Oxygen quantification & forecasting

The COVID-19 pandemic highlighted the urgent need for tools to support a range of users seeking to understand oxygen supply and demand. This includes for example:

• Clinicians at the bedside trying to understand how long their supply will last or how much oxygen a new delivery device might consume
• Hospital operations lead or biomedical engineer/technician trying to estimate supply capacity or how often to order refills of LOX or cylinders
• Hospital administrator trying to estimate costs
• A Ministry of Health trying to design distribution of national or regional capacity to care for a surge in patients
• Advocacy or policy teams seeking to improve access to oxygen locally or globally
• Planners trying to determine which oxygen supply systems are optimal for a given setting

Oxygen consumption is commonly estimated based on need (e.g. number of beds, gas wall outlets, historical consumption), however, such estimates have major limitations and challenges. Flow measurement systems are uncommon in many facilities including LMICs, and also may not account for true need (e.g. waste, leak, rationing etc).

Below are descriptions of some widely used tools. A comparison summary table is coming soon.

Click to see description above

The formulas described below are used in the OCC Oxygen Calculator.

Manufacturer specifications must always be referenced especially when using delivery devices with bias flow, turbines and compressors.

When estimating device consumption one must always consider device leak or leak at the patient interface which is commonly encountered.

What is the weight of gaseous oxygen (O2)?

This calculation is relevant as in some settings oxygen quantity may be described by the volume of gaseous oxygen in liters (or other units) or the weight of gaseous oxygen in kg (or other units). First, remember the atomic and molecular weight of oxygen:  O = 15.99 g/mol and O2 = 32 g/mol

Use the ideal gas law: PV = nRT

P = pressure (in atm); V = volume (in Liters); n = amount of substance (in moles); R = ideal gas constant = 0.0821 (units are (Liters*atm)/(Kelvin*n) ); T = absolute temperature (in Kelvin)

To get the gaseous volume of 1 mole of gas:  V=nRT/P

(1 mol)(0.0821 L/atm/K/mol)(273K)/1atm = 22.4 L gas

1 mole gas (STP) = 22.4L = 32g of O2

(32g/mol)(1L/22.4L/mol)= 1.428 g O2 per gaseous liter at STP

Standard temperature and pressure is 1 atm and 273K or O C

If we assume a ‘room temperature’ (NTP) of 20 degrees C, then using the same formula with this temperature:

V=nRT/P

(1 mol)(0.0821 L/atm/K/mol)(293K)/1atm = 24.05 L gas

(32g/mol)(1L/24.05 L/mol) = 1.33 g of O2 per gaseous liter at 20 degrees C (Normal Temperature and Pressure – NTP)

So if you have 1000 L of gaseous oxygen at room temperature, then the weight is: 1.33 g/L (1000L) = 1.33 kg

For calculators that modeled facility scenarios (e.g. OCC Oxygen Demand Calculator), users can manipulate the size of the ward and the severity of hypoxemia for patients. Often estimates of oxygen consumption by patient are derived from expert opinion and limited data. Although cross-sectional oxygen usage data have been published from early in the COVID-19 pandemic, the evolution of respiratory support practices—particularly the timing of intubation and the roles of non-invasive ventilation and high flow nasal oxygen—has limited the degree to which these data could be used to guide present-day estimates of oxygen demand.

Early WHO estimates postulated that 75% of hospitalized COVID19 patients would be classified as ‘severe’ (10 L/min O2 requirement) and 25% classified as ‘critical’ (30 L/min O2 requirement). These numbers have not been validated and how oxygen need changed over time for patients with COVID19, different strains of COVID19, and for other respiratory illnesses is poorly characterized.

Below is a summary table of select data to date.

Below are cylinder constants used in the OCC cylinder duration calculations that follow:

• ‘Size C’: 0.085
• ‘Size D’: 0.17
• ‘Size E’: 0.34
• ‘Size F’: 0.68
• ‘Size G’: 1.7
• ‘Size J’: 3.40
• ‘Size K’: 3.55

Remaining Supply = 

Remaining Time =

Pressure in psi and Flow in LPM

* Of note: cylinder size terminology and volumes are not universally standard. You must check with the local manufacturer for cylinder capacity and size/capacity.

*Service pressure for aluminum cylinders is approximately 2000-2200 psi (137-150 bar), while service pressure for steel cylinders may vary more widely. Always check with the manufacturer for specifications.

