# ⚛  L1 Principle — Compositional Reservoir Simulation

**ID:** `L1-459` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Petroleum Engineering — *EOS-based simulation*
> **🎯 Problem class:** parameter estimation · **🧮 Solution space:** 3D composition pressure
> **📡 Carrier:** acoustic · **🌫 Noise:** measurement gaussian
> **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555279

---

## 🧠 1. Introduction

**Compositional Reservoir Simulation** is a **parameter-estimation problem** whose unknown lives in **3D composition pressure** space, within the **EOS-based simulation** sub-domain of **Petroleum Engineering**.

Measurements consist of acoustic pressure waves recorded by transducers via a **compositional eos flow** sensing mechanism.

The forward operator applies, in order: applies a smooth nonlinear function element-wise; S · flash · rachford rice operator; O · material balance · compositional operator.

Observations are corrupted by measurement gaussian. Existence of the recovered 3D_composition_pressure is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 5000); EOS_tuning_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor.

## ⚙ 2. Forward Model

Physical chain: **x** → Pointwise nonlinearity → S · flash · rachford rice → O · material balance · compositional → **y** (detector).

```
y = `O.material_balance.compositional` `S.flash.rachford_rice` f(·) x
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `N.pointwise` | Applies a smooth nonlinear function element-wise |
| `S.flash.rachford_rice` | S · flash · rachford rice operator |
| `O.material_balance.compositional` | O · material balance · compositional operator |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Petroleum Engineering |
| Sub domain | EOS-based simulation |
| Carrier | acoustic |
| Problem class | parameter_estimation |
| Solution space | 3D_composition_pressure |
| Noise model | measurement_gaussian |
| Integration axis | 3d_compositional |
| Difficulty delta | 5 |
| L dag | 4.5 |

## 📡 4. Measurement Model

Existence of the recovered 3D_composition_pressure is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 5000); EOS_tuning_uncertainty dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor.

| Metric | Value |
|---|---|
| Metric | GOR_prediction_RMSE_percent |
| Secondary | dew_point_pressure_error_psi |

## 📏 5. Operating Range (Ω)

**Center problem class:** `parameter_estimation` · **Forward operator:** `compositional_eos_flow`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| N cells | — | 5000 |
| Gor scf stb | — | 1000 |
| N components | — | 6 |
| Reservoir pressure psi | — | 5000 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| N cells | — | 100 – 100000 |
| Gor scf stb | — | 100 – 100000 |
| N components | — | 2 – 20 |
| Reservoir pressure psi | — | 500 – 15000 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 10 GOR_prediction_RMSE_percent

| Metric | Range |
|---|---|
| Gor prediction rmse percent | 2 – 50 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **GOR_prediction_RMSE_percent**, with κ = `1000000.0` and δ = `5`.

## 💾 8. Reference Dataset

- **primary** · weight 1.0 · IPFS _(not pinned yet)_

## 9. On-chain Registration

- **Chain hash:** `0x7c7a6c2b230eb5a08a88ad03ecdbd0879fcf36f3644e44abffa1964814dc9300`
- **Chain tx hash:** `0xbf6fee84fbb5f60f894e27831bebdf564c6ea7e0ece0931e965d45b0721588f4`
- **Chain block:** `41555279`

---

## File Mapping

This bundle consists of: `L1-459.md`, `L1-459.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-459.md` | Source of truth — edit this | Human or LLM |
| `L1-459.json` | Structured metadata for the registry | LLM regenerates from the sections above |

**Prompt for your LLM after editing this Markdown:**

> Read the attached Markdown. Regenerate the sibling `.json` so every field matches.
> Preserve the schema documented in the rows above.
> Output each file in its own fenced code block tagged with the filename.
> Output only the JSON object.

_This Markdown was auto-synthesized from the catalog row for `L1-459`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._