Multiphase flow
Fast, physically grounded computation for complex gas–liquid flow, measurement, and real-time operational decisions.
Research · Computation · Field Intelligence
Mathematics for systems
that refuse to be simple.
DigitronX, LLC is a Missouri research and scientific-software company developing computational methods for multiphase flow, carbon capture, utilization and storage, stiff dynamical systems, and behavioral health measurement.
Springfield, MissouriEstablished 2026Independent research
Research programs
Where hard science meets usable computation.
Our work is organized around problems in which conventional computation becomes too slow, too fragile, or too detached from physical reality.
CCUS measurement
Methods for CO₂ transport, impurity effects, custody transfer, and defensible uncertainty assessment.
Stiff systems
Singular-perturbation and composite methods designed to turn severe stiffness from a burden into a computational advantage.
Computational psychiatry
Mathematical approaches to diagnostic agreement, population heterogeneity, biomarkers, and clinical decision-making.
Current work
Problems under active investigation.
DigitronX is building a focused research portfolio rather than a catalog of generic services. These programs share a common aim: results that are mathematically sound, physically interpretable, and useful on the timescale of a real decision.
Energy systems
Near-real-time computation for CO₂ transport
Composite stiff-system methods for rapid estimates of phase behavior, impurity effects, and operational transitions in carbon-dioxide pipelines.
Measurement
Defensible CCUS custody transfer
A measurement framework linking equation-of-state uncertainty, multiphase behavior, instrument response, and the evidence required for an auditable transfer certificate.
Numerical methods
The stiffer the better
A renewed program in singular perturbation: identify the fast structure, replace brute-force integration where justified, and preserve physical constraints across regimes.
Behavioral health
The mathematics of diagnostic reliability
Research showing how apparent agreement depends not only on diagnosticians, but also on thresholds, population heterogeneity, and where subjects lie relative to a decision boundary.
Research descriptions identify active directions; they are not claims of completed commercial products.
Phase-flow capability
Models fast enough for the control room—and honest enough to say when they should not be trusted.
DigitronX works at the intersection of stiff numerical methods, field measurement of two-phase pipeline flow, and CO₂/acid-gas process chemistry.
Real-time transient modeling
Reduced-order and composite methods for stiff pipeline dynamics, transient forecasting, virtual flow metering, and continuous recalibration against sparse pressure and temperature measurements.
Two-phase flow measurement
Interpretation of gas–liquid flow regimes in offshore and hilly-terrain pipelines, grounded in firsthand field measurement and the practical limits of instrumentation.
CO₂ transport and acid-gas chemistry
Analysis of impurity effects, selective H₂S removal, high-pressure gas purification, phase behavior, and measurement consequences for CCUS transport.
Measurement models and diagnostics
Meter, densitometer, and analyzer models at the interface level: measurement equations, uncertainty structure, dynamic response, failure signatures, and self-validating diagnostics.
Stability, safety, and control criteria
Perturbation-derived, criterion-based analysis for stiff reacting and transport systems—designed to produce interpretable go/no-go boundaries rather than opaque numerical output.
Field and scientific foundation
Digitron, Inc. field systems studied offshore and hilly-terrain gas-condensate pipelines for Shell, Mobil, and Standard Oil of California (Chevron), with results reported through the American Gas Association. Related peer-reviewed work addressed stiff computation, CO₂/H₂S separation, gas purification, stability, and process control.
Engagements
Technical consulting and algorithm development · CCUS measurement strategy · independent technical review · advisory work with metering, digital-twin, and virtual-flow-metering teams · lecturing and training
Why the method is different
Conventional solvers can spend their greatest effort resolving dynamics that have already relaxed. DigitronX uses singular-perturbation structure to remove that unnecessary computational burden—while retaining a diagnostic that indicates when the reduced model is no longer trustworthy.
What DigitronX can deliver
Technical work products—not generic advice.
- 01Reduced-order transient models
- 02Virtual-flow-metering algorithms
- 03In-line model-validity diagnostics
- 04CO₂ impurity and phase-transition analyses
- 05Measurement uncertainty assessments
- 06Prototype scientific software and computational proofs of concept
Selected field record
Measurement where the physics becomes inconvenient.
1985 · Hilly-terrain system
Rickman–Painter
Two-phase measurement in a hilly-terrain gas-condensate pipeline, where elevation changes, liquid accumulation, and intermittent behavior complicated conventional interpretation.
1986 · Offshore system
Matagorda offshore system
Field observations using gamma-transmission measurement to characterize gas–liquid behavior through a steel offshore pipeline system under operating conditions.
Selected technical foundations
Evidence behind the capability.
A selective record of the field, computational, chemical, and stability work underlying current DigitronX programs.
Rickman–Painter
Two-phase flow measurement in a hilly-terrain pipeline system; American Gas Association research publication.
Matagorda offshore system
Field observations of two-phase flow in an offshore pipeline system; American Gas Association research publication.
Parameter estimation
Stage-wise parameter estimation for stiff differential equations, published in AIChE Journal.
CO₂ and H₂S chemistry
Peer-reviewed work on selective H₂S removal from CO₂ streams and high-pressure selective gas purification.
Stability criteria
A graded damping-factor criterion for explosion limits in H₂–O₂ kinetics, published in Combustion and Flame.
Stiff computation
Composite asymptotic methods that exploit separated time scales instead of resolving every fast transient by brute force.
Underlying methods
The stiffer,
the better.
DigitronX revives a distinctive line of work: using asymptotic structure to extract reliable answers from systems that defeat ordinary numerical approaches.
- 01Composite asymptotic methods for stiff differential equations
- 02Near-real-time scientific computation
- 03Multiphase-flow measurement and interpretation
- 04CO₂ and H₂S thermodynamics
- 05Diagnostic reliability and psychometric modeling
- 06Translation between mathematical theory and field practice
1983 → 2026
From measurement in the field to computation at decision speed.
The original Digitron, Inc. combined gamma-ray sensing, mathematical inversion, and field engineering to examine multiphase flow through steel pipelines for major oil and gas operators.
DigitronX, LLC is a newly established and legally distinct company. It carries forward the intellectual method—not a claim of continuous corporate operation: begin with the physics, respect the measurement, and make the mathematics serve the field decision.
Founder
Richard C. Aiken, MD, PhD
A career spanning numerical analysis, field engineering, psychiatry, and scientific entrepreneurship.
Dr. Aiken earned his PhD at Princeton University and developed early composite asymptotic methods for stiff chemical systems. His academic and research work has included the University of Utah, ETH Zürich, KTH Stockholm, Washington University in St. Louis, and the University of Illinois.
In 1983 he founded Digitron, Inc., applying gamma-ray measurement and mathematical modeling to multiphase petroleum pipelines. DigitronX is a new company—and a new chapter—bringing that combination of theory, measurement, and field judgment to today’s energy and behavioral-health problems.
Company
Serious work.
Independent thinking.
DigitronX, LLC
Research and scientific software
Springfield, Missouri, USA
Current programs include computational methods for multiphase flow and CCUS, with selected work in behavioral-health measurement.