Hydrocyclone Separator: Composition, Performance, and How It Is Used Across Industries

Types of Hydrocyclone Separators

A hydrocyclone separator is a highly efficient device used in industrial processes for liquid-solid or liquid-liquid separation. By harnessing centrifugal force, hydrocyclones classify particles based on size, density, and shape without the need for moving parts. The feed slurry is injected tangentially into a conical chamber, creating a vortex that forces heavier particles to the outer wall, where they exit through the underflow, while lighter or finer materials exit through the overflow at the top.

Key operational variables such as feed pressure, flow rate, slurry density, and particle size distribution significantly influence separation efficiency. Structurally, a hydrocyclone consists of three main components: the inlet (feed entry), overflow outlet (top discharge), and underflow outlet (bottom discharge). Design variations are tailored to specific industrial applications, from mining and wastewater treatment to food processing and oil refining.

General Hydrocyclone

Designed for basic particle classification by size and density in slurry mixtures. Commonly used in mineral processing and industrial recycling.

Advantages

• Simple and robust design
• No moving parts, low maintenance
• High separation efficiency for coarse particles
• Adjustable performance via feed pressure

Limitations

• Less effective for very fine particles
• Susceptible to wear in abrasive applications
• Requires consistent feed conditions

Best for: Primary classification in mining, aggregate processing, and general industrial separation

Multiclass Hydrocyclone

Advanced design capable of separating multiple particle size fractions in a single unit, enhancing process efficiency and reducing equipment footprint.

Advantages

• Simultaneous multi-grade separation
• Reduces need for multiple cyclones
• Improves plant throughput and efficiency
• Customizable cut points for specific fractions

Limitations

• More complex design and setup
• Higher initial cost
• Requires precise control of feed parameters

Best for: Mineral beneficiation, sand processing, and multi-product recovery operations

Degerming Hydrocyclone

Specialized for removing lightweight components such as germ, husk, or bran in grain and cereal processing, particularly in corn milling.

Advantages

• Effective separation of low-density impurities
• Improves purity and quality of final product
• Non-thermal, preserving nutritional content
• High throughput capacity

Limitations

• Limited to specific agricultural applications
• Requires clean feed to prevent clogging
• May need pre-screening of feed material

Best for: Corn wet milling, cereal processing, and starch production

Desander Hydrocyclone

Engineered to remove coarse sand, grit, and heavy particulates early in the process to protect downstream equipment and ensure product purity.

Advantages

• High-efficiency removal of abrasive particles
• Larger diameter for high-volume processing
• Prevents wear on pumps and valves
• Essential for protecting sensitive equipment

Limitations

• Not suitable for fine particle separation
• Higher energy requirement due to pressure needs
• Can experience plugging if not maintained

Best for: Oil & gas production, water treatment, mining, and dredging operations

Degreasing Hydrocyclone

Used to separate oily contaminants—such as petroleum, animal fats, or vegetable oils—from water or solid slurries based on density differences.

Advantages

• Efficient oil/water separation
• Compact and cost-effective vs. skimmers
• Continuous operation capability
• Low environmental impact when properly managed

Limitations

• Performance drops with emulsified oils
• Requires stable flow and pressure
• May need coalescing aids for optimal results

Best for: Wastewater treatment, food processing, and oil recovery systems

Refiner Hydrocyclone

Precisely designed for recovering fine, high-value materials such as starch, sugar, or fine minerals with exceptional separation accuracy.

Advantages

• High precision for fine particle recovery
• Maximizes yield of valuable products
• Compact design with high efficiency
• Optimized for low-density valuable materials

Limitations

• Not suitable for coarse separation
• Sensitive to feed fluctuations
• Higher maintenance due to fine tolerances

Best for: Starch extraction, sugar refining, pharmaceuticals, and specialty chemical processing

Type	Primary Function	Particle Size Target	Key Industries	Efficiency Level
General Hydrocyclone	Size classification	Coarse to medium	Mining, aggregates	High
Multiclass Hydrocyclone	Multi-fraction separation	Multiple cuts	Mineral processing	Very High
Degerming Hydrocyclone	Remove low-density organics	Light components	Food processing	High
Desander Hydrocyclone	Remove sand/grit	Coarse (>50µm)	Oil & gas, water treatment	Very High
Degreasing Hydrocyclone	Oil/fat separation	Immiscible liquids	Wastewater, food	High
Refiner Hydrocyclone	Recover fine valuable solids	Fine (<20µm)	Starch, sugar, pharma	Very High

Expert Tip: For optimal performance, ensure hydrocyclones operate within their designed pressure range (typically 15–30 psi). Too low pressure reduces separation efficiency, while excessive pressure increases wear and energy consumption. Regular inspection of wear liners and vortex finders is recommended to maintain consistent performance.

