. Image by RegBarc — Own work. Licensed under CC BY-SA 3.0, via Wikimedia Commons.

Designing TDD patches is a challenge for many reasons. One design challenge is that the skin is a little too good at protecting the body from foreign substances. To get drugs past the body’s natural defenses, the patch needs to contain a chemical permeation enhancer. The stronger the enhancer, the better it is at transporting the drug. But a stronger permeation enhancer is also more likely to irritate the skin. Therefore, when designing an optimal TDD patch, we must consider both its effectiveness and patient comfort.

To find a balance between these factors, we can analyze the drug diffusion process in a TDD patch with simulation. Alireza Kermani and Nagi Elabbasi from Veryst Engineering, a COMSOL Certified Consultant, demonstrated this by modeling a TDD patch in COMSOL Multiphysics and comparing the results to those from an experiment.

Modeling a TDD Patch in COMSOL Multiphysics®

To model the TDD patch, the researchers at Veryst Engineering first set up a 2D axisymmetric model. For their model, the skin and patch both have a thickness of 50.8 μm and the radius of the patch is 0.9 cm. The team also assumed that the drug and enhancer dissolve uniformly.

A cross section of Veryst Engineering’s TDD patch model, displaying the normalized initial drug concentration (not to scale). Image by A. Kermani and N. Elabbasi and taken with permission from their COMSOL Conference 2016 Boston paper.

The team then set up the appropriate physics and boundary conditions to accurately model the drug’s movement from the patch into the skin. They used a pointwise constraint in COMSOL Multiphysics to enforce the flux continuity and partitioning of the drug and enhancer at the interface. They also accounted for the nonlinear diffusion caused by the coupling of the drug and enhancer and specified the drug’s diffusion, which varies linearly with the enhancer’s concentration. Since drugs do not exit the top or sides of TDD patches, the team added boundary conditions to their model to stop the drug flux in those areas.

The lower boundary of the skin acts as a sink for both the drug and enhancer. Therefore, the concentration was set to zero at that boundary. This represents the drug and enhancer leaving the skin. Using a sink boundary condition means that the concentration is zero.

Next to the lower boundary of the skin is the dermis layer, which is not modeled in this research. However, the researchers still considered its effect. The dermis layer undergoes blood microcirculation, so when a drug reaches the lower boundary of the skin, it is removed via microcirculation and transferred to the rest of the body. The team assumed that the concentration of the drug or enhancer is zero at the skin’s lower boundary and added a sink boundary condition.

Analyzing the Drug Diffusion Process

The group at Veryst Engineering tested their model to see how it performed in three different cases:

1. When there is no permeation enhancer in the patch
2. When the permeation enhancer’s initial concentration is 0.08 g/cm³
3. When the permeation enhancer’s initial concentration is 0.12 g/cm³

In all cases, the drug had an initial concentration of 0.06 g/cm³.

The drug diffusion process for the 2D model of the TDD patch. Animation courtesy of Veryst.

The simulation results show that the drug flux increases when there’s a permeation enhancer present, especially when it has a higher initial concentration. The plot below shows the normalized drug flux over time for the three enhancer concentrations.

The normalized drug flux in the skin for the three levels of permeation enhancer concentration. Image courtesy of Veryst.

Comparing the Model to Experimental Results

The Veryst Engineering team validated their model by comparing the results to a previous experiment. The experiment used the drug fentanyl at a concentration of 0.06 g/cm³ and the permeation enhancer lauryl pyroglutamate at an initial concentration of 0.12 g/cm³.

Veryst’s model accounts for the maximum flux value in the TDD patch as well as how this value increases with a higher concentration of enhancer. However, the model doesn’t account for the flux’s broad peak and quick decay, which are investigated in the experiment. The simulation also does not predict the drug flux accurately over long periods of time.

Comparison of the simulation results and experimental results for different permeation enhancer concentrations. Image courtesy of Veryst.

The engineers at Veryst suspect several factors may contribute to the difference in results. For instance, the Fickian diffusion model does not represent drug diffusion over a long period of time. Also, the assumption that drug diffusion increases linearly with a higher enhancer concentration is too simple to describe the drug diffusion process, which is time dependent. This means that the linear increase is not accurate for longer time periods.

Other components of the model, such as the boundary condition at the skin’s bottom layer, also need further investigation. A sink boundary condition for the enhancer may not be the right approach, since the solubility of the enhancer is not significant in the skin. On the other end of the spectrum, the team could have assumed that the enhancer has zero flux at the bottom boundary of the skin. The Zero Flux boundary condition increases the concentration of the enhancer in the skin, therefore increasing the drug flux. The true approach to describing this boundary is neither of these boundary conditions, but instead, something in between.