The OCC cylinder size calculator uses volumetric calculations based on height, circumference (or width), and wall thickness to estimate volume of the cylinder (see formulas below). This calculator assumes the shape of a cylinder which will vary from the actual shape of a gas cylinder – see ISO 7866 and ISO 9809 for details. Steel and aluminum cylinders have different wall thicknesses and knowing which type of cylinder you have is necessary for accurate estimations.

Calculated cylinder volume may vary from actual or manufacturer reported cylinder volume due to differences between the entered and actual wall thickness, shape of the bottom or top of the cylinder, or the fill pressure used to define capacity, among other potential factors. See ISO7866 and ISO9809

Liquid water volume capacity: Liquid volume is given by approximating the volume of a cylinder, by

(We do not multiply the wall thickness x2, as for this estimate we account for the thickness of the cylinder base only and not the dome)

Gaseous oxygen volume: Boyle’s Law is used to convert from a known volume and pressure to another known volume and pressure. For example, if we have an E cylinder with a volume of 4.7 L water and 2000 PSI (137 bar), and convert that to gaseous volume at ambient atmospheric pressure (P = pressure; V = Volume):

Further simplified, Pressure (bar) × Cylinder water volume (L) = Total gas volume (L) at sea level.  If pressure units are in PSI, then this must be accounted for (1 atm pressure at sea level = 14.70 psi):

If you have the dimensions of the cylinder, the pressure in the cylinder and know ambient pressure, then the above equations can be arranged as follows:

(Volume in liters; Pressure in any unit; diameter, wall thickness and height in mm)

In the OCC O2 supply calculator, user inputs quantity per unit of time and we convert to Liters per day * % day safely run * leakage factor

For concentrators, user inputs number of concentrators and calculator multiplies above by number of concentrators.

For the OCC liquid oxygen supply calculator, the user inputs total quantity in gallons or Liters. We eliminated height remaining in the insulated storage tank as an option for quantifying since this is dependent on the variable geometry of the storage tank.  

To calculate gaseous oxygen supply from liquid oxygen supply, multiply liquid liters by 861 to convert to gaseous liters, then multiply by a system leakage factor. This comes from the ideal gas law, and we assume conditions of ‘room temperature’ (20C-22C) and standard pressure (1 atm). The following explains where how this conversion factor for liquid to gaseous oxygen is derived. 

Ideal gas law: PV = nRT

P = pressure (in atm); V = volume (in Liters); n = amount of substance (in moles); R = ideal gas constant = 0.0821 (units are (Liters*atm)/(Kelvin*n) ); T = absolute temperature (in Kelvin)

• To calculate volume (in Liters) of gaseous oxygen from liquid oxygen (in Liters), convert Liters of liquid oxygen to moles of oxygen.
• Multiply the Liters of liquid oxygen by 1000 to convert from Liters to mL, then multiply by its density, 1.14g/mL to obtain mass of oxygen. Divide mass of oxygen by its molecular mass (O2 so 32g/mole) to obtain moles (n) of oxygen.
• Convert temperature to Kelvin (if Celsius, add 273.15).
• This input is entered into the ideal gas law: Liters of gaseous oxygen = V = (nRT) / P

When sea level and room temperature are assumed, this simplifies to:

• Liters of liquid oxygen * 861 = Liters of gaseous oxygen
• Leakage factor is then included to take into account leaks from equipment.

As used in the OCC Demand Calculator, FiO2 is assumed to be 1.0 and flow rates are adjustable in liters per minute.

As used in the OCC Demand Calculator, FiO2 is adjustable (defaulted to 1.0) and flow rate is adjustable in liters per minute.

As used in the OCC Demand Calculator, FiO2 is adjustable (defaulted to 1.0) and flow rate is adjustable in liters per minute and dependent on multiple factors.

Notes: on bias flow and FiO2.

SaO₂ = user input range 0 to 100%

FiO₂ = user input range 0 to 100%

Imputed PO₂ =

( 11700 / ( (1/SaO₂) – 1 ) + ( 50^3 + (11700 / ( (1/SaO₂) – 1 ))^2 ) ^1/2 ) ^ ⅓

Non-linear equation derived in brown et al. Chest 2016 (formula above and below in image)

Imputed P:F = Imputed PO₂ / FiO₂

S:F = (SaO₂ * 100) / FiO₂