FLAC3D Theory and Background • Fluid-Mechanical Interaction

Fluid-Flow Boundary Conditions, Initial Conditions, Sources and Sinks

Boundaries are impermeable by default; all gridpoints are initially “free” (i.e., the pore pressure at such gridpoints is free to vary according to the net inflow and outflow from neighboring zones). This condition may be declared explicitly by using the command zone gridpoint free pore-pressure at the appropriate gridpoints. The opposite condition, zone gridpoint fix pore-pressure, may also be set at any gridpoint. In general, fluid may enter or leave the grid at an external boundary if the pore pressure is fixed. The effect of these two boundary conditions is summarized:

1. Pore-pressure free — This is an impermeable boundary, and is the default condition. There is no exchange between the grid and the outside world. Pressure and saturation changes are computed according to this equation or this equation, depending on the current value of saturation and whether the fluid has “cavitated” (fallen below the tensile limit).

2. Pore-pressure fixed — This is a permeable boundary across which fluid flows to and from the outside world. The saturation may only vary if the set pressure is exactly zero. Otherwise, saturation is forced to be 1 (to conform with FLAC3D’s assumption that pore pressures can only exist in a fully saturated material). Pore pressure cannot be fixed at a value less than the tensile limit; FLAC3D will reset any such pressures to the tensile limit.

As noted above, certain combinations of conditions are impossible (e.g., pore pressure fixed at a value less than the tensile limit). FLAC3D “corrects” such conditions before executing any calculation step. Pore pressure is fixed at some pressure by using the zone gridpoint fix pore-pressure command. Alternatively, the command zone face apply pore-pressure can be used for either external or internal boundaries. It is important to note that the optional keyword interior must be specified if the condition is to be applied at a non-surface node. The use of zone face apply pore-pressure has the advantage that the pressure may be controlled directly by a history (supplied by a FISH function).

Fluid-flow boundary conditions can be applied to individual, or ranges of, gridpoints, zone faces or zones via the zone face apply pore-pressure command. The zone gridpoint fix well command causes a prescribed inflow or outflow to be applied to a boundary gridpoint. If the interior keyword is added, the condition can be applied to an interior gridpoint. The zone face apply discharge and zone face apply leakage commands specify either a fluid flux or a leaky boundary condition to faces of boundary zones. The zone apply well command applies a volume rate of flow to zones within a specified range. All of these fluid-flow boundary conditions except zone face apply leakage can refer to a history (via the history keyword). See Input Instructions for Fluid-Flow Analysis for a more detailed description and format for these commands.

Fixed-pressure gridpoints may act as a source or sinks. There is no explicit command that can be used to measure the inflow or outflow at these points. However, the FISH grid variable gp.flow records unbalanced nodal flows: a simple function that allows inflows and outflows to be printed or plotted for any range of gridpoints can be written.

Initial distributions of pore pressure, porosity, saturation and fluid-flow properties may be specified with the zone gridpoint initialize or zone fluid property command, as noted in Input Instructions for Fluid-Flow Analysis. If gravity is also given (with the model gravity command), it is important that the initial distributions are consistent with the gravitational gradient implied by the value of gravity, the given density of water and the values of saturation and porosity within the grid. If the initial distributions are inconsistent, then flow may occur in all zones at the start of a run. When setting up a simulation, a few steps should be taken to check for this possibility. Stress and Pore-Pressure Initialization with a Phreatic Surface provides a detailed description of the procedure for setting up initial conditions.

If a model contains interfaces, effective stresses will be initialized along the interfaces (i.e., the presence of pore pressures will be accounted for within the interface stresses when stresses are initialized in the grid). This occurs either with or without model configure fluid specified. For example, the zone water command (in non-model configure fluid mode) will include pore pressures along the interface, because pore pressures are defined at gridpoints for interpolation to interface nodes for this mode. Note that flow takes place, without resistance, from one surface to the other surface of an interface, if they are in contact. Preferential flow along an interface (e.g., fracture flow) is not computed.