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(Description of poster presented at International Conference on Analytic-based Modeling of Groundwater flow, 7-10 April 1997, Nunspeet, The Netherlands. Slightly adapted version)


by P.R. Nienhuis
Eerste Oosterparkstraat 183, 1091 HA Amsterdam, The Netherlands. E-mail:


A description is given of the analytical multiaquifer model code MLPU. The program is capable of simulating groundwater flow in systems of up to nine aquifers, each aquifer being homogeneous and of infinite extent. Two options for background flow are provided. An example of the use of the model is given.


In many local-scale groundwater investigations like groundwater pollution studies, quick insight is required in the horizontal and vertical groundwater flow situation and in the effects of vertical hydraulic heterogeneity of the aquifer system. In addition, there is often need to get exploratory insight in the effects of e.g. well emplacement on the local 3D groundwater flow. Modeling tools used for this purpose should allow rapid and easy adaptations to new data and/or new insights and so contribute to the efficient design of additional data collection strategies and to efficient setup of more complex numerical models.

Analytical groundwater model codes are especially useful in such cases because of (1) the relatively easy setup (2) the relatively rapid calculations and (3) incorporation of boundary conditions in a less explicit and therefore sometimes more flexible way when compared to numerical models. However, most of the available analytical model codes can handle only one single aquifer. Currently available analytical multiaquifer model codes are either too costly for quick and simple models or suffer from undue hardware demands or discouraging data input/visualization procedures. Another issue is that background flow, treated on local scales, is not easily and/or satisfactory incorporated in analytical multiaquifer groundwater models.

Multiaquifer model code MLPU

MLPU is a relatively simple and interactive, user-friendly multi-aquifer groundwater model for steady-state and transient groundwater flow with modest memory requirements. It is especially designed for use as (1) "exploratory" model (2) pre-model before setting up a more complex numerical model or (3) a learning tool to gain general insight in multi-aquifer groundwater flow. In addition, hydraulic parameters can be optimized given sufficient head measurements and proper aquifer scheme and boundary conditions. MLPU employs superposition of various analytical solutions cf. the AEM (Strack, 1989). The following multiaquifer analytical elements are implemented: (1) Wells screened in any aquifer, using the solution of Hemker (1984); (2) Circular recharge ponds, using solutions of Hunt (1985) and Strack (1989); (3) Recharge in an infinite strip, using a solution of Hunt (1985); (4) Linesinks using the solution for single aquifers of Strack (1989) and for multiaquifer systems employing numerical integration of the well solution of Hemker (1984); (5) transient wells using a solution of Hemker and Maas (1987). In case of wells or linesinks with unknown discharge, extra reference heads are needed, one for each unknown discharge. Although most of the implemented analytical solutions are only valid for semi-confined multi-aquifer flow, unconfined multi-aquifer flow can be modeled too, provided the relative change in saturated thickness of the upper aquifer across the modeled domain remains limited.


Background flow on a local scale is actually caused by hydrological phenomena operating on a much larger scale than the problem at hand. Depending on the actual situation it can be an obvious step to model this background flow as being completely independent of the local scale phenomena to be simulated. For a single-aquifer model, simply adding a proper uniform flow component to the groundwater flow induced by local scale phenomena like wells etc. will do.
Background flow in multiaquifer analytical models is more complicated: in each aquifer the background flow can have a distinct strength and direction and vertical cross-flow between adjacent aquifers may be considerable. There are two alternatives: (1) explicit modeling of the background flow component with regard to both strength and direction separately in each aquifer ("uniform flow"), ignoring the so induced vertical groundwater exchange between adjacent aquifers, or (2) assuming parallel background flow in all aquifers and properly taking into account the vertical groundwater exchange through aquitards caused by background flow. Depending on the local situation, vertical water balance errors associated with modeled uniform flow may be acceptable. In case of parallel flow, heads in all aquifers are specified at two reference points which lie on the same flowline if only background flow is considered. One reference point lies upstream and the other one downstream of the area of interest. Both horizontal and vertical background flow components in each aquifer can then be computed for every location in a strip between the reference locations.


In MLPU the uniform flow option is implemented straightforwardly following Strack (1989). For parallel flow use is made of a solution of Hemker (1994) based on eigenvalue analysis (Hemker, 1984):

h = V.D-1.r + V.D.s + c

where h is a vector containing the computed heads in all aquifers, V is a matrix depending on the hydraulic properties of the aquifer system, D is a diagonal matrix of order m with entries exp(x.wi2), m is the number of aquifers, x is relative position between the reference points, wi-2 are leakage factors of the aquifer system, r and s are vectors containing information on D, the reference heads and geometry of the situation, and c is a vector depending on boundary conditions. One of the reference heads also serves as reference head for all other analytic elements.
In case of parallel background flow a distinction has to be made between calibration ("actual" situation) and simulation ("future" situation after adding capture wells etc.). Vectors r and s are computed during the calibration stage after subtracting the influence of all other modeled analytic elements from the heads at the reference locations. Once these vectors are known, their values have to be fixed during the ensuing simulation stage. An obvious way is to choose a new reference head location on the bisectrix of the line connecting the original reference locations, sufficiently far away from the actual modeling domain (point c in fig. 1). (In semi-confined systems no relocation is needed.)
In case of modeled wells or linesinks with unknown discharge, MLPU is able to compute vectors r and s and the unknown discharges during the calibration stage of parallel background flow.


The example refers to a case of groundwater pollution in a small village in the province of Overijssel, The Netherlands. MLPU was used for preliminary setup of a remediation system; detailed design was to be carried out with a numerical model code later on. Because emphasis is laid here on the use of MLPU rather than the problem itself, the site description is limited to what is needed for explanation of the graphs. The aquifer at the site has a thickness of about 140 m and is covered by about 10 m of glacially pushed till; the piezometric level lies at about or just below the base of this till. The groundwater flow at the site of interest is dominated by the nearby water supply pumping station of 4.5 x 106 m3/a, with wells screened deeper than about 45 m below surface level. Due to the location of these wells in a long row, the groundwater flows more or less uniformly towards the wells. The polluted plume is found in the upper 35 m of the aquifer (fig. 2B). It was intended to try to incorporate two already emplaced interception wells in the design of the remediation system. The aquifer was provisionally schematized as 4 subaquifers separated by layers representing the vertical resistance of a representative depth range of the subaquifers. Five streamlines (labeled a-e) traced upstream from the interception wells are shown in plan view (fig. 2A) and cross-section (fig. 2B). In the modeled situation, these streamlines envelope the plume. The undulating streamline pattern seen in cross-section is caused by the locally dominating influence of injection and abstraction wells.


A simple analytical multi-aquifer model code has been developed which allows easy and rapid modeling of local scale groundwater flow problems.


Hemker, C.J., 1984. Steady groundwater flow in multiple leaky aquifer systems. J. Hydr. (72) p.355-374
Hemker, C.J., 1994. Personal communication
Hemker, C.J. and C. Maas, 1987. Unsteady flow to wells in layered and fissured aquifer systems. J. Hyd. (90), p.231-249
Hunt, B., 1985. Solutions for steady state groundwater flow in multi-layer aquifer systems. Tr. Por. Med. 1, p.419-429
Strack, O.D.L., 1989. Groundwater Mechanics. Prentice-Hall, NJ, 675 pp

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Figure 1: Modeling parallel background flow. (A): Principle; (B): Relocating reference point to C for simulation

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Figure 2A: Plan view of modeled area with wells, pollution plume and computed streamlines. Dashed: approximate plume limit

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Figure 2B: Cross-section A-A' across modeled area with streamlines

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