Technical
May / June 2019

Inline Dilution: An Agile Capability for Downstream Manufacturing

Lindsey E. Daniel, PE
Avril J. Vermunt
Article

As the global population demands faster and more affordable drugs, biopharmaceutical companies are continually trying to find ways to produce their drug products more economically and efficiently. Today, the competition and need for drugs are greater than ever before. Companies have been considering operational alternatives to reduce production costs and increase manufacturing rates.1 2   Inline dilution provides an agile solution by reducing long-term costs and increasing process flexibility.


  • 1Kelley, Brian. “Very Large Scale Monoclonal Antibody Purification: The Case for Conventional Unit Operations.” Biotechnology Progress 23, no. 5 (September–October 2007): 995–1008. https://doi.org/10.1021/bp070117s
  • 2Noble, John. “The Capacity Challenge—Shifting Paradigms in Biopharmaceutical Facility Development: Point of View.” Pharmaceutical Engineering 37, no. 6 (November 2017): 50–1.

Automated inline dilution has been a growing solution for downstream bioprocessing since the 1980s. Because upstream productivity increases titers, downstream processes have been targeted as potential bottlenecks that require more efficient and flexible solutions.3   To address the increased need for a responsive capability in downstream processing, manufacturing facilities are implementing inline dilution for optimum throughput in their facilities.4

Inline dilution is an added capability to chromatography systems that brings multiple process streams together to dilute or blend a solution at the point of use. Buffer and process solutions are mixed with water to meet the targeted final buffer composition. There are several advantages to inline dilution, but like any process, there are also challenges. Inline dilution systems can increase process efficiency and flexibility, but they require a design that reflects the individual process and the company’s manufacturing philosophies. Every process has unique buffer profiles and chemistry requirements. Therefore, the key to successful processing using inline dilution is choosing a design option that best fits the specific process needs. Exploring different design options and understanding the pros and cons of each are critical aspects of inline dilution. This article offers an overview of inline dilution basics, the benefits and challenges of implementing an inline dilution system, and the types of designs implemented in today’s manufacturing environments.

Buffers or Process Solutions?

Chromatography is a powerful separation tool that takes advantage of different molecular attributes to separate target molecules and impurities. To optimize these techniques, conditions that promote specific chemical interactions must be controlled. These conditions include pH, conductivity, and other attributes.5   For this reason, chromatography conditions are thoroughly screened and selected during development work.6   Buffers are solutions containing a conjugate acid and base designed to maintain a specific pH during component additions, such as a small addition of a strong titrant.7   Throughout the industry, chromatography process solutions are inappropriately called “buffers” even though they have no buffering capacity. For example, the sodium chloride (NaCl) solution from Figure 1 does not have capacity to resist the pH change because of a titrant addition. Nevertheless, all chromatography process solution compositions, buffers or not, are important to the unit’s operation performance and product quality.8   Therefore, dilution of process solutions and buffers is essential to secure the expected chromatography results.

Major Benefits of Inline Dilution

Inline dilution allows for more efficient and flexible design by blending or diluting multiple buffers to required concentrations at the point of use, resulting in smaller buffer batch sizes and thus a smaller facility footprint. Furthermore, if the hold times can be validated, concentrated buffers can also be used for multiple batches, which then results in reduced utility and equipment costs. Although long-term inline dilution usually results in cost savings, the up-front capital costs can be greater.

Figure 1: Inline dilution concept for a chromatography example
Figure 1: Inline dilution concept for a chromatography example

One of the greatest drivers for inline dilution is long-term cost savings. Implementing inline dilution usually results in a smaller facility footprint; materials usage optimization; waste reduction; and validation, labor, and utility savings.9   The design utilizes buffer concentrates that supply the same amount of buffer as use-strength solutions with a fraction of the volume. If a company requires a 1000 liter (L) 1 molar(M) NaCl solution, it can implement a 250 L 4 M NaCl concentrate solution and dilute it at the point of use, as shown in Figure 1. That not only reduces the tank size but also allows companies to use disposable systems, which further cuts the costs of utilities and cleaning validation.10   Even if disposables are not implemented, this process still results in utility savings because cleaning a 250 L tank requires less water, steam, and cleaning solutions than cleaning a 1000 L tank. Reduction of classified space for buffer preparation and storage operations saves in up-front capital as well as maintenance costs over time. Facilities that have space limitations will also benet from the smaller footprint of concentrate vessels.

