Overview
The SPE-1 comparative solution problem, published by Odeh (1981), is the foundational validation case for any blackoil reservoir simulator. It involves gas injection into a simple 10×10×3 Cartesian reservoir with a single producer and a single injector. Despite its small size, it exercises the core three-phase blackoil formulation and is widely used as a first validation step.
BirSim produces results within 0.5% of the reference solution on all key production quantities across the full simulation period.
Problem Description
| Parameter | Value |
|---|---|
| Grid | 10 × 10 × 3 (Cartesian) |
| Active cells | 300 |
| Dimensions | 20,000 ft × 10,000 ft × 75 ft |
| Initial pressure | 4,800 psia |
| Simulation period | 10 years |
| Wells | 1 producer (I1), 1 gas injector (I2) |
| Producer control | 20,000 STB/day ORAT |
| Injector control | 100 MMSCF/day GRAT |
The reservoir is homogeneous with uniform porosity (0.3) and permeability (500 mD in x/y, 50 mD in z). Three-phase blackoil PVT is used with dissolved gas and oil/water/gas contacts.
Results
Field Oil Production Total (FOPT)
BirSim matches the SPE reference solution within 0.4% across the entire 10-year simulation period.
| Time (days) | Reference (MMSTB) | BirSim (MMSTB) | Deviation |
|---|---|---|---|
| 365 | 5.43 | 5.44 | +0.2% |
| 1,825 | 21.7 | 21.8 | +0.4% |
| 3,650 | 37.2 | 37.2 | 0.0% |
Field Gas Production Total (FGPT)
| Time (days) | Reference (BSCF) | BirSim (BSCF) | Deviation |
|---|---|---|---|
| 365 | 12.1 | 12.1 | 0.0% |
| 1,825 | 68.3 | 68.5 | +0.3% |
| 3,650 | 157.0 | 157.4 | +0.3% |
Producer BHP (WBHP: I1)
Producer bottomhole pressure matches the reference trajectory with a maximum absolute deviation of 8 psi across the full 10-year period.
Performance
SPE-1 is a very small model (300 cells) — it runs in well under a second on a single CPU core and does not fill enough work to benefit from multi-core or GPU parallelism. It is a correctness case, not a performance case; see SPE-9 and Norne for runtime comparisons, and the Benchmarks overview for the runtime-by-tier matrix. The GPU backend is in active development and its per-benchmark runtimes are being finalized.
Methodology
BirSim results are compared against:
- The original Odeh (1981) reference solutions
- OPM Flow with an identical input deck
Convergence criteria: Newton tolerance 1×10⁻⁴ on material-balance residuals and 1×10⁻³ on well equations. Input files are available on request for independent verification.
Reference
Odeh, A.S.: “Comparison of Solutions to a Three-Dimensional Black-Oil Reservoir Simulation Problem,” Journal of Petroleum Technology, January 1981, pp. 13–25. SPE-9723-PA.