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A mathematical model study of an aquifer with significant dewatering
Journal of Hydrology, 62 (1983) 143--158
143
Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
[2] A MATHEMATICAL MODEL STUDY OF AN A Q U I F E R WITH SIGNIFICANT DEWATERING
K.R. RUSHTON and D.C.H. SENARATH
Department of Civil Engineering, University of Birmingham, Birmingham B15 2TT (Great Britain) (Received January 6, 1982; revised and accepted May 8, 1982)
ABSTRACT
Rushton, K.R. and Senarath, D.C.H., 1983. A mathematical model study of an aquifer with significant dewatering. J. Hydrol., 62: 143--158. A finite-differencenumerical technique is used to study the behaviour of a Chalk aquifer in southeast England. In the neighbourhood of certain of the abstraction boreholes partial dewatering takes place due to prolonged pumping. A technique is devised for including this local dewatering in a regional model. The numerical model is used to understand the flow mechanisms within the aquifer with special emphasis on the balance between inflows from the unconfined region and water released from storage due to dewatering. The simulation covers a time period of over 100 yr.
INTRODUCTION
When increasing abstraction causes groundwater levels to show a continuing decline, there is a need to ascertain the length of time for which an adequate quantity of water may be available. This is particularly important when an aquifer, which is initially confined, becomes unconfined in the vicinity of abstraction sites. There is then a significant risk that the saturated depth in the vicinity of the abstraction sites will decrease so much that the yield of the wells will fall off dramatically. A typical example of this situation is provided b y a Chalk aquifer system in Essex. The aquifer dips from o u t c r o p at ~ 0 . 3 ° beneath the impermeable L o n d o n Clay. Before abstraction c o m m e n c e d in the confined region the flow through the confined aquifer was small. Increasing abstraction from the confined region over the past 100 years has caused an increase in the groundwater gradient and therefore in the flow from the unconfined region; yet this inflow is only ~ 7 5 % of the current abstraction rate. The additional water is provided b y localised dewatering around certain of the abstraction sites. In order to examine the future of the aquifer as a resource it is important to identify the various flow mechanisms within the aquifer and then investigate the consequences of various future abstraction patterns.
0022-1694/83/0000--0000/$03.00 © 1983 Elsevier Scientific Publishing Company
144
This paper describes a mathematical model study of this Chalk aquifer. It relies on a detailed hydrogeological study which has been carried out b y the Anglian Water Authority. The mathematical model brings together the various facets of the aquifer system and allows the different items of information to be cross-checked. Issues that are resolved include the apparent lack of balance between the recharge, dewatered volume and abstraction rate. The number of years that need to be included in the simulation is another important feature. New techniques in the mathematical modelling of aquifers are introduced in this study. The growth of the dewatered region around an abstraction borehole is simulated b y a gradual change in the effective storage coefficient at nodal points on the finite-difference grid. Modifications to standard techniques were also required to represent the long period over which gradual changes in the aquifer conditions have occurred. Finally, it was helpful to devise a new m e t h o d of presenting information a b o u t the flow balance in the confined region. ESSEX CHALK AQUIFER
The area under consideration, which is shown in Fig. 1, includes the catchments o f the Rivers Chelmer, Pant and Colne while to the south it extends to the Thames estuary. The surface topography dips generally from the northwest to the south and southeast at a gradient of ~ 1 . 5 m km -1 . The river valleys are ~ 40--45 m below the level of the intervalley areas. N
S, ud, Aroa bounded b ~ ; ~ ~ ~ ' ~ oashed ine ~ "
~"
x__~~' .;^ ''=~r \."--~.C," Colne
~__ ~," ",~COiCHESTER ~ . ~
~
ef X-.../ .J'-2,-'-,d" \
, f-"E. _.j ~ C ;
kt '~ \
,n-v-~
_ j~"
"\ J ...... groundwaterhead
~-;
contourslmJ
"-x)-/-
"'a0 _ _
~
0
10
20
Fig. 1. Details of the Essex Chalk c a t c h m e n t and a l o c a t i o n plan.
Km
145
Hydrogeology A brief description of the hydrogeology of the area is given below; a much fuller account is presented b y Lloyd et al. (1981). The area lies in a major syncline with an east--west main axis. Cretaceous strata outcrop in the north and b e y o n d the b o u n d a r y of the study area in the south. Tertiary strata o c c u p y the core of the syncline and are present everywhere except in the far north of the area where the Cretaceous outcrops. Superficial deposits consisting of muds, silts, sands, gravels and clays cover much of the solid strata throughout the area. A generalised NW--SE section through the catchment is shown in Fig. 2. The Boulder Clay, which is of glacial origin, is an unstratified clay containing stones which are mainly chalk and flint. Streaks and lenses of sand, gravel and loam are intercalated within the mass of the Boulder Clay. The presence of stones, sands and gravels means that the permeability is inhomogeneous thereby allowing some percolation of water. The thickness of the boulder clay varies significantly with a maximum of 30 m in the intervalley areas. Glacial Sands and Gravels generally lie under the Boulder Clay and rest directly on the solid formations. In most of the river valleys in the outcrop area, the Boulder Clay has been removed b y erosion and the Glacial Sands and Gravels are bare. Elsewhere, water that percolates through the Boulder Clay, flows through the Glacial Sands and Gravels towards the river valleys; even in the summer this flow is maintained. The L o n d o n Clay is a stiff clay containing a number of more or less continuous layers of a clayey limestone. In general, the beds of the L o n d o n Clay dip very gently southwards with a m a x i m u m thickness of 70 m; in the Braintree area the thickness is ~ 4 0 m. Being a stiff clay formation, movement of water through the pores is prevented and therefore it is generally regarded as an impervious formation. Underlying the L o n d o n Clay are the Lower L o n d o n Tertiaries. They consist of clays, silts, loams and sands b u t the actual composition is extremely variable. In thickness they vary from 10 to 30 m. Though the Lower L o n d o n Tertiaries are poor aquifers in the sense that the boreholes do not produce a good yield, nevertheless t h e y do contain water which can be withdrawn slowly b y dewatering. Therefore, their specific yield of ~ 0.05 can be significant when local dewatering takes place. -
~ --I
~
A
l
l
u
v
i
u
r
n
A
~_~ndon
Clay
I
Lower
London
Tertiaries
'
-~ , , ,
0
Fig. 2. Generalised section o f the c a t c h m e n t .
10
,~,
~ , ~, , 2i0 km
"
146 The chalk is a mainly soft fine-grained fissured limestone; the total thickness is ~ 2 5 0 m. Little movement of water occurs through the solid chalk b u t the presence of fissures, which generally coincide with bedding planes or joint systems, allows water to flow. Water passing through the chalk fissures dissolve some of the calcium carbonate thereby increasing the size of the fissures. Pumping tests indicate that in the valley areas the chalk transmissivity is of the order of 250 m 2 day -1 b u t in the intervalley areas it is less than 20 m: day -1 (Woodland, 1946). The specific yield is taken to be 0.02.
