Methodology

Overview

IPRS solves the production system as three coupled layers, each with its own governing physics. The layers are advanced simultaneously through time: reservoir pressure depletes via material balance, well rates respond to the resulting drawdown, and a surface network propagates backpressure from sales meter to wellhead. No empirical decline curve is used — every rate emerges from physics.

Layer 1 — Reservoir Material Balance

For a dry-gas reservoir, the p/Z method gives the canonical material balance:

For multi-reservoir cases with inter-layer transmissibility, the volumetric form is solved bisectionally per timestep:

Z-factor uses the Dranchuk-Abou-Kassem correlation; B_g follows directly from the real-gas law.

Layer 2 — Well Inflow (Darcy + Nodal)

Well productivity index in pseudo-pressure form:

The pseudo-pressure m(p) is built once per timestep via Simpson's rule from 50 psia to 1.2·p_i, with a lookup table for fast evaluation. When multi-rate test data is uploaded, J is calibrated via Houpeurt log-log regression and overrides the Darcy estimate.

Layer 3 — Surface Network

The gathering system is a directed graph from wells through stations to a sales meter (sink). The solver walks the graph in two passes:

1. Forward pass — Kahn topological sort propagates flow from upstream stations to downstream sinks.
2. Backward pass — pressure propagates from the sink upstream via Weymouth pipe pressure-drop, then through flowlines to each wellhead.

Tubing pressure drop uses Cullender-Smith with static head + friction terms.

Coupling Across Layers

At each timestep, all three layers iterate to a self-consistent solution:

1. Solve network for wellhead pressure given current well rates.
2. For each well, find the q ↔ p_wf Nodal intersection (VLP curve meets IPR curve) by damped fixed-point iteration.
3. Apply new rates to reservoir material balance; update average pressure.
4. Recompute network with new rates. Repeat until rates change less than 1% of average.

Calibration Workflow

Each component can be in one of two calibration states:

• Default — uses theoretical inputs (k, h, skin from petrophysics; OGIP from volumetrics).
• Matched — uses observed history (pressure surveys for reservoirs, multi-rate tests for wells).

A mixed calibration is fully supported: matched components use calibrated parameters, unmatched components fall back to defaults. The forecast runs end-to-end regardless.