Hydrogeological Parameters

Even before considering contaminants, a simulation relies on the representation of flow: where the water comes from, where it goes, at what speed, and with what recharge and discharge points. This page details how to configure these parameters in IsoFind, in conjunction with the already defined stratigraphic layers and the domain's boundary conditions.

Hydraulic Gradient

The driving force behind groundwater flow is the hydraulic gradient, which is the slope of the potentiometric surface. IsoFind offers three modes to define it, ranging from the most straightforward to the most field-accurate.

Mode	Expected Query Fields	Usage
Mode A: Direct Input	flow_direction_deg and flow_velocity_m_j	Darcy velocity and direction already estimated externally
Mode B: Darcy Calculation	hydraulic_gradient, K_ms, porosity	Gradient and permeability known; velocity derived via Darcy's Law
Automatic Fallback	No fields provided	Estimation based on sample potentiometric gradients (estimate_flow_velocity)

The two modes cannot be combined: if Mode A fields are provided, they take precedence and Mode B fields are ignored. The automatic fallback is only triggered when neither mode is configured, which is typical for an initial exploratory run on a well-instrumented site.

For a first draft, leaving hydrogeological fields empty and relying on the automatic fallback provides a workable result if samples include water level measurements. Switching later to Mode B with K and porosity derived from the dominant lithology improves accuracy. Mode A is most relevant when a previous hydrogeological study has already provided a validated Darcy velocity.

Darcy Velocity vs. Effective Velocity

The velocity calculated by Darcy's Law is an apparent velocity: the volume of water per unit area per unit time. The effective velocity of the contaminant is obtained by dividing this by the effective porosity. This distinction is crucial because contaminants actually travel much faster than a naive reading of permeability would suggest.

$$v_{Darcy} = -K \cdot \frac{\partial h}{\partial x} \quad \quad v_{effective} = \frac{v_{Darcy}}{\theta}$$

Where $K$ is the hydraulic conductivity of the layer, $h$ is the hydraulic head, and $\theta$ is the effective porosity. IsoFind displays both velocities in the simulation outputs to ensure correct interpretation.

Flow Boundary Conditions

Beyond the internal velocity field, the behavior at the domain boundaries must be specified. The same types of conditions (Dirichlet, Neumann, Cauchy) used for transport apply to flow, with adapted physical meanings.

Type	Meaning for Flow	Use Case
Specified Head (Dirichlet)	Fixed potentiometric level	Water body, gaining stream
Specified Flux (Neumann)	Fixed inflow or outflow rate	Meteoric recharge, pumping well
No-Flow Boundary (Zero Neumann)	No flux across the boundary	Impermeable bedrock, tectonic limit
Head-Dependent Flux (Cauchy)	Flux proportional to head difference	Partial contact between aquifer and clogged riverbed

Meteoric Recharge

Recharge from rainfall infiltration can be represented as a vertical inflow at the top of the water table. IsoFind allows for either a uniform value in mm/year (useful for average estimates) or a variable field by zone (useful when land use changes recharge, such as rooftops and roads versus agricultural soils).

Land Cover	Indicative Recharge (mm/year)
Permeable Bare Soil	150 to 300
Permanent Grassland	100 to 250
Annual Crops	100 to 200
Temperate Forest	50 to 150
Permeable Urban Area	50 to 100
Impermeable Urban Area	0 to 50

These values vary significantly based on regional climate and the underlying soil type. They are provided as guidelines and should be adjusted based on local data if available (water balance studies, water level time series).

Internal Sources and Sinks

In addition to boundary conditions, the simulation can manage injection or extraction points internal to the domain. Four types are handled:

Type	Representation	Parameters
Continuous Point Source	3D point with constant flow	Coordinates, flow rate, injected concentration, duration
Instantaneous Source	3D point with total mass at t=0	Coordinates, mass, initial isotopic signature
Surface or Volume Source	2D or 3D zone with flux per unit area	Polygon or volume, flux, duration
Pumping Well	3D point with negative flow	Coordinates, pumping rate

Sources can be activated or deactivated over time to simulate intermittent leaks, remediation campaigns, or operational shutdowns. Each source carries its own isotopic signature, enabling the simulation of cases where multiple sources with different origins coexist.

Intra-Layer Heterogeneity

A stratigraphic layer is rarely perfectly homogeneous. IsoFind allows for internal heterogeneity through two mechanisms:

Mechanism	Principle	Usage
Stochastic Field	Permeability drawn from a log-normal distribution with spatial correlation	Alluvial sediments, representing natural variability
Specified Zones	Sub-regions with specific values	Buried channels, known clay lenses

Introducing heterogeneity significantly increases complexity and computation time. It is justified when homogeneity predicts a result clearly contradicted by observations. Otherwise, keeping it simple is almost always preferable.

Typical Hydrogeological Setup Path

Simulation > Hydrogeological Parameters > Gradient Mode > Boundary Conditions > Recharge > Sources and Sinks > Validate

Once these parameters are set, IsoFind calculates the flow field and displays a preview with streamlines. This preview should be checked before launching the actual transport simulation: visual consistency between the streamlines and the known hydrogeological context prevents many unpleasant surprises later on.

Learn More

Engine Principles: How these parameters are integrated into the equations.
Speciation and Propagation: Coupling between flow and reactions.
Stratigraphic Layers: Where the permeability and porosity values come from.