Material and energy balances, reactor design, separations (distillation, absorption, extraction), transport phenomena, process control and reservoir and petroleum basics.
Chemical Engineering (chemical-engineering-ai999x) is an offline Python package for chemical engineering. It covers material and energy balances, reactor design, separations (distillation, absorption, extraction), transport phenomena, process control and reservoir and petroleum basics.
It has 91 capabilities — 91 computational procedures — in 10 topics, the largest being Separations, Reactor design, Process control, Property estimation, Energy balances and Material balances. Ask a question in words with ask(), or call a capability by name with typed inputs with solve(). Every answer carries its value and unit, the steps that produced it and the formula in LaTeX.
When a question is not determined — a value is missing, an input is out of range, or the request is outside the package — it says so and names what it needs, instead of guessing. It runs on an ordinary CPU without a network connection (Python >=3.10), and the same question always gets the same answer.
pip install chemical-engineering-ai999x hf download AI999X/chemical-engineering-ai999x --local-dir chemical-engineering-ai999x
Each question below was put to chemical-engineering-ai999x and the answer shown is the one it returned, with the steps it took.
First-order CSTR volume: v0 = 36 m^3/h, k = 0.06 1/min, X = 90%
v0 = 36 m^3/h, k = 0.06 1/min, X = 0.9V = 90 m^3, tau = 9000 sCombustion flue gas: fuel = CH4, excess_air = 20%
fuel = CH4, excess_air = 0.2O2_theoretical = 2, air = 11.42857143, n_CO2 = 1, n_H2O = 2, n_SO2 = 0, n_O2 = 0.4, n_N2 = 9.028571429, y_CO2_dry = 0.09589041096, y_O2_dry = 0.03835616438, y_H2O_wet = 0.1609195402, AFR_mass = 20.55283933Bubble-point temperature: x = [0.4, 0.6], ant = [[6.90565, 1211.033, 220.79], [6.95464, 1344.8, 219.482]], units = mmHg_degC, base = log10, P = 1 atm
x = [0.4, 0.6], ant = [6.90565 1211.03 220.79; 6.95464 1344.8 219.482], units = mmHg_degC, base = log10, P = 1 atmT = 368.2916947 K, y = [0.6218490537, 0.3781509463] KRadial Darcy flow: k = 100 md, h = 30 ft, mu = 1.5 cP, pe = 3000 psi, pw = 2500 psi, re = 1000 ft, rw = 0.3 ft
k = 9.869233e-14 m^2, h = 30 ft, mu = 0.0015 (Pa*s), pe = 20684271.88 Pa, pw = 17236893.23 Pa, re = 1000 ft, rw = 0.3 ftq = 0.001606511475 m^3/s, PI = 4.660095801e-10 m^3/(s*Pa)m.solve("chemeng_mccabe_thiele_stages", alpha=2.5, zF=0.5, xD=0.95, q=1, xB=0.05, R=2) alpha = 2.5, zF = 0.5, xD = 0.95, q = 1, xB = 0.05, R = 2N = 11, Rmin = 1.1Adiabatic flame temperature: fuel = CH4, excess_air = 0.0, T_in = 300.0 K
fuel = CH4, excess_air = 0, T_in = 300 KT_ad = 2326.321765 KNPSH available: p_s = 101325.0 Pa, p_v = 2339.0 Pa, rho = 998.0 kg/m^3, z_s = 2.0 m, h_f = 0.5 m
p_s = 101325 Pa, p_v = 2339 Pa, rho = 998 kg/m^3, z_s = 2 m, h_f = 0.5 mNPSHa = 11.61399089 m, pressure_head = 10.35298049 m, vapour_head = 0.2389896014 mExponential decline: qi = 0.0018401307283333335 m^3/s, Di = 9.506426344208685e-09 1/s, t = 63115200.0 s
qi = 0.001840130728 m^3/s, Di = 9.506426344e-09 1/s, t = 63115200 sq = 0.001009885156 m^3/s, Np = 87335.19228 m^3Every snippet was run as shown; the output under it is what it printed.
import chemical_engineering_ai999x as m
a = m.ask("First-order CSTR volume: v0 = 36 m^3/h, k = 0.06 1/min, X = 90%")
print(a.outcome)
print(a.values)
for step in a.steps:
print(step["name"])SOLVED
{'V': 90.0, 'tau': 9000.0}
CSTR volume for a conversion (first order)
import chemical_engineering_ai999x as m
a = m.solve("chemeng_mccabe_thiele_stages", alpha=2.5, zF=0.5, xD=0.95, q=1, xB=0.05, R=2)
print(a.outcome)
print(a.values)SOLVED
{'N': 11, 'Rmin': 1.1}
import chemical_engineering_ai999x as m
# an input is missing: the answer says what it needs instead of guessing
a = m.solve("chemeng_mccabe_thiele_stages")
print(a.outcome)
print(a.message)NEEDS_INPUT
chemeng_mccabe_thiele_stages needs alpha, zF, xD, q, xB, R (relative volatility of the light component (constant); mole fraction of the light component in the feed; mole fraction of the light component in the distillate; feed quality q: 1 saturated liquid, 0 saturated vapour, > 1 subcooled, < 0 superheated; mole fraction of the light component in the bottoms; reflux ratio L/D). Example: solve('chemeng_mccabe_thiele_stages', alpha=2.5, zF=0.5, xD=0.95, q=1, xB=0.05, R=2).
chemical-engineering-ai999x "First-order CSTR volume: v0 = 36 m^3/h, k = 0.06 1/min, X = 90%"
V = 90 m^3, tau = 9000 s 1. CSTR volume for a conversion (first order): design equation V = F_A0 X/(-r_A) at the exit concentration: V = v0 X/(k (1 - X)) with v0 = 36 m^3/h, k = 0.06 1/min, X = 0.9 -> V = 90 m^3, tau = 9000 s Assumptions: 0 <= X < 1; steady state, perfect mixing, constant density, -r_A = k C_A …
Every value in these figures was computed by the package, each point a run of solve(); in a notebook, plot() and plot_relation() draw a capability's curves the same way.
12 of its 91 formulas; every one is in the capability browser below.