Specifications and Maintenance of Hydrocyclone Separators

Hydrocyclone separators are essential in industrial processes for efficient solid-liquid separation, particularly in mining, wastewater treatment, and petrochemical applications. Understanding their key specifications ensures optimal performance, while consistent maintenance enhances durability and prevents unplanned downtime.

Key Specifications of Hydrocyclone Separators

Each specification plays a critical role in determining the separator’s efficiency, capacity, and suitability for specific materials and operating conditions.

Size (Apex Base Diameter)

The size of a hydrocyclone is defined by its apex base diameter, typically ranging from 10 mm to 1000 mm. Smaller units (10–50 mm) are highly effective for fine particle separation due to higher centrifugal forces, making them ideal for precision applications such as de-sliming or ultrafine classification.

Larger hydrocyclones (300–1000 mm) are designed for high-volume throughput and are commonly used in primary separation stages where large feed volumes must be processed efficiently, such as in mineral processing plants.

Throughput Capacity

Throughput refers to the volume of slurry or feed material processed per hour (measured in m³/h). It is directly influenced by the hydrocyclone’s diameter—larger cones handle higher flow rates. However, actual throughput also depends on several factors including feed density, particle size distribution, inlet pressure, and viscosity.

For consistent performance, it's crucial to match the hydrocyclone size and number of units in a bank to the system’s total flow requirements. Overloading can reduce separation efficiency and increase wear.

Separation Efficiency

Hydrocyclones separate particles based on size, shape, and density using centrifugal force. Denser and finer particles are forced toward the outer wall and exit through the apex (underflow), while lighter and coarser particles move inward and are discharged via the vortex finder (overflow).

Efficiency is typically measured by the d50 cut point—the particle size at which 50% report to underflow and 50% to overflow. Efficiency can exceed 90% when the unit is correctly sized and operated under optimal conditions. Design features like vortex finder depth, apex diameter, and inlet geometry significantly affect performance.

Working Pressure

Optimal operation occurs within a working pressure range of 0.1 to 2.0 MPa. Higher pressures increase centrifugal force, enhancing separation efficiency and enabling the processing of dense or viscous slurries.

However, excessively high pressure can accelerate wear, especially at the inlet and apex, and may cause instability in the air core. Pressure must be regulated using pumps and control valves to maintain consistent performance and protect downstream equipment.

Construction Material

The material of construction directly impacts the hydrocyclone’s resistance to abrasion, corrosion, and chemical degradation. Common materials include:

• Hard Metal (e.g., cast steel): Excellent wear resistance; suitable for abrasive slurries in mining.
• Ceramic (e.g., alumina): Superior abrasion resistance compared to metal; ideal for high-wear environments but more brittle.
• Polyurethane: Flexible, corrosion-resistant, and quieter in operation; widely used in mineral processing and petrochemical industries.
• Rubber: Resists corrosion and moderate abrasion; often used in acidic or caustic environments.

Material selection should balance durability, chemical compatibility, and cost based on the application.

Specification	Typical Range	Performance Impact
Apex Diameter	10 – 1000 mm	Smaller = finer separation; Larger = higher capacity
Throughput	0.5 – 100+ m³/h	Depends on size, pressure, and slurry properties
Working Pressure	0.1 – 2.0 MPa	Higher pressure improves efficiency and cut sharpness
Separation Cut Point (d50)	5 – 300 µm	Depends on design, pressure, and feed characteristics
Common Materials	Metal, Ceramic, Polyurethane, Rubber	Affects lifespan, corrosion resistance, and maintenance needs

Essential Maintenance Practices

Proper maintenance ensures reliable operation, extends service life, and minimizes costly downtime. A structured maintenance routine should include the following key tasks:

Regular Cleaning: Remove accumulated solids, scale, or debris from the inlet, vortex finder, and apex to prevent clogging. Use water flushes or cleaning agents compatible with the cyclone material. Clean more frequently in high-solids or sticky slurry applications.

