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Hydraulic Fracture Propagation Modeling L1-461

Petroleum EngineeringWell stimulationδ=5 · challengingL_DAG = 4📋 Stub — not mineable
📋

Unclaimed Principle — open for contribution

This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.

To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.

Forward model E

dp/dt = q/(V_f + C_L\cdot A_f); w = (K_Ic/(E'\cdot \sqrt{L))) for PKN/KGD model

Hydraulic Fracture Propagation Modeling: Hydraulic fracture modeling: infer fracture geometry (length, height, width) from treatment pressure and microseismic data. The forward operator produces the measurement through a 3-node primitive DAG (M.pkn.fracture_model…); recovery is posed as a nonlinear_inverse problem. Difficulty tier delta=5 with effective condition number kappa_eff~500; stress_shadow_complexity, natural_fracture_interaction set the accuracy floor at the Omega boundary. See the forward_model field for the closed-form equation.

L-DAG

N.pointwise -> S.pressure_decline.analysis -> O.microseismic.inversion
N.pointwiseS.pressure_decline.analysisO.microseismic.inversion

Well-posedness W

Existence:
true
Uniqueness:
true
Stability:
conditional
κ:
10000

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.

Solvability C

Solver class:
sparse-recovery [PKN_KGD_analytical or UFM_complex_fracture or GEOS_3D]
Convergence rate q:
2
Complexity:
O(N_timesteps * N_elements) for numerical fracture propagation per iteration

Specs (0)

No L2 specs registered yet for this principle.