Aquifer mechanism Natural recharge occurs over the region to the north of the L o n d o n Clay boundary. The magnitude of the recharge is influenced by the Boulder Clay cover and b y the conditions within the confined region of the aquifer. Recharge that cannot be accepted b y the confined aquifer finds its way directly into streams or b y upward leakage through the L o n d o n Clay close to its northern limit where the thickness is small. Most of the abstraction from the Chalk occurs in the confined region. Initially boreholes were sited in towns and in the vicinity of industrial sites. More recently, boreholes for public water supply have been sited in river valleys principally because the Chalk transmissivity is higher in these valleys. Abstraction of water from the Chalk aquifer started around 1850. The borehole at Notley Road, Braintree, was completed in 1854 and yielded a supply of 0.25 M1 day -1 . In 1950 the estimated abstraction reached 15M1 day -1 from 46 boreholes. There was a rapid increase in the next few years and in 1976 the abstraction rate reached 26 M1 day -1 . This increased abstraction has caused a serious decline in the water levels. Fig. 6 shows that at Notley Road the decline b e t w e e n 1860 and 1950 was over 40 m. There was some recovery in the next 20 years followed b y a further serious decline in the 1970's. This decline was mirrored in other boreholes and it was considered that at some stage the yield of the aquifer system could fall off rapidly. Therefore, the purpose of the study is to understand the aquifer response since 1860 and, in particular, to examine the reasons for the serious decline in water levels.
Sources of borehole data Reliable long-term data a b o u t water levels and abstraction data are essential for an adequate analysis. Systematic records of abstraction rates and groundwater levels are currently collected b u t information concerning earlier periods must be deduced from the sparse records. Records were frequently made of the rest and p u m p e d levels at the time when the borehole was constructed. Occasional records of the subsequent borehole water levels axe also available. Estimates can be made of the likely abstraction rates b y noting when the borehole was deepened, new pumps
147
installed or additional boreholes drilled nearby. In this way an acceptable picture of the abstraction pattern from the aquifer can be built up. One feature that often causes some difficulty is that groundwater heads in pumped boreholes are quoted either as pumped levels or rest levels. The pumped level includes the effect of the seepage face in unconfined aquifers and is therefore below the aquifer level given by the numerical model. On the other hand, the rest levels, which are usually taken after the pump has been switched off for an hour or so, correspond to an incomplete recovery and may be higher than the levels given by the numerical model. Consequently, the numerical model results should usually lie between the pumped and rest field levels.
Recharge In estimating the recharge to the aquifer account must be taken of the influence of the Boulder Clay cover in the outcrop region and also the ability of the confined region to accept the recharge. A routing model has been devised to represent the various flow paths through the Boulder Clay and the Glacial Sands and Gravels (Senarath and Rushton, 1983) and allows an estimate to be made of the time variant recharge to the unconfined region. Distribution factors between the various flow paths are estimated by means of a sensitivity analysis and delays in the transfer of water are deduced from one-dimensional numerical solutions. The limited quantity of water that can be accepted by the confined region is also incorporated in the routing model. Comparisons between the predicted and field values of the river hydrographs at the point where the river starts to flow over the boulder clay are used as the objective functions for assessing the adequacy of the routing model. In the routing model, the whole outcrop region is idealised as one typical cross-section, yet, despite such limitations, adequate agreement can be obtained between the model and the field stream hydrograph. This agreement was achieved when the effective recharge was ~20% of the recharge as calculated by the conventional recharge calculation based on the approach of Penman (1949) and Grindley (1969) using soil moisture deficits and the difference between precipitation and actual evaporation.
MATHEMATICAL MODEL
One of the most useful methods of attempting to understand aquifer behaviour is by means of a mathematical model. The flow of water through the aquifer is described by a differential equation. To specify a particular problem such as the North Essex Chalk it is also necessary to define boundary and initial conditions and make special modifications for features such as local dewatering around an abstraction well.
148
Since the main purpose of the study is to investigate the dewatering in the vicinity of Braintree, the modelled area is restricted to the areas which influence the groundwater flow in the Braintree area. The part of the aquifer considered is therefore as shown in outline in Fig. 1 and in detail in Fig. 3. To the north and east the area extends to a groundwater divide or to a zone of very low transmissivity. To the west a boundary is chosen which coincides with a flowline as deduced from the groundwater contours. The eastern b o u n d a r y is taken along an intervalley region where the transmissivity is low. This line of the intervalley region is n o t precisely at right angles to the groundwater contours; such an occurrence is not unexpected since in a region of varying transmissivity the flow lines are n o t necessarily at right angles to lines of equal groundwater head (Rushton and Redshaw, 1979). The boundary to the south is poorly defined physically. Groundwater levels in the Maldon area have been falling steadily yet there is evidence that in the early 19th century the groundwater heads were significantly above sea
of Lower i'ertiaries
lit of ~Clay
Fig. 3. Details of the numerical model.
149 level suggesting that originally there was a flow towards the sea. Therefore, because detailed information is n o t required in this area, the b o u n d a r y is represented as a line of zero head along the Thames estuary. Transmissivity values were deduced from pumping test analyses. In the valley areas the transmissivities exceed 250 m 2 day -1 b u t in the intervalley areas they are 20 m 2 day -1 or less (Woodland, 1946). A confined storage coefficient of 2.5 • 10 -s is deduced from the pumping tests. Fig. 3 shows the mesh subdivision selected to represent the aquifer. The mesh spacing of 2 km is just adequate provided that corrections are made for the radial flow towards boreholes as described below. A backwarddifference finite-difference approximation to the governing differential equation is used; the resultant simultaneous equations are solved b y the iterative point successive over-relaxation method. This m e t h o d is particularly useful when including non-linear effects such as intermittent springs and localised dewatering around the abstraction sites. Initial conditions The representation of initial conditions is important in most aquifer simulations. It is advisable to start a simulation from the time when the aquifer was in a state of equilibrium. For this particular aquifer gradual changes in the aquifer conditions have occurred since 1860 and therefore it is necessary to use the conditions existing in the mid 1800's as initial conditions. To represent the conditions in 1860 the recharge to the unconfined region is taken as the average value deduced from the routing model. Before significant abstraction occurred, much of this recharge could not flow into the confined region and so it flowed o u t of the aquifer system through springs and the bed of streams at positions as indicated in Fig. 3. Some water also escaped from the aquifer through thin layers of the L o n d o n Clay into the beds of the rivers Pant and Colne. The magnitudes of these outflows are thought to have decreased as the abstraction from the confined region increased; since 1950 these outflows became very small. By enforcing these conditions a reasonable representation of the historical aquifer response becomes possible. Time steps Representation of over 100 years of aquifer behaviour can make heavy demands on computing time. For the modelling of recent years a detailed solution is warranted since information is available with which comparisons can be made. In the period prior to 1950, the basic requirement is that the flow balance should be adequately represented. This can best be achieved b y obtaining solutions in terms of decades. Rather than changing the time step an alternative approach is to artificially reduce the storage coefficient to one-tenth of its normal value so that each year in effect represents a decade.