Fastener Inspection & Tightening: Check bolts, clamps, and flanges regularly, especially those connecting the hydrocyclone to feed pipes and support structures. Vibration and pressure fluctuations can loosen fittings, leading to leaks or misalignment.

Lubrication of Moving Parts: While most hydrocyclones have no moving internal parts, external components such as support brackets or adjustment mechanisms may require periodic lubrication with appropriate grease or oil to prevent seizing and corrosion.

Frequent Visual Inspection: Inspect for signs of wear (especially at the apex and inlet), cracks, leaks, or deformation. Replace worn liners or entire units before failure occurs. Use wear indicators if available.

Important: Always follow the manufacturer’s maintenance schedule and operating guidelines. Using incorrect materials, exceeding pressure limits, or neglecting inspections can lead to premature failure, safety hazards, or reduced separation efficiency. Regular monitoring and proactive maintenance not only extend the life of your hydrocyclone but also ensure consistent process performance and product quality.

Applications of Hydrocyclone Separators

Hydrocyclone separators are highly efficient, compact, and cost-effective devices used across a wide range of industries for separating solid particles from liquids using centrifugal force. Their ability to handle high flow rates with minimal maintenance makes them indispensable in processes requiring rapid and reliable solid-liquid separation.

Mining and Mineral Processing

In the mining industry, hydrocyclones play a critical role in ore processing by classifying and concentrating valuable minerals from raw slurry. The slurry is fed tangentially into the hydrocyclone, where centrifugal forces cause denser mineral particles to move outward and settle at the bottom (underflow), while lighter waste materials and water exit through the overflow.

• Used in grinding circuits to separate coarse and fine particles for recirculation
• Enables efficient dewatering of mineral concentrates before further processing
• Reduces tailings volume and improves recovery rates of target minerals
• Commonly used in gold, copper, iron ore, and coal processing plants

Key benefit: Enhances process efficiency and reduces energy consumption in milling operations

Oil and Gas Industry

Hydrocyclones are essential in crude oil processing for desalting and removing emulsified water. Salt content in crude oil can cause severe corrosion in refining equipment, while water reduces heating value and can lead to operational inefficiencies.

• De-oiling hydrocyclones remove oil droplets from produced water before discharge or reinjection
• Desalting units use cyclonic action to separate brine and impurities from crude oil
• Compact design allows integration into offshore platforms with space constraints
• Improves product quality and protects downstream refining equipment

Technical advantage: Achieves separation efficiencies of over 90% for water-in-oil and oil-in-water emulsions

Food and Beverage Production

In food processing, hydrocyclones ensure product purity and clarity by removing unwanted solids from liquids such as fruit juices, wine, beer, and fermentation broths. This enhances both shelf life and consumer appeal.

• Clarifies fruit juices by removing pulp, seeds, and fine particulates
• Used in starch and sugar processing to separate insoluble impurities
• Improves fermentation efficiency by pre-cleaning mash and broth
• FDA-compliant materials (e.g., stainless steel, food-grade polymers) ensure safety

Quality impact: Delivers consistent product clarity and reduces downstream filtration load

Pulp and Paper Manufacturing

Pulp and paper mills rely on hydrocyclones for cleaning and refining pulp by removing contaminants such as ink, sand, filler particles, and fiber bundles that compromise paper quality.

• Installed in deinking lines to separate ink particles from recycled fiber
• Removes abrasive contaminants that can damage paper machine components
• Improves brightness and smoothness of the final paper product
• Operates continuously with low maintenance requirements

Sustainability benefit: Supports high-efficiency recycling of paper products

Water and Wastewater Treatment

Hydrocyclones are widely used in municipal and industrial wastewater treatment plants to remove sand, silt, and other heavy particulates from effluent streams before biological or chemical treatment.

• Serves as a primary clarification step in sewage treatment
• Protects pumps and pipelines from abrasive wear caused by grit
• Used in stormwater management systems to capture sediment
• Reduces sludge volume and improves overall treatment efficiency

Environmental role: Helps meet regulatory discharge standards for suspended solids

Pharmaceuticals and Specialty Industries

In pharmaceutical manufacturing, hydrocyclones are employed to purify fermentation broths by removing cellular debris and particulate matter prior to crystallization or filtration, ensuring high-purity end products.