Search by name, formula, input or topic. Each capability opens to show what it takes, what it returns, when it applies, and a question it answered.
chemeng_adiabatic_flame_temperatureAdiabatic flame temperature of a gaseous fuel burned with excess dry air at constant pressure, complete combustion without dissociation, from NASA 7-coefficient polynomials (GRI-Mech 3.0 data).
fuel fuel: CH4, C2H6, C3H8, H2, CO, C2H4, C2H2, CH3OH choiceexcess_air excess air as a fraction of theoretical (0 = stoichiometric)T_in temperature of the fuel and air entering [K]T_ad adiabatic flame temperature [K]chemeng_adiabatic_reactor_temperatureOutlet temperature of an adiabatic reactor from the feed, the conversion of the limiting reactant, the heat of reaction at a reference temperature and polynomial heat capacities.
n0 feed amounts of each species, mol (or mol/s) on one basis vectornu stoichiometric coefficients, negative for reactants vectorcp heat-capacity coefficients, one row (a, b, c, d) per species; cp = a + bT + cT^2 + dT^3 in J/(mol K) matrixdH heat of reaction at T_ref, per mole of extent [J/mol]T_ref reference temperature of dH [K]T_in feed temperature [K]key number of the limiting reactant in the species list (1 = first) integerX conversion of the limiting reactantT_out adiabatic outlet temperature [K]chemeng_batch_coil_coolingTemperature of a well-stirred batch after time t when a coolant (or heating liquid) flows once through a coil and leaves warmer (Kern's batch cooling).
M mass of liquid in the tank [kg]cp specific heat of the batch liquid [J/(kg*K)]W coolant mass flow [kg/s]cp_c specific heat of the coolant [J/(kg*K)]t_in coolant inlet temperature [K]UA overall heat-transfer coefficient times coil area [W/K]T0 initial batch temperature [K]t time [s]T batch temperature at time t [K]chemeng_batch_heating_temperatureTemperature of a well-stirred batch heated or cooled by a medium at constant temperature (condensing steam, boiling refrigerant) after time t.
m mass of liquid in the tank [kg]cp specific heat of the liquid [J/(kg*K)]UA overall heat-transfer coefficient times area of the coil or jacket [W/K]T_s temperature of the heating or cooling medium (constant, e.g. condensing steam) [K]T0 initial liquid temperature [K]t heating time [s]T liquid temperature at time t [K]chemeng_batch_heating_timeTime for a well-stirred batch heated or cooled by a medium at constant temperature to reach a stated temperature.
m mass of liquid in the tank [kg]cp specific heat of the liquid [J/(kg*K)]UA overall heat-transfer coefficient times area of the coil or jacket [W/K]T_s temperature of the heating or cooling medium (constant, e.g. condensing steam) [K]T0 initial liquid temperature [K]T temperature to reach [K]t time needed [s]chemeng_reaction_enthalpy_at_temperatureThe heat of reaction at T from its value at T0 and the polynomial heat capacities of the species (Kirchhoff's law).
nu stoichiometric coefficients, negative for reactants and positive for products vectorcp heat-capacity coefficients, one row (a, b, c, d) per species in the order of nu; cp = a + bT + cT^2 + dT^3 in J/(mol K) matrixdH0 heat of reaction at T0, per mole of extent [J/mol]T0 temperature of the known heat of reaction [K]T temperature wanted [K]dH heat of reaction at T, per mole of extent [J/mol]chemeng_sensible_heat_cp_polynomialHeat needed to take n moles from T1 to T2 when cp = a + bT + cT^2 + dT^3 (J/(mol K), T in K), and the mean heat capacity over the range.
n amount of substance [mol]a cp coefficient a, J/(mol K)b cp coefficient b, J/(mol K^2)c cp coefficient c, J/(mol K^3) (default 0) optionald cp coefficient d, J/(mol K^4) (default 0) optionalT1 initial temperature [K]T2 final temperature [K]Q heat added (negative when cooled) [J]cp_mean mean heat capacity between T1 and T2 [J/(mol*K)]chemeng_npsh_availableThe net positive suction head available at a pump inlet, NPSHa = (p_s - p_v)/(rho g) + z_s - h_f, from the pressure on the liquid surface, the vapour pressure, the static head and the suction-line loss; with the required NPSH, the margin.
p_s absolute pressure on the suction liquid surface [Pa]p_v vapour pressure of the liquid at the pumping temperature [Pa]rho liquid density [kg/m^3]z_s liquid surface above the pump inlet (negative for a suction lift) [m]h_f friction head loss in the suction line [m]NPSHr required NPSH of the pump (optional) [m] optionalNPSHa NPSH available [m]pressure_head p_s/(rho g) [m]vapour_head p_v/(rho g) [m]margin NPSHa - NPSHr (with NPSHr) [m]chemeng_pump_headThe total head a pump adds between its suction and discharge, H = (p2 - p1)/(rho g) + (z2 - z1) + (v2^2 - v1^2)/(2g), with the hydraulic power rho g Q H and the shaft power for an efficiency.
p1 suction pressure (absolute) [Pa]p2 discharge pressure (absolute) [Pa]rho liquid density [kg/m^3]dz elevation of the discharge gauge above the suction gauge (default 0) [m] optionalv1 suction velocity (default 0) [m/s] optionalv2 discharge velocity (default 0) [m/s] optionalQ volumetric flow (optional, for the power) [m^3/s] optionaleta pump efficiency (optional, with Q) optionalH total head [m]dp_equivalent head as a pressure rho g H [Pa]P_hydraulic hydraulic power rho g Q H [W]P_shaft shaft power rho g Q H/eta [W]chemeng_blending_flowsThe mass flow of each feed stream needed to make a product of stated flow and composition, from the component balances (as many feeds as components).
W mass fractions of the feed streams: one row per feed stream, one column per component (rows sum to 1) matrixp mass fractions of the product, one per component (sum to 1) vectorP product mass flow [kg/s]F1 flow of the first feed stream [kg/s]F flow of every feed stream, in kg/s, in the order of the rows of Wchemeng_combustion_flue_gasTheoretical oxygen, air supplied, flue-gas moles and wet and dry compositions, and the air-fuel mass ratio for complete combustion of a fuel with excess dry air (21 % O2, 79 % N2).
fuel molecular formula of the fuel (C, H, O, N and S), e.g. CH4, C3H8, C2H5OH textexcess_air excess air as a fraction of the theoretical air (20% = 0.2)O2_theoretical theoretical O2, mol per mol fuelair air supplied, mol per mol fueln_CO2 CO2 in the flue gas, mol per mol fueln_H2O H2O, mol per mol fueln_SO2 SO2, mol per mol fueln_O2 O2, mol per mol fueln_N2 N2, mol per mol fuely_CO2_dry CO2 mole fraction, dry basisy_O2_dry O2 mole fraction, dry basisy_H2O_wet H2O mole fraction, wet basisAFR_mass air-fuel ratio, kg air per kg fuelchemeng_variable_volume_tankVolume and concentration of a well-mixed tank whose inflow and outflow differ, at time t.