150
For the modelling of the period from 1970 onwards, normal values of storage coefficient are used with each month divided into three time steps. Confined--unconfined
change and dewatering
The importance of modifying the storage coefficient when the aquifer conditions change from the confined to the unconfined state has been discussed by Rushton and Wedderburn (1971) and Prickett (1975). Numerical model solutions incorporating this change have been described by Prickett and Lonnquist (1971) and Oakes and Skinner (1975) amongst others. In these studies the storage coefficient at a nodal point changes suddenly as the groundwater head falls below the confining layer. Though this approach is often acceptable when an overall lowering of the water table occurs, it is unacceptable when dewatering only occurs in the vicinity of an abstraction well. In the study of the Essex Chalk, the problem is complicated further by the fact that water is released from storage from both the Lower London Tertiaries and the Chalk. Consider a nodal point which represents an abstraction borehole such that the groundwater head close to the borehole is below the confining layer, but the groundwater head at some distance from the well is above the confining layer. This situation can be included in a numerical model by modifying the storage coefficient. Fig. 4 illustrates the situation of a groundwater head profile which crosses the base of the confining layer at a radius rc ; the elevation of the confining layer above datum is zc. Before considering the modifications due to the presence of the confining layer, allowance in the regional groundwater simulation must be made for the fact that the standard finite-difference approximation does not account for the radial flow towards a well. Both Rushton and Herbert (1966) and Prickett (1967) showed that a correction must be made to account for the radial flow towards a well. Assuming a constant saturated thickness, the equation for radial steady-state flow towards a well is: h a --h 0 = (Q/2~T) ln(ra/ro)
(1}
where ha and h 0 are groundwater heads at radial distances ra and r0, respectively. If h a is the average head at a distance Ax from the well, then: h a -- h o = ( Q / 2 ~ T ) l n ( A x / r o )
The next step in the derivation is to deduce the equivalent radius represented by the nodal point of a standard finite~lifference mesh. The governing differential equation (Rushton and Redshaw, 1979} is:
where q is the inflow per unit area.
151
i'r° 1 J ~, I
oJ
z/
(a)
/
I
datum h2
FI I
l-
OI
t h3
(b)
I
o t
I
1
I
0.5Ax
0-5Ax
1
I I _[~.
h4 t-
Ax
~,
/~x
Fig 4. Dewatering in the vicinity of an abstraction well.
For a square mesh when Ax = Ay and with constant transmissivity, the governing differential equation can be written in finite-difference form as: 4 (hn - - h o )
=
Q/T
(2)
n=l
where Q, the total discharge from node 0 equals - - q A x A y . The mesh positions are indicated in Fig. 4b. Taking the average o f heads h 1, h2, h3 and h4 as ha, eq. 2 can be rewritten as: h a --h o =
0.25Q/T
(3)
Combining eqs. 1 and 3 shows that when the standard finite-difference mesh is used in a region where the flow is radial, the equivalent radius of the mesh point is:
152
r0 = exp(--0.5u)Ax = 0.208Ax
(4)
This is illustrated in Fig. 4a which shows that the head h 0 as obtained from a standard finite-difference solution refers to a distance r 0 from the axis of the well. If a finite-difference mesh of i km is used the head h 0 at an abstraction well node actually represents the groundwater head at a distance of 208 m from the axis of the well. For the next step in the derivation, eqs. 1 and 4 can be used to show that the groundwater head on the face of a well of radius rw is: hw
= ho - - ( Q / 2 n T ) l n [ e x p ( - O . 5 n )
Ax/r w ]
= ho - - ( Q / 2 n T ) l n ( O . 2 O S A x / r w )
(5)
A similar procedure can be used to deduce the radius, re, at which the groundwater head coincides with the underside of the confining layer (Fig. 4a). At this radius the groundwater head equals the elevation of the confining layer, zc, thus: Zc -- ho = ( Q / 2 n T ) l n ( r c / r o ) or
rc = ro e x p [ ( 2 7 r T / Q ) ( z ¢ - - h o )
] = 0.208Ax exp[(21rT/Q)(z c --h0) ]
(6)
Provided that r c is less than 0.5Ax, an "effective storage" coefficient can be defined as ( a ) a n area 7rr~ with unconfined storage coefficient Su ; and (b) the shaded area of Fig. 4b which equals Ax 2 -- rr~ at the confined storage value of S¢. Hence the effective nodal storage coefficient is: 1 S -
Ax2[~r~Su
+ (Ax 2 -- 7rrfc)S~]
(7)
This derivation is based on steady-state equations. Nevertheless, because of the discrete time step used in finite-difference solutions, the time variant solution can be considered as a series of steady-state solutions. Consequently, the radius to the confined region is recalculated at each time step and the new effective storage coefficient, deduced from eq. 7, is incorporated in the finite-difference solution for the following time step. The validity of this approach has been checked by comparing a simulation using a square finite-difference grid with the storage coefficient modified according to eq. 7 and a more detailed and accurate solution, using the time variant radial flow numerical model (Rushton and Redshaw, 1979). This shows that even when a rectangular mesh of 2 km is used, the radius at which conditions change from confined to unconfined according to eq. 6 never differs by more than 20 m from the value given by the radial flow model. In the particular problem of the Essex Chalk aquifer there are two regions t h a t can be dewatered; initially water drains from the Lower L o n d o n Tertiaries b u t when the water table falls still further, part of the Chalk can be dewatered. Following Fig. 5, the radius, rL, where the drawdown curve
153 Stora0e Coefficient
ro=0r.2L0 8~,•
/~nfined
-1
RTIARIES
"~
unconfined S L
zL ho
CHALK
unconfined ScH
IZc I
i Datum
m
Vertical
_
Section
ewatered area within the ower London Tertiaries
ewatered area within the Chalk
Plan
Fig. 5. Dewatering in the Lower London Tertiaries and in the Chalk. intersects the interface of the base of the L o n d o n Clay and top of the Lower L o n d o n Tertiaries is: r L = 0.208 Ax exp
[(27rT/Q)(z
L --
h0) ]
(8)
Eq. 6 gives the radius where the water table intercepts the top of the Chalk. Consequently, the effective storage coefficient becomes: S -
1 Ax: [~(r~ --r~)SL + 7rr~ScH + (Ax 2 --~r~)S¢]
(9)
where SL is the specific yield of the Lower London Tertiaries; ScH is the specific yield of the Chalk; and Sc is the confined storage coefficient of the aquifer system. Values used in the simulation are: SL = 0.05,
ScH = 0.02
and
Sc = 0.000025
154
Since the dewatering only causes a small decrease in the saturated depth of the Chalk, it is acceptable to leave the transmissivity unchanged. Results
When all of the features described above are included in the mathematical model, detailed results are obtained which can be compared with the field data. This is a very important part of the study for the inability of the model to represent any of the reliable field data suggest that the mathematical model may not be providing a reliable representation of the actual flow mechanisms. In the early stages of the model development, considerable difficulty was encountered in representing the falling heads in the confined region. This lead to a careful rethinking of the historical behaviour of the aquifer and a review and fresh interpretation of the hydrogeological evidence. Modifications were made to the down-dip model boundaries and the representation of spring outflows. Many comparisons were made between the results of the final mathematical model and field evidence. These forms of comparison are summarised below: variation of groundwater head with time at pumped boreholes variation of groundwater head with time at observation boreholes groundwater head contours throughout the aquifer area of dewatered regions at abstraction sites groundwater components of stream hydrographs travel times of groundwater compared with evidence from hydrochemistry
Full details of all these comparisons are given in Senarath (1981); an example of a typical comparison is given in Fig. 6. Field values of pumped and rest water levels at Notley Road pumping station are shown by crosses and circles, respectively; since the numerical model results, which are shown recerdedrest I evel + pumped level
40 g
•~
rical model O
O
+
~
o
~" =
base of London Clay
~
"~/
+
"1-+
+
"1"++ =
40 1860
decades
~,1
O0
°
+
t
÷ -I-
4-
!70,71 ,72,73,74,75,76,7
1970
Fig. 6. Groundwater heads at Notley Road pumping station.
