16-Civ-B5 Water Supply and Wastewater Treatment · December 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examination, December 2014 — 98-Civ-B5 Water Supply and Wastewater Engineering. Three hours; closed book with one two-sided aid sheet and an approved calculator. Question 1 is compulsory and any three of Questions 2–5 are attempted; every question carries 25 marks. All five questions are solved below, because the set is intended as a study resource rather than an exam script.
Reference texts.
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
A rapid gravity sand filter is the polishing step of a conventional surface-water treatment train — coagulation, flocculation, sedimentation, filtration, disinfection — and its purpose is to remove the residual floc and the pathogens that settling leaves behind. It is called rapid because it is operated at a filtration rate of roughly $5$ to $15\ \text{m}^3\,\text{m}^{-2}\,\text{h}^{-1}$, some fifty to a hundred times the rate of a slow sand filter, and it achieves that rate by removing particles within the depth of the bed rather than on its surface, and by being cleaned mechanically at intervals of hours rather than being scraped at intervals of weeks.
Referring to Figure 5.1, the filter is an open rectangular reinforced-concrete box, typically $25$ to $100\ \text{m}^2$ in plan, containing from the bottom upward: an underdrain floor of nozzles or laterals set in a plenum that distributes wash water and air and collects filtrate; a graded gravel support layer $0.3$ to $0.45\ \text{m}$ deep, coarse at the bottom and fine at the top, which prevents the sand from entering the underdrain while spreading the wash flow evenly; and the filter medium proper, a $0.6$ to $0.75\ \text{m}$ bed of silica sand with an effective size $d_{10}$ of $0.45$ to $0.6\ \text{mm}$ and a uniformity coefficient below about 1.6. Above the bed sits $1.0$ to $1.5\ \text{m}$ of supernatant water, which supplies the driving head, and wash-water troughs set high enough to clear the expanded bed during backwash. A rate-of-flow controller, a loss-of-head gauge and an effluent turbidimeter complete the installation, and a plant is always built with several cells so that one can be washed while the others remain in service.
Straining plays only a minor part. The pores between $0.5\ \text{mm}$ sand grains are of the order of $80\ \text{µm}$, whereas the particles being removed — floc fragments, clay, bacteria, Giardia cysts and Cryptosporidium oocysts — are one to two orders of magnitude smaller. Removal is instead a two-step depth-filtration process. First comes transport: as water follows the tortuous path between grains, particles are brought to a grain surface by interception, by sedimentation onto the upper surfaces of grains, by Brownian diffusion for the smallest colloids, and by inertial impaction. Then comes attachment: the particle must stick, which it will do only if the electrostatic repulsion between the negatively charged particle and the negatively charged sand has been suppressed. That is the job of the upstream coagulant, and it is why a rapid filter is only as good as the chemistry ahead of it — an uncoagulated water passes through a sand bed almost unchanged. Deposition therefore begins at the top of the bed and progresses downward as the upper layers fill, which is what allows the whole depth to be used and gives the filter its long run between washes.
Two consequences follow. Head loss rises through the run, from a clean-bed value of $0.3$ to $0.6\ \text{m}$ predicted by the Carman–Kozeny or Rose equation, to a terminal value of $2$ to $3\ \text{m}$; and effluent turbidity follows a characteristic curve — a brief ripening period of degraded quality after each wash while fresh collection sites are conditioned, a long stable plateau, and finally breakthrough as the shear at the deposits exceeds their strength and previously captured material is re-entrained. The filter is taken out of service at whichever comes first, terminal head loss or turbidity breakthrough, and it must never be run to breakthrough, because that is precisely when the pathogens it has stored are released. In Canadian practice the operating target set by the Guidelines for Canadian Drinking Water Quality for chemically assisted filtration is a filtered turbidity of $0.3\ \text{NTU}$ or less in at least 95 percent of measurements, which underwrites the 3-log Giardia and Cryptosporidium removal credit assigned to the filtration barrier.
The term — German for “dirt blanket” — properly belongs to the slow sand filter, and the distinction is the most instructive point in the whole question. In a slow sand filter, operated at only $0.1$ to $0.3\ \text{m}^3\,\text{m}^{-2}\,\text{h}^{-1}$, a living biological mat of algae, bacteria, protozoa, diatoms and their extracellular polymer develops over several days to weeks in the top few millimetres of the bed. That mat is the principal treatment mechanism: it strains, it biologically oxidises dissolved organic matter and ammonia, and its predatory protozoa consume bacteria, so a mature slow sand filter can achieve two to three log removal of coliforms with no coagulant at all. Ripening it is essential, cleaning is by scraping off the top $20$ to $25\ \text{mm}$, and the filter must be re-ripened afterwards.
