Dual-Representation Mondrian Conformal Assignment of Pressure-Transient GeoTypes: An Independent Reproduction and Extension for Fractured-Reservoir Flow

Version 2 (comprehensive). Fractured reservoirs exhibit recurring fluid-flow behaviours hidden in the shape of their pressure-transient responses. A recent study clusters geologically consistent discrete-fracture-network (DFN) ensembles into flow-behaviour classes and attributes each class to fracture-network properties. This preprint first independently reproduces that pipeline, DFN pressure transients, Bourdet-derivative features, dynamic-time-warping (DTW) k-medoids clustering into a GeoType catalogue, and random-forest / TreeSHAP attribution, from permissively licensed components on the original open 4TU corpus and on analytic dual-porosity families. The reproduction recovers clean clusters, with the real transients clustering more cleanly (silhouette up to 0.86) than the analytic families (0.15-0.27), and it recovers the finding that fracture intensity (log I) is the top attributed control. It then extends the pipeline in two ways. First, it makes the assignment coverage-controlled, which the base random-forest attribution is not, with a class-conditional (Mondrian) split-conformal assigner on a DTW nonconformity score that emits per-class p-values, a prediction set, and an out-of-catalogue flag (empirical coverage 0.85-0.94 at target across the rich-method cases). Second, and the methodological contribution, it introduces a dual-representation Mondrian conformal assigner that conformalizes jointly across two nonconformity scores (the DTW shape distance and a physics-descriptor implausibility from the attribution forest) and accepts a GeoType only in the per-class conjunction of the two prediction sets. This excludes curves that are shape-close to the wrong physics, which single-score conformal accepts: across five rich-method cases the dual conjunction trades marginal coverage (e.g. 0.85 to 0.73, 0.94 to 0.87) for tighter, physics-consistent sets. The shape machinery is signal-agnostic and is exercised on real hydrogeology pumping-test field data as well as reservoir transients. The manuscript includes the reproduced pipeline over twenty-one committed cases, three purpose-driven figures generated deterministically from the committed traces, the dual-conformal equations, and a per-case appendix. The contribution is a faithful, independent reproduction plus a coverage-controlled assignment that fuses shape space and physics-descriptor space, with every number backed by a committed deterministic artifact. Code, artifacts, and workbench (MIT): https://github.com/fsantibanezleal/CAOS_RES_Pulso . Reusable shape machinery (Apache-2.0): https://github.com/fsantibanezleal/CAOS_GeoTypes .