L1 ⚛ L1-192 ⊙ Testnet

Buckley-Leverett — two-phase displacement saturation

Fluid Dynamics · Buckley-Leverett in petroleum reservoirs

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⬇ L1-192.md

# ⚛ L1 Principle — Buckley-Leverett — two-phase displacement saturation **ID:** `L1-192` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Fluid Dynamics — *Buckley-Leverett in petroleum reservoirs* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** saturation shock > **📡 Carrier:** mechanical · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41553978 --- ## 🧠 1. Introduction **Buckley-Leverett — two-phase displacement saturation** is a **linear inverse problem** whose unknown lives in **saturation shock** space, within the **Buckley-Leverett in petroleum reservoirs** sub-domain of **Fluid Dynamics**. Measurements consist of mechanical vibrations or strain signals via a **well production** sensing mechanism. The forward operator applies, in order: L · flux function operator; L · shock admissible operator; L · fractional flow 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 · flux function → L · shock admissible → L · fractional flow → Temporal integration → **y** (detector). ``` y = ∫_t dt `L.fractional_flow` `L.shock_admissible` `L.flux_function` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `L.flux_function` | L · flux function operator | | `L.shock_admissible` | L · shock admissible operator | | `L.fractional_flow` | L · fractional flow operator | | `int.temporal` | Detector accumulates flux over the exposure window | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Fluid Dynamics | | Sub domain | Buckley-Leverett in petroleum reservoirs | | Carrier | mechanical | | Problem class | linear_inverse | | Solution space | saturation_shock | | 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 | PSNR_dB | | Secondary | SSIM | ## 📏 5. Operating Range (Ω) **Center problem class:** `bl` · **Forward operator:** `bl_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | Snr db | dB | 30 | | N cells | — | 100 | | N times | — | 1000 | | Relperm error | — | 0 | | Capillary error | — | 0 | | Mobility ratio error | — | 0 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Snr db | dB | 0 – 40 | | N cells | — | 10 – 100000 | | N times | — | 100 – 100000 | | Relperm error | — | 0.0 – 0.3 | | Capillary error | — | 0.0 – 0.3 | | Mobility ratio error | — | 0.0 – 0.2 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 24.0 | Metric | Range | |---|---| | Psnr db | 10.0 – 45.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **PSNR_dB**, with κ = `300` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xb5d96e0f7bd9783b2718a08a9ec3928333aea9fca4152e3c8fbabdacaad67e69` - **Chain tx hash:** `0x0af50dc66db6aeccdff0295e67dcff4107b9391b886e495aefa182b796ae97a1` - **Chain block:** `41553978` --- ## File Mapping This bundle consists of: `L1-192.md`, `L1-192.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-192.md` | Source of truth — edit this | Human or LLM | | `L1-192.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 `L1-192`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-192.md).
Regenerate L1-192.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-192-001 Buckley-Leverett — two-phase displacement saturation Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41553978,
  "chain_hash": "0xb5d96e0f7bd9783b2718a08a9ec3928333aea9fca4152e3c8fbabdacaad67e69",
  "chain_tx_hash": "0x0af50dc66db6aeccdff0295e67dcff4107b9391b886e495aefa182b796ae97a1",
  "domain": "Fluid Dynamics",
  "hardness_fn": {
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    "kappa": 300,
    "metric": "PSNR_dB",
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    "regime": "Conditional stability; mismatch parameters dominate at Omega bounds.",
    "secondary": "SSIM"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "mechanical",
    "difficulty_delta": 3,
    "domain": "Fluid Dynamics",
    "integration_axis": "temporal",
    "noise_model": "gaussian",
    "primitives": [
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      "L.shock_admissible",
      "L.fractional_flow",
      "int.temporal"
    ],
    "problem_class": "linear_inverse",
    "sensing_mechanism": "well_production",
    "solution_space": "saturation_shock",
    "sub_domain": "Buckley-Leverett in petroleum reservoirs",
    "title": "Buckley-Leverett \u2014 two-phase displacement saturation"
  },
  "size_tiers": {
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    "allowed_omega_dimensions": [
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      "N_times",
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      "capillary_error",
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        "relperm_error": 0.0
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    "epsilon_bounds": {
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        45.0
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    },
    "omega_bounds": {
      "N_cells": [
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        100000
      ],
      "N_times": [
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        100000
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      "SNR_dB": [
        0,
        40
      ],
      "capillary_error": [
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      ],
      "mobility_ratio_error": [
        0.0,
        0.2
      ],
      "relperm_error": [
        0.0,
        0.3
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Buckley-Leverett in petroleum reservoirs",
  "title": "Buckley-Leverett \u2014 two-phase displacement saturation"
}

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