155
by the full line, generally lie between the field values the results are adequate. In the early stages of the development of the model significant differences occurred between the field and model results. All the comparisons suggested that the mathematical model provides a fair representation of the aquifer response in the confined region. However, the simulation within the unconfined region requires further refinement, particularly the interaction between streams and the aquifer in regions where abstraction sites are positioned close to streams.
FLOW BALANCE OF THE CONFINED REGION
Since the main objective of this study is to understand the nature of the dewatering in the Braintree area, it is helpful to consider how the inflows and outflows of the confined region have varied with time. The flow balance of the confined region is illustrated in Fig. 7; the quantities are average annual values expressed as M1 day-1.
10 Mltd
recharge to unconfinedaquifer Unconfined Recharge
5 0
results in decades
.~ 70 71 72 73 74 75 76 7i I
I
1970
1860
I
[
I
I
I
I
t
c----
from unconfined to confined region ~
inflow
/ release from
0
-- """
"" "-'~
~'- --i
Mild
-5 Bzlanc~aCti° e for Confined Region
"~
-10 Fig. 7. Water balance of confined region.
,---~__..~. . . . . r--~*-I
I
I
I
I
I
156
In the upper part of the figure, values are plotted of the annual estimated recharge to the unconfined region as deduced from the routing model. Prior to 1970, that is to the left of the break in the diagram, the time scale is compressed and due to lack of reliable information a uniform value is assumed for the recharge. For the period 1970--1977, significant changes occurred in the annual recharge values. The lower part of Fig. 7 shows the flow balance for the confined region. The components are: ( 1 ) i n f l o w from the unconfined region; ( 2 ) w a t e r released from storage in the confined region; (3) abstraction from the confined region; and (4) flow across the southern boundary. Annual values of (1), (2) and (3) are plotted in the figure, flow across the southern b o u n d a r y is n o t included since it is always less than 0.12 M1 day -1 . Despite the significant variations in recharge during the period 1970-1977, the quantity flowing from the unconfined into the confined region changes only slowly. F o r instance, the actual recharge to the unconfined region in 1974 is l l . 8 M l d a y -~ higher than for 1973, y e t the inflow from the unconfined region to the confined region only increases b y 0.2 M1 day-1. After 1910 the inflow from the unconfined region is always less than the abstraction and in the 1970's it levels off at a value of ~ 8 M l d a y -1 . However, the increasing groundwater gradient brought a b o u t b y the abstraction has increased this inflow from 1.4 M1 day -1 in 1860 to 8.3 M1 day -t in 1977. The difference b e t w e e n the abstraction and the inflow from the unconfined region is met b y water released from storage in the confined region. During the period 1970--1977, the annual values for the water released from storage show significant changes, mirroring the changes in annual abstraction. N o w that an adequate groundwater gradient has been set up between the unconfined and confined regions there should be a reliable supply of ~ 8 M1 day -1 . Provided that the confined abstraction rate does not exceed this value there should be no overall depletion in the groundwater levels in the confined region, though some local readjustments in level are likely to occur. If the abstraction rates were maintained at a value of ~ 1 2 M l d a y -1 , serious reductions in the yields of certain boreholes in the confined region are likely to occur.
CONCLUSIONS
This study has demonstrated that the occurrence of partial dewatering around abstraction boreholes as indicated b y recorded field data can be represented satisfactorily by a regional groundwater model with special modifications for the dewatering. The adequacy of these modifications has also been confirmed b y comparisons with a radial flow numerical model. The mathematical model of the Essex Chalk aquifer indicated that when the groundwater gradient towards the abstraction area is insufficient to transmit enough water to meet the abstraction demands, partial dewatering
157
takes place. The limited ability of the aquifer to transmit water also means that only a small proportion of the potential recharge is able to enter the confined region; the remainder escapes to streams in the recharge area. The mathematical model simulation which extends over a time period of more than 100 years is essential to gaining an understanding of the changes in aquifer conditions that have occurred since significant abstraction commenced. Also the method of presenting the overall annual flow balances for the confined region is invaluable in understanding the aquifer response. This method of presenting the overall flow balance also demonstrates that the amount of water supplied by dewatering is very sensitive to the changes in the groundwater gradients and variations in the abstraction rates. Consequently, a numerical model is necessary to gain an adequate understanding of the development of the dewatered region. Once a numerical model has been tested successfully, it can be used for predictive purposes. An improved utilization of the aquifer resources may be achieved by a careful selection of locations for abstraction boreholes and by controlling the abstraction rates to make a maximum use of the available resources.
ACKNOWLEDGEMENT
This work was carried out in association with the Essex River Division of the Anglian Water Authority. The authors wish to acknowledge the help and encouragement of the staff of the Essex River Division and in particular Mr. D. Harker and Mr. A. Powell.
REFERENCES Grindley, J., 1969. The calculation of actual evaporation and soil moisture deficits over specified catchment areas. Meteorol. Off. Hydrol., Bracknell, Memo No. 38. Lloyd, J.W., Harker, D. and Baxendale, R.A., 1981. Recharge mechanisms and groundwater flow in the chalk and drift deposits of southern East Anglia. Q.J. Eng. Geol. London, 14: 87--96. Oakes, D.B. and Skinner, A.C., 1975. The Lancashire conjunctive use scheme groundwater model. Water Res. Cent., Medmenham, TR 12, 36 pp. Penman, H.L., 1949. The dependence of transpiration on weather and soil conditions. J. Soil Sci., Oxford, 1: 74--89. Prickett, T.A., 1967. Designing pumped well characteristics into electrical analogue models. Ground Water, 5: 38--46. Prickett, T.A., 1975. Modelling techniques for groundwater evaluation. In: V.T. Chow (Editor), Advances in Hydroscience, Vol. 10. Academic Press, New York, N.Y., pp. 1--143. Prickett, T.A. and Lonnquist, C.G., 1971. Selected digital computer techniques for groundwater resources evaluation. Ill. State Water Surv., Bull. 55. Rushton, K.R. and Herbert, R., 1966. Groundwater flow studies by resistance network. Geotechnique, 16: 264--267.
158
Rushton, K.R. and Redshaw, S.C., 1979. Seepage and Groundwater Flow. Wiley, Chichester, 332 pp. Rushton, K.R. and Wedderburn, L.A., 1971. Aquifers changing between the confined and unconfined state. Ground Water, 9: 30--39. Senarath, D.C.H., 1981. Regional groundwater flow simulation using a numerical model including aquifer dewatering and recharge estimation. Ph.D. Thesis, University of Birmingham, Birmingham. Senarath, D.C.H. and Rushton, K.R., 1983. A routing technique for estimating aquifer recharge. Ground Water (submitted). Woodland, A.W., 1946. Water supply from underground sources of Cambridge--Ipswich District.Geol. Surv. Mus., London, Wartime Pamphlet No. 20.