V0 liquid volume at t = 0 [m^3]q_in volumetric inflow [m^3/s]q_out volumetric outflow [m^3/s]C_in inlet concentration [mol/m^3]C0 concentration in the tank at t = 0 [mol/m^3]t time [s]V liquid volume at time t [m^3]C concentration at time t [mol/m^3]chemeng_mass_to_mole_fractionsMole fractions of a mixture and its mean molar mass from the mass fractions and the molar masses of the components.
w mass fractions (sum to 1) vectorMW molar masses of the components, g/mol vectorz mole fractionsMW_mean mean molar mass of the mixture [kg/mol]chemeng_recycle_purgeSteady-state flows of a reactor A -> B with complete product separation, recycle of unreacted A and inert, and a purge that removes a fraction of the recycle stream to stop the inert accumulating.
F0 fresh feed flow (reactant A plus inert) [mol/s]zA mole fraction of A in the fresh feed (the rest is inert)X single-pass conversion of A in the reactorf purge fraction: the fraction of the separator overhead (unreacted A + inert) that is purgedR recycle flow [mol/s]P purge flow [mol/s]reactor_feed combined reactor feed flow [mol/s]X_overall overall conversion of A (fresh feed to product)product production rate of B [mol/s]y_inert mole fraction of inert in the recycle and purgechemeng_binary_separator_balanceDistillate and bottoms flows of a binary separator from the feed flow and the three compositions, with the recoveries of the light component in the distillate and of the heavy component in the bottoms.
F feed molar flow [mol/s]zF mole fraction of the light component in the feedxD mole fraction of the light component in the distillate (top product)xB mole fraction of the light component in the bottomsD distillate flow [mol/s]B bottoms flow [mol/s]recovery_D fraction of the light component recovered in the distillaterecovery_B fraction of the heavy component recovered in the bottomschemeng_unsteady_mixing_tankConcentration in a constant-volume well-mixed tank at time t after the inlet concentration changes (inflow equals outflow).
V liquid volume of the tank [m^3]q volumetric flow in and out [m^3/s]C_in inlet concentration [mol/m^3]C0 concentration in the tank at t = 0 [mol/m^3]t time [s]C concentration in the tank (and outlet) at time t [mol/m^3]chemeng_exponential_declineProduction rate and cumulative production at time t of a well in exponential (constant-percentage) decline (Arps b = 0).
qi initial rate (bbl/day and STB/day are converted here) [m^3/s]Di initial nominal decline rate, e.g. 0.3 1/yr [1/s]t time since the start of the decline [s]q rate at time t [m^3/s]Np cumulative production to time t [m^3]chemeng_gas_well_backpressureExponent n, coefficient C and absolute open flow of a gas well from multi-rate test data fitted to q = C (pr^2 - pwf^2)^n.
q test gas rates, in q_unit vectorpwf flowing bottom-hole pressures at those rates, in p_unit vectorq_unit unit of the rates: m3_per_day or Mscf_per_day choicep_unit unit of the flowing pressures choicepr average reservoir (shut-in) pressure [Pa]n back-pressure exponentlog10_C log10 of the coefficient C, with q in m^3/s and pressures in PaAOF absolute open flow (rate at pwf = 0) [m^3/s]chemeng_harmonic_declineProduction rate and cumulative production at time t of a well in harmonic decline (Arps b = 1).
qi initial rate (bbl/day and STB/day are converted here) [m^3/s]Di initial nominal decline rate, e.g. 0.3 1/yr [1/s]t time since the start of the decline [s]q rate at time t [m^3/s]Np cumulative production to time t [m^3]chemeng_hyperbolic_declineProduction rate and cumulative production at time t of a well in hyperbolic decline with Arps exponent 0 < b < 1.
qi initial rate (bbl/day and STB/day are converted here) [m^3/s]Di initial nominal decline rate, e.g. 0.3 1/yr [1/s]b Arps decline exponent (0 < b < 1)t time since the start of the decline [s]q rate at time t [m^3/s]Np cumulative production to time t [m^3]chemeng_closed_loop_stabilityWhether a feedback loop with a proportional controller Kc around a process G(s) = num(s)/den(s) is stable: the largest real part of the closed-loop poles and how many lie in the right half-plane.
num numerator coefficients of G(s), highest power of s first vectorden denominator coefficients of G(s), highest power of s first vectorKc controller gainmax_real largest real part of the closed-loop poles, 1/(time unit of the coefficients)n_rhp number of closed-loop poles in the right half-planestable stable or unstable (text)chemeng_pid_controller_outputOutput of a digital position-form PID controller at each sample for a stated history of errors (rectangular integration, derivative on the error, loop at rest before the first sample).
Kc controller gaintauI integral (reset) time [s]tauD derivative time (0 for PI) [s]dt sampling interval [s]e error samples e_1 ... e_n (set point minus measurement) vectorbias controller output bias (output when the error has always been zero)u_last controller output at the last sampleu controller output at every samplechemeng_fopdt_step_responseDeviation of the output of a first-order process with dead time at time t after a step of size M in its input.
K process gain (output change per unit input change)tau process time constant [s]theta dead time [s]M size of the input step (deviation)t time after the step [s]y output deviation at time t (in the output's units)chemeng_lag_frequency_responseAmplitude ratio and phase angle of a process made of one to three first-order lags in series, at angular frequency w.
K process gaintaus time constants of the lags, in t_unit vectort_unit unit of the time constants choicew angular frequency of the input sinusoid [rad/s]AR amplitude ratio (output amplitude per input amplitude)phase_deg phase angle in degrees (negative: lag)chemeng_pi_loop_marginsGain margin, phase margin and the two crossover frequencies of a loop with a PI controller and a process of three to five first-order lags.
