Introduction of MODFLOW Yangxiao Zhou [email protected] General Information • Developed by McDonald & Harbaugh of the USGS, in 1983 • Public Domain available in 1988 • Block-Centered, 3D, modular structural, finite difference groundwater flow model • Most widely used groundwater flow model • Steady-state or transient saturated flow in porous medium • Currently MODFLOW-2000 and MODFLOW-2005 are used • MODFLOW 6 is recently released in 2017 • Download site: https://water.usgs.gov/ogw/modflow/ Mathematical model 3D groundwater flow in the saturated heterogeneous and anisotropic porous media: ∂ ∂h ∂ ∂h ∂ ∂h ∂h ( Kxx ) + ( K yy ) + ( Kzz ) −W = Ss ∂x ∂x ∂y ∂y ∂z ∂z ∂t where: -1 Kxx, Kyy, Kzz = values of hydraulic conductivity along xyz axes (LT ) h = total head (L) W = Sources and sinks (T-1) -1 Ss = Specific storage (L ) t = time (T) Finite Difference Model Model grid: • Rows, columns, layers • Count from the upper left corner • At the centre point of each cell (called a "node" ), groundwater head is to be calculated Finite Difference Model Model grid: • Block-centred grid • Horizontal grid: rectangular cell varies with size Finite Difference Model Model grid: • Block-centred • Vertical layers: layer thickness varies • Avoiding very thin layer MODFLOW flowchart The period of simulation is divided into a series of "stress periods" within which specified stress data are constant. Each stress period, in turn, is divided into a series of time steps. For each time step, the finite difference equation is formulated and solved numerically. When the solution is converged, results (head, water budget) are saved. MODFLOW packages • Basic • Changing Head Boundary • Flow Package • General Head Boundary – BCF • Horizontal Flow Barrier – LPF – HUF • Stream-Aquifer Interaction • River • Solvers • Drain • PCG • Well • SIP • Recharge • Output Control • Evapotranspiration MODFLOW Basic Package (BAS) Functions: • Discretization of model domain; • Selection of major options and the designation of their input unit numbers; • Specifying initial and boundary conditions, and • Discretization of time. MODFLOW Basic Package (BAS) Definition of model grids and boundaries • Number of rows, columns and layers • Cells outside model domain are marked as inactive • Cells inside model domain are marked as active • Cells with constant head are marked as constant head • Controlled through IBOUND array MODFLOW Basic Package (BAS) Definition of stress periods and time steps • Simulation time is divided into stress periods • The values of transient stresses are constant at each stress period • Each stress period is further subdivided into time steps. MODFLOW Basic Package (BAS) Initial heads • Provides initial set of heads for iterative solver • Defines head values at specified head cells • Provide initial conditions for transient modelling • Typical approaches – Assign a constant value or land surface elevation for the steady-state model – Interpolate from scatter points of measured values for the transient model – Use head solution from the steady-state model for the transient model MODFLOW Flow Package (BCF) • Each layer is assigned a layer type – Type 0: Confined layer: transmissivity and storage coefficient are constant. – Type 1: Unconfined layer: transmissivity varies, specific yield is used to calculated the change of the storage. – Type 2: Confined/Unconfined: transmissivity remains constant, storage parameter may alternates between storage coefficient and specific yield. – Type 3: Confined/Unconfined: transmissivity varies, storage parameter may alternates between storage coefficient and specific yield. South North Layer 1 2 3 4 5 MODFLOW Flow Package (BCF) • Layer data are entered depending on the type – Hydraulic conductivity K – Top and bottom elevation – Transmissivity – Leakance – Effective porosity – Specific yield and storage • Data input – Map of parameter zones – Parameter values – Contour map of layer elevations MODFLOW Layer Property Package (LPF) • Replacement of BCF package • Layer data are entered depending on the type – Confined or Convertible – Hydraulic conductivity must be specified – Top and bottom layer elevations must be specified – Specific yield and specific storage must be specified – Every layer is simulated with horizontal and vertical flow MODFLOW Hydrological Unit Flow Package (HUF) • Replacement of BCF package • Aquifer stratigraphy represented in a grid-independent fashion • Equivalent Kh, Kv computed at runtime Hydrogeological units are defined together with parameter values MODFLOW Recharge Package (RCH) Areal recharge: QRi,j = Ii,j*DELRj*DELCi QRi,j is the recharge flow rate to the cell (i,j) expressed as a fluid volume per unit time; Ii,j is the recharge flux to the cell (i,j) in units of length per unit time; can be constant or transient; The units of length and time are consistent with the units used in all other model parameters. MODFLOW Recharge Package (RCH) • Options of application of recharge to model layers: • Option 1: top layer (C); • Option 2: user