AN ANALYTICAL STUDY ON RIVERBED AND RIVERBANK FILTRATION

Abstract

Surface water as a source of drinking water requires costly treatment to make it free from physical, chemical, and bacteriological contamination. Therefore, the managers of various water utilities are exploring the other sources, wherein, the cost of treatment is low. Groundwater is considered as a sustainable source of drinking water in many parts of the world as it requires minimal treatment. Most of the urban areas are located on the banks of the river which are generally contaminated due to various anthropogenic activities. River water as a source of water supply, therefore, results in heavy treatment cost. In such situations, water collected through a collector pipe laid under a riverbed or through a radial well constructed adjacent to the river is the best choice. The flow through collector pipes in such cases shall be free from suspended particles as well as from bacterial contamination as the riverbed/ riverbank filtration work as slow sand filter. Riverbank filtration (RBF) is a process during which surface water is subjected to subsurface flow prior to extraction from the wells. In RBF process, surface water is subject to a combination of physical, chemical, and biological processes such as filtration, dilution, sorption, and biodegradation that significantly improve the raw water quality. RBF is widely used for drinking water purposes as the water utilities strive to meet increasingly stringent drinking water regulations, especially with respect to the provisions of multiple barriers for protection against microbial pathogens and tighter regulations related to Disinfectant-by-Products (DBPs). It has been noticed that only a few studies have been carried out to model such systems mathematically which resulted in analytical solutions. In this study, an attempt has been made to analyse the system of riverbed and riverbank filtration mathematically and to derive the analytical solutions corresponding to various flow characteristics under steady flow condition through such a system. ii A radial collector well, commonly known as “Ranney Well”, collects water from underground aquifer through slotted radial pipes extended horizontally outward from a caisson. Like infiltration galleries, they are located in or close to rivers and other surface-water bodies. A collector pipe is the primary component of a radial collector well constructed either for riverbed or riverbank filtration. Assuming the collector pipe as a line sink and applying the conformal mapping technique, Aravin and Numerov (1965) have derived an analytical solution for computing potential and flow to the collector pipe laid under riverbed under steady state flow condition. They have considered the origin of the physical domain at the centre of the collector pipe, which restricts the convenience of analysis. In this study, the origin of the physical flow domain is considered at the lower impervious base of the aquifer, which makes the analysis easier as compared to Aravin and Numerov (1965). Analytical expressions have been derived for (i) the potential at different location in the flow domain, (ii) quantity of flow to the collector pipe, (iii) entrance velocity, and (iv) travel time of a parcel of water from the riverbed to the collector pipe along the shortest path. Further, using the travel time and the logistic function approach, the number of log cycle reduction in bacterial concentration has been found out. It has been noticed that this expression is non-linear in nature which depends on the reproduction and decay rate of micro-organisms. Based on the dimensionless parameters obtained and the analysis related to flow characteristics, following conclusions are drawn: Yield of a collector pipe is linearly proportional to (i) hydraulic conductivity of the riverbed material, (ii) drawdown in the well caisson, (iii) length of the collector pipe, and iii Nonlinearly dependent on (i) the diameter of the collector pipe, (ii) thickness of the aquifer, (iii) height above the impervious base at which the collector pipe laid. Further, the present study has been extended to two more cases, i.e., (i) assuming the collector pipe as a line slit, and (ii) collector pipe with a square cross-section having constant finite head boundary condition at their periphery. In both the cases, collector pipe is laid under fully penetrating riverbed. It is found that whether the collector pipe is assumed as a line sink with infinite head boundary or as a line slit or as a collector pipe with square cross-section with finite head boundary; there is no appreciable difference in the estimated flow to the collector pipe. In case of riverbank filtration, Zhan and Cao (2000) have put forward the philosophy that during late pumping stage, horizontal pseudo-radial flow takes place towards a horizontal collector pipe. This postulation supports the assumption of sheet flow condition in a thin aquifer system with horizontal collector pipe(s). In the present study, using this philosophy for applying Schwartz-Christoffel conformal mapping technique, radial collector well systems having several coplanar laterals located near a straight river reach have been analyzed. The collector well systems with different lengths of laterals, orientation of laterals and distance of the collector well from the river, etc, have been analyzed for safe yield. In case of a collector well with 4 laterals of equal length, it has been found that the maximum flow occurs when angle between the laterals oriented towards the river is + 3  and π for 5 2  l R (see Fig. 5.2 (a)). For 5 2  l R , flow to the collector well is maximum for   0.5. A radial collector well with 3 radials is a particular case of 4 laterals in which one of the collectors (l3) (which is perpendicular to the river axis but away from river) is zero. The flow iv in such well system is maximum, if the other two laterals are oriented at an angle   0.5 for R/l2 <5. For 5 2  l R , the flow to the collector well is maximum if 3   2 . In case of a collector well with three radials of equal length in which one of them orient away from the river, the other two should be oriented at an angle 3 0.2   1 for 5 2  l R to obtain near maximum yield. For 5 2  l R , their orientation should be 2 1 3 1   . In order to validate the results using the concept of sheet flow, an exact solution of flow computation to a line sink in a confined aquifer with collector pipe laid parallel to the river is suggested. In the study, using the conformal mapping technique, an exact analytical solution for two-dimensional flow in vertical plane normal to a collector pipe laid parallel to a fully penetrating river in the middle of a confined aquifer is obtained. While estimating flow to a radial collector well with sheet flow condition, the thickness of aquifer and diameter of the collector pipe are not considered. Therefore, in order to account for thickness of the aquifer, it is suggested to multiply the estimated flow by the thickness of aquifer. As the flow does not increase linearly with thickness of the aquifer, a correction factor needs to be applied. It has been found that the correction factor increases marginally as the thickness of the aquifer decreases. It decreases as the distance of the collector pipe from the riverbank increases. It has been noticed that as the correction factor is very much less than 1, Broom’s postulation          y C p kD w   of flow estimation using sheet flow concept overestimates the collector pipe yield, and hence need a correction factor. It may be noticed that the derived correction factors may be applied to estimate the collector well yield with more than 2 collector pipes. Further, yield of collector well increases as it is located nearer to the water body but will decrease the travel time and hence the number of log cycle reduction. It also increases with increase in length and diameter of the collector pipe.