Introduction to Solid-Liquid Filtration
The goal of filtration is to :
Key Process Parameters Affecting Filtration Efficiency
Filtration performance is influenced by fluid properties, solids characteristics, and system design.
A. Viscosity and Temperature Effects
- Higher viscosity fluids (e.g., resins, oils, slurries) reduce permeability, lowering throughput. • Example Flux Rates:
- Water-like viscosity (1 cP): 0.4 gpm/ft²
- 3000 cP fluid: 0.1 gpm/ft²
- Temperature increases may lower viscosity, improving flow
- Thermal Management Strategies: Heat tracing or controlled temperature operation can improve flow in high-viscosity applications.
B. Pressure Drop Considerations
- Low-pressure drop (2-15 PSI) : Maintains efficiency and extends media life.
- Excessive ΔP (>15 PSI) : Leads to compaction/compression, drag pressure reducing void fraction that can be countered with filter aid addition.
- Optimized Driving Force : By balancing and controlling the driving force—treating pressure differential as a metered expenditure—steady flow is maintained without excessive cake compression.
Governing Equations of Filtration
The efficiency of a filtration process is governed by fluid dynamics and resistance models.
A. Darcy’s Law (Fundamental Filtration Equation)
The flow of liquid through a porous medium is described by Darcy’s Law.
Where :
K = Porosity of the filter cake (darcy)
Delta p = Pressure drop across the filter (atmosphere)
- As cake thickness increases, the flow rate decreases due to higher resistance.
B. Cake Thickness and Volume Relationship
Where :
The increase in cake thickness is described by the equation L=CVDAL = \frac{CV}{DA}L=DACV, where L is the cake thickness, C represents the mass of solids per unit volume of liquid (g/L), V is the volume of liquid filtered (L), D is the bulk density of cake solids (g/cm³), and A is the filtration area (cm²).
C. Constant-Rate vs. Constant-Pressure Filtration
Where :
Constant-Rate Filtration:
- Pressure increases over time as cake thickens.
- Best for systems requiring consistent throughput.
Constant-Rate Filtration:
- Flow rate decreases as cake thickness increases
- Used in batch operations and laboratory testing.
- Helps prevent excessive cake compaction in compressible solids.