L1 ⚛ L1-465 ⊙ Testnet

Well Productivity Index Inversion

Petroleum Engineering · Well performance

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⬇ L1-465.md

# ⚛ L1 Principle — Well Productivity Index Inversion **ID:** `L1-465` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Petroleum Engineering — *Well performance* > **🎯 Problem class:** parameter estimation · **🧮 Solution space:** reservoir property vector > **📡 Carrier:** acoustic · **🌫 Noise:** measurement gaussian > **⚖ Difficulty (δ):** 3 · **⛓ Block:** 41555280 --- ## 🧠 1. Introduction **Well Productivity Index Inversion** is a **parameter-estimation problem** whose unknown lives in **reservoir property vector** space, within the **Well performance** sub-domain of **Petroleum Engineering**. Measurements consist of acoustic pressure waves recorded by transducers via a **pressure transient analysis** sensing mechanism. The forward operator applies, in order: gradient / divergence with respect to position; S · pta · derivative analysis operator; O · semi log · straight line operator. Observations are corrupted by measurement gaussian. Existence of the recovered reservoir_property_vector 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 ~= 25); wellbore_storage_distortion 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** → Spatial derivative → S · pta · derivative analysis → O · semi log · straight line → **y** (detector). ``` y = `O.semi_log.straight_line` `S.pta.derivative_analysis` ∇ x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `D.space` | Gradient / divergence with respect to position | | `S.pta.derivative_analysis` | S · pta · derivative analysis operator | | `O.semi_log.straight_line` | O · semi log · straight line operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Petroleum Engineering | | Sub domain | Well performance | | Carrier | acoustic | | Problem class | parameter_estimation | | Solution space | reservoir_property_vector | | Noise model | measurement_gaussian | | Integration axis | radial_wellbore | | Difficulty delta | 3 | | L dag | 2.5 | ## 📡 4. Measurement Model Existence of the recovered reservoir_property_vector 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 ~= 25); wellbore_storage_distortion dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | permeability_estimation_error_percent | | Secondary | skin_factor_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `parameter_estimation` · **Forward operator:** `pressure_transient_analysis` **Center point:** | Parameter | Unit | Value | |---|---|---| | K md | — | 50 | | Skin factor | — | 5 | | N pressure points | — | 500 | | Wellbore storage c bbl psi | — | 0.01 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | K md | — | 0.1 – 10000 | | Skin factor | — | -5 – 50 | | N pressure points | — | 50 – 5000 | | Wellbore storage c bbl psi | — | 0.001 – 1.0 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 15 permeability_estimation_error_percent | Metric | Range | |---|---| | Permeability estimation error percent | 2 – 50 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **permeability_estimation_error_percent**, with κ = `500` and δ = `3`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x8a1ccb9a2ebaacf2e139043aa5ad760ae46b7d6e4c022b3242e85b99d5d470a7` - **Chain tx hash:** `0xbf8e44adcebeb838bc2c456575091cfb34c09e4034b0c7d52174b07343673dec` - **Chain block:** `41555280` --- ## File Mapping This bundle consists of: `L1-465.md`, `L1-465.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-465.md` | Source of truth — edit this | Human or LLM | | `L1-465.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 `L1-465`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-465.md).
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L2-465-001 Well Productivity Index Inversion — Nominal + Mismatch Specs

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📋 JSON metadata

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  "chain_block": 41555280,
  "chain_hash": "0x8a1ccb9a2ebaacf2e139043aa5ad760ae46b7d6e4c022b3242e85b99d5d470a7",
  "chain_tx_hash": "0xbf8e44adcebeb838bc2c456575091cfb34c09e4034b0c7d52174b07343673dec",
  "domain": "Petroleum Engineering",
  "hardness_fn": {
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    "kappa": 500,
    "metric": "permeability_estimation_error_percent",
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    "regime": "Existence of the recovered reservoir_property_vector 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 ~= 25); wellbore_storage_distortion dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Measurement gaussian sets the irreducible data-fidelity floor.",
    "secondary": "skin_factor_error"
  },
  "physics_fingerprint": {
    "L_DAG": 2.5,
    "carrier": "acoustic",
    "difficulty_delta": 3,
    "domain": "Petroleum Engineering",
    "integration_axis": "radial_wellbore",
    "noise_model": "measurement_gaussian",
    "primitives": [
      "D.space",
      "S.pta.derivative_analysis",
      "O.semi_log.straight_line"
    ],
    "problem_class": "parameter_estimation",
    "sensing_mechanism": "pressure_transient_analysis",
    "solution_space": "reservoir_property_vector",
    "sub_domain": "Well performance",
    "title": "Well Productivity Index Inversion"
  },
  "size_tiers": {
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      "pressure_transient_analysis"
    ],
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      "N_pressure_points",
      "k_mD",
      "skin_factor",
      "wellbore_storage_C_bbl_psi"
    ],
    "allowed_problem_classes": [
      "parameter_estimation"
    ],
    "center_spec": {
      "epsilon_fn_center": "15 permeability_estimation_error_percent",
      "forward_operator": "pressure_transient_analysis",
      "input_format": "measurement_only",
      "omega": {
        "N_pressure_points": 500,
        "k_mD": 50,
        "skin_factor": 5,
        "wellbore_storage_C_bbl_psi": 0.01
      },
      "problem_class": "parameter_estimation"
    },
    "epsilon_bounds": {
      "permeability_estimation_error_percent": [
        2,
        50
      ]
    },
    "omega_bounds": {
      "N_pressure_points": [
        50,
        5000
      ],
      "k_mD": [
        0.1,
        10000
      ],
      "skin_factor": [
        -5,
        50
      ],
      "wellbore_storage_C_bbl_psi": [
        0.001,
        1.0
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Well performance",
  "title": "Well Productivity Index Inversion"
}

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