Another aspect to consider moving forward is the hydration in the skin and patch. The skin sample in the experiment is fully hydrated and when the patch is applied, the patch hydration level increases. The patch begins to swell, changing the concentrations of the drug and enhancer. This effect is not accounted for in the model.

Next Steps for Modeling a TDD Patch

The model designed by the team at Veryst Engineering demonstrates that, with additional information, it’s possible to simulate TDD patches in COMSOL Multiphysics. According to the team, the COMSOL software made it easy to include the continuity of flux, partitioning of the drug and enhancer, and the effect of coupling the drug’s diffusion coefficient with the concentration of the enhancer.

To get an accurate representation of the diffusion process, more research needs to be done on selecting the appropriate boundary conditions as well as choosing the correct factors to investigate, including hydration.

After building an optimized TDD patch model for future research, it is possible to couple it with other types of physics. For example, we can account for heat transfer in the patch model to determine how heat affects the drug diffusion process.

Additional Resources

• Learn more about Veryst Engineering
• Read the full paper from the COMSOL Conference 2016 Boston: Transdermal Drug Delivery with Permeation Enhancer
• Browse the COMSOL Blog to see more about how Veryst uses simulation:
  • Preventing Airborne Infection with CFD Modeling
  • Modeling Phononic Band Gap Materials and Structures
  • Simulating a Valveless Micropump Mechanism

The Advantages and Functionality of Vacuum Dryers

Humans have used drying as a method for preserving food since ancient times. Since then, the drying process has expanded from open-air drying or sun drying to other drying techniques, such as solar drying, freeze drying, and vacuum drying. Drying is also a key process in many other application areas, from the pharmaceutical industry to plastics.

Today, we’ll focus on the chemical process of vacuum drying, which is particularly useful when drying heat-sensitive materials such as food and pharmaceutical drugs. Vacuum dryers, commonly called vacuum ovens in the pharmaceutical industry, also offer other benefits. Because they require lower temperatures to operate, vacuum dryers use less energy and therefore, reduce costs. They also recover solvents and avoid oxidation.

A rotary vacuum dryer. Image by Matylda Sęk — Own Work. Licensed under CC BY-SA 3.0, via Wikimedia Commons.

Vacuum dryers remove water and organic solvents from a wet powder. The dryer operates by reducing the pressure around a liquid in a vacuum, thereby decreasing the liquid’s boiling point and increasing the evaporation rate. As a result, the liquid dries at a quicker rate — another major benefit of this process.

For vacuum drying to be effective, we need to decrease drying times without harming the products, which means that we need to maintain a strict control of the operating conditions. To balance these goals and to understand how operating conditions influence the product, you can use the multiphysics modeling capabilities of COMSOL Multiphysics.

Analyzing the Drying Speed of a Vacuum Dryer Using Multiphysics Modeling

Today, we’ll analyze the vacuum drying process of a Nutsche filter-dryer model. The dryer works by heating a wet cake from the bottom and the side walls of a container and by decreasing the pressure in the gas phase on the top of the cake. This example is based on a paper published by Murru et al. (Ref. 1 in the model documentation).

Let’s start by taking a closer look at our model. The vacuum dryer is comprised of a cylindrical drum filled with wet cake, which consists of three different phases: solid powder particulates, a liquid solvent, and a gas. As such, the cake’s material properties need to include the properties of all three individual phases, which vary depending on the proportion of each phase in the cake. The portion of each phase is determined by the volume fraction, which is one of our modeled variables.

The cake is modeled as a rectangular geometry with a radius of 40 cm and height of 10 cm in a 2D axisymmetric component. At the top, our model is exposed to a low-pressure head space. Meanwhile, heat flux boundary conditions at the filter dryer’s side and bottom boundaries account for a 60°C heating fluid.

The vacuum drying process in an axisymmetric Nutsche filter dryer.

Moving on, our tutorial combines evaporation and heat transfer modeling in order to study the cake’s liquid phase profiles and temperature. We calculate the cake’s solvent volume fraction with the Coefficient Form PDE interface and simulate heat transfer with the Heat Transfer in Solids interface. To solve the moisture transport in porous media, we use a predefined multiphysics interface in the Heat Transfer Module. We also include solvent evaporation by using both a heat-sink and mass-sink term and approximate the solvent transport as a diffusion process.