143
Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
[2] A MATHEMATICAL MODEL STUDY OF AN A Q U I F E R WITH SIGNIFICANT DEWATERING
K.R. RUSHTON and D.C.H. SENARATH
Department of Civil Engineering, University of Birmingham, Birmingham B15 2TT (Great Britain) (Received January 6, 1982; revised and accepted May 8, 1982)
ABSTRACT
Rushton, K.R. and Senarath, D.C.H., 1983. A mathematical model study of an aquifer with significant dewatering. J. Hydrol., 62: 143--158. A finite-differencenumerical technique is used to study the behaviour of a Chalk aquifer in southeast England. In the neighbourhood of certain of the abstraction boreholes partial dewatering takes place due to prolonged pumping. A technique is devised for including this local dewatering in a regional model. The numerical model is used to understand the flow mechanisms within the aquifer with special emphasis on the balance between inflows from the unconfined region and water released from storage due to dewatering. The simulation covers a time period of over 100 yr.
INTRODUCTION
When increasing abstraction causes groundwater levels to show a continuing decline, there is a need to ascertain the length of time for which an adequate quantity of water may be available. This is particularly important when an aquifer, which is initially confined, becomes unconfined in the vicinity of abstraction sites. There is then a significant risk that the saturated depth in the vicinity of the abstraction sites will decrease so much that the yield of the wells will fall off dramatically. A typical example of this situation is provided b y a Chalk aquifer system in Essex. The aquifer dips from o u t c r o p at ~ 0 . 3 ° beneath the impermeable L o n d o n Clay. Before abstraction c o m m e n c e d in the confined region the flow through the confined aquifer was small. Increasing abstraction from the confined region over the past 100 years has caused an increase in the groundwater gradient and therefore in the flow from the unconfined region; yet this inflow is only ~ 7 5 % of the current abstraction rate. The additional water is provided b y localised dewatering around certain of the abstraction sites. In order to examine the future of the aquifer as a resource it is important to identify the various flow mechanisms within the aquifer and then investigate the consequences of various future abstraction patterns.
0022-1694/83/0000--0000/$03.00 © 1983 Elsevier Scientific Publishing Company
144
This paper describes a mathematical model study of this Chalk aquifer. It relies on a detailed hydrogeological study which has been carried out b y the Anglian Water Authority. The mathematical model brings together the various facets of the aquifer system and allows the different items of information to be cross-checked. Issues that are resolved include the apparent lack of balance between the recharge, dewatered volume and abstraction rate. The number of years that need to be included in the simulation is another important feature. New techniques in the mathematical modelling of aquifers are introduced in this study. The growth of the dewatered region around an abstraction borehole is simulated b y a gradual change in the effective storage coefficient at nodal points on the finite-difference grid. Modifications to standard techniques were also required to represent the long period over which gradual changes in the aquifer conditions have occurred. Finally, it was helpful to devise a new m e t h o d of presenting information a b o u t the flow balance in the confined region. ESSEX CHALK AQUIFER
The area under consideration, which is shown in Fig. 1, includes the catchments o f the Rivers Chelmer, Pant and Colne while to the south it extends to the Thames estuary. The surface topography dips generally from the northwest to the south and southeast at a gradient of ~ 1 . 5 m km -1 . The river valleys are ~ 40--45 m below the level of the intervalley areas. N
S, ud, Aroa bounded b ~ ; ~ ~ ~ ' ~ oashed ine ~ "
~"
x__~~' .;^ ''=~r \."--~.C," Colne
~__ ~," ",~COiCHESTER ~ . ~
~
ef X-.../ .J'-2,-'-,d" \
, f-"E. _.j ~ C ;
kt '~ \
,n-v-~
_ j~"
"\ J ...... groundwaterhead
~-;
contourslmJ
"-x)-/-
"'a0 _ _
~
0
10
20
Fig. 1. Details of the Essex Chalk c a t c h m e n t and a l o c a t i o n plan.
Km
145
Hydrogeology A brief description of the hydrogeology of the area is given below; a much fuller account is presented b y Lloyd et al. (1981). The area lies in a major syncline with an east--west main axis. Cretaceous strata outcrop in the north and b e y o n d the b o u n d a r y of the study area in the south. Tertiary strata o c c u p y the core of the syncline and are present everywhere except in the far north of the area where the Cretaceous outcrops. Superficial deposits consisting of muds, silts, sands, gravels and clays cover much of the solid strata throughout the area. A generalised NW--SE section through the catchment is shown in Fig. 2. The Boulder Clay, which is of glacial origin, is an unstratified clay containing stones which are mainly chalk and flint. Streaks and lenses of sand, gravel and loam are intercalated within the mass of the Boulder Clay. The presence of stones, sands and gravels means that the permeability is inhomogeneous thereby allowing some percolation of water. The thickness of the boulder clay varies significantly with a maximum of 30 m in the intervalley areas. Glacial Sands and Gravels generally lie under the Boulder Clay and rest directly on the solid formations. In most of the river valleys in the outcrop area, the Boulder Clay has been removed b y erosion and the Glacial Sands and Gravels are bare. Elsewhere, water that percolates through the Boulder Clay, flows through the Glacial Sands and Gravels towards the river valleys; even in the summer this flow is maintained. The L o n d o n Clay is a stiff clay containing a number of more or less continuous layers of a clayey limestone. In general, the beds of the L o n d o n Clay dip very gently southwards with a m a x i m u m thickness of 70 m; in the Braintree area the thickness is ~ 4 0 m. Being a stiff clay formation, movement of water through the pores is prevented and therefore it is generally regarded as an impervious formation. Underlying the L o n d o n Clay are the Lower L o n d o n Tertiaries. They consist of clays, silts, loams and sands b u t the actual composition is extremely variable. In thickness they vary from 10 to 30 m. Though the Lower L o n d o n Tertiaries are poor aquifers in the sense that the boreholes do not produce a good yield, nevertheless t h e y do contain water which can be withdrawn slowly b y dewatering. Therefore, their specific yield of ~ 0.05 can be significant when local dewatering takes place. -
~ --I
~
A
l
l
u
v
i
u
r
n
A
~_~ndon
Clay
I
Lower
London
Tertiaries
'
-~ , , ,
0
Fig. 2. Generalised section o f the c a t c h m e n t .
10
,~,
~ , ~, , 2i0 km
"
146 The chalk is a mainly soft fine-grained fissured limestone; the total thickness is ~ 2 5 0 m. Little movement of water occurs through the solid chalk b u t the presence of fissures, which generally coincide with bedding planes or joint systems, allows water to flow. Water passing through the chalk fissures dissolve some of the calcium carbonate thereby increasing the size of the fissures. Pumping tests indicate that in the valley areas the chalk transmissivity is of the order of 250 m 2 day -1 b u t in the intervalley areas it is less than 20 m: day -1 (Woodland, 1946). The specific yield is taken to be 0.02.