Kc controller gaintauI integral time [s]K process gaintaus time constants of the lags, in t_unit (the integral time is converted to this unit too) vectort_unit unit of the time constants choiceGM gain margin (ratio)PM_deg phase margin, degreesw_pc phase-crossover frequency (phase -180 degrees) [rad/s]w_gc gain-crossover frequency (|L| = 1) [rad/s]chemeng_first_order_step_fitGain and time constant of a first-order process (dead time known) fitted by least squares to the recorded response of a step test.
t sample times from the moment of the step, in t_unit vectory output deviations at those times vectort_unit unit of the times choiceM size of the input steptheta dead time (known) [s]K process gaintau time constant [s]chemeng_p_control_offsetSteady-state output (as a fraction of a set-point step) and the offset of a P-only feedback loop around a process of first-order lags in series, after checking the loop is stable.
Kc controller gainK process gaintaus time constants of the first-order lags in series, in t_unit vectort_unit unit of the time constants choicey_ss final output change per unit set-point changeoffset steady-state offset per unit set-point changechemeng_ziegler_nichols_tuningUltimate gain and period of a process of first-order lags in series, and the Ziegler-Nichols closed-loop settings of a P, PI or PID controller.
K process gaintaus time constants of the lags (three or more), in t_unit vectort_unit unit of the time constants choicecontroller controller type: P, PI or PID choiceKu ultimate gainPu ultimate period [s]Kc controller gaintauI integral time (PI, PID) [s]tauD derivative time (PID) [s]chemeng_virial_compressibilitySecond virial coefficient from the Abbott (Pitzer) correlation and the compressibility factor Z = 1 + BP/(RT) of a gas at moderate pressure.
T temperature [K]P pressure [Pa]Tc critical temperature [K]Pc critical pressure [Pa]omega acentric factorB second virial coefficient [m^3/mol]Z compressibility factorchemeng_watson_heat_of_vaporizationHeat of vaporisation at T from a known value at T_ref and the critical temperature (Watson's correlation, exponent 0.38).
T temperature wanted [K]T_ref temperature of the known value [K]Hvap_ref heat of vaporisation at T_ref [J/mol]Tc critical temperature [K]Hvap heat of vaporisation at T [J/mol]chemeng_riedel_heat_of_vaporizationHeat of vaporisation at the normal boiling point from the boiling point and critical constants (Riedel's equation, Pc in bar).
Tb normal boiling point [K]Tc critical temperature [K]Pc critical pressure [Pa]Hvap_b heat of vaporisation at the normal boiling point [J/mol]chemeng_pitzer_heat_of_vaporizationHeat of vaporisation at T from the critical temperature and acentric factor (Pitzer's corresponding-states correlation as fitted by Carruth and Kobayashi).
T temperature [K]Tc critical temperature [K]omega acentric factorHvap heat of vaporisation [J/mol]chemeng_peng_robinsonCompressibility factors (vapour and liquid roots) and fugacity coefficients of a pure substance at T and P from the Peng-Robinson equation of state.
Tc critical temperature [K]Pc critical pressure [Pa]omega acentric factorT temperature [K]P pressure [Pa]Z_vapour compressibility factor of the vapour-like (largest) rootZ_liquid compressibility factor of the liquid-like (smallest) rootphi_vapour fugacity coefficient on the vapour rootphi_liquid fugacity coefficient on the liquid rootn_roots number of real roots above the covolume (1 or 3)chemeng_rackett_liquid_volumeMolar volume of a saturated liquid from the critical constants and the critical compressibility factor (Rackett equation).
T temperature [K]Tc critical temperature [K]Pc critical pressure [Pa]Zc critical compressibility factorVm saturated liquid molar volume [m^3/mol]chemeng_srkCompressibility factors (vapour and liquid roots) and fugacity coefficients of a pure substance at T and P from the Soave-Redlich-Kwong equation of state.
Tc critical temperature [K]Pc critical pressure [Pa]omega acentric factorT temperature [K]P pressure [Pa]Z_vapour compressibility factor of the vapour-like (largest) rootZ_liquid compressibility factor of the liquid-like (smallest) rootphi_vapour fugacity coefficient on the vapour rootphi_liquid fugacity coefficient on the liquid rootn_roots number of real roots above the covolume (1 or 3)chemeng_lee_kesler_vapour_pressureVapour pressure of a pure substance from its critical constants and acentric factor (Lee-Kesler corresponding-states correlation).
T temperature [K]Tc critical temperature [K]Pc critical pressure [Pa]omega acentric factorPsat vapour pressure [Pa]chemeng_batch_conversion_first_orderConversion reached in an isothermal batch reactor after time t for a first-order reaction.
k first-order rate constant [1/s]t reaction time [s]X conversion of Achemeng_batch_conversion_second_orderConversion and concentration reached in an isothermal batch reactor after time t when -r_A = k C_A^2.
k second-order rate constant (-r_A = k C_A^2) [m^3/(mol*s)]CA0 feed (initial) concentration of A [mol/m^3]t reaction time [s]X conversion of ACA concentration of A at time t [mol/m^3]chemeng_batch_time_first_orderReaction time an isothermal batch reactor needs to reach conversion X for a first-order reaction.
k first-order rate constant [1/s]X conversion of A wantedt reaction time [s]chemeng_batch_time_second_orderReaction time an isothermal batch reactor needs to reach conversion X when -r_A = k C_A^2.
k second-order rate constant (-r_A = k C_A^2) [m^3/(mol*s)]CA0 feed (initial) concentration of A [mol/m^3]X conversion of A wantedt reaction time [s]chemeng_cstr_conversion_first_orderSteady-state conversion of a CSTR of volume V for a first-order liquid-phase reaction.
v0 volumetric feed flow [m^3/s]V reactor volume [m^3]k first-order rate constant [1/s]X conversion of Achemeng_cstr_conversion_second_orderSteady-state conversion and exit concentration of a CSTR of volume V when -r_A = k C_A^2.
v0 volumetric feed flow [m^3/s]V reactor volume [m^3]k second-order rate constant (-r_A = k C_A^2) [m^3/(mol*s)]CA0 feed (initial) concentration of A [mol/m^3]X conversion of ACA exit concentration of A [mol/m^3]chemeng_cstr_volume_first_orderVolume and space time of a CSTR that reaches conversion X for a first-order liquid-phase reaction.
v0 volumetric feed flow [m^3/s]k first-order rate constant [1/s]X conversion of A wantedV reactor volume [m^3]tau space time V/v0 [s]chemeng_cstr_volume_second_orderVolume and space time of a CSTR that reaches conversion X when -r_A = k C_A^2 (liquid phase, constant density).
