Sedimentation Principles and Design of Facilities Part 2 Pradeep Kumar S. Sarkar Type I and II sedimentation Zone settling occurs when a flocculent suspensions with high initial concentration (on the order of500 mg/L) settles by gravity. Flocculant forces between particles causes settling as a matrix(particles remain in a fixed position relative to each other as they settle).(Type III settling) When matrix sedimentation is constrained from the bottom, the matrixbegins to compress. Such a situation occurs when the matrix encounters the bottom oftank in which it is settling. This is called compression (Type IV) settling. Time or Distance Down the Tank Depth t=0 Vs Vc Clarified water zone Interfacial zone Transition zone Compaction zone Interface 1 Interface 2 Clarified water zone Interfaces meet and coalesce Compaction zone Hc Xc Xu Hu t=tu t=tc tc>t>0 H0 ZONE SETTLING AND COMPRESSION SETTLING Type III and IV sedimentation ZONE SETTLING AND COMPRESSION SETTLING t=0 Vs Vc Clarified water zone Interfacial zone Transition zone Compaction zone Interface 1 Interface 2 Clarified water zone Interfaces meet and coalesce Compaction zone Hc Xc Xu Hu t=tu t=tc tc>t>0 H0 Uniform sludgeconc. X0 Beginning of compaction End of compaction Clarification Process ThickeningProcess Below Interface 1, the solids settle at a uniform velocity and the blanket of solids moves at a constant velocity of Vs. The solids that has reached at the bottom, starts getting compacted as the water gets squeezed out from the compacted sludge. This compaction zone also has a uniform concentration.This zone increases in volume over time. The interface 2 moves upward at a velocity Vc. The two interfaces meet at a critical time tc and the transition zone fades away. At this time the settled sludge show an uniform concentration Xc, (critical concentration). Compaction starts and reaches an ultimate concentration Xu. Height of Interface 1 Settling Time,t (min) A Bt1 t Slope svdtdhSlope cvdtdh0 dtdhC 0 t=0 Vs Vc Clarified water zone Interfacial zone Transition zone Compaction zone Interface 1 Interface 2 Clarified water zone Interfaces meet and coalesce Compaction zone Hc Xc Xu Hu t=tu t=tc tc>t>0 H0 Protocol for Designing Secondary Clarifier 1. Calculate the minimum surface area required to allow for clarification of sludge 2. Calculate the minimum surface area required to provide for thickening of sludge to the desired underflow condition. 3. Take the larger of these two area as the design area for clarifier. Sedimentation Tank Mass Balance InfluentEffluent Underflow Q0, X0 Qe, Xe Qu, Xu Liquid balance, u eQ Q Q 0u u e eX Q X Q X Q 0 0Solids balance, ) () (0 0e uueX XX X QQe uQ Q Q 0Findingout the Minimum Area for Clarification PurposeMinimum area required for clarification = Acl

It depends on the velocity vs with which the suspension in the interfacial zone settles before reaching the critical concentration Xc Therefore, under continuous flow conditions, velocity of water over the overflow weir cannot exceed vs if clarification is to take place efficiently.

