Overview
Most reservoirs are supported by an underlying or flanking aquifer — a body of water that expands into the reservoir as pressure declines, providing natural pressure support and driving water influx. BirSim models aquifers three ways, all validated against OPM Flow:
- Fetkovich (
AQUFETP) — a lumped material-balance tank. - Carter-Tracy (
AQUCT) — a van Everdingen–Hurst radial influence function. - Numerical (
AQUNUM/AQUCON) — explicit water-filled grid cells.
The analytic aquifers connect to reservoir boundary faces via AQUANCON and are
coupled implicitly through the Jacobian, so the influx and the reservoir
pressure solve together each Newton iteration.
Fetkovich (AQUFETP)
A lumped tank with initial encroachable water W_ei = c_t · V_w · P_a0. The
aquifer pressure declines linearly with cumulative influx,
P_a = P_a0 · (1 − W_e / W_ei), and the per-step influx is the analytic
Fetkovich decay:
ΔW_e = (W_ei / P_a0) · (P_a − P_res) · (1 − e^(−J · P_a0 · Δt / W_ei))
where J is the aquifer productivity index.
Carter-Tracy (AQUCT)
A radial aquifer evaluated with the superposition-free Carter-Tracy update of the
van Everdingen–Hurst solution, using the Edwardson dimensionless-pressure P_D
polynomial approximation for the influence function. Parameterized by permeability,
porosity, total compressibility, inner radius, thickness, and influence angle.
Numerical (AQUNUM / AQUCON)
AQUNUM overrides a named grid cell into a large water-filled aquifer cell (its
own area, length, porosity, permeability, depth, and P_init); AQUCON connects
it to reservoir faces. BirSim uses per-side-area half-transmissibilities and a
water-balance ANQR so the numerical aquifer conserves water and matches the
analytic behavior in the appropriate limit.
Validation
Each aquifer type was run against an OPM Flow reference case: the OPM
aquifer-fetkovich benchmark, a Carter-Tracy variant, and a numerical-aquifer box.
| Aquifer | Reference | Pressure | Cumulative influx |
|---|---|---|---|
| Fetkovich | OPM aquifer-fetkovich | ~1% | within ~10–40% |
| Carter-Tracy | OPM Carter-Tracy variant | ~1% | within ~10–40% |
| Numerical | OPM numerical-aquifer box | ~1% | within ~7–9% |
Aquifer and field pressure match OPM to ~1% across all three models — the quantity that governs the reservoir’s pressure support. The influx totals agree within the analytic spread (~10–40% for the analytic tanks, tighter ~7–9% for the numerical aquifer), consistent with the sensitivity of the influence-function integral to the aquifer parameterization.
Why it matters
Aquifer support determines how a reservoir depletes and when water breaks through — often the single biggest uncertainty in a field forecast. Supporting all three industry-standard models (two analytic, one numerical) with implicit coupling, and matching OPM Flow on pressure to ~1%, lets BirSim run the aquifer-driven decks that dominate real field studies.
Reference
Fetkovich, M.J. (1971); Carter, R.D. & Tracy, G.W. (1960); van Everdingen, A.F. &
Hurst, W. (1949). BirSim is validated against OPM Flow’s AQUFETP / AQUCT /
AQUNUM implementations on the same decks; deck paths and command lines are
available on request.