Use a formula sheet for a quick reference and a review checklist to record the assumptions behind a calculation. When several results depend on the same inputs, use a linked workflow to keep the geometry, pressure basis and time units consistent. Each workflow includes its equations, source references, reproducible example and model limits; it does not infer missing field measurements or replace an approved engineering procedure.
Solve vapor, two liquids and pure C18 crystal amounts together, with a depleted-fluid flash, crystal complementarity and component-balance checks.
Model boundary: 280-315 K and 0.1-1 MPa absolute; propane/n-heptane/water/n-octadecane only. One vapor, at most two PR liquids and one pure C18 crystal. This is not an arbitrary-composition commercial VLLS simulator.
Solve coupled cross-sectional Navier-Stokes velocity and relative pressure in a rotating eccentric annulus with mesh, momentum and energy checks.
Model boundary: Steady, fully developed, isothermal, incompressible Newtonian flow on one 2-D cross-section with three velocity components. No axial variation except constant pressure gradient, no ends/inlet development and no moving mesh.
Compare sI and sII hydrate onset for a methane-rich gas using guest fugacities, supplied water activity and explicit Langmuir cage occupancies.
Model boundary: 273.15-303.15 K, 3-10 MPa(a), water activity 0.8-1; fixed CH4-rich gas only. Condensation, failed gas stability and unbracketed onset fail explicitly.
Trace both C1-C6 bubble and dew branches through the critical neighborhood, correcting native continuation seeds and auditing every returned equilibrium state.
Model boundary: C1-C6 only, all kij=0, classical PR without volume translation. This is not a tuned composition/interaction regression, water association model or arbitrary multi-liquid phase topology.
Minimize Gibbs energy for one regular-solution liquid and separate C18/C20 crystals with material balance, convexity and solid-stability checks.
Model boundary: 250-330 K, increasing interval no wider than 60 K. The sufficient convexity gate deliberately rejects some potentially solvable cases; it is not an LLE solver.
Solve axial pressure-driven and rotational annular flow together with one HB stress invariant, no-slip constraints and mechanical power closure.
Model boundary: Steady, concentric, uniform annulus, 0.2<=Ri/Ro<=0.9. Fully developed creeping flow, no end losses or axial wall motion.
Solve all three velocity components and cross-sectional pressure in an eccentric annulus using regularized HB rheology and mixed finite elements.
Model boundary: Fully developed, isothermal creeping regularized HB, stationary outer cylinder. No exact plug-boundary claim, no turbulent correction or full Taylor stability analysis.
Trace pressure waves after prescribed downstream velocity closure with a fixed reservoir, Darcy friction, grid refinement and absolute-pressure cavitation rejection.
Model boundary: One horizontal uniform pipe with constant density/wave speed, V/a<0.01 and quasi-steady Darcy friction. No branches, variable diameter or arbitrary terminal equipment.
Track a well segment and surrounding rock through heating/cooling, shut-in and restart using radial heat diffusion, thermal storage and energy-conserving matrix exponentials.
Model boundary: One local axial segment, uniform initial state and constant properties. No axial advection, geothermal gradient, full circulating well profile, casing-layer resolution or phase change.
Split a measured C7+ mean into four bounded gamma cuts and inspect the PR phase split, cut properties and molecular-weight closure.
Model boundary: A deliberately bounded four-cut approximation over 100-300 g/mol, not a complete Whitson C7-to-C80 assay. Every cut uses the same supplied 60/60 F SG. Reject an unbracketed mean, retained gamma probability below 1e-6, Tb>=Tc or omega outside 0-1. Shape does not determine aromaticity or a measured carbon-number distribution.
Fit one methane/heavy-cut interaction parameter to fixed-temperature pressure and vapor-mole-fraction observations, with sensitivity and residual checks.
Model boundary: A deliberately bounded four-cut approximation over 100-300 g/mol, not a complete Whitson C7-to-C80 assay. Every cut uses the same supplied 60/60 F SG. Reject an unbracketed mean, retained gamma probability below 1e-6, Tb>=Tc or omega outside 0-1. Shape does not determine aromaticity or a measured carbon-number distribution.
Solve a heavy-mixture pressure-drop energy flash using an explicitly supplied heavy ideal-gas heat-capacity fit and four characterized C7+ cuts.
Model boundary: A deliberately bounded four-cut approximation over 100-300 g/mol, not a complete Whitson C7-to-C80 assay. Every cut uses the same supplied 60/60 F SG. Reject an unbracketed mean, retained gamma probability below 1e-6, Tb>=Tc or omega outside 0-1. Shape does not determine aromaticity or a measured carbon-number distribution.