In a rapid filter the analogous surface layer is a purely physical deposit of coagulated floc — sometimes loosely called the schmutzdecke by analogy, and shown as the thin dark band in Figure 5.1 — and its role is entirely different. It is not living, it is not the main removal mechanism, and it is not wanted. Because the filtration rate is so high, any material retained at the surface blinds the bed, drives the head loss up steeply and shortens the run; the design intent is to push penetration deep into the bed, which is exactly why dual-media filters place a coarse, low-density anthracite layer (effective size $0.9$ to $1.1\ \text{mm}$, specific gravity about 1.5) above the finer, denser sand. Coarse-to-fine in the direction of flow distributes the deposit through the depth, doubling the run length for the same terminal head loss. A rapid filter is therefore cleaned by removing its surface layer at every wash, whereas a slow sand filter is cleaned around its schmutzdecke and depends on it; a candidate who treats the two as the same mechanism has inverted the design logic of both processes.
Backwashing reverses the flow to fluidise the bed and carry the accumulated solids to waste. The sequence, all of it visible in Figure 5.1, is as follows. The filter is taken off line and the supernatant is drawn down to just above the wash troughs. Air scour is applied first (see below). Wash water, drawn from a treated-water storage tank or an elevated washwater tank, is then admitted through the same underdrain plenum at a rate of about $0.6$ to $0.9\ \text{m}^3\,\text{m}^{-2}\,\text{min}^{-1}$ — roughly $36$ to $54\ \text{m/h}$, some five times the filtration rate — which lifts the bed into a fluidised state and expands it by $20$ to $50$ percent in depth. Grains circulate, the deposits are stripped by the hydrodynamic shear and by grain-to-grain abrasion, and the dirty water spills over the troughs and goes to the washwater recovery basin, typically for recycling to the head of the plant. Washing continues for $5$ to $10$ minutes, until the spent wash water clears; on returning to service the first filtrate is run to waste or recycled for the few minutes of the ripening period.
Three design points govern the operation. The expansion must be sufficient to fluidise but not so great that media are carried into the troughs — hence the trough elevation is set from the expanded-bed height, and the wash rate must be corrected for water temperature, because cold water is more viscous and fluidises the bed at a lower velocity. The gravel support must not be disturbed, or the graded layers intermix and the bed develops the permanent short-circuiting known as gravel upset. And the wash-water volume must be accounted for in the plant water balance: at 2 to 4 percent of the water filtered, it is a real loss and, since it carries the concentrated pathogen load stripped from the bed, its recycling must be managed rather than assumed.
Water alone is a comparatively inefficient cleaning agent, for a reason that is easy to overlook: once the bed is fluidised the grains are separated by water and there is little grain-to-grain contact, so the abrasion that dislodges firmly attached deposits is largely absent. Increasing the wash rate does not fix this; it simply risks washing media out. The remedy is to introduce air, at $0.9$ to $1.5\ \text{m}^3\,\text{m}^{-2}\, \text{min}^{-1}$, through the same nozzle floor. The rising bubbles violently agitate the medium in an unexpanded or only partly expanded bed, producing exactly the grain collisions that shear the deposits from the grain surfaces, and they break up the mudballs — agglomerations of floc and sand that otherwise sink, accumulate and permanently reduce capacity.
Air scour is applied either as a separate first stage — air alone for two to three minutes, then water alone — or, in the more effective modern practice, as a simultaneous combined air-and-water wash at a sub-fluidisation water rate, followed by a water-only rinse to carry the released solids out over the troughs. The combined wash typically halves the wash-water volume for the same or better cleaning, which is why it is standard on new Canadian plants. It demands a robust nozzle underdrain designed for two-phase flow, and the air must be shut off before the final high-rate rinse so that bubbles do not carry medium into the troughs. Where air scour is not provided, the usual alternative is a mechanical or fixed-nozzle surface wash sweeping the top of the bed during the wash — less effective on mudballs, but simpler.
Taken together the three elements answer the question’s logic: the rapid filter works by depth removal rather than surface straining, so the surface layer that a slow sand filter cultivates is here a nuisance to be removed; backwash fluidises the bed to carry that material away; and air scour supplies the grain-to-grain abrasion that fluidisation alone destroys. Omit the air and the bed slowly accumulates mudballs and loses capacity; omit the coagulant upstream and no amount of washing will make the filter perform at all.