Our model makes the following assumptions:

1. Evaporation stops when the value of the liquid phase reaches zero, indicating that the liquid is fully evaporated.
2. Evaporation stops when the local vapor pressure is less than the head-space water vapor pressure, indicating that evaporation has no driving force.
3. Diffusion in the solvent stops when the liquid phase’s volume fraction dips below the critical value.

In these situations, we can use a step function to smoothly ramp both the evaporation rate and diffusion coefficient down to zero.

How Quickly Does Our Dryer Function?

We see that our simulation results are as predicted. Let’s start by examining our analysis of the cake after 30 hours have passed. As seen below, the cake’s temperature is close to that of the heating fluid (60°C) at both the side and bottom boundaries, and the liquid phase’s volume fraction is lowest near these heated boundaries and highest at the cake’s center. Additionally, the apparent moisture diffusivity is highest at the cake’s center and almost zero in places where the liquid phase has evaporated. Considering our model’s assumptions, these results are all expected.

The cake’s temperature (left), volume fraction of the liquid phase (middle), and apparent moisture diffusivity (right) after 30 hours.

Switching gears, let’s expand our timescale to look at the evaporation rate after 10, 20, and 30 hours. This study also yields expected results, since it shows evaporation beginning at the heated walls and decreasing when the amount of solvent at these boundaries lessens. During this process, the evaporation front shifts toward the cake’s center.

The evaporation rate after 10 (left), 20 (middle), and 30 (right) hours.

The quantitative results generated by our simulation study are in good agreement with previous research, confirming their validity. As such, we can use this model to accurately predict how dry a product is as a function of time. Using this information, we can minimize the amount of time that a product is exposed to elevated temperatures. Additionally, we can change the dryer’s size if we want to reduce the drying time when working with heat-sensitive products. Through multiphysics simulation, we can design more efficient and effective vacuum dryers for use in a variety of industries.

Explore More Modeling Applications for the Food and Pharmaceutical Industries

• Try it yourself: Download the Vacuum Drying tutorial featured in this blog post
• Check out these related blog posts:
  • Using Simulation to Optimize Biopharmaceutical Processes
  • Sensing the Bio in Biosensor Design with a Simulation App
  • Using Apps to Optimize Induction Heating for Food Processing
  • Optimizing the Hydration Operation in the Thermal Processing of Dates

From Descriptive to Hypothesis-Driven Research

Theory and simulations, assisted by clever experimental techniques, have allowed for an increased detailed mechanistic understanding of biological systems, at the molecular level. This understanding has resulted in a myriad of methods for detection of biomolecules that play significant roles in drug discovery and targeting, microbial and virus detection, gene therapy, and other processes in biotechnology. The applications are countless in fields such as health care, agri-food, and environmental technology.

Biosensors are key components of the analytical techniques for detection and measurement of biomolecules. The Biosensor Design demo app, included in the latest version of COMSOL Multiphysics, predicts the results from measurements of a biomolecule’s concentration (or activity) from an understanding of this molecule’s attachment to an enzyme. The simulation app can be used as an example of how to optimize the design of the detector in order to achieve a well-defined signal.

Enzymes as Detectors

The figure below shows one possible arrangement of detector micropillars in a biosensor subjected to an analyte flow from left to right. The gold-colored concave parts of the pillars are coated with an enzyme that can only attach to a specific group of biomolecules.

Micro flow cell with pillars coated with enzymes, designed to detect a specific biomolecule.

The biomolecules are adsorbed to the enzyme-coated pillars, where they can be measured by, for example, fluorescent detection. Enzymes serve as excellent receptors, since they can only attach to one biomolecule or to a very specific group of biomolecules. A second reaction quenches the adsorbed biomolecule, decreasing fluorescence and so weakening the signal from the detector.

The measured biomolecules are contained in a solution that flows over the detector surface (1). The biomolecules attach to the enzyme-coated surface, causing excitation and fluorescence (2). A quenching molecule is also contained in the solution (3) and this can react with the biomolecule attached to the enzyme (4). The quenched molecules no longer emit light and can therefore not be detected.

Introducing the Biosensor Design App

We recently introduced a new Biosensor Design demo app, where the user can change the following parameters:

• The diameter of the pillars
• The number of pillars in the pillar array
• The flow velocity
• The simulated concentration of biomolecules
• The simulation time

Here is what the user interface (UI) looks like, with annotations for where the input is entered and the results are visualized:

The app’s UI is very easy to use. A few relevant input fields and command buttons are available together with the most important output.