Calculate PR phase equilibrium for C1-C6, iC4/iC5, N2, CO2 and H2S with pinned ChemSep PR pairs and explicit missing-pair assumptions.
Model boundary: Classical PR, no volume translation, at most one vapor and one liquid phase, 180-450 K, 0.1-10 MPa(a). Fixed component list only. No heavy ends, reactions, ionic species, adsorption, wax or hydrates. Numerical stability search is not proof of stability against arbitrary additional phases.
Explore vapor and up to two PR liquids with water, light hydrocarbons and noncondensables, while identifying assumed versus database interaction parameters.
Model boundary: Classical PR, no volume translation, at most one vapor and two liquid phases, 280-450 K, 0.1-10 MPa(a). Fixed component list only. No heavy ends, reactions, ionic species, adsorption, wax or hydrates. Numerical stability search is not proof of stability against arbitrary additional phases.
Find a fixed-composition PR outlet state at equal entropy and a specified pressure, with ideal shaft work and equilibrium closure checks.
Model boundary: Six components C1-C6, normal C4-C6, classical PR and all kij=0. No water, isomers, sour gas, heavy fractions, reactions, solids or volume translation. Use the expanded-mixture tools for their explicitly supported alternatives, not by inserting a new species in these fixed feed slots.
Calculate thirty audited PR saturation endpoints across a bounded temperature band without claiming a complete critical or retrograde phase envelope.
Model boundary: Six components C1-C6, normal C4-C6, classical PR and all kij=0. No water, isomers, sour gas, heavy fractions, reactions, solids or volume translation. Use the expanded-mixture tools for their explicitly supported alternatives, not by inserting a new species in these fixed feed slots.
Remove vapor at three prescribed PT stages, carry only liquid forward and check overall component and interstage energy balances.
Model boundary: Six components C1-C6, normal C4-C6, classical PR and all kij=0. No water, isomers, sour gas, heavy fractions, reactions, solids or volume translation. Use the expanded-mixture tools for their explicitly supported alternatives, not by inserting a new species in these fixed feed slots.
Solve local PR equilibrium, pressure and temperature together with prescribed heat transfer, friction, elevation and changing kinetic energy.
Model boundary: Six components C1-C6, normal C4-C6, classical PR and all kij=0. No water, isomers, sour gas, heavy fractions, reactions, solids or volume translation. Use the expanded-mixture tools for their explicitly supported alternatives, not by inserting a new species in these fixed feed slots.
Couple local PR phase change, prescribed drift-flux holdup, pressure and total energy along a short upward hydrocarbon interval.
Model boundary: Six components C1-C6, normal C4-C6, classical PR and all kij=0. No water, isomers, sour gas, heavy fractions, reactions, solids or volume translation. Use the expanded-mixture tools for their explicitly supported alternatives, not by inserting a new species in these fixed feed slots.
Find a bounded isentropic ideal-nozzle mass-flux maximum with PR phase equilibrium, rather than applying an ideal-gas choke formula to a changing mixture.
Model boundary: Six components C1-C6, normal C4-C6, classical PR and all kij=0. No water, isomers, sour gas, heavy fractions, reactions, solids or volume translation. Use the expanded-mixture tools for their explicitly supported alternatives, not by inserting a new species in these fixed feed slots.
Inspect ideal liquid/pure-solid equilibrium for one wax molecule using supplied fusion data and an explicit component material balance.
Model boundary: Ideal one-solute liquid plus pure crystalline solid; constant Hfus, deltaCp=0 and negligible pressure dependence. No petroleum multicut wax, solid solutions, nonideal activity model, asphaltenes or vapor equilibrium. An ideal onset is not a measured crude-oil WAT.
Invert the IAPWS ice Ih melting curve at absolute pressure and compare it with a supplied pure-water temperature.
Model boundary: Pure ordinary water only; no brine, dissolved gas, methanol/glycol inhibition, gas hydrate, pore-size effects or ice polymorph beyond Ih. This model must not be used as a natural-gas hydrate prediction.
Solve low-inertia concentric-cylinder HB rotation, torque, yielded radius and dissipation with exact stress balance and no-slip integral closure.
Model boundary: Concentric steady creeping azimuthal HB flow only. No axial/helical flow, eccentricity, end effects, wall slip, cuttings, elasticity, thixotropy or temperature variation. Do not superpose this torque with axial HB pressure loss; nonlinear helical shear components are coupled.
Estimate one C7+ pseudocomponent from measured molecular weight and specific gravity, then calculate its Peng-Robinson equilibrium split with C1-C6.