specified cells (D); • Option 3: highest active cells (E), preferred option since recharge is also available • Data input • Map of recharge zones • Recharge rates MODFLOW ET Package (ET) Evapotranspiratoion rate: QET = QETM h > hs QET = QETM (h - hd)/d hd < h < hs QET = 0 h < hd h: groundwater level in the cell (i,j) hs: ET surface QETM : maximum ET rate (length per unit time) when h > hs d: ET extinction depth: hd = hs – d MODFLOW ET Package (ET) • Lump sum of E and T • Linear function • QETM • d • Data input: • Map of ET zones • ET surface • Max ET rate • Extinction depth MODFLOW River Package (RIV) Discretization of a river into reaches MODFLOW River Package (RIV) A. Cross section of a stream-aquifer system B. Conceptual representation of stream- aquifer interconnection in simulation • If head is above river stage, flow is from aquifer to river • If head is below river stage, flow is from river to aquifer MODFLOW River Package (RIV) Exchange flux between the river and aquifer: QRIV = CRIV*(HRIV-hi,j,k), hi,j,k > RBOT QRIV = CRIV*(HRIV-RBOT), hi,j,k < RBOT QRIV is the flow between the river and the aquifer; HRIV is the river water level; hi,j,k is the groundwater head in the cell underlying the river reach; RBOT is the elevation of the bottom of the streambed layer; CRIV =K*L*W/M, is the hydraulic conductance of river-aquifer; K is the conductivity of the riverbed, L is the length of the river reach, W is the width of the river reach, and M is the thickness of the riverbed. MODFLOW River Package (RIV) • Suitable for permanent rivers • Exchange of water will not cause large change of river stages • Data input: • Map of rivers • River stages • Riverbed bottom elevation • River conductance MODFLOW River Package (RIV) River conductance: L = Length of reach Direction of flow K = Hydraulic conductivity of river bed M = material Thickness of river bed W = Width of river K * (area of flow) KLW Cond = = (length of flow) M MODFLOW Drain Package (DRN) Underground drain (A), Open drain (B), Wetland drain B Used to simulate • Agricultural drains • Springs • Creek beds A C MODFLOW Drain Package (DRN) Simulation of drainage rate: QDi,j,k = CDi,j,k*(hi,j,k - di,j,k) for hi,j,k > di,j,k QDi,j,k = 0 for hi,j,k < di,j,k CDi,j,k is a lumped (or equivalent) conductance describing all of head losses mentioned above; di,j,k is the drain elevation. MODFLOW Drain Package (DRN) • Simulation of discharge by springs and drains • Data input: − Map of drains − Elevation of drains − Drain conductance • Spring discharge measurements should be used to calibrate conductance MODFLOW Well Package (DRN) • Assigned to individual cells • Q can be steady state or transient • Extraction well (negative Q) • Injection well (positive Q) • Well package is used to simulate individual well rate, or well field rate • Well package is often used to simulate flow boundaries MODFLOW Drain Package (DRN) The discharge of the multi-layer well: Ql/Qw = Tl/ T where: Ql is the discharge from layer l to a multi-layer well in a given stress period; Qw is the total discharge of the multi-layer well in that stress period; Tl is the transmissivity of the layer l; and T is the sum of the transmissivities of all layers penetrated by the wells. MODFLOW General Head Boundary Package (GHB) • Assigned to individual cells • Used to simulate head dependent flow boundaries and lakes • Required parameters – Head hbi,j,k – Conductance Cbi,j,k Qbi,j,k = Cbi,j,k * (hbi,j,k - hi,j,k) MODFLOW General Head Boundary Package (GHB) Lake Lake Cell bottom sediments Flow Direction KA C = Area = A cell Thickness = L L MODFLOW General Head Boundary Package (GHB) • Use of simulating third boundary conditions • Assume continuous hydraulic contact • Exchange of water between aquifer and sources/sinks MODFLOW HFB Package (HFB) Horizontal Flow Barrier • Not part of original MODFLOW packages • Used to simulate low permeability barriers such as sheet pile walls, impermeable fault, or slurry trenches • Assigned to cell boundaries • Each instance is assigned a hydraulic characteristic = K/thickness MODFLOW input files Name Abbr. Description Input files Basic BAS Handles a number of administrative tasks, such as selection of BAS.DAT packages, specification of boundaries, time-step length, initial conditions, and printing of results. Block- BCF Formulates finite-difference equations representing flow within BCF.DAT Centered Flow porous medium Well WEL Adds flow by wells to the finite difference equations. WEL.DAT Recharge RCH Adds flow by areally distributed recharge to the equations. RCH.DAT River RIV Adds flow by rivers to the finite difference equations. RIV.DAT Drain DRN Adds flow by drains to the finite difference equations DRN.DAT Evapotran- EVT Adds flow by ET to the finite difference equations. EVT.DAT spiration General- Head GHB Adds flow by general-head boundaries to the finite-difference GHB.DAT Boundary equations. Strongly SIP Solves the system of finite-difference equations iteratively using SIP.DAT Implicit the Strongly Implicit Procedure.