There is minimal hassle when defining the simulation and you do not have to be an expert in simulations to benefit from accurate multiphysics modeling, by gaining understanding, and optimizing your biosensor system.

The embedded model defines and solves the fluid flow equations and the equations for transport and reaction of biomolecules, including the kinetics for the surface reactions.

Simulation of Injection and Detection of Biomolecules

The animation below shows the time-dependent concentration field of the measured biomolecules as a 3D surface (where the height and color of the surface indicates concentration), after injection of the analyte.

Animation showing the concentration field of a biomolecule in the analyte sweeping over the pillars like a wave. The color legend and height of the wave represent concentration in mol/m³.

The sweeping wave of biomolecules caused by the injection of analyte is also seen on the concentration at the surface of the pillars, as you can see in the app screenshot below. The blue solid line shows the concentration in the first row of pillars and in the middle of the channel. The blue dash-dotted line shows the detected concentration at the surface of the pillars in the back row in the middle of the channel. The red solid curve represents the concentration of the biomolecule at the surface of the pillars positioned in the first row close to the wall of the cell. The red dash-dotted line shows the concentration measured by the pillars in the back row but close to the wall of the cell. The pillars close to the walls and at the back of the cell both contribute to a broadening of the signal from the biosensor. In this case, it may be a good idea to decrease the number of pillars at the cost of a weaker but more well-defined signal.

Concentration of the measured biomolecule at the surface of the enzyme-coated pillars at different positions in the cell.

The app demonstrated here is one example of countless possible biosensor design configurations. This specific configuration may not be optimal for your purposes, but the app can be broadly used by you to build similar apps with clear and simple interfaces that inspire users to simulate and improve the design of biosensors.

Get Started Building Your Own Biosensor App

• Download the demo app: Biosensor Design
• Read more about the behind-the-scenes of app building in this blog post featuring another demo app

The Relationship Between the Product and the Process

When looking at the future direction of the pharmaceutical industry, biopharmaceuticals are noted as a sector of rapid growth and interest. These products — which include vaccines, allergenics, and gene therapies — are developed with biotechnology, which uses biological processes to design or manufacture drugs or other useful products. In the development of these drugs, the end goal is to provide patients with a product of the highest possible quality.

With modeling, designers can advance the design of biopharmaceutical products and analyze how they work in vivo (i.e., investigate the product’s intended function). Researchers can study how different biomolecules, which are also manipulated by viruses and bacteria, affect a living mechanism. In our Model Gallery, you will find several examples of simulating the function of biopharmaceutical products.

Modeling can also be a valuable resource for enhancing the design of production processes for biopharmaceutical products. This is often considered the second step. After designing a biomolecule, the question then becomes how to manufacture these products on a larger scale through optimized production processes. While often different from the previous type of modeling, both of these analyses may occur in a living system (e.g., production with the use of living cells in a process). Our Model Gallery features many examples of simulating these production processes, some of which we will discuss below.

As a whole, simulation is a powerful tool for improving the design of biopharmaceuticals and the processes behind their production. In addition to faster results, this method of testing fosters innovation and offers a simplified way of improving product designs and the mechanisms used in their development.

Modeling Biopharmaceutical Processes with COMSOL Multiphysics

The COMSOL Multiphysics simulation software is a valuable tool for advancing the design and performance of biopharmaceuticals. In a recent webinar, my colleague Ahsan Munir highlighted several examples from our Model Gallery that demonstrate the use of simulation in analyzing various stages of biopharmaceutical processes.

The production stage of biopharmaceuticals often involves the use of mixers and reactors. Using COMSOL Multiphysics, you can investigate the reaction mechanisms and kinetics within these designs as well as the influence of process parameters. For instance, the Laminar Flow in a Baffled Stirred Mixer model investigates the flow within the mixer, with the opportunity to add mass transport and heat transfer in order to study the flow’s impact on the concentration and temperature fields. In the Porous Reactor with Injection Needle model, you can visualize the flow and reactions within the catalytic porous bed in a reactor, addressing the flow of fluid in porous and free regions.

Chemical reactor model with flow streamlines and concentration isosurfaces for one of the reactants and the product species. Two species enter the reactor from different inlets and then undergo a reaction in a catalytic porous bed placed downstream from an injection needle in the reactor.