Aquifer mechanism Natural recharge occurs over the region to the north of the L o n d o n Clay boundary. The magnitude of the recharge is influenced by the Boulder Clay cover and b y the conditions within the confined region of the aquifer. Recharge that cannot be accepted b y the confined aquifer finds its way directly into streams or b y upward leakage through the L o n d o n Clay close to its northern limit where the thickness is small. Most of the abstraction from the Chalk occurs in the confined region. Initially boreholes were sited in towns and in the vicinity of industrial sites. More recently, boreholes for public water supply have been sited in river valleys principally because the Chalk transmissivity is higher in these valleys. Abstraction of water from the Chalk aquifer started around 1850. The borehole at Notley Road, Braintree, was completed in 1854 and yielded a supply of 0.25 M1 day -1 . In 1950 the estimated abstraction reached 15M1 day -1 from 46 boreholes. There was a rapid increase in the next few years and in 1976 the abstraction rate reached 26 M1 day -1 . This increased abstraction has caused a serious decline in the water levels. Fig. 6 shows that at Notley Road the decline b e t w e e n 1860 and 1950 was over 40 m. There was some recovery in the next 20 years followed b y a further serious decline in the 1970's. This decline was mirrored in other boreholes and it was considered that at some stage the yield of the aquifer system could fall off rapidly. Therefore, the purpose of the study is to understand the aquifer response since 1860 and, in particular, to examine the reasons for the serious decline in water levels.
Sources of borehole data Reliable long-term data a b o u t water levels and abstraction data are essential for an adequate analysis. Systematic records of abstraction rates and groundwater levels are currently collected b u t information concerning earlier periods must be deduced from the sparse records. Records were frequently made of the rest and p u m p e d levels at the time when the borehole was constructed. Occasional records of the subsequent borehole water levels axe also available. Estimates can be made of the likely abstraction rates b y noting when the borehole was deepened, new pumps
147
installed or additional boreholes drilled nearby. In this way an acceptable picture of the abstraction pattern from the aquifer can be built up. One feature that often causes some difficulty is that groundwater heads in pumped boreholes are quoted either as pumped levels or rest levels. The pumped level includes the effect of the seepage face in unconfined aquifers and is therefore below the aquifer level given by the numerical model. On the other hand, the rest levels, which are usually taken after the pump has been switched off for an hour or so, correspond to an incomplete recovery and may be higher than the levels given by the numerical model. Consequently, the numerical model results should usually lie between the pumped and rest field levels.
Recharge In estimating the recharge to the aquifer account must be taken of the influence of the Boulder Clay cover in the outcrop region and also the ability of the confined region to accept the recharge. A routing model has been devised to represent the various flow paths through the Boulder Clay and the Glacial Sands and Gravels (Senarath and Rushton, 1983) and allows an estimate to be made of the time variant recharge to the unconfined region. Distribution factors between the various flow paths are estimated by means of a sensitivity analysis and delays in the transfer of water are deduced from one-dimensional numerical solutions. The limited quantity of water that can be accepted by the confined region is also incorporated in the routing model. Comparisons between the predicted and field values of the river hydrographs at the point where the river starts to flow over the boulder clay are used as the objective functions for assessing the adequacy of the routing model. In the routing model, the whole outcrop region is idealised as one typical cross-section, yet, despite such limitations, adequate agreement can be obtained between the model and the field stream hydrograph. This agreement was achieved when the effective recharge was ~20% of the recharge as calculated by the conventional recharge calculation based on the approach of Penman (1949) and Grindley (1969) using soil moisture deficits and the difference between precipitation and actual evaporation.
MATHEMATICAL MODEL
One of the most useful methods of attempting to understand aquifer behaviour is by means of a mathematical model. The flow of water through the aquifer is described by a differential equation. To specify a particular problem such as the North Essex Chalk it is also necessary to define boundary and initial conditions and make special modifications for features such as local dewatering around an abstraction well.
148
Since the main purpose of the study is to investigate the dewatering in the vicinity of Braintree, the modelled area is restricted to the areas which influence the groundwater flow in the Braintree area. The part of the aquifer considered is therefore as shown in outline in Fig. 1 and in detail in Fig. 3. To the north and east the area extends to a groundwater divide or to a zone of very low transmissivity. To the west a boundary is chosen which coincides with a flowline as deduced from the groundwater contours. The eastern b o u n d a r y is taken along an intervalley region where the transmissivity is low. This line of the intervalley region is n o t precisely at right angles to the groundwater contours; such an occurrence is not unexpected since in a region of varying transmissivity the flow lines are n o t necessarily at right angles to lines of equal groundwater head (Rushton and Redshaw, 1979). The boundary to the south is poorly defined physically. Groundwater levels in the Maldon area have been falling steadily yet there is evidence that in the early 19th century the groundwater heads were significantly above sea
of Lower i'ertiaries
lit of ~Clay
Fig. 3. Details of the numerical model.
149 level suggesting that originally there was a flow towards the sea. Therefore, because detailed information is n o t required in this area, the b o u n d a r y is represented as a line of zero head along the Thames estuary. Transmissivity values were deduced from pumping test analyses. In the valley areas the transmissivities exceed 250 m 2 day -1 b u t in the intervalley areas they are 20 m 2 day -1 or less (Woodland, 1946). A confined storage coefficient of 2.5 • 10 -s is deduced from the pumping tests. Fig. 3 shows the mesh subdivision selected to represent the aquifer. The mesh spacing of 2 km is just adequate provided that corrections are made for the radial flow towards boreholes as described below. A backwarddifference finite-difference approximation to the governing differential equation is used; the resultant simultaneous equations are solved b y the iterative point successive over-relaxation method. This m e t h o d is particularly useful when including non-linear effects such as intermittent springs and localised dewatering around the abstraction sites. Initial conditions The representation of initial conditions is important in most aquifer simulations. It is advisable to start a simulation from the time when the aquifer was in a state of equilibrium. For this particular aquifer gradual changes in the aquifer conditions have occurred since 1860 and therefore it is necessary to use the conditions existing in the mid 1800's as initial conditions. To represent the conditions in 1860 the recharge to the unconfined region is taken as the average value deduced from the routing model. Before significant abstraction occurred, much of this recharge could not flow into the confined region and so it flowed o u t of the aquifer system through springs and the bed of streams at positions as indicated in Fig. 3. Some water also escaped from the aquifer through thin layers of the L o n d o n Clay into the beds of the rivers Pant and Colne. The magnitudes of these outflows are thought to have decreased as the abstraction from the confined region increased; since 1950 these outflows became very small. By enforcing these conditions a reasonable representation of the historical aquifer response becomes possible. Time steps Representation of over 100 years of aquifer behaviour can make heavy demands on computing time. For the modelling of recent years a detailed solution is warranted since information is available with which comparisons can be made. In the period prior to 1950, the basic requirement is that the flow balance should be adequately represented. This can best be achieved b y obtaining solutions in terms of decades. Rather than changing the time step an alternative approach is to artificially reduce the storage coefficient to one-tenth of its normal value so that each year in effect represents a decade.