Reduced buffer volumes require fewer raw materials and consumables—such as preparation filters and samples—per manufacturing lot, and the savings accumulate over a manufacturing campaign. By cutting buffer preparation volumes, the filter area is also decreased because buffer filters are typically sized volumetrically for aqueous solutions. For volumes that span multiple preparations, using a concentrate that reduces the volume to a single preparation eliminates an equal number of samples. In cases where concentrates can be used for multiple operations or production lots, release testing is also reduced. Although it is easy to overlook these simple reductions, they collectively add up to long-term savings.

If buffer concentrates are used for multiple batches, companies also benefit from labor and utility savings because they do not need to make batches as often and systems require fewer cleaning cycles. For higher titer processes, cell culture media preparations may require a similar number and similar volumes of buffer preparations as lower titer processes. However, the trade-off for more productivity is an increased need for chromatographic cycles, and therefore more buffer volume and preparations.11   In some cases, this burden requires that existing facilities make multiple buffer batches for multiple cycles in one product lot. If concentrates are used for multiple lots and require fewer preparations, a company can redirect the resources and labor that would have been required for preparation—that is, the setup and teardown time of buffer equipment, the sampling and testing of buffers, etc.—to more critical unit operations. That could represent a significant potential reallocation. Furthermore, utilities are also reduced when employing a multiple-lot buffer concentrate strategy because clean-in-place and sterilize-in-place processing of vessels is not required between process runs. Fewer cleaning cycles also can lead to a faster and more flexible manufacturing schedule.

The flexibility of inline dilution is another factor that appeals to many companies. Different concentrations of the same solution may be required throughout the process. This is especially common for companies that use a process platform to develop, scaleup, and deploy for multiproduct facilities.12 With the implementation of inline dilution, companies that use a process platform create maximum flexibility for future products by validating and proving the makeup of multiple buffer concentrates. Buffer concentrates allow for one concentration to be made and then diluted to various use-strength concentrations. The concepts that allow for appropriate inline dilution are also applicable in a chromatography gradient elution where the dilution rate will change over time to achieve the product elution.

Challenges

Inline dilution provides benefits but also presents challenges. One of the greatest challenges to inline dilution is maintaining and confirming the quality of the buffers. Inline blending/mixing, flow control, and inline feedback and monitoring must be robust for inline dilution to be successful. Demonstrating and maintaining good mixing, whether in a vessel or inline, is a challenge in itself. However, mixing a solution in a vessel over a period of time with an agitator is often better understood than mixing inline, as fluid flows through in one pass. A robust design for inline mixing and confirmation of mixing is a major component to be considered in the design. A chromatography system can be validated for mixing by inline feedback control or through commissioning and validation data. Although good mixing and maintaining a controlled solution composition are important, many companies have found that slight variations in the concentration have no impact on the product.13   To ensure inline dilution is feasible for the process, the allowed variation must first be determined in process development. Inline dilution usually requires pump turndown with lower flow rates because multiple streams are utilized. Depending on the type of pump implemented, greater turndowns can be harder to control and maintain across the full flow rate range.

Figure 2: Inline dilution design examples
Figure 2: Inline dilution design examples

The other major challenge with inline dilution is the up-front costs. Although the long-term costs of inline dilution will likely result in cost savings for some companies, companies, especially startups, may not have the up-front cash to implement such a solution. An existing facility requires greater modifications if inline dilution is implemented. The design usually requires at least two pumps, or at least three pumps if performing dilution and gradients, and will likely involve more inline instrumentation for control and monitoring. The startup time required for inline dilution is generally greater because inline dilution requires additional system characterization, including flow ratio capability, instrumentation accuracy, and system mixing.

Because the buffer chemistry is critical to unit operations, successful chromatography and product quality also depend on a firm understanding of the chemistry of buffer concentrates.14   The concentrate recipe must account for common ion effects to ensure that the use-strength composition has the correct pH and conductivity for the process.15

Although inline dilution may increase the number of process batches that can be made with one preparation of concentrate process solutions, multiple-lot buffers introduce additional challenges related to stability and the risk of contamination. Before multiple-lot buffer systems are implemented, extended hold-time validation and growth-promoting studies are required. Traditional quality programs may need to adapt to the testing and release of concentrates and may have to consider new approaches for the release of real-time use-strength solutions.

Inline dilution provides an agile solution by reducing long-term costs and increasing process flexibility.

