Injectivity-Floor Calculator for Power-Law Fluids in Blended Porous Packs
A screening module for reservoir and process engineers that certifies minimum flow capacity (injectivity) for non-Newtonian, power-law fluids moving through Minkowski-blended porous or packed geometries, using two reference solves instead of full nonlinear simulations.
Concept
A screening tool for engineers who inject non-Newtonian (shear-thinning, power-law) fluids — polymer floods, chemical floods, polymer-laden slurries — into packed or porous media. Because the p-Laplace equation is the standard model for steady power-law flow, the A-capacity studied in [0] serves as an injectivity/conductivity-type figure of merit for a pore or grain geometry. The module takes the measured or once-simulated flow capacities of two reference microstructure geometries (e.g., two grain-size packs or graded-filter layouts) and returns certified lower bounds on the flow capacity of any Minkowski blend of them — mixed or graded packings — with no further nonlinear flow simulation. Engineers use it to pre-screen pack and flood designs for a guaranteed minimum injectivity before committing to full field-scale simulation.
Why now
Paper [0] establishes the Brunn–Minkowski inequality for the nonlinear A-capacity tied to a p-Laplace-type PDE: the capacity of any Minkowski blend of two convex sets is bounded below by the weighted combination of the individual capacities (each raised to 1/(n−p)). Paper [2] demonstrates that effective behavior of fluid-filled porous microstructures can be rigorously derived by averaging as pore size shrinks (homogenization). Together, these justify certified, closed-form flow-capacity floors for blended and averaged pack geometries — a cheap guarantee that was not available for nonlinear (power-law) flow before [0].
Written by GLM · 2 Oct 2026
AI assessment
A highly specialized engineering tool that leverages a new mathematical inequality to provide guaranteed flow-capacity floors for non-Newtonian fluids, offering a significant speed-up for reservoir design screening.
- Evidence strength 4/5
- The idea directly applies the proven Brunn-Minkowski inequality for A-capacity from the full text of [2] to the physical problem of power-law fluid flow, supported by the homogenization theory in [1].
- Market pull 3/5
- While the target companies (SLB, Halliburton) have clear needs for polymer-flood optimization, the specific demand for a 'lower bound' screener versus a full simulation is a niche workflow requirement.
- Novelty & moat 3/5
- It is a domain-specific application of the same mathematical mechanism used in the 'Certified Capacitance-Floor Screener' (similarity 0.50), but it targets a distinct industrial physics problem (fluid injectivity vs. electrical capacitance).
- Feasibility 5/5
- The core value is a closed-form calculation based on two reference solves, making the MVP a simple calculator rather than a complex simulation engine.
- Wedge clarity 4/5
- The focus on 'injectivity screening' for polymer-flood designs provides a sharp, high-value entry point for reservoir engineers.
- Simplicity / focus 5/5
- The product is a single, focused screening module with one clear mathematical function and a specific output.
Scored by Gemma 4 · 8 Oct 2026. Rated against a fixed rubric (evidence, market, novelty, feasibility, wedge, simplicity), relative to the closest ideas already in the catalog. A prior estimate to compare ideas before real-world signal arrives.
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Who benefits
Its STARS simulator is a standard tool for polymer/chemical EOR; a certified injectivity-floor screening module is a natural pre-simulation add-on for its customers.
- SLB (Schlumberger)company
Provides EOR services and reservoir simulation; closed-form injectivity bounds would cut the cost of screening polymer-flood designs across rock and pack scenarios.
- Halliburtoncompany
Same EOR evaluation need — cheap certified screening of non-Newtonian injection scenarios before expensive field-scale modeling.
- Baker Hughescompany
Screens chemical and polymer EOR projects; guaranteed minimum injectivity for blended pack designs supports go/no-go decisions.
- SNFcompany
The world's largest polyacrylamide (EOR polymer) producer could use certified injectivity floors to position polymer grades by guaranteed flow performance in blended packs.
Research it builds on
- Transactions of the American Mathematical Society2026 · 1772 citationsAll ideas from this paper →
- Memoirs of the American Mathematical SocietyAkman, Murat, Gong, Jasun, Hineman, Jay et al. · 2026 · 662 citationsAll ideas from this paper →