150
For the modelling of the period from 1970 onwards, normal values of storage coefficient are used with each month divided into three time steps. Confined--unconfined
change and dewatering
The importance of modifying the storage coefficient when the aquifer conditions change from the confined to the unconfined state has been discussed by Rushton and Wedderburn (1971) and Prickett (1975). Numerical model solutions incorporating this change have been described by Prickett and Lonnquist (1971) and Oakes and Skinner (1975) amongst others. In these studies the storage coefficient at a nodal point changes suddenly as the groundwater head falls below the confining layer. Though this approach is often acceptable when an overall lowering of the water table occurs, it is unacceptable when dewatering only occurs in the vicinity of an abstraction well. In the study of the Essex Chalk, the problem is complicated further by the fact that water is released from storage from both the Lower London Tertiaries and the Chalk. Consider a nodal point which represents an abstraction borehole such that the groundwater head close to the borehole is below the confining layer, but the groundwater head at some distance from the well is above the confining layer. This situation can be included in a numerical model by modifying the storage coefficient. Fig. 4 illustrates the situation of a groundwater head profile which crosses the base of the confining layer at a radius rc ; the elevation of the confining layer above datum is zc. Before considering the modifications due to the presence of the confining layer, allowance in the regional groundwater simulation must be made for the fact that the standard finite-difference approximation does not account for the radial flow towards a well. Both Rushton and Herbert (1966) and Prickett (1967) showed that a correction must be made to account for the radial flow towards a well. Assuming a constant saturated thickness, the equation for radial steady-state flow towards a well is: h a --h 0 = (Q/2~T) ln(ra/ro)
(1}
where ha and h 0 are groundwater heads at radial distances ra and r0, respectively. If h a is the average head at a distance Ax from the well, then: h a -- h o = ( Q / 2 ~ T ) l n ( A x / r o )
The next step in the derivation is to deduce the equivalent radius represented by the nodal point of a standard finite~lifference mesh. The governing differential equation (Rushton and Redshaw, 1979} is:
where q is the inflow per unit area.
151
i'r° 1 J ~, I
oJ
z/
(a)
/
I
datum h2
FI I
l-
OI
t h3
(b)
I
o t
I
1
I
0.5Ax
0-5Ax
1
I I _[~.
h4 t-
Ax
~,
/~x
Fig 4. Dewatering in the vicinity of an abstraction well.
For a square mesh when Ax = Ay and with constant transmissivity, the governing differential equation can be written in finite-difference form as: 4 (hn - - h o )
=
Q/T
(2)
n=l
where Q, the total discharge from node 0 equals - - q A x A y . The mesh positions are indicated in Fig. 4b. Taking the average o f heads h 1, h2, h3 and h4 as ha, eq. 2 can be rewritten as: h a --h o =
0.25Q/T
(3)
Combining eqs. 1 and 3 shows that when the standard finite-difference mesh is used in a region where the flow is radial, the equivalent radius of the mesh point is:
152
r0 = exp(--0.5u)Ax = 0.208Ax
(4)
This is illustrated in Fig. 4a which shows that the head h 0 as obtained from a standard finite-difference solution refers to a distance r 0 from the axis of the well. If a finite-difference mesh of i km is used the head h 0 at an abstraction well node actually represents the groundwater head at a distance of 208 m from the axis of the well. For the next step in the derivation, eqs. 1 and 4 can be used to show that the groundwater head on the face of a well of radius rw is: hw
= ho - - ( Q / 2 n T ) l n [ e x p ( - O . 5 n )
Ax/r w ]
= ho - - ( Q / 2 n T ) l n ( O . 2 O S A x / r w )
(5)
A similar procedure can be used to deduce the radius, re, at which the groundwater head coincides with the underside of the confining layer (Fig. 4a). At this radius the groundwater head equals the elevation of the confining layer, zc, thus: Zc -- ho = ( Q / 2 n T ) l n ( r c / r o ) or
rc = ro e x p [ ( 2 7 r T / Q ) ( z ¢ - - h o )
] = 0.208Ax exp[(21rT/Q)(z c --h0) ]
(6)
Provided that r c is less than 0.5Ax, an "effective storage" coefficient can be defined as ( a ) a n area 7rr~ with unconfined storage coefficient Su ; and (b) the shaded area of Fig. 4b which equals Ax 2 -- rr~ at the confined storage value of S¢. Hence the effective nodal storage coefficient is: 1 S -
Ax2[~r~Su
+ (Ax 2 -- 7rrfc)S~]
(7)
This derivation is based on steady-state equations. Nevertheless, because of the discrete time step used in finite-difference solutions, the time variant solution can be considered as a series of steady-state solutions. Consequently, the radius to the confined region is recalculated at each time step and the new effective storage coefficient, deduced from eq. 7, is incorporated in the finite-difference solution for the following time step. The validity of this approach has been checked by comparing a simulation using a square finite-difference grid with the storage coefficient modified according to eq. 7 and a more detailed and accurate solution, using the time variant radial flow numerical model (Rushton and Redshaw, 1979). This shows that even when a rectangular mesh of 2 km is used, the radius at which conditions change from confined to unconfined according to eq. 6 never differs by more than 20 m from the value given by the radial flow model. In the particular problem of the Essex Chalk aquifer there are two regions t h a t can be dewatered; initially water drains from the Lower L o n d o n Tertiaries b u t when the water table falls still further, part of the Chalk can be dewatered. Following Fig. 5, the radius, rL, where the drawdown curve
153 Stora0e Coefficient
ro=0r.2L0 8~,•
/~nfined
-1
RTIARIES
"~
unconfined S L
zL ho
CHALK
unconfined ScH
IZc I
i Datum
m
Vertical
_
Section
ewatered area within the ower London Tertiaries
ewatered area within the Chalk
Plan
Fig. 5. Dewatering in the Lower London Tertiaries and in the Chalk. intersects the interface of the base of the L o n d o n Clay and top of the Lower L o n d o n Tertiaries is: r L = 0.208 Ax exp
[(27rT/Q)(z
L --
h0) ]
(8)
Eq. 6 gives the radius where the water table intercepts the top of the Chalk. Consequently, the effective storage coefficient becomes: S -
1 Ax: [~(r~ --r~)SL + 7rr~ScH + (Ax 2 --~r~)S¢]
(9)
where SL is the specific yield of the Lower London Tertiaries; ScH is the specific yield of the Chalk; and Sc is the confined storage coefficient of the aquifer system. Values used in the simulation are: SL = 0.05,
ScH = 0.02
and
Sc = 0.000025
154
Since the dewatering only causes a small decrease in the saturated depth of the Chalk, it is acceptable to leave the transmissivity unchanged. Results
When all of the features described above are included in the mathematical model, detailed results are obtained which can be compared with the field data. This is a very important part of the study for the inability of the model to represent any of the reliable field data suggest that the mathematical model may not be providing a reliable representation of the actual flow mechanisms. In the early stages of the model development, considerable difficulty was encountered in representing the falling heads in the confined region. This lead to a careful rethinking of the historical behaviour of the aquifer and a review and fresh interpretation of the hydrogeological evidence. Modifications were made to the down-dip model boundaries and the representation of spring outflows. Many comparisons were made between the results of the final mathematical model and field evidence. These forms of comparison are summarised below: variation of groundwater head with time at pumped boreholes variation of groundwater head with time at observation boreholes groundwater head contours throughout the aquifer area of dewatered regions at abstraction sites groundwater components of stream hydrographs travel times of groundwater compared with evidence from hydrochemistry
Full details of all these comparisons are given in Senarath (1981); an example of a typical comparison is given in Fig. 6. Field values of pumped and rest water levels at Notley Road pumping station are shown by crosses and circles, respectively; since the numerical model results, which are shown recerdedrest I evel + pumped level
40 g
•~
rical model O
O
+
~
o
~" =
base of London Clay
~
"~/
+
"1-+
+
"1"++ =
40 1860
decades
~,1
O0
°
+
t
÷ -I-
4-
!70,71 ,72,73,74,75,76,7
1970
Fig. 6. Groundwater heads at Notley Road pumping station.