A final challenge involves material compatibility evaluation of the preparation and hold vessels or facility and system piping. Materials of construction for tanks, piping, and associated components such as instruments, valving, and seals must be selected to withstand the conditions posed by concentrates, including pH levels and temperatures. Process concentrates should be assessed for extractables and leachables in single-use vessels and evaluated for corrosivity in stainless steel vessels.16 17

Fundamental Design Considerations

When designing an inline dilution system, stakeholders need to ask questions up front to determine the design best suited for their process. Here are a few examples of points to consider prior to implementing inline dilution:

  • How many buffers does the process require?
  • How many different concentrations of a single buffer are there?
  • Are there varying flow rates? What are the flow rate ranges?
  • How critical is the buffer composition to the process? Is gradient or step elution used?
  • How accurate are the monitoring and control instruments?
  • Are the use-strength buffer and concentrate recipes well understood? Will concentrates pose solubility or viscosity issues? Are there shifts in pH after dilution? Is the dilution exothermic?
  • Do any buffers or concentrates require specialty construction materials? Are there corrosive buffers that need additional safety assessments, such as double-contained piping? Do any require a higher alloy metal for vessels, piping, and components?

These questions will drive the design as well as the monitoring and control strategy.

Engineering Design

Design options for inline dilution systems include a variety of system components, control options, and inlet supply flow paths. Some systems use multiple pumps to blend concentrated buffer with water, whereas others use blending tanks and inlet control valves, as shown in Figure 2.

When designing a system with inline dilution, five key design components need to be explored:

  • Mixing, including piping and optional static mixer and/or break tank
  • Pumps, including types, accuracy, and turndown
  • Flow measurement for monitoring and/or control
  • pH and/or conductivity for measurement and/or control
  • Control valves

Example 1 in Figure 2 shows a break tank that provides hydrostatic decoupling of the upstream inlet supplies and combined process stream through the chromatography system. This type of break tank uses an agitator and sometimes baffles, which help with mixing solutions but result in a costlier design. The residence time in the tank helps balance the dilution but can increase buffer losses.18   A 100 liters-per-minute (LPM) system that has a 5- to 10-second residence time will result in an approximately 30 L break tank. If it is assumed that piping volume is approximately 20 L, a 5 system-volume flush would result in 250 L of buffer use rather than 100L of buffer use without the break tank. Over multiple uses, that additional 150 L of buffer can be costly. This is another example of why a company needs to discuss the points to consider at the beginning of their design and business strategy implementation.

Table 1: Pros and cons of pumps used for inline dilution
Type
of Pump
Pros Cons
Diaphragm • Easy maintenance
• Prevents backflow
• Can be self-priming
• Low shear
• Pulsing/lack of precise flow control
• Flow control can be improved by multiple pump heads, but that adds cost
Peristaltic • Disposable/easy to clean
• Feed rate is less affected by varying pressures
• Pulsing/lack of precise flow control
• Can trap air
• Pressure limitations (back pressure from column)
Rotary lobe • Flow control is more precise and efficient
• Low shear
• Hard to clean/maintain
• Less efficient when operated at high pressure
• Prone to slip

Achieving a homogenous solution is a critical performance requirement for inline dilution and can be further challenging based on the miscibility of process solutions, especially at higher concentrations. Processes that have greater viscosity may benefit from a break tank that can use baffles or an agitator, but an inline mixer is sufficient for most systems.

Simple things that can have a long-term impact, such as pipe hold-up volume, are frequently overlooked.19   Designing a system that assesses dead legs is critical. Several options for valves minimize dead legs, but best practices include minimizing system hold-up volumes and reducing dead-leg distances. An example of a design component able to achieve this is block body valves. The design, performance, and cost should be balanced to achieve the appropriate system for the intended use. Systems that use pumps require robust flow accuracy, and the type of pump selected is therefore key to the system design.20   Positive displacement pumps are generally preferred for chromatography systems because they pose low shear risk to the product. The main types of pumps used for large-scale chromatography are diaphragm, peristaltic, and rotary lobe.21   The pros and cons of various pump types are highlighted in Table 1.

