# ⚛  L1 Principle — Well Test Analysis — transient pressure testing

**ID:** `L1-291` · **Status:** ⊙ Testnet (genesis catalog)

> **🌐 Domain:** Geophysics — *Pressure-transient analysis (PTA) for reservoir properties*
> **🎯 Problem class:** linear inverse · **🧮 Solution space:** kh skin params
> **📡 Carrier:** mechanical · **🌫 Noise:** gaussian
> **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41554066

---

## 🧠 1. Introduction

**Well Test Analysis — transient pressure testing** is a **linear inverse problem** whose unknown lives in **kh skin params** space, within the **Pressure-transient analysis (PTA) for reservoir properties** sub-domain of **Geophysics**.

Measurements consist of mechanical vibrations or strain signals via a **downhole pressure** sensing mechanism.

The forward operator applies, in order: L · diffusivity operator; L · radial flow operator; L · boundary detect operator; detector accumulates flux over the exposure window.

Observations are corrupted by additive Gaussian noise. Conditional stability; mismatch parameters dominate at Omega bounds.

## ⚙ 2. Forward Model

Physical chain: **x** → L · diffusivity → L · radial flow → L · boundary detect → Temporal integration → **y** (detector).

```
y = ∫_t dt `L.boundary_detect` `L.radial_flow` `L.diffusivity` x + n,    n ~ 𝒩(0, σ²)
```

**Measurement DAG:**

| Primitive | What it does |
|---|---|
| `L.diffusivity` | L · diffusivity operator |
| `L.radial_flow` | L · radial flow operator |
| `L.boundary_detect` | L · boundary detect operator |
| `int.temporal` | Detector accumulates flux over the exposure window |

## 🔬 3. Physics Fingerprint

| Property | Value |
|---|---|
| Domain | Geophysics |
| Sub domain | Pressure-transient analysis (PTA) for reservoir properties |
| Carrier | mechanical |
| Problem class | linear_inverse |
| Solution space | kh_skin_params |
| Noise model | gaussian |
| Integration axis | temporal |
| Difficulty delta | 3 |
| L dag | 3 |

## 📡 4. Measurement Model

Conditional stability; mismatch parameters dominate at Omega bounds.

| Metric | Value |
|---|---|
| Metric | kh_rel_error_percent |
| Secondary | SSIM |

## 📏 5. Operating Range (Ω)

**Center problem class:** `pta` · **Forward operator:** `pta_forward`

**Center point:**

| Parameter | Unit | Value |
|---|---|---|
| Snr db | dB | 30 |
| N times | — | 1000 |
| Boundary error | — | 0 |
| Kh prior error | — | 0 |
| Skin factor error | — | 0 |

**Allowed bounds:**

| Parameter | Unit | Range |
|---|---|---|
| Snr db | dB | 0 – 40 |
| N times | — | 10 – 100000 |
| Boundary error | — | 0.0 – 0.3 |
| Kh prior error | — | 0.0 – 0.2 |
| Skin factor error | — | 0.0 – 0.3 |

## 🎯 6. Tolerance (ε)

**Center tolerance:** 3.0

| Metric | Range |
|---|---|
| Kh rel | 0.3 – 30.0 |

## ⚖ 7. Hardness Function

Hardness scales as **`epsilon_fn`** on **kh_rel_error_percent**, with κ = `240` and δ = `3`.

## 💾 8. Reference Dataset

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

## 9. On-chain Registration

- **Chain hash:** `0xf2f70ea25462cf3734fda6ba48bf768ec5f568d7fd503ad2d79395df61dd62a4`
- **Chain tx hash:** `0xb9ecb7293132bb57e67a4f5db71a9ceb9a1cfd6403db78207e0f4937b088161f`
- **Chain block:** `41554066`

---

## File Mapping

This bundle consists of: `L1-291.md`, `L1-291.json`.

| File | Role | How to regenerate |
|------|------|-------------------|
| `L1-291.md` | Source of truth — edit this | Human or LLM |
| `L1-291.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 `L1-291`._
_Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._