v0 volumetric feed flow [m^3/s]k second-order rate constant (-r_A = k C_A^2) [m^3/(mol*s)]CA0 feed (initial) concentration of A [mol/m^3]X conversion of A wantedV reactor volume [m^3]tau space time V/v0 [s]chemeng_cstrs_in_series_first_orderConversion leaving N equal CSTRs in series, each of volume V, for a first-order liquid-phase reaction.
v0 volumetric feed flow [m^3/s]V volume of EACH tank [m^3]k first-order rate constant [1/s]N number of equal tanks in series integerX overall conversion of Achemeng_cstrs_in_series_second_orderConversion leaving N equal CSTRs in series, each of volume V, when -r_A = k C_A^2.
v0 volumetric feed flow [m^3/s]V volume of EACH tank [m^3]k second-order rate constant (-r_A = k C_A^2) [m^3/(mol*s)]CA0 feed (initial) concentration of A [mol/m^3]N number of equal tanks in series integerX overall conversion of ACA exit concentration of A [mol/m^3]chemeng_pfr_gas_volume_first_orderVolume of an isothermal, isobaric gas-phase plug-flow reactor for conversion X of a first-order reaction whose mole number changes (factor eps).
FA0 molar feed flow of A [mol/s]CA0 concentration of A at the inlet [mol/m^3]k first-order rate constant [1/s]eps volume-change factor eps = y_A0 * (change in moles per mole of A); e.g. A -> 2B with pure A: eps = 1X conversion of A wantedV reactor volume [m^3]chemeng_pfr_gas_volume_second_orderVolume of an isothermal, isobaric gas-phase plug-flow reactor for conversion X when -r_A = k C_A^2 and the mole number changes (factor eps).
FA0 molar feed flow of A [mol/s]CA0 concentration of A at the inlet [mol/m^3]k second-order rate constant (-r_A = k C_A^2) [m^3/(mol*s)]eps volume-change factor eps = y_A0 * (change in moles per mole of A); e.g. A -> 2B with pure A: eps = 1X conversion of A wantedV reactor volume [m^3]chemeng_pfr_conversion_first_orderConversion at the exit of an isothermal plug-flow reactor of volume V for a first-order constant-density reaction.
v0 volumetric feed flow [m^3/s]V reactor volume [m^3]k first-order rate constant [1/s]X conversion of Achemeng_pfr_conversion_second_orderExit conversion and concentration of an isothermal plug-flow reactor of volume V when -r_A = k C_A^2 (constant density).
v0 volumetric feed flow [m^3/s]V reactor volume [m^3]k second-order rate constant (-r_A = k C_A^2) [m^3/(mol*s)]CA0 feed (initial) concentration of A [mol/m^3]X conversion of ACA exit concentration of A [mol/m^3]chemeng_pfr_volume_first_orderVolume of an isothermal plug-flow reactor that reaches conversion X for a first-order constant-density reaction.
v0 volumetric feed flow [m^3/s]k first-order rate constant [1/s]X conversion of A wantedV reactor volume [m^3]chemeng_pfr_volume_second_orderVolume of an isothermal plug-flow reactor that reaches conversion X when -r_A = k C_A^2 (constant density).
v0 volumetric feed flow [m^3/s]k second-order rate constant (-r_A = k C_A^2) [m^3/(mol*s)]CA0 feed (initial) concentration of A [mol/m^3]X conversion of A wantedV reactor volume [m^3]chemeng_recycle_reactor_first_orderOverall conversion of a plug-flow reactor with recycle ratio R (recycled flow / product flow) for a first-order constant-density reaction.
v0 fresh volumetric feed flow [m^3/s]V reactor volume [m^3]k first-order rate constant [1/s]R recycle ratio: recycled flow divided by the flow leaving the systemX overall conversion of Achemeng_rtd_momentsMean residence time, variance and the equivalent number of tanks in series from a pulse-tracer response C(t) (trapezoidal rule, uneven spacing allowed).
t sample times, in the unit t_unit vectorC tracer concentrations at those times (any unit) vectort_unit unit of the times: s, min or h choicet_mean mean residence time [s]variance variance of the RTD [s^2]N_tanks equivalent number of equal tanks in series, t_mean^2/variancechemeng_reversible_first_order_batchConcentrations and conversion after time t, and the equilibrium conversion, for A <-> B with first-order forward and reverse steps.
k1 forward rate constant (A -> B) [1/s]k2 reverse rate constant (B -> A) [1/s]CA0 feed (initial) concentration of A [mol/m^3]CB0 initial concentration of B [mol/m^3]t reaction time [s]CA concentration of A at t [mol/m^3]CB concentration of B at t [mol/m^3]X conversion of A at tX_eq equilibrium conversion of Achemeng_series_reaction_maximumTime (or plug-flow space time) at which the intermediate B of first-order series reactions A -> B -> C peaks, starting from pure A, and the concentrations there.
k1 rate constant of A -> B [1/s]k2 rate constant of B -> C [1/s]CA0 feed (initial) concentration of A [mol/m^3]t_max time (or space time) of the maximum of B [s]CB_max maximum concentration of B [mol/m^3]CA concentration of A at the maximum [mol/m^3]CC concentration of C at the maximum [mol/m^3]chemeng_gas_pz_material_balanceOriginal gas in place of a volumetric gas reservoir from the straight line of p/z against cumulative gas production.
p average reservoir pressures, in p_unit vectorz gas deviation factors at those pressures vectorGp cumulative gas production at standard conditions, in gp_unit vectorp_unit unit of the pressures choicegp_unit unit of Gp: m3, MMscf or Bscf choiceG original gas in place at standard conditions [m^3]pz_initial p/z extrapolated to no production [Pa]chemeng_havlena_odeh_gas_capOil initially in place and the gas-cap ratio m from the straight line F/Eo = N + N m Eg/Eo of successive surveys (no water influx).
F underground withdrawals, in v_unit at reservoir conditions vectorEo oil and dissolved-gas expansion per unit of oil in place vectorEg gas-cap expansion term per unit of oil in place vectorv_unit unit of F: m3 or bbl choiceN oil initially in place (stock-tank volume) [m^3]m ratio of initial gas-cap to oil-zone reservoir volumechemeng_havlena_odeh_oil_in_placeStock-tank oil initially in place from the underground withdrawal F and the total expansion term Et of successive pressure surveys (no water influx), by the straight line F = N Et through the origin.