When utilizing pumps for flow control, the varying inlet pressures from the upstream fluid pose a challenge. Example 2 in Figure 2 shows that a back pressure regulator can be installed to prevent slippage through pumps and to help control flow. Rotary lobe pumps provide great flow control; however, if there is a high-pressure differential across the pump, there is likely to be some slip. Peristaltic pumps are a great option because they require no cleaning, but the tubing usually has a low-pressure rating. Diaphragm pumps are easy to maintain, but they offer less efficient flow control due to pulsing. Flow control can be improved by using multiple pumps, but this strategy adds cost. As more applications look to disposable flow paths, understanding pump technology and performance becomes more time-sensitive because the technology is rapidly changing in this area.

Table 2: Control modes used for inline dilution
Type of Control Mode Pros Cons
Open-loop ratio control • Simplest design
• Simple speed set point automation
• No reaction to actual conditions
• Actual flow dependent on back pressure
Total-flow feedback with ratio control • Ensures total flow-rate range is achieved • Actual flow dependent on back pressure observed by each pump
Flow feedback control • Ensures flow parameters for each channel as well as total flow are achieved • Requires more instrumentation and control components
• May require fine-tuning depending on turndown
Conductivity feedback with ratio or flow control • Achieves process stream condition specifically required by unit operation • Temperature compensation needs to be considered
pH feedback with ratio or flow control • Achieves process stream condition specifically required by unit operation • Requires precise pH instrumentation
• May require special handling as pH probes may be susceptible to process solutions (especially at extreme pH)
• Concentrates must account for dilution and salt effects on pH
• Standardization practices and managing drift should be considered

Buffer concentrates require lower inlet flow rates because there are multiple streams. For example, a 4x buffer of NaCl that has an outlet flow rate of 100 LPM will use an inlet flow rate of 25 LPM of 4x NaCl and 75 LPM of purified water. This lower flow rate of 25 LPM could be affected by ow-through of the higher flow pump, making it harder to achieve precise flow control and, therefore, dilution ratios. A back pressure regulator can be used downstream of the pump to prevent flow through the pumps, but it does not always resolve the lack of flow accuracy. A flow meter is usually placed downstream of the pumps to monitor the flow and can tie into the pumps or control valves to provide closed-loop feedback control. Flow-meter accuracy should ensure that typical flow rate operating ranges are ±5%–10%, but acceptable operating ranges may be tightened depending on process needs. The three key operating parameters to control and/or monitor for inline dilution are flow, pH, and conductivity. Flow control may be sufficient to create a process stream with the desired pH and conductivity and can be controlled through pumps or control valves, as shown in Figure 2. Confirming good mixing and proper flow control can be achieved by monitoring pH and conductivity. When instrumentation is selected, the design should consider the chromatography solutions’ attributes. For instance, pH may need to be within ±0.2 units and conductivity may need to be within ±10% of the process target for most applications. For cases where parameters for pH and conductivity need to be more precise, measurement tolerances of ±0.05 pH units and ±2% conductivity target may be implemented.

Finally, more advanced designs address the use of more than two or three inlet supply streams being blended and controlled to deliver use-strength solutions to chromatography unit operations. These systems incorporate multiple pumps of various sizes, which add cost but meet performance and quality expectations and provide flexibility to address a large range of buffer recipes.22

Automation, Monitoring, and Controls

One of the biggest challenges with utilizing multiple pumps is balancing the flow to minimize overshoot and provide a continuous flow of concentrate and water within a specified range. If the flow rate varies, a slower-acting proportional–integral–derivative control loop may be required so that the system keeps the process solutions in a steadier range rather than oscillating significantly. An acceptable oscillation must be within the operating range of key operating parameters, such as ±0.2 pH units or ±10% for conductivity. The controller response time should be balanced with the overall ramp to ensure concentrate and water are not wasted. A typical ramp should be less than a few minutes, but the duration depends on the low-rate set point relative to the overall range.

The control of inline dilution generally comes with two options: inline feedback control and ratio control. Both options involve monitoring of pH, conductivity, or flow to confirm the buffers are in range. The pros and cons of these options are highlighted in Table 2.

The type of control is generally based on how much risk is acceptable. Control modes for inline dilution should consider the distance of the normal operating range from the critical design range, and they may include pH and conductivity monitoring as an additional engineering control to verify that process stream composition is as expected.

Open-loop ratio control does not include any feedback control and is based on commissioned or standardized ratios. If a 4x concentrate were used, the pumps would run at a flow ratio of 3:1 to achieve the required use-strength buffer concentration. Open-loop ratio control is a cheaper option, especially when a system is running at high flow rates relative to design range, which are easier to control. The main concern with ratio control is that if the buffer pH or conductivity goes out of specification, the ratio will not automatically adjust. The system may be programmed to activate an alarm, and manual intervention may be required. Being out of specification could pose a risk to the product if the deviation substantially affects the quality or yield. However, some processes may accept varying buffer concentrations without product impact.23   For example, for many chromatography cleaning steps, the cleaning solution has a design range that is much wider than the operating range, allowing for more variability to be accepted by the process. The acceptable degree of variability should be considered for each process step.