Model boundary: One light-to-medium C7+ lump only: M=100-300 g/mol and SG=0.65-0.90. This is a deliberately restricted correlation use, not a universal heavy-oil/asphaltene characterization. Reject Tb>=Tc or omega outside 0-1. No fallback to Pedersen, multicut/gamma splitting, carbon-number distribution, volume translation, sulfur/aromatic calibration or measured-PVT matching.
Solve PR outlet temperature and equilibrium compositions after a pressure drop with prescribed heat input; zero heat input gives an isenthalpic C1-C6 flash.
Model boundary: C1-C6 only with normal C4-C6, zero binary interaction parameters, no volume translation and the pinned ideal-gas caloric functions. No C7+ heat-capacity assumption, wet/sour gas, arbitrary mixture, chemical reaction, multiple liquids or solid phase. Agreement with an independent implementation does not replace measured-PVT validation.
Solve SRK outlet temperature and equilibrium compositions after a pressure drop with prescribed heat input; zero heat input gives an isenthalpic C1-C6 flash.
Model boundary: C1-C6 only with normal C4-C6, zero binary interaction parameters, no volume translation and the pinned ideal-gas caloric functions. No C7+ heat-capacity assumption, wet/sour gas, arbitrary mixture, chemical reaction, multiple liquids or solid phase. Agreement with an independent implementation does not replace measured-PVT validation.
Flash a C1-C6 hydrocarbon mixture with Peng-Robinson: equilibrium phase compositions, vapor mole/mass fractions, densities and closure checks.
Model boundary: Screening PT vapor-liquid equilibrium for mixtures of C1, C2, C3, nC4, nC5 and nC6 only, with conventional quadratic attraction/linear covolume mixing and kij=0. No isobutane/isopentane, C7+ pseudocomponents, water, CO2, H2S, nitrogen, brine, hydrates, wax, solids, adsorption or multiple liquid phases. Zero kij is a disclosed assumption, not a verified interaction fit for any particular sample.
Calculate a C1-C6 hydrocarbon equilibrium split with the SRK EOS and compare phase compositions, vapor fractions and densities with Peng-Robinson.
Model boundary: Screening PT vapor-liquid equilibrium for mixtures of C1, C2, C3, nC4, nC5 and nC6 only, with conventional quadratic attraction/linear covolume mixing and kij=0. No isobutane/isopentane, C7+ pseudocomponents, water, CO2, H2S, nitrogen, brine, hydrates, wax, solids, adsorption or multiple liquid phases. Zero kij is a disclosed assumption, not a verified interaction fit for any particular sample.
Calculate eccentric yield-power-law annular friction with a self-consistent local flow index, effective diameter and roughness-aware turbulent branch.
Model boundary: Stationary uniform eccentric circular annulus, incompressible time-independent HB liquid. This is the generalized empirical AADE hydraulic method, not an exact eccentric HB solution or a field-calibrated turbulence closure. No rotation, skew, cuttings bed, elasticity, gas, wall slip, local/entrance losses, hydrostatic head or temperature-dependent rheology.
Integrate water/steam pressure, enthalpy, temperature and equilibrium vapor fraction with heat exchange, friction, acceleration and elevation.
Model boundary: Steady one-dimensional pure-water homogeneous equilibrium screening model: equal phase velocities and instantaneous thermal/phase equilibrium. No hydrocarbon composition flash, salts/brine, dissolved/noncondensable gas, slip/holdup correlation, metastable nucleation delay, severe slugging, countercurrent flow or reservoir coupling. This is not a general petroleum PVT/production-well simulator.
Estimate eccentric annular laminar/turbulent friction using power-law rheology, effective diameter and wall roughness, with both branch losses.
Model boundary: Power-law, time-independent incompressible liquid in a stationary uniform eccentric annulus. No yield stress/Herschel-Bulkley extrapolation, pipe rotation, cuttings bed, wall slip, gas, thermal feedback, local/entrance losses or hydrostatic head. This is friction-only, not a complete standpipe-pressure, ECD, hole-cleaning or well-control design.
Estimate liquid temperature and heat exchange along a wellbore with geothermal gradient, tubing resistance and long-time formation conduction.
Model boundary: Ramey's approximate single-phase incompressible-liquid case at one fixed operating time, with constant flow rate, heat capacity, U and formation thermal properties. Radial formation conduction and quasi-steady wellbore heat transfer; linear geothermal background along one uniform interval. It does not solve an early-time thermal transient or arbitrary injection/shut-in history.