F underground withdrawals at each survey, in v_unit at reservoir conditions vectorEt total expansion per unit of oil in place at each survey (reservoir volume per stock-tank volume) vectorv_unit unit of F: m3 or bbl choiceN oil initially in place (stock-tank volume) [m^3]chemeng_horner_buildupPermeability and the extrapolated pressure p* from the semilog straight line of shut-in pressure against the Horner time ratio (tp + dt)/dt.
dt shut-in times, in t_unit vectorpws shut-in bottom-hole pressures, in p_unit vectort_unit unit of the shut-in times choicep_unit unit of the pressures choicetp producing time before shut-in [s]q flow rate before shut-in at reservoir conditions [m^3/s]mu fluid viscosity [Pa*s]h net pay thickness [m]m semilog slope, pressure change per log cycle [Pa]k permeability [m^2]p_star extrapolated pressure p* at (tp + dt)/dt = 1 [Pa]chemeng_radial_darcy_flowSteady-state reservoir flow rate into a vertical well from a circular drainage area, with an optional skin factor, and the productivity index.
k permeability (md is converted here) [m^2]h net pay thickness [m]mu fluid viscosity (cP is converted here) [Pa*s]pe pressure at the drainage radius [Pa]pw flowing bottom-hole pressure [Pa]re drainage radius [m]rw wellbore radius [m]S skin factor (default 0: undamaged well) optionalq flow rate at reservoir conditions [m^3/s]PI productivity index q/(pe - pw) [m^3/(s*Pa)]chemeng_line_source_drawdownPressure drop and pressure at radius r and time t after a well starts producing at a constant rate in an infinite reservoir (line-source, exponential-integral solution).
q flow rate at reservoir conditions [m^3/s]mu fluid viscosity [Pa*s]k permeability [m^2]h net pay thickness [m]phi porosity (fraction)ct total compressibility (1/psi is converted here) [1/Pa]r radius from the well [m]t time since production started [s]pi initial reservoir pressure [Pa]dp pressure drop at r and t [Pa]p pressure at r and t [Pa]chemeng_kremser_absorberSolute mole fraction in the gas leaving a countercurrent absorber of N ideal stages, and the fraction of solute absorbed, for dilute gas with linear equilibrium y = m x.
N number of ideal stages integerA absorption factor A = L/(m V)m slope of the equilibrium line y = m xy_in solute mole fraction in the entering gasx_in solute mole fraction in the entering liquid (solvent)y_out solute mole fraction in the leaving gasrecovery fraction of the entering solute absorbedchemeng_nrtl_activity_coefficientsActivity coefficients and excess Gibbs energy of a liquid mixture from NRTL interaction parameters tau_ij and non-randomness parameters alpha_ij.
x liquid mole fractions vectortau NRTL parameters tau_ij (dimensionless, tau_ii = 0) at the temperature of interest matrixalpha non-randomness parameters alpha_ij (symmetric, alpha_ii = 0) matrixgamma1 activity coefficient of component 1gamma activity coefficients of every componentGE_RT excess Gibbs energy over RTchemeng_uniquac_activity_coefficientsActivity coefficients of a liquid mixture from UNIQUAC volume and area parameters r, q and interaction parameters tau_ij (coordination number 10).
x liquid mole fractions vectorr UNIQUAC volume parameters r_i vectorq UNIQUAC area parameters q_i vectortau UNIQUAC parameters tau_ij = exp(-a_ij/T) at the temperature of interest (tau_ii = 1) matrixgamma1 activity coefficient of component 1gamma activity coefficients of every componentchemeng_wilson_activity_coefficientsActivity coefficients of every component and the excess Gibbs energy of a liquid mixture from Wilson parameters Lambda_ij.
x liquid mole fractions vectorLam Wilson parameters Lambda_ij (dimensionless, Lambda_ii = 1) at the temperature of interest matrixgamma1 activity coefficient of component 1gamma activity coefficients of every componentGE_RT excess Gibbs energy over RTchemeng_antoine_boiling_temperatureTemperature at which a pure liquid boils at pressure P, from Antoine coefficients written in a stated convention.
A Antoine coefficient AB Antoine coefficient BC Antoine coefficient Cunits units the Antoine coefficients are written for: pressure_temperature, e.g. mmHg_degC (P in mmHg, T in degC) or kPa_K choicebase logarithm of the Antoine equation: log10 or ln choiceP pressure [Pa]Tsat saturation temperature [K]chemeng_raoult_bubble_pressurePressure at which a liquid of composition x starts to boil at temperature T, and the composition of the first bubble, for an ideal solution (Raoult's law, Antoine vapour pressures).
x liquid mole fractions vectorant Antoine coefficients, one row (A, B, C) per component, in the stated convention matrixunits units the Antoine coefficients are written for: pressure_temperature, e.g. mmHg_degC (P in mmHg, T in degC) or kPa_K choicebase logarithm of the Antoine equation: log10 or ln choiceT temperature [K]P bubble-point pressure [Pa]y vapour mole fractions of the first bubblechemeng_modified_raoult_bubble_pressureThe bubble-point pressure P = sum x_i gamma_i P_i^sat of a non-ideal liquid with stated activity coefficients and vapour pressures (low pressure, ideal vapour), and the vapour composition y_i = x_i gamma_i P_i^sat/P.
x liquid mole fractions (sum to 1) vectorgamma activity coefficient of each component at this composition vectorPsat vapour pressure of each pure component at the temperature, in the unit p_unit vectorp_unit unit of the vapour pressures: Pa, kPa, MPa, bar, atm or psi choiceP bubble-point pressure [Pa]y1 vapour mole fraction of the first componenty vapour mole fractions, in the order of xchemeng_raoult_bubble_temperatureTemperature at which a liquid of composition x starts to boil at pressure P, and the first-bubble composition (Raoult's law, Antoine vapour pressures; iterative).
x liquid mole fractions vectorant Antoine coefficients, one row (A, B, C) per component, in the stated convention matrixunits units the Antoine coefficients are written for: pressure_temperature, e.g. mmHg_degC (P in mmHg, T in degC) or kPa_K choicebase logarithm of the Antoine equation: log10 or ln choiceP pressure [Pa]T bubble-point temperature [K]y vapour mole fractions of the first bubblechemeng_countercurrent_extractionRaffinate and extract solute ratios and the fraction extracted for N ideal countercurrent stages with immiscible carrier and solvent and a constant distribution ratio Y = K X (solute-free mass-ratio basis).