155
by the full line, generally lie between the field values the results are adequate. In the early stages of the development of the model significant differences occurred between the field and model results. All the comparisons suggested that the mathematical model provides a fair representation of the aquifer response in the confined region. However, the simulation within the unconfined region requires further refinement, particularly the interaction between streams and the aquifer in regions where abstraction sites are positioned close to streams.
FLOW BALANCE OF THE CONFINED REGION
Since the main objective of this study is to understand the nature of the dewatering in the Braintree area, it is helpful to consider how the inflows and outflows of the confined region have varied with time. The flow balance of the confined region is illustrated in Fig. 7; the quantities are average annual values expressed as M1 day-1.
10 Mltd
recharge to unconfinedaquifer Unconfined Recharge
5 0
results in decades
.~ 70 71 72 73 74 75 76 7i I
I
1970
1860
I
[
I
I
I
I
t
c----
from unconfined to confined region ~
inflow
/ release from
0
-- """
"" "-'~
~'- --i
Mild
-5 Bzlanc~aCti° e for Confined Region
"~
-10 Fig. 7. Water balance of confined region.
,---~__..~. . . . . r--~*-I
I
I
I
I
I
156
In the upper part of the figure, values are plotted of the annual estimated recharge to the unconfined region as deduced from the routing model. Prior to 1970, that is to the left of the break in the diagram, the time scale is compressed and due to lack of reliable information a uniform value is assumed for the recharge. For the period 1970--1977, significant changes occurred in the annual recharge values. The lower part of Fig. 7 shows the flow balance for the confined region. The components are: ( 1 ) i n f l o w from the unconfined region; ( 2 ) w a t e r released from storage in the confined region; (3) abstraction from the confined region; and (4) flow across the southern boundary. Annual values of (1), (2) and (3) are plotted in the figure, flow across the southern b o u n d a r y is n o t included since it is always less than 0.12 M1 day -1 . Despite the significant variations in recharge during the period 1970-1977, the quantity flowing from the unconfined into the confined region changes only slowly. F o r instance, the actual recharge to the unconfined region in 1974 is l l . 8 M l d a y -~ higher than for 1973, y e t the inflow from the unconfined region to the confined region only increases b y 0.2 M1 day-1. After 1910 the inflow from the unconfined region is always less than the abstraction and in the 1970's it levels off at a value of ~ 8 M l d a y -1 . However, the increasing groundwater gradient brought a b o u t b y the abstraction has increased this inflow from 1.4 M1 day -1 in 1860 to 8.3 M1 day -t in 1977. The difference b e t w e e n the abstraction and the inflow from the unconfined region is met b y water released from storage in the confined region. During the period 1970--1977, the annual values for the water released from storage show significant changes, mirroring the changes in annual abstraction. N o w that an adequate groundwater gradient has been set up between the unconfined and confined regions there should be a reliable supply of ~ 8 M1 day -1 . Provided that the confined abstraction rate does not exceed this value there should be no overall depletion in the groundwater levels in the confined region, though some local readjustments in level are likely to occur. If the abstraction rates were maintained at a value of ~ 1 2 M l d a y -1 , serious reductions in the yields of certain boreholes in the confined region are likely to occur.
CONCLUSIONS
This study has demonstrated that the occurrence of partial dewatering around abstraction boreholes as indicated b y recorded field data can be represented satisfactorily by a regional groundwater model with special modifications for the dewatering. The adequacy of these modifications has also been confirmed b y comparisons with a radial flow numerical model. The mathematical model of the Essex Chalk aquifer indicated that when the groundwater gradient towards the abstraction area is insufficient to transmit enough water to meet the abstraction demands, partial dewatering
157
takes place. The limited ability of the aquifer to transmit water also means that only a small proportion of the potential recharge is able to enter the confined region; the remainder escapes to streams in the recharge area. The mathematical model simulation which extends over a time period of more than 100 years is essential to gaining an understanding of the changes in aquifer conditions that have occurred since significant abstraction commenced. Also the method of presenting the overall annual flow balances for the confined region is invaluable in understanding the aquifer response. This method of presenting the overall flow balance also demonstrates that the amount of water supplied by dewatering is very sensitive to the changes in the groundwater gradients and variations in the abstraction rates. Consequently, a numerical model is necessary to gain an adequate understanding of the development of the dewatered region. Once a numerical model has been tested successfully, it can be used for predictive purposes. An improved utilization of the aquifer resources may be achieved by a careful selection of locations for abstraction boreholes and by controlling the abstraction rates to make a maximum use of the available resources.
ACKNOWLEDGEMENT
This work was carried out in association with the Essex River Division of the Anglian Water Authority. The authors wish to acknowledge the help and encouragement of the staff of the Essex River Division and in particular Mr. D. Harker and Mr. A. Powell.
REFERENCES Grindley, J., 1969. The calculation of actual evaporation and soil moisture deficits over specified catchment areas. Meteorol. Off. Hydrol., Bracknell, Memo No. 38. Lloyd, J.W., Harker, D. and Baxendale, R.A., 1981. Recharge mechanisms and groundwater flow in the chalk and drift deposits of southern East Anglia. Q.J. Eng. Geol. London, 14: 87--96. Oakes, D.B. and Skinner, A.C., 1975. The Lancashire conjunctive use scheme groundwater model. Water Res. Cent., Medmenham, TR 12, 36 pp. Penman, H.L., 1949. The dependence of transpiration on weather and soil conditions. J. Soil Sci., Oxford, 1: 74--89. Prickett, T.A., 1967. Designing pumped well characteristics into electrical analogue models. Ground Water, 5: 38--46. Prickett, T.A., 1975. Modelling techniques for groundwater evaluation. In: V.T. Chow (Editor), Advances in Hydroscience, Vol. 10. Academic Press, New York, N.Y., pp. 1--143. Prickett, T.A. and Lonnquist, C.G., 1971. Selected digital computer techniques for groundwater resources evaluation. Ill. State Water Surv., Bull. 55. Rushton, K.R. and Herbert, R., 1966. Groundwater flow studies by resistance network. Geotechnique, 16: 264--267.
158
Rushton, K.R. and Redshaw, S.C., 1979. Seepage and Groundwater Flow. Wiley, Chichester, 332 pp. Rushton, K.R. and Wedderburn, L.A., 1971. Aquifers changing between the confined and unconfined state. Ground Water, 9: 30--39. Senarath, D.C.H., 1981. Regional groundwater flow simulation using a numerical model including aquifer dewatering and recharge estimation. Ph.D. Thesis, University of Birmingham, Birmingham. Senarath, D.C.H. and Rushton, K.R., 1983. A routing technique for estimating aquifer recharge. Ground Water (submitted). Woodland, A.W., 1946. Water supply from underground sources of Cambridge--Ipswich District.Geol. Surv. Mus., London, Wartime Pamphlet No. 20.