L1 ⚛ L1-461 ⊙ Testnet

Hydraulic Fracture Propagation Modeling

Petroleum Engineering · Well stimulation

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⬇ L1-461.md

# ⚛ L1 Principle — Hydraulic Fracture Propagation Modeling **ID:** `L1-461` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Petroleum Engineering — *Well stimulation* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** fracture geometry vector > **📡 Carrier:** acoustic · **🌫 Noise:** microseismic gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41555279 --- ## 🧠 1. Introduction **Hydraulic Fracture Propagation Modeling** is a **nonlinear inverse problem** whose unknown lives in **fracture geometry vector** space, within the **Well stimulation** sub-domain of **Petroleum Engineering**. Measurements consist of acoustic pressure waves recorded by transducers via a **fracture geometry inversion** sensing mechanism. The forward operator applies, in order: applies a smooth nonlinear function element-wise; S · pressure decline · analysis operator; O · microseismic · inversion operator. Observations are corrupted by microseismic gaussian. Existence of the recovered fracture_geometry_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 ~= 500); stress_shadow_complexity dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Microseismic gaussian sets the irreducible data-fidelity floor. ## ⚙ 2. Forward Model Physical chain: **x** → Pointwise nonlinearity → S · pressure decline · analysis → O · microseismic · inversion → **y** (detector). ``` y = `O.microseismic.inversion` `S.pressure_decline.analysis` f(·) x ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `N.pointwise` | Applies a smooth nonlinear function element-wise | | `S.pressure_decline.analysis` | S · pressure decline · analysis operator | | `O.microseismic.inversion` | O · microseismic · inversion operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Petroleum Engineering | | Sub domain | Well stimulation | | Carrier | acoustic | | Problem class | nonlinear_inverse | | Solution space | fracture_geometry_vector | | Noise model | microseismic_gaussian | | Integration axis | fracture_surface | | Difficulty delta | 5 | | L dag | 4 | ## 📡 4. Measurement Model Existence of the recovered fracture_geometry_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 ~= 500); stress_shadow_complexity dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Microseismic gaussian sets the irreducible data-fidelity floor. | Metric | Value | |---|---| | Metric | fracture_half_length_RMSE_m | | Secondary | pressure_match_RMSE_psi | ## 📏 5. Operating Range (Ω) **Center problem class:** `nonlinear_inverse` · **Forward operator:** `fracture_geometry_inversion` **Center point:** | Parameter | Unit | Value | |---|---|---| | Stage spacing ft | — | 200 | | Young modulus gpa | — | 30 | | Fluid viscosity cp | — | 50 | | Injection rate bbl min | — | 15 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | Stage spacing ft | — | 50 – 500 | | Young modulus gpa | — | 5 – 80 | | Fluid viscosity cp | — | 5 – 5000 | | Injection rate bbl min | — | 2 – 50 | ## 🎯 6. Tolerance (ε) **Center tolerance:** 30 fracture_half_length_RMSE_m | Metric | Range | |---|---| | Fracture half length rmse m | 5 – 200 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **fracture_half_length_RMSE_m**, with κ = `10000.0` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xf11d527efd059c6ee9e552f27b84d4d426762705d8a099c84e865ca7d60990a0` - **Chain tx hash:** `0x03496d371ad73925d841e6ca6858681f36cb1ac3ede4aec81e437f78a55ad215` - **Chain block:** `41555279` --- ## File Mapping This bundle consists of: `L1-461.md`, `L1-461.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-461.md` | Source of truth — edit this | Human or LLM | | `L1-461.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 `L1-461`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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📋 JSON metadata

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  "artifact_id": "L1-461",
  "chain_block": 41555279,
  "chain_hash": "0xf11d527efd059c6ee9e552f27b84d4d426762705d8a099c84e865ca7d60990a0",
  "chain_tx_hash": "0x03496d371ad73925d841e6ca6858681f36cb1ac3ede4aec81e437f78a55ad215",
  "domain": "Petroleum Engineering",
  "hardness_fn": {
    "delta": 5,
    "kappa": 10000.0,
    "metric": "fracture_half_length_RMSE_m",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
    {
      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "fracture_half_length_RMSE_m",
    "regime": "Existence of the recovered fracture_geometry_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 ~= 500); stress_shadow_complexity dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Microseismic gaussian sets the irreducible data-fidelity floor.",
    "secondary": "pressure_match_RMSE_psi"
  },
  "physics_fingerprint": {
    "L_DAG": 4.0,
    "carrier": "acoustic",
    "difficulty_delta": 5,
    "domain": "Petroleum Engineering",
    "integration_axis": "fracture_surface",
    "noise_model": "microseismic_gaussian",
    "primitives": [
      "N.pointwise",
      "S.pressure_decline.analysis",
      "O.microseismic.inversion"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "fracture_geometry_inversion",
    "solution_space": "fracture_geometry_vector",
    "sub_domain": "Well stimulation",
    "title": "Hydraulic Fracture Propagation Modeling"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "fracture_geometry_inversion"
    ],
    "allowed_omega_dimensions": [
      "Young_modulus_GPa",
      "fluid_viscosity_cP",
      "injection_rate_bbl_min",
      "stage_spacing_ft"
    ],
    "allowed_problem_classes": [
      "nonlinear_inverse"
    ],
    "center_spec": {
      "epsilon_fn_center": "30 fracture_half_length_RMSE_m",
      "forward_operator": "fracture_geometry_inversion",
      "input_format": "measurement_only",
      "omega": {
        "Young_modulus_GPa": 30,
        "fluid_viscosity_cP": 50,
        "injection_rate_bbl_min": 15,
        "stage_spacing_ft": 200
      },
      "problem_class": "nonlinear_inverse"
    },
    "epsilon_bounds": {
      "fracture_half_length_RMSE_m": [
        5,
        200
      ]
    },
    "omega_bounds": {
      "Young_modulus_GPa": [
        5,
        80
      ],
      "fluid_viscosity_cP": [
        5,
        5000
      ],
      "injection_rate_bbl_min": [
        2,
        50
      ],
      "stage_spacing_ft": [
        50,
        500
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Well stimulation",
  "title": "Hydraulic Fracture Propagation Modeling"
}

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