F solute-free carrier flow in the feed [kg/s]S solute-free solvent flow [kg/s]K distribution ratio Y = K X (mass ratios)N number of ideal stages integerXF solute ratio in the feed, kg solute per kg carrierYS solute ratio in the entering solvent, kg solute per kg solventXN solute ratio in the final raffinateY1 solute ratio in the final extractrecovery fraction of the solute extractedchemeng_crosscurrent_extractionRaffinate solute ratio after N ideal stages, each fed with the same amount of fresh solvent, for immiscible solvents and a constant distribution ratio.
F solute-free carrier flow (or mass) in the feed [kg/s]S solute-free solvent flow (or mass) added to EACH stage [kg/s]K distribution ratio Y = K X (mass ratios)N number of stages integerXF solute ratio in the feed, kg solute per kg carrierXN solute ratio in the final raffinaterecovery fraction of the solute extractedchemeng_raoult_dew_pressurePressure at which a vapour of composition y starts to condense at temperature T, and the composition of the first drop (Raoult's law, Antoine vapour pressures).
y vapour mole fractions vectorant Antoine coefficients, one row (A, B, C) per component, in the stated convention matrixunits units the Antoine coefficients are written for: pressure_temperature, e.g. mmHg_degC (P in mmHg, T in degC) or kPa_K choicebase logarithm of the Antoine equation: log10 or ln choiceT temperature [K]P dew-point pressure [Pa]x liquid mole fractions of the first dropchemeng_raoult_dew_temperatureTemperature at which a vapour of composition y starts to condense at pressure P, and the first-drop composition (Raoult's law, Antoine vapour pressures; iterative).
y vapour mole fractions vectorant Antoine coefficients, one row (A, B, C) per component, in the stated convention matrixunits units the Antoine coefficients are written for: pressure_temperature, e.g. mmHg_degC (P in mmHg, T in degC) or kPa_K choicebase logarithm of the Antoine equation: log10 or ln choiceP pressure [Pa]T dew-point temperature [K]x liquid mole fractions of the first dropchemeng_wilson_k_flashVapour fraction and phase compositions of a hydrocarbon feed at T and P with K-values estimated by Wilson's correlation from critical constants and acentric factors.
z feed mole fractions vectorTc critical temperatures, K vectorPc critical pressures, in the unit p_unit vectoromega acentric factors vectorp_unit unit of the critical pressures: Pa, kPa, MPa, bar, atm or psi choiceT flash temperature [K]P flash pressure [Pa]VF vapour fraction V/Fx liquid mole fractionsy vapour mole fractionsK Wilson K-valueschemeng_raoult_isothermal_flashVapour fraction and phase compositions of a feed flashed at temperature T and pressure P, with Raoult's-law K-values from Antoine vapour pressures.
z feed mole fractions vectorant Antoine coefficients, one row (A, B, C) per component, in the stated convention matrixunits units the Antoine coefficients are written for: pressure_temperature, e.g. mmHg_degC (P in mmHg, T in degC) or kPa_K choicebase logarithm of the Antoine equation: log10 or ln choiceT flash temperature [K]P flash pressure [Pa]VF vapour fraction V/Fx liquid mole fractionsy vapour mole fractionschemeng_rachford_rice_flashVapour fraction and the liquid and vapour compositions of a feed flashed at conditions where the K-values are known.
z feed mole fractions vectorK equilibrium ratios K_i = y_i/x_i vectorVF vapour fraction V/Fx liquid mole fractionsy vapour mole fractionschemeng_mccabe_thiele_stagesNumber of theoretical stages (the partial reboiler counted as one) of a binary column at reflux ratio R, by stepping between the operating lines and a constant-alpha equilibrium curve, with the feed switched at the intersection of the operating lines.
alpha relative volatility of the light component (constant)zF mole fraction of the light component in the feedxD mole fraction of the light component in the distillateq feed quality q: 1 saturated liquid, 0 saturated vapour, > 1 subcooled, < 0 superheatedxB mole fraction of the light component in the bottomsR reflux ratio L/DN theoretical stages including the partial reboilerRmin minimum reflux ratiochemeng_fenske_minimum_stagesThe minimum number of equilibrium stages of a binary distillation at total reflux by the Fenske equation (constant relative volatility), counting the partial reboiler as a stage.
alpha relative volatility of the light component (constant)xD mole fraction of the light component in the distillatexB mole fraction of the light component in the bottomsNmin minimum number of equilibrium stages (partial reboiler included)Nmin_trays minimum number of trays (Nmin - 1, the reboiler excluded)chemeng_multicomponent_underwoodThe minimum reflux ratio of a multicomponent distillation with constant relative volatilities by Underwood's equations: the root theta between the key volatilities of sum alpha_i z_i/(alpha_i - theta) = 1 - q, then R_min + 1 = sum alpha_i x_D,i/(alpha_i - theta).
alpha relative volatility of each component (any common reference, constant) vectorz feed mole fractions (sum to 1) vectorxD distillate mole fractions at minimum reflux (sum to 1) vectorq feed quality q (1 saturated liquid, 0 saturated vapour)lk light key: its position in the lists (1 = first) integerhk heavy key: its position in the lists integertheta Underwood root between the key volatilitiesRmin minimum reflux ratio L/Dchemeng_binary_minimum_refluxMinimum reflux ratio of a binary distillation with constant relative volatility, for any feed condition q (Underwood's equations).
alpha relative volatility of the light component (constant)zF mole fraction of the light component in the feedxD mole fraction of the light component in the distillateq feed quality q: 1 saturated liquid, 0 saturated vapour, > 1 subcooled, < 0 superheatedRmin minimum reflux ratio L/Dchemeng_absorber_transfer_unitsNumber of overall gas-phase transfer units and packed height of a dilute countercurrent absorber with linear equilibrium (Colburn's equation).
y1 solute mole fraction in the gas entering (bottom)y2 solute mole fraction in the gas leaving (top)x2 solute mole fraction in the liquid entering (top)m slope of the equilibrium line y = m xA absorption factor A = L/(m V)HOG height of an overall gas-phase transfer unit [m]NOG number of overall gas-phase transfer unitsZ packed height [m]chemeng_kremser_stripperSolute mole fraction in the liquid leaving a countercurrent stripper of N ideal stages, and the fraction stripped, for dilute liquid with linear equilibrium y = m x.