Total-flow feedback with ratio control has enhanced automation and therefore generates a lower risk of the buffer concentrate being out of specification, as long as concentrates are well characterized and have accounted for any pH shifts upon dilution.24   Total-flow feedback with ratio control is likely the best option for risk-adverse companies and in situations when processes require tight process stream composition. It is impossible to completely guarantee that a process will never go out of range; however, with inline controls and proper tuning, the system can adjust accordingly and have good control over the process. Alarms can be used to alert operators when the process deviates from its specific range. This design is generally more expensive and requires automation and control tuning, which results in greater startup and commissioning investment. Not all systems require feedback control. When considering whether to use it, companies should evaluate the amount of risk they are willing to take, how confident they are in commissioning the system, and their requirements for concentration.

Regardless of the control strategy adopted, automated inline dilution provides benefits such as:25

  • Eliminating risk of release sample contamination or failure
  • Generating trends to support validation and continuous improvement
  • Supporting ongoing buffer preparation and downstream process monitoring
  • Enabling online, real-time release

Testing and Performance

When implementing inline dilution, several areas should be addressed before engineering and operational decisions are finalized. Objectives for the system that will meet expected performance should be based on process definitions. Once the objectives are clear to decision makers and stakeholders, further details can be evaluated for proper selection. The criteria for performance should drive design and be revisited periodically through the design and execution milestones.

Once a system has been engineered and assembled, it should be tested to ensure the performance meets expected requirements. 25   Commissioning and qualification tests should be developed in accordance with the system requirements and risk assessment. These tests could include simple checks of the system components such as pump curves and flow control that cover the full range of the respective operating parameters. If needed, a more complex set of tests could include blending and dilution of concentrates with analysis of the subsequent resulting output response—for instance, conductivity, pH, or ultraviolet absorbance. Output trends can be analyzed using linear least squares and normalized to provide a percent error. Finally, when specific operational conditions are considered to be high risk, a process qualification can include tests for those conditions. For example, it may be prudent to run tests to verify that the system accounts for pKa changes from concentrates or heat of dissolution when diluted.23   Another test might evaluate whether the system demonstrates the critical control needed to create a gradient for a chromatographic elution.

These tests may not be relevant for every system, especially when mathematical models inform design, or when duplicating systems already utilized in a facility.26   A family approach to commissioning and qualification may be taken for functional performance, or a design qualification may be all that is necessary once system designs have been previously implemented and fully characterized. To understand what to test and the performance needed, it is helpful to conduct a risk assessment that includes experience with the design and the criticality of buffer composition to the process. This assessment can also help feed into defense-in-depth activities that inform deviation investigations undertaken during manufacturing.

Conclusion

The bioprocessing industry is becoming more agile with increased design and technology solutions. As manufacturers find ways to increase titers, the bottleneck is shifting to downstream operations such as buffer preparation and chromatography. As long as biopharmaceutical processes continue to intensify, scale-up, and scale-out, inline dilution will be a useful tool for avoiding bottlenecks in solution preparation and decreasing buffer hold capacity. Although there are many questions to address when implementing inline dilution, careful consideration of system design, components, instrumentation, and control strategies can ensure successful integration. The use of inline dilution in chromatography unit operations optimizes manufacturing throughput by providing an agile capability in downstream manufacturing.

Additional Resources

Baek, Youngbin, Deyu Yang, Nripen Singh, Abhiram Arunkumar, Sanchayita Ghose, Zheng Jian Li, and Andrew L. Zydney. “pH Variations During Diafiltration due to Bu er Nonidealities.” Biotechnology Progress 33, no. 6 (November 2017): 1555–60. https://doi.org/10.1002/btpr.2544

Min, Byeong Jo, Seong Woo Kang, Yoon Seok Song, Jong Ho Lee, Seung Heon Lee, Chulhwan Park, Seung Wook Kim, and Chan-Wha Kim. “Verification of the Final Anion Exchange Chromatography in the r-hGH Manufacturing Process.” Biotechnology and Bioprocess Engineering 15, no. 3 (June 2010): 488–96. https://doi.org/10.1007/s12257-009-3053-9