• Used in antibiotic and enzyme production for cell separation
• Applied in ceramic and pigment industries for particle size classification
• Supports spice and starch processing by removing impurities
• Utilized in HVAC systems for separating air-borne particulates in liquid refrigerants

Precision advantage: Enables tight control over particle size distribution in high-value products

Industry Insight: Hydrocyclone performance depends on feed pressure, particle size distribution, and slurry density. Proper sizing and material selection (e.g., polyurethane for abrasion resistance, stainless steel for hygiene) are crucial for maximizing efficiency and longevity in each application. Regular monitoring of underflow and overflow streams ensures optimal operation.

Industry	Primary Function	Typical Feed Material	Separation Efficiency
Mining	Mineral classification & concentration	Ore slurry (60–70% solids)	85–95%
Oil & Gas	Crude desalting & water removal	Crude oil with emulsified water	90–98%
Food & Beverage	Liquid clarification	Juices, ferment, starch slurries	80–90%
Pulp & Paper	Contaminant removal	Recycled pulp slurry	85–93%
Wastewater	Grit and sand removal	Raw sewage or industrial effluent	90–95%
Pharmaceuticals	Ferment purification	Biological broths with cells	75–85%

Additional Applications and Benefits

• Ceramics & Pigments: Classifies fine particles to achieve uniform grain size for improved product consistency
• Textile Industry: Recovers cellulose fibers from process water, supporting sustainable manufacturing
• Chemical Processing: Separates catalyst particles from reaction mixtures for reuse
• Compact Design: Requires minimal footprint compared to sedimentation tanks or filters
• Low Maintenance: No moving parts result in reduced downtime and operating costs
• Scalability: Multiple units can be operated in parallel for high-capacity processing

How to Choose a Hydrocyclone Separator: A Comprehensive Guide

Selecting the right hydrocyclone separator is crucial for achieving efficient solid-liquid separation in industrial processes such as mining, wastewater treatment, oil & gas, and chemical processing. A well-chosen hydrocyclone improves process efficiency, reduces operational costs, and ensures compliance with environmental standards. This guide outlines the key factors to consider when selecting a hydrocyclone separator, providing practical insights to help you make an informed decision based on your specific application needs.

Important Note: Improper selection of a hydrocyclone can lead to poor separation efficiency, increased wear, higher energy costs, and frequent maintenance. Always analyze your process requirements thoroughly before finalizing equipment choices.

Key Selection Criteria for Hydrocyclone Separators

1. Feed Characteristics Analysis

   Understanding the physical and chemical properties of the feed slurry is the foundation of proper hydrocyclone selection. Key parameters include:

   • Particle size distribution: Determines the required cut size (d50) of the hydrocyclone. Finer particles may require smaller-diameter cyclones or multi-stage configurations.
   • Density difference between solids and liquid: Impacts separation efficiency—greater density differences improve separation performance.
   • Slurry viscosity: High-viscosity fluids reduce separation efficiency and may require larger cyclones or temperature adjustments.
   • Flow rate (volumetric and mass): Directly influences the required cyclone diameter and number of units in parallel operation.

   Tip: Conduct lab-scale testing with representative samples to simulate real-world performance before full-scale implementation.

2. Separation Efficiency and Accuracy

   The primary goal of a hydrocyclone is to achieve precise particle classification or solid-liquid separation. Consider the following:

   • Cut size (d50): The particle size at which 50% of particles report to the underflow and 50% to the overflow. Select a hydrocyclone design that matches your target d50 value.
   • Sharpness of cut: Refers to how cleanly the separation occurs. A steeper partition curve indicates better classification accuracy.
   • Overflow and underflow quality: Define acceptable limits for solids content in overflow (typically low) and liquid clarity in underflow (minimized water loss).
   • Capacity vs. efficiency trade-off: Higher throughput often reduces separation precision—optimize for your process priorities.

   Advanced models offer adjustable spigots or vortex finders to fine-tune performance dynamically during operation.