N number of ideal stages integerS stripping factor S = m V/Lm slope of the equilibrium line y = m xx_in solute mole fraction in the entering liquidy_in solute mole fraction in the entering stripping gasx_out solute mole fraction in the leaving liquidrecovery fraction of the entering solute strippedchemeng_antoine_vapour_pressureVapour pressure of a pure liquid at temperature T from Antoine coefficients written in a stated convention (logarithm and units).
A Antoine coefficient AB Antoine coefficient BC Antoine coefficient Cunits units the Antoine coefficients are written for: pressure_temperature, e.g. mmHg_degC (P in mmHg, T in degC) or kPa_K choicebase logarithm of the Antoine equation: log10 or ln choiceT temperature [K]Psat vapour pressure [Pa]chemeng_cake_filtration_volumeVolume of filtrate collected after time t in constant-pressure cake filtration (Ruth equation with cake and medium resistances).
A filter area [m^2]dP pressure difference across cake and medium [Pa]mu filtrate viscosity [Pa*s]alpha specific cake resistance [m/kg]c mass of dry cake deposited per volume of filtrate [kg/m^3]Rm filter medium resistance [1/m]t filtration time [s]V filtrate volume collected [m^3]chemeng_stefan_diffusion_fluxSteady molar flux of A diffusing through a stagnant film of non-diffusing B in an ideal gas (evaporation, absorption through an inert).
D diffusivity of A in B [m^2/s]P total pressure [Pa]T temperature [K]L film thickness (diffusion path length) [m]yA1 mole fraction of A at the start of the pathyA2 mole fraction of A at the end of the pathNA molar flux of A [mol/(m^2*s)]chemeng_equimolar_counterdiffusionThe molar flux of A through a film of thickness L in equimolar counterdiffusion (N_B = -N_A, ideal gas): N_A = c D (y_A1 - y_A2)/L with c = P/(R T).
D diffusivity of A in B [m^2/s]P total pressure [Pa]T temperature [K]L film (path) thickness [m]yA1 mole fraction of A at z = 0yA2 mole fraction of A at z = LNA molar flux of A [mol/(m^2*s)]NB molar flux of B (= -N_A) [mol/(m^2*s)]chemeng_mass_transfer_coefficientThe convective mass-transfer coefficient k_c = Sh D/L from the Reynolds and Schmidt numbers by a stated correlation: a sphere (Ranz-Marshall), a flat plate in laminar flow (average) or turbulent flow in a pipe (Linton-Sherwood).
geometry correlation: sphere (Ranz-Marshall), flat_plate (laminar, average) or pipe (Linton-Sherwood, turbulent) choiceu fluid velocity [m/s]L characteristic length: sphere or pipe diameter, plate length [m]D diffusivity of the solute in the fluid [m^2/s]rho fluid density [kg/m^3]mu fluid viscosity [Pa*s]Re Reynolds number rho u L/muSc Schmidt number mu/(rho D)Sh Sherwood numberkc mass-transfer coefficient Sh D/L [m/s]chemeng_carman_pressure_dropPressure drop through a packed bed from Carman's correlation of the bed friction factor (180/Re' + 2.87/Re'^0.1 form).
dp particle diameter [m]eps bed voidage (porosity)vs superficial velocity [m/s]rho fluid density [kg/m^3]mu fluid viscosity [Pa*s]L bed depth [m]dP pressure drop across the bed [Pa]chemeng_ergun_pressure_dropPressure drop of a fluid flowing through a packed bed of spheres from the particle size, voidage, superficial velocity and fluid properties (Ergun equation).
dp particle diameter [m]eps bed voidage (porosity)vs superficial velocity [m/s]rho fluid density [kg/m^3]mu fluid viscosity [Pa*s]L bed depth [m]dP pressure drop across the bed [Pa]chemeng_filtration_constants_fitSpecific cake resistance and filter-medium resistance from a constant-pressure filtration test (times and filtrate volumes), by the straight line of t/V against V.
t times at which the filtrate volumes were read, in t_unit vectorV cumulative filtrate volumes, in v_unit vectort_unit unit of the times choicev_unit unit of the volumes choiceA filter area [m^2]dP constant pressure difference [Pa]mu filtrate viscosity [Pa*s]c dry cake mass per volume of filtrate [kg/m^3]alpha specific cake resistance [m/kg]Rm filter medium resistance [1/m]slope slope of t/V against V, s/m^6intercept intercept of t/V against V, s/m^315 files, 35 MB in total. The largest:
| File | Size |
|---|---|
| model.safetensors | 18.9 MB |
| dist/chemical_engineering_ai999x-1.0.0-py3-none-any.whl | 6.2 MB |
| onnx/search/encoder.int8.onnx | 4.9 MB |
| docs/chemical_engineering_ai999x_capabilities.pdf | 3.8 MB |
| onnx/search/index.json | 403.3 KB |
| docs/chemical_engineering_ai999x_capabilities.html | 331.4 KB |
| docs/chemical_engineering_ai999x_capabilities.md | 257.6 KB |
| onnx/search/tokenizer.json | 176.4 KB |
| README.md | 25.6 KB |
| LICENSE | 11.4 KB |
| evaluation/release_gate.md | 2.3 KB |
| evaluation/KNOWLEDGE_CARD.md | 1.4 KB |
Chemical Engineering answers questions in chemical engineering: material and energy balances, reactor design, separations (distillation, absorption, extraction), transport phenomena, process control and reservoir and petroleum basics. Each answer gives the value with its unit, the steps and the formula in LaTeX.
With pip: pip install chemical-engineering-ai999x. The same files are on Hugging Face (hf download AI999X/chemical-engineering-ai999x --local-dir chemical-engineering-ai999x) and GitHub.
Yes. It is a Python package that runs on an ordinary CPU without a network connection (Python >=3.10); no GPU and no API key are needed.
91 capabilities in 10 topics, including Separations, Reactor design, Process control, Property estimation, Energy balances.
Field: Engineering. Tasks: Question Answering, Sentence Similarity, Feature Extraction.
Asked "First-order CSTR volume: v0 = 36 m^3/h, k = 0.06 1/min, X = 90%", it answers: V = 90 m^3, tau = 9000 s.
It says so and names what is missing or out of range, instead of guessing a number.