Thömmes, Jörg, and Mark Etzel. “Alternatives to Chromatographic Separations.” Biotechnology Progress 23, no. 1 (2007): 42–45. https://doi.org/10.1021/bp0603661

Van Beijeren, Peter, Peter Kreis, and Tim Zeiner. “Ion Exchange Membrane Adsorption of Bovine Serum Albumin: Impact of Operating and Bu er Conditions on Breakthrough Curves.” Journal of Membrane Science 415–416 (October 2012): 568–76. https://doi.org/10.1016/j.memsci.2012.05.051

  • 14Tindall, G. William. “Mobile-Phase Buffers, Part III—Preparation of Buffers.” LCGC North America, January 2003, 28–32.
  • 15Challener, Cynthia A. “Improving Process-Scale Chromatography.” BioPharm International 29, no. 11 (November 2016): 14–7. http://www.biopharminternational.com/improving-process-scale-chromatography
  • 16Ding, Weibing, Gary Madsen, Ekta Mahajan, Seamus O’Connor, and Ken Wong. “Standardized Extractables Testing Protocol for Single-Use Systems in Biomanufacturing.” Pharmaceutical Engineering 34, no. 6 (November–December 2014): 74–85.
  • 17Lopolito, Paul, Dijana Hadziselimovic, Amanda Deal, and Amy Thanavaro. “Cleaning Buffer Preparation Tank Air–Liquid Interface Rings.” Pharmaceutical Engineering 36, no. 1 (January–February 2016): 66–72.
  • 18Faanes, Audun, and Sigurd Skogestad. “Buffer Tank Design for Acceptable Control Performance.” Industrial & Engineering Chemistry Research 42, no. 10 (May 2003): 2198–208. https://doi.org/10.1021/ie020525v
  • 19Dolan, John W. “Reducing Column Diameter in Gradient Elution—A Case Study.” LCGC North America, December 2000, 1228–32.
  • 20Majors, Ronald E., Howard G. Barth, and Charles H. Lochmueller. “Column Liquid Chromatography.” Analytical Chemistry 54, no. 5 (1982): 323–63. https://doi.org/10.1021/ac00242a028
  • 21Markarian, Jennifer. “Pumping Fluids in Biopharmaceutical Processing.” Biopharm International 30, no. 2 (February 2017): 26–9. http://www.biopharminternational.com/pumping-fl uids-biopharmaceutical-processing-2
  • 22Fabbrini, Davide, Carlo Simonini, Joakim Lundkvist, Enrique Carredano, and Debora Otero. “Addressing the Challenge of Complex Buffer Management: An In-Line Conditioning Collaboration.” BioProcess International. December 13, 2017. https://bioprocessintl.com/downstream-processing/separation-purification/addressing-the-challenge-of-complex-buffer-management-an-in-line-conditioningcollaboration
  • 23 a b
  • 24Carredano, Enrique N., Roger Nordberg, Susanne Westin, Karolina Busson, Tomas M. Karlsson, Torbjörn S. Blank, Henrik Sandegren, and Günter Jagschies. “Simplification of Buffer Formulation and Improvement of Buffer Control with In-Line Conditioning (IC).” In Biopharmaceutical Processing: Development Design and Implementation of Manufacturing Processes, edited by Günter Jagschies, Eva Lindskog, Karol Lacki, and Parrish M. Galliher, 513–525. Amsterdam: Elsevier, 2018. https://doi.org/10.1016/B978-0-08-100623-8.00027-X
  • 25 a b Castillo, Francisco C., Brendan Cooney, and Howard L. Levine. “Biopharmaceutical Manufacturing Process Validation and Quality Risk Management.” Pharmaceutical Engineering 36 no. 2 (May–June 2016): 82–92.
  • 26Kaltenbrunner, Oliver, and Jungbauer Alois. “Simple Model for Blending Aqueous Salt Buffers—Application to Preparative Chromatography.” Journal of Chromatography A 769, no. 1 (May 1997): 37–48. https://doi.org/10.1016/S0021-9673(97)00161-1

Acknowledgments

The authors would like to thank Madhu Raghunathan, Enrique Carredano, Chris Krein, and the Pharmaceutical Engineering Editorial Review Board for their thoughtful review of this article. A special thanks to Josh Van Kirk for his review and support, and for introducing the authors to each other.