3. Material and Construction

   Durability is critical, especially in abrasive or corrosive environments. Material selection affects both performance and lifecycle cost:

   • Ceramic linings: Offer superior abrasion resistance for high-wear applications like mineral processing.
   • Polyurethane bodies: Provide excellent wear and impact resistance with lighter weight and lower cost than metal alternatives.
   • Stainless steel: Ideal for corrosive slurries or high-pressure systems where structural integrity is paramount.
   • Composite materials: Combine chemical resistance with mechanical strength for specialized chemical or pharmaceutical uses.

   Ensure seals, gaskets, and internal components are compatible with your slurry chemistry to prevent premature failure.

4. Energy Consumption

   Hydrocyclones themselves are passive devices, but they rely on feed pumps to generate the necessary pressure (typically 10–60 psi). Energy efficiency considerations include:

   • Pressure drop optimization: Smaller cyclones require higher inlet pressure, increasing pump energy use.
   • Pump efficiency: Pair the hydrocyclone with a properly sized, high-efficiency slurry pump to minimize operating costs.
   • Multi-stage arrangements: Sometimes more efficient than single large units for fine separations.
   • Variable frequency drives (VFDs): Allow pump speed adjustment to match changing process conditions and save energy.

   Look for hydrocyclone designs with streamlined internal geometry to reduce turbulence and pressure losses.

5. Maintenance and Servicing

   Minimizing downtime is essential for continuous operations. Evaluate the following maintenance aspects:

   • Wear monitoring: Choose models with wear indicators or accessible inspection points to anticipate liner replacement.
   • Modular design: Units with replaceable liners, vortex finders, and spigots allow quick servicing without replacing the entire assembly.
   • Accessibility: Ensure adequate space around the unit for disassembly and maintenance activities.
   • Parts availability: Confirm that spare parts (especially consumables like spigots) are readily available from the supplier.
   • Installation flexibility: Some hydrocyclones support vertical or horizontal mounting depending on space constraints.

   Regular inspection schedules and preventive maintenance can extend component life by up to 40%.

6. Regulatory Compliance

   Ensure the hydrocyclone system meets all applicable industry and environmental standards:

   • Effluent discharge standards: Verify that overflow quality meets local regulations for suspended solids and chemical content.
   • Safety certifications: Look for compliance with ASME, ISO, or ATEX standards where applicable.
   • Material traceability: Required in food, pharmaceutical, and nuclear industries for quality assurance.
   • Noise and vibration levels: Important in enclosed or urban facilities.

   Documentation such as Material Test Reports (MTRs), CE marking, or FDA compliance may be required depending on your sector.

Selection Factor	Key Questions to Ask	Common Mistakes	Recommended Actions
Feed Characteristics	What is the typical and peak flow rate? What are the particle size and density ranges?	Using average data without considering variability	Conduct comprehensive slurry sampling over multiple shifts
Separation Efficiency	What d50 is required? How sharp must the cut be?	Overestimating achievable efficiency	Request performance curves from the manufacturer
Material Selection	Is the slurry abrasive, corrosive, or temperature-sensitive?	Choosing low-cost materials that wear quickly	Invest in premium liners for high-wear zones
Energy Use	What is the available pump pressure? Can VFDs be used?	Ignoring total cost of ownership (TCO)	Perform a lifecycle cost analysis including power consumption
Maintenance	How often do parts need replacement? Is training available?	Underestimating labor and downtime costs	Select modular, user-serviceable designs
Compliance	Which environmental or safety standards apply?	Assuming all cyclones meet regulatory requirements	Verify certifications in writing before purchase

Expert Tip: When in doubt, consult with application engineers from reputable hydrocyclone manufacturers. Many offer free process audits, simulation software, and pilot testing services to validate performance before full-scale deployment.

Additional Selection Best Practices

• Consider using computational fluid dynamics (CFD) modeling to predict hydrocyclone performance under your specific conditions.
• Evaluate the possibility of using a hydrocyclone cluster (multiple units in parallel) for large-volume applications.
• Integrate instrumentation such as pressure gauges, flow meters, and density sensors for real-time monitoring and control.
• Plan for future scalability—design systems that can accommodate increased capacity or tighter separation requirements.
• Document all selection criteria and performance expectations for future reference and troubleshooting.

Choosing the right hydrocyclone separator involves balancing technical performance, operational demands, and economic factors. By systematically evaluating feed characteristics, efficiency goals, construction materials, energy use, maintenance needs, and regulatory requirements, you can select a solution that delivers reliable, cost-effective separation for years to come. Remember that expert consultation and real-world testing can significantly reduce risk and improve long-term outcomes.