Next, we can turn to the clarification stage, which hones in on the separation of particles. Dielectrophoresis, a common method for transporting and separating different kinds of particles, is used extensively in the medical field, as biological cells possess dielectric characteristics. The Dielectrophoretic Particle Separation model shows the separation of platelets from red blood cells. This example indicates the particle trajectories both with and without the applied dielectrophoresis force as well as the electric field within the microchannel. You may also want to read my colleague Bjorn Sjodin’s blog post featuring a dielectrophoretic separation app.

This brings us to the purification stage. High-performance liquid chromatography is a technique that separates closely related chemical species within a mixture and then identifies and quantifies them. Valued for its well-controlled nature and versatility, this separation technology is often used in the development of pharmaceutical and biological products. With the Liquid Chromatography model, you can investigate the concentrations of the components in the mobile phase as well as how external heating affects the material behavior.

Last is the finishing phase. When looking to dry heat-sensitive substances like blood plasma and antibiotics, freeze-drying is a viable option. Along with helping to preserve products for a longer period of time, this technique also makes it easier to transport the products by removing water from them, thus making them lighter. COMSOL Multiphysics features A Transient Analysis of Freeze-Drying model that demonstrates a common test case for many set-ups of this technique: Ice sublimation within a vial in vacuum-chamber conditions. Using this example, you can explore how the temperature and heat changes from the beginning to the end of the drying process.

A model depicting the temperature and heat flux at the end of the drying period.

Concluding Thoughts and Next Steps

This blog post and our recent webinar provide just a brief introduction to the many benefits of modeling biopharmaceutical processes. We encourage you to further explore our Model Gallery to find additional models that can be applied to the analysis and optimization of biopharmaceutical processes. Please contact us if you would like to learn more.

• Watch the archived webinar

About the HPLC Method

High-performance liquid chromatography (HPLC) is a multistep process designed to separate the chemical components in a mixture. There are many other liquid chromatography methods out there, but HPLC is the most versatile due to its ability to be well controlled and provide relatively high through-puts. The system is much like column chromatography, pushing solvents through at a high pressure, instead of gravity like traditional methods. The high pressure allows for a much faster run-time.

In essence, HPLC involves mixing a solvent (mobile phase) from a reservoir (#1 in the image below) with a sample zone containing the analytes that are to be separated (#4) and then pumping (#5) the mixture into an injector (#7). The injection is an automated step of the process. Then, the mobile phase carries the analyte through a column that contains a solid stationary phase (#9). If the analyte is not colored, a detector (#10) is needed in order to know when it has passed through the column. The detection data is stored for analysis (#11) and the waste is collected (#12).

An HPLC apparatus. Image credit: Yassine Mrabet.

Here’s another, simpler version of the diagram above:

A simplified schematic of an HPLC system.

Applications of Liquid Chromatography

Liquid chromatography is used in many settings. It is commonly used in research and development (R&D), quality control, and manufacturing at biotech and pharmaceutical companies, for instance. Additionally, the separation technique may be used for monitoring water, food, and environmental effects. Liquid chromatography is also used in medical or forensic scenarios directly involving patients or clients.

High-Performance Liquid Chromatography Modeling Example

If you want to analyze the separation of two species, you could set up a lab experiment according to the numbered diagram above. Alternatively, you could set up a simulation using COMSOL Multiphysics and the Chemical Reaction Engineering Module.

Suppose there are two components in the mobile phase and we want to determine their concentration levels after flowing through the column. Before modeling the increased concentrations, we need to solve for low initial injector concentrations. That way we can compare the different results. Then, we increase the concentration of analyte carried by the mobile phase, so that the chromatography is nonlinear. We’ll skip the detailed steps here, but you can follow them by reading the model documentation.

Linear Chromatography Results

The initial analyte concentration is low (both components are of 0.1 mol/m³). This means that the solution will be in the linear domain. Plotting our results, we can see that the sample zones are normally distributed and symmetrical:

Initial injector concentrations of 0.1 mol/m³ for both components.

Nonlinear Chromatography Results

Now, what happens when we increase the two components’ concentrations to one and ten mol/m³, respectively? Well, we can see that the behavior changes dramatically, as the solution is now in the nonlinear domain:

Nonlinear chromotography: Concentrations of the two components (1 is shown as solid and 2 is dashed) in the mobile phase while flowing through the column at 0, 80, and 160 seconds. The initial injector concentrations for c₀₁ = 1 mol/m³ and c₀₂ = 10 mol/m³.

Model Download

• Liquid Chromatography model