Thus, seclvQA BAdtdhvs00 Settling velocity can be obtained from the zone settling curves But, the clarifier designed with this criteria may not necessarily mean that desired concentration of solid (Xu) shall be achieved at the underflow Clarified water zone Xi Zone Settling of Sludge in a Batch Reactor Such as in a Laboratory Column The capacity of the clarifier for carrying solids downwards at a concentration Xi under gravity is given by i i Bv X G GB = batch Solids flux, mass/(unit area. Time) Xi= Sludge concentration,vi = Zone Settling velocity at Xi Unlike discrete particle or flocculent Settling, here thezone settling velocity of sludge gradually decreasesover time after the critical concentration is reached. At this situation, the water needs to be squeezed out in order to allow for the sludge blanket to settle down. The greater the particle density, the more difficult is to allow the water to pass through the settling sludge. vi As the sludge blanket settles down, Xi increases, due to water being continuously squeezed out. At very high concentrations the suspension is almost compacted and approaches vi0, and from the above equation GB0. On the other hand, at a low concentrations, xi0, then also, GB0. This suggests that a maximum for GB should occur at some intermediate value of xi. GB Xi Solids Concentration Solids Flux InfluentEffluent Underflow Q0, X0 Qe, Xe Qu, Xu MASS BALANCE AT A CLARIFIER u u e eX Q X Q X Q 0 00 eXu uX Q X Q 0 0Ideally, the outlet solids concentration should be zero or may be much less than the concentration at the underflow. u eX X Or, In either case, Mass of the solids removed at the underflow, 0 0X Q X Q Mu u If the area of the thickener is At, then this mass M should have settled down through this thickener area. In such a case, T tG A M TGTotal Solids Fluxthrough the thickener (unit mass/area) 0 0X Q G A MT t TtGX QA0 0How do we find out GT? What is the physical significance of GT? InfluentEffluent Underflow Q0, X0 Qe, Xe Qu, Xu Zone Settling in a Continuous-Flow Clarifier 1. Sludge settles down (corresponds to solids flux in batch reactor 2. Settled Sludge is continuously being taken out as the underflowu i uv X G u B TG G G Total Solid flux =Solids flux in Batch reactor + Underflow fluxThe total solid fluxcan becontrolled by manipulating vu as it can be controlled by operating the valve at the outlet or changing the underflow pumping rate.i i Bv X G Xi vu is the sludge velocity due to underflow removal At any solids concentration Xi of the settling sludge blanket, vi is the sludge velocity due to fall under gravity But, how to ensure that we obtain the target concentration of solids (Xu) at the underflow? We need to choose an appropriate area for thickening so that the target solids concentration at the underflow is achieved. GB GT Gu T B Xu Xi Underflow velocity,tuuAQv uTu tT tu t u t u tu uuXGX AG AX AMX A X QX A X Qv 0 0A 0 uuTuvXGXB 00taniiBivXGXA 00tan Plot Xu on the x-axis Solids Concentration Solids Flux Draw tangent to the Batch-flux curve from the point Xu and extend it to meet the y-axis at B Batch-flux curve u B TG G G Slope of the tangent provides the underflow velocity (vu) required to achieve the underflow concentration of Xu BG A 0TG B 0uG AB T TtGX QGMA0 0 Thickener Area, Finding Thickener Area Example: A laboratory batch thickening experiment with variable solids concentration produced the following results: Solids concentration (mg/L)Settling Velocity (m/hr) 9004.2 14003.0 22001.85 30001.21 37000.76 45000.45 52000.28 65000.13 82000.089 The influent concentration is MLSS 3000 mg/L, flow Rate is 8000 cum/day. Design a secondary settling tank that will thicken the solids so that the underflow solids concentration is 10,000 mg/L.STEP 1. Calculate the solids flux based on the laboratory column analysis data Solids concentration (mg/L) Settling Velocity (m/hr) Solids Flux(kg/sqm.hr) (col 1 X col 2) 00 9004.23.78 14003.04.2 22001.854.07 30001.213.63 37000.762.80 45000.452.03 52000.281.46 65000.130.90 82000.0890.73 .hr m10 2 . 410mg10 2 . 4Lmg3 1400263 3 -3mghrmXmXhrmX X STEP 2. Plot Solids Flux vs. Concentration STEP 3. Draw Tangent to the curve with starting point , Xu = 10,000 mg/L, Find out the ordinate. This is the solids flux GT. GT = 2.4 kg/sqm.hr GT= 2.4 GB=0.8 GT Gu=1.6 T TtGX QGMA0 0 Required area of the clarifier so that it satisfies the thickening requirements, sq.m. 7 . 416kg/sqm.hr 4 . 2mg/L 3000 * cum/d 80000 0 TtGX QACheck for the thickener clarification ability. 23m 275m/hr 21 . 1/ m 8000 dvQAsClFrom the data table, the settling velocity of the sludge blanket with concentration of 3000 mg/L is 1.21 m/hr Cl tA A So, area required for thickening will govern the process design. Hence, the surface area of the clarifier shall be 417 sq m. The Diameter shall be 23 m.