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d) ( * If we keep the filtration process going, please predict the volume of the total filtrate collected at the filtration time t = 3 min. II

d) ( * If we keep the filtration process going, please predict the volume of the total filtrate collected at the filtration time t = 3 min. II

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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In a filtration experiment, the slurry in water at 25 °C was filtered through a plate and frame filter system at a constant pressure (−ΔP) of 300 kPa. The filtration time and the obtained filtrate volume (m³) were recorded as shown in the following table: | Time (s) | V (m³) | Time (s) | V (m³) | Time (s) | V (m³) | |----------|------------|----------|------------|----------|------------| | 10 | 1.05E-03 | 50 | 3.15E-03 | 90 | 4.51E-03 | | 20 | 1.73E-03 | 60 | 3.53E-03 | 100 | 4.80E-03 | | 30 | 2.27E-03 | 70 | 3.88E-03 | 110 | 5.08E-03 | | 40 | 2.74E-03 | 80 | 4.21E-03 | 120 | 5.35E-03 | The filter's total area was A = 0.05 m² and the slurry concentration was 20 kg/m³. a) Calculate the specific cake resistance \( \alpha \); b) Calculate the total resistance due to the filter medium \( R_m \); c) Calculate the total resistance due to the filter cake \( R_c \) when 5 liters of filtrate was collected; d) If we keep the filtration process going, please predict the volume of the total filtrate collected at the filtration time \( t = 3 \) min.
Transcribed Image Text:In a filtration experiment, the slurry in water at 25 °C was filtered through a plate and frame filter system at a constant pressure (−ΔP) of 300 kPa. The filtration time and the obtained filtrate volume (m³) were recorded as shown in the following table: | Time (s) | V (m³) | Time (s) | V (m³) | Time (s) | V (m³) | |----------|------------|----------|------------|----------|------------| | 10 | 1.05E-03 | 50 | 3.15E-03 | 90 | 4.51E-03 | | 20 | 1.73E-03 | 60 | 3.53E-03 | 100 | 4.80E-03 | | 30 | 2.27E-03 | 70 | 3.88E-03 | 110 | 5.08E-03 | | 40 | 2.74E-03 | 80 | 4.21E-03 | 120 | 5.35E-03 | The filter's total area was A = 0.05 m² and the slurry concentration was 20 kg/m³. a) Calculate the specific cake resistance \( \alpha \); b) Calculate the total resistance due to the filter medium \( R_m \); c) Calculate the total resistance due to the filter cake \( R_c \) when 5 liters of filtrate was collected; d) If we keep the filtration process going, please predict the volume of the total filtrate collected at the filtration time \( t = 3 \) min.
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