**2.2. Groundwater water model**

Channels with a very low slope are modeled as water storage. The level dependent upper bound for the channel outflow is derived from a steady state level-flow relation like e.g. Chezy-Manning friction formula and is directly added as constraint to the optimization

The Structure of the Beijing water supply system is shown in Fig. 2. Firstly, there are the four main reservoirs Miyun, Huairou, Baihebao and Guanting. Further sources are groundwater storages and water transfers. Secondly, there are the water transportation systems such as channels and rivers. Miyun reservoir and Huairou reservoir are connect‐ ed to Beijing by the Miyun-Beijing water diversion. In the simulation model the arrows describe hydraulic behavior of water flow. Baihebao and Guanting reservoir are connect‐ ed by tunnel and river Guishui. From Guanting water runs into the Yongding river wa‐ ter diversion system to Beijing. Existing retention areas for flood control are also

The surface water from channels and rivers is delivered to the customers in different ways, directly or through the surface waterworks. Groundwater is distributed to the customers through ground waterworks as well as motor-pumped wells. Therefore, the waterworks build the third part of the Beijing water supply system. The last category is made up of all the customer groups (agriculture, industry, households and environment). To complete up the cycle, catchments area models are integrated in the system to take into account precipita‐

problem.

considered in the simulation model.

26 Water Supply System Analysis - Selected Topics

tion and evapotranspiration.

**Figure 2.** Structure of the Beijing water supply system

The most important water resource in the considered area is groundwater that is modeled by a dynamic spatially distributed finite element groundwater model. The governing equa‐ tion for groundwater flow is Darcy's law [6] describing slow streams through unconfined aquifers. Combining Darcy's law with mass conservation yields the partial differential equa‐ tion (4) which is a diffusion equation.

$$\mathbf{S}\_0 \dot{\mathbf{h}} - \nabla \cdot \left( \mathbf{k}\_f \nabla \mathbf{h} \right) = \mathbf{Q}\_{rech} - \mathbf{Q}\_{\text{expl}} \tag{4}$$

In (4) denotes *h* the hydraulic head (which corresponds to the groundwater level) and *kf* the hydraulic conductivity that governs the hydrogeological properties of the soil. S0 denotes the specific storage coefficient. The terms on the right hand side of (4) summarize all sources and sinks that coincide with the time dependent groundwater exploitation due to industry, households and agriculture (Qexpl) and recharge e. g. due to precipitation and irrigation (Qrech) in Ω.

The partial differential equation (4) is an initial-boundary value problem which has to be solved numerically for *h* in the 3 dimensional model domain Ω. The groundwater model has been implemented using FEFLOW, which is a Finite Element (FEM) software specialized on subsurface flow [7]. The initial condition is h (Ω,t0) (groundwater surface) at the initial time t0. The inflow/outflow is described by Dirichlet boundary conditions, i.e. h (∂Ω) at the boun‐ dary ∂Ω and by well boundary conditions, that define a particular volume rate into or out of Ω. The advantage of the latter one is that they are scalable. The 3D FEM model consists of more than 150,000 nodes, distributed on 25 layers (cf. Fig. 3). Huge computational costs re‐ sult from this high resolution. The simulation of 5 years needs ~15 Minutes on an Intel Core 2 Duo CPU (2.5 GHz). Hence it is very time consuming to calculate optimal water allocation strategies with the 3D FEM groundwater model. This is the motivation for model reduction (see subsection 2.3).

The main task with respect to the groundwater model is the parameterization of the largescaled model covering an area of 6,300 km². On the one hand the time independent soil pa‐ rameters kf , S0 have to be estimated and generalized for the whole domain Ω by a (small) set of measured values. On the other hand the source / sink terms Qexpl, Qrech have to be calculat‐ ed time dependent. For these calculations time dependent maps of precipitation and water demand are needed. The water demand is splitted into the three user groups households, industry and agriculture (see [8] for details). This parameterization issue is supported by powerful geographical information systems (GIS).

mogeneous. Regions of high abundance and high yielding porous groundwater aquifers are the piedmont plains and the northeastern districts of Miyun, Huairou and Shunyi whereas less yielding aquifers are found in the Yangqing and Tong districts. In the transition zone from the Taihang Mountains to the NCP the quarternary sediments with low thickness of e.

Model Based Sustainable Management of Regional Water Supply Systems

http://dx.doi.org/10.5772/51973

29

In the mountainous districts unstable groundwater distributions were assumed in depend‐ ence on the form of the rocks with geological discontinuities (fractures, joints, dissolution features) and the groundwater flow. In the transition area from the Taihang and Yanshan Mountains to the NCP stratigraphic sequences of various ages ranging from archaean meta‐ morphic rocks to quaternary are documented in the geological and hydrogeological maps. A detailed description of the geological and hydrogeological conditions can be found in [10]. On the base of a conceptual geological model and a structured horizontal (2D) groundwater model, a horizontal and vertical structured 3D - groundwater model was developed describ‐ ing the saturated zone till approx. 200 m depth below ground surface (bgs.) in the area of the quaternary sediments of the NCP. In addition the borehole data from approx. 125 drill‐ ings situated in the model area were used in the groundwater model. Although a quite ho‐ mogeneous distribution of the boreholes was given, one measurement point represents an

which is only a rare database for modelling subsurface conditions.

There can be found strong variations in structure and thickness of the loose stratum sedi‐ ments in the model area. The evaluation of all data (borehole data, geological and hydrogeo‐ logical maps and profiles, ground water levels from observation wells, literature etc.) shows that the large number of the water bearing layers can be summarised in up to three essential ground water aquifers according to present knowledge on regional level. These aquifer sys‐

The aquifers are separated by less permeable layers or aquitards, above all fine sands, silts and clays. It can be assumed that the three essential aquifers are not completely independent from each other, i.e. a groundwater exchange takes place between them in a certain range. Where low permeable layers or aquitards are absent or have a low thickness two aquifers can form a hydraulic unity as in the area of piedmont plains. Thus in the piedmont plains only one porous aquifer between the unsaturated loess top set layers and the bedrock was assumed. In regions, in which the separating layers have bigger thickness and larger exten‐ sion, local confined aquifers can appear. Because of morphology and evolution processes perched aquifers can appear within the loess deposits. All these local effects are summarised

The piedmont areas of the Taihang Mountains and the Yanshan Mountains along the western boundary and the northern/northeastern boundary of the area are the areas where groundwater inflow into the plains contributes to the groundwater recharge of the

g. some tens of meters are lying on the older rock formations of the regions.

area of about 50 km2

tems are from top to down:

**•** Aquifer I: Shallow aquifer in approx. 5 m to 30 m depth bgs.

**•** Aquifer III in the depth area of approx. 120/140 m to 200/260 m bgs

**•** Aquifer II: Primary aquifer, till approx. 120 m depth bgs.

in the above mentioned three essential aquifers.

**Figure 3.** Mesh of the 3D Finite Element groundwater model of the region of Beijing