Hydrocyclone Separator: Frequently Asked Questions

Q1: What materials are hydrocyclones made of?

Hydrocyclone separators are constructed from durable, wear-resistant materials to withstand harsh industrial environments and prolonged use. The choice of material depends on the application, operating conditions, and the type of slurry being processed:

• Polyurethane (PU): Offers excellent abrasion resistance and flexibility, making it ideal for applications involving coarse particles and high wear. It is lightweight and corrosion-resistant, commonly used in mining and mineral processing.
• Ceramic (e.g., alumina ceramic): Provides superior hardness and longevity in extremely abrasive conditions. Ceramic liners or inserts are often used in critical wear zones to extend service life.
• Stainless Steel (e.g., SS304, SS316): Used in corrosive environments where chemical resistance is essential—such as in water treatment, chemical processing, and offshore oil operations. Stainless steel housings resist rust and degradation from acidic or saline fluids.
• Cast Iron with Linings: Sometimes used as a base structure with internal linings of rubber or ceramic for added protection.

These materials ensure that hydrocyclones maintain structural integrity and performance over time, reducing downtime and maintenance costs in demanding industrial settings.

Q2: How does a hydrocyclone work?

A hydrocyclone operates on the principle of centrifugal separation to classify, separate, or sort particles in a liquid suspension (slurry) without any moving parts. Here's how it works:

1. Feed Entry: The slurry is pumped tangentially into the cylindrical chamber of the hydrocyclone at high velocity, creating a swirling motion.
2. Centrifugal Force: As the mixture spins, heavier and larger particles are forced outward toward the wall of the cyclone due to centrifugal force, while lighter and finer particles remain closer to the center.
3. Separation Process: The heavier particles spiral downward along the cone wall and exit through the underflow outlet (apex), which carries concentrated solids or waste.
4. Overflow: The lighter, cleaner fluid with fine particles moves upward in a helical path through the center and exits via the overflow outlet at the top.

This efficient separation mechanism allows hydrocyclones to function as classifiers, desanders, de-sliming units, or thickening devices depending on the setup and design parameters such as diameter, inlet size, and pressure.

Q3: Why are hydrocyclones used in industry?

Hydrocyclones are widely adopted across various industries due to their efficiency, reliability, and versatility in separating solids from liquids or differentiating particle sizes. Key applications include:

• Mining & Mineral Processing: Used to separate valuable minerals (like gold, copper, or iron ore) from gangue (waste rock) by particle size classification. They play a critical role in grinding circuits and flotation feed preparation.
• Oil & Gas Industry: Employed in offshore platforms and production facilities to remove sand and water from crude oil streams, protecting downstream equipment and improving product quality.
• Water & Wastewater Treatment: Applied in purifying drinking water by removing suspended solids, silt, and contaminants. Also used in industrial effluent treatment to meet environmental discharge standards.
• Pulp & Paper Industry: Utilized for cleaning and thickening pulp by removing contaminants like sand and filler materials.
• Chemical & Food Processing: Used for clarification, concentration, and recovery of fine particles in process streams.

Their compact footprint, low operational cost, and ability to handle large volumes make hydrocyclones indispensable in continuous industrial processes.

Q4: What are the advantages of using a hydrocyclone separator?

Hydrocyclones offer numerous benefits that contribute to their widespread use in industrial separation processes:

Advantage	Description
No Moving Parts	Hydrocyclones have no motors, gears, or rotating components, resulting in minimal maintenance, reduced wear, and lower operating costs compared to mechanical separators.
High Efficiency	Capable of separating fine particles down to 10–20 microns with high precision, especially when operated under optimal pressure and flow conditions.
Compact Design	Takes up less space than traditional settling tanks or thickeners, making it ideal for installations with limited footprint.
Scalability	Multiple hydrocyclones can be grouped into clusters (manifolds) to increase capacity for large-scale operations.
Cost-Effective	Low capital and operational expenses with fast return on investment due to improved process efficiency and reduced waste.
Versatility	Can be adapted for various functions including classification, de-sliming, dewatering, and clarification across multiple industries.

While hydrocyclones rely on feed pressure and proper design for optimal performance, their simplicity and effectiveness continue to make them a preferred solution for solid-liquid separation in modern industrial systems.