Estimate short-segment gas/liquid pressure loss and holdup with Beggs-Brill regime selection, inclination corrections and measured local properties.
Model boundary: Empirical smooth-pipe co-current gas/liquid correlation. Constant local phase density, viscosity and surface tension; no oil/water emulsion, flashing, thermal change, roughness extension, countercurrent flow, choking, terrain-slug dynamics, severe slugging or automatic measured-data calibration. No Payne/Palmer correction or NeqSim thermodynamic engine is included.
Solve concentric laminar yield-power-law annular flow at a specified rate, retaining radial curvature, both yield surfaces and a moving plug.
Model boundary: Incompressible, time-independent HB liquid; fully developed laminar axial flow in a stationary concentric circular annulus with no wall slip. No eccentricity, pipe rotation, turbulence, entrance losses, thixotropy, viscoelasticity, cuttings transport, gas or thermal/property variation is modeled.
Compare slip-aware and no-slip upward gas/liquid profiles using calibrated drift-flux inputs, phase momentum, friction and liquid holdup.
Model boundary: Steady, vertical upward, co-current, isothermal gas/liquid screening only. No downward, counter-current, horizontal or inclined slip model; no regime selection, empirical Shi/Hagedorn-Brown/Beggs-Brill implementation, phase flash, dissolution, heat transfer, slug transients or reservoir coupling. This is a reduced model, not the full T2Well simulator.
Calculate exact Newtonian concentric-annulus friction loss and the radial velocity profile, with geometry and conservative laminar-range checks.
Model boundary: Single incompressible Newtonian liquid, stationary concentric circular walls and fully developed laminar axial flow only. No eccentricity, pipe rotation, roughness-driven turbulence, washouts, yield stress, shear thinning, cuttings, gas or wall slip is modeled. Do not substitute a Herschel-Bulkley apparent viscosity and call this a non-Newtonian annular solution.
Integrate an isothermal no-slip gas/liquid screening profile with friction, elevation and gas-expansion acceleration, checked against momentum closure.
Model boundary: This is explicitly a homogeneous no-slip isothermal screening model, not Beggs-Brill, Hagedorn-Brown, drift-flux, a mechanistic flow-regime solver or three-phase PVT. It does not model slugging, slip, actual liquid holdup, gas liberation/dissolution, phase change, heat transfer, compositional properties or flow assurance.
Fit a local log-linear porosity/permeability transform to measured core pairs, with residuals, extrapolation warnings and portable saved-work files.
Model boundary: This is a locally calibrated empirical log-linear transform, not a universal porosity-to-permeability equation, Kozeny-Carman pore-geometry model, NMR transform or effective-permeability upscaling method. Porosity alone does not identify pore connectivity, grain size, diagenesis, fracture contribution or directional permeability.
Solve DAK and Hall-Yarborough gas compressibility factors from reduced pressure and temperature, with checked residuals and a pressure comparison curve.
Model boundary: This comparison deliberately supports only 0.2 <= P_pr <= 15 and 1.2 <= T_pr <= 3. The software envelope is narrower than the cited DAK range; near-critical, subcritical and higher-pressure extensions are not implemented. Bounds are enforced, not treated as extrapolation warnings.
Fit yield stress, consistency and flow exponent to shear-rate/stress measurements with bounded nonlinear least squares, residuals and saved-work exports.
Model boundary: A fitted Herschel-Bulkley yield stress is an extrapolated model intercept, not gel strength or an independently measured static yield point. No confidence intervals, outlier removal, measurement weighting, thixotropy, wall-slip correction or instrument-to-SI conversion is inferred.
Calculate annular cement volume, planned excess, whole sacks and mixing water from hole geometry and laboratory slurry yield.
Model boundary: One uniform concentric interval only. Add shoe-track, rat-hole and other volumes separately; washouts and caliper data are not inferred.
Forecast production rate and cumulative oil with exponential, hyperbolic and harmonic decline over a defined time horizon.
Model boundary: A parameter-driven, single-segment forecast, not an automatic history match or reserve estimate. No economic cutoff, downtime or operating change is included.
Compare saturated solution gas-oil ratio correlations over absolute pressure, with transparent coefficient selection and applicability checks.
Model boundary: Correlation agreement is not validation. Select or calibrate against measured PVT data; this tool does not rank accuracy or replace a laboratory study.
Link hydrostatic pressure, measured annular pressure loss, ECD, annular velocity and volume using one consistent set of drilling inputs.
Model boundary: One constant-density, uniform annular section. No cuttings loading, eccentricity, compressibility or temperature-density profile is modelled.