1.4. Units and Conversions
We have used “oilfield” units throughout the text, even though this system of units is inherently inconsistent. We chose this system because more petroleum engineers “think” in bbl/day and psi than in terms of m^{3}/s and Pa. All equations presented include the constant or constants needed with oilfield units. To employ these equations with SI units, it will be easiest to first convert the SI units to oilfield units, calculate the desired results in oilfield units, then convert the results to SI units. However, if an equation is to be used repeatedly with the input known in SI units, it will be more convenient to convert the constant or constants in the equation of interest. Conversion factors between oilfield and SI units are given in Table 1-1.
Table 1-1 Typical Units for Reservoir and Production Engineering Calculations
Variable |
Oilfield Unit |
SI Unit |
Conversion (Multiply SI Unit) |
Area |
acre |
m^{2} |
2.475 × 10^{–4} |
Compressibility |
psi^{–1} |
Pa^{–1} |
6897 |
Length |
ft |
m |
3.28 |
Permeability |
md |
m2 |
1.01 × 10^{15} |
Pressure |
psi |
Pa |
1.45 × 10^{–4} |
Rate (oil) |
STB/d |
m^{3}/s |
5.434 × 10^{5} |
Rate (gas) |
Mscf/d |
m^{3}/s |
3049 |
Viscosity |
cp |
Pa-s |
1000 |
Example 1-1. Conversion from Oilfield to SI Units
The steady-state, radial flow form of Darcy’s law in oilfield units is given in Chapter 2 as
for p in psi, q in STB/d, B in res bbl/STB, μ in cp, k in md, h in ft, and r_{e} and r_{w} in ft (s is dimensionless). Calculate the pressure drawdown (p_{e} – p_{wf}) in Pa for the following SI data, first by converting units to oilfield units and converting the result to SI units, then by deriving the constant in this equation for SI units.
Data
q = 0.001 m^{3}/s, B = 1.1 res m^{3}/ST m^{3}, μ = 2 × 10^{–3} Pa-s, k = 10^{–14} m^{2}, h = 10 m, r_{e} = 575 m, r_{w} = 0.1 m, and s = 0.
Solution
Using the first approach, we first convert all data to oilfield units. Using the conversion factors in Table 1-1,
Since r_{e} is divided by r_{w}, the units for these radii do not have to be converted. Now, from Equation (1-10),
and converting this results to Pascals,
Alternatively, we can convert the constant 141.2 to the appropriate constant for SI units, as follows (including only-to-be-converted variables):
or
The constant derived, 0.159, is 1/2π, as it should be for this consistent set of units. Substituting the parameters in SI units directly into Equation (1-19), we again calculate that p_{e} – p_{wf} = 3.043 × 10^{7} Pa.
Often, in regions where metric units are customary, a mix of SI and non-SI units is sometimes employed. For example, in using Darcy’s law, the units for flow rate may be m^{3}/d; for viscosity, cp; for permeability, md; and so on. In this instance, units can be converted to oilfield units in the same manner demonstrated here for consistent SI units.