2 API MPMS CHAPTER 11.
1—ADDENDUM 1
correlated to this same base density and the temperature t at which the compression occurs. The forms for these
correlations are:
K 0 + K1ρ* + K 2 ρ*2 K 0 K1
α 60 = = *2 + * + K 2 (16)
ρ*2 ρ ρ
⎧ C + Dt ⎫
FP = exp ⎨ A + Bt + ⎬ (17)
⎩ ρ*2 ⎭
There was one set of coefficients for the FP compressibility factor (A = -1.99470, B = 0.00013427, C = 793920,
D = 2326; based on density in kg/m3 at 60°F the A, B, C, and D values) but several sets of coefficients for the α60
thermal expansion coefficient (the K0 , K1 , and K2 values) depending upon the liquid’s classification and density
at 60°F.
To recognize differences between the current ITS-90 temperature scale and the IPTS-68 temperature scale in effect
when the data for this Standard were measured, this Standard makes small corrections to the temperature t and the
base temperature T and a non-zero base temperature correction factor, denoted as δ60 , is used. Also, the density
used in the correlations, ρ* , is slightly different from a ρ60 measured consistent with ITS-90. See 11.1.5.3 for the
procedure to convert ITS-90 temperatures to an IPTS-68 basis, Appendix C for the origin of the δ60 correction
factor, and 11.1.6.1 for the calculation of ρ* from ρ60 .
Equations (16) and (17) are directly expressed in terms of ρ* . However, since ρ* can be directly related to ρ60 ,
then these equations can also be thought of as being a direct function of ρ60 , too.
11.1.3.4 Base Pressure in This Standard
For volatile hydrocarbons, the base pressure is the saturation pressure for the liquid (i.e., its “bubble point”
pressure). It is generally assumed that if the saturation pressure is less than atmospheric pressure then there is little
error in applying the correction at a constant base pressure of 1 atmosphere. For liquids with equilibrium vapor
pressure less than atmospheric pressure (0 psig or 14.696 psia) the Pe value used in Equation 15 shall be atmospheric
pressure (0 psig or 14.696 psia). The heavier liquids covered by this Standard are fairly non-volatile — the
saturation pressure is less than the atmospheric pressure over the entire temperature range of this Standard. It is only
the lightest of the liquids covered by this Standard whose vapor pressures may exceed atmospheric pressure at the
higher temperatures.
For simplicity of application, this Standard will neglect any effects of the liquid’s saturation pressure exceeding
atmospheric pressure. In all equations, this Standard will use Pe = 0 (gauge) and the CPL equation reduces to:
1
C PL = . (18)
1 − FP P
For liquids with an equilibrium vapor pressure greater than atmospheric, the equilibrium vapor pressure (Pe) should
be subtracted from the pressure input values before entering the calculation sequences given in 11.1.5.1, 11.1.6.1,
11.1.6.2, 11.1.6.3, 11.1.7.1, 11.1.7.2, and 11.1.7.3.
11.1.3.9 Rounding of Values
Previous versions of the Table values required rounding at various stages of the calculation procedures. The
Implementation Procedures are now written with no rounding of initial or intermediate values. The final CTPL is
rounded as specified in API MPMS Chapter 12. If there is no guidance for a specific application, round to five
decimal places. VCF is rounded to five decimal places. Rounding of input values is only to be used when creating
tabular representations of the results from these Implementation Procedures. When the tabular representations are
calculated, the initial and final values are to be rounded for display, but intermediate values are never to be rounded.
Addendum 1 to API MPMS Ch. 11.1-2004—
Temperature and Pressure Volume Correction Factors
for Generalized Crude Oils, Refined Products,
and Lubricating Oils
Note: Added text is highlighted yellow. Deleted text is indicated by strikethrough.
11.1.2.2 Scope
This Standard provides the algorithm and implementation procedure for the correction of temperature and pressure
effects on density and volume of liquid hydrocarbons which fall within the categories of crude oil, refined products,
or lubricating oils; NGLs and LPGs are excluded from consideration in this Standard. The combination of density
and volume correction factors for both temperature and pressure is collectively referred to in this Standard as a
Correction for Temperature and Pressure of a Liquid (CTPL) (VCF). The temperature portion of this correction is
termed the Correction for the effect of Temperature on Liquid (CTL), also historically known as VCF (Volume
Correction Factor). The pressure portion is termed the Correction for the effect of Pressure on Liquid (CPL). As
this Standard will be applied to a variety of applications the output parameters specified in this Standard (CTL, Fp,
CPL, and CTPL) may be used as specified in other API Manual of Petroleum Measurement Standards (MPMS)
Chapters.
Including the pressure correction in this Standard represents an important change from the "temperature only" 1980
Tables. However, if the pressure is one atmosphere (the standard pressure) then there is no pressure correction and
this Standard will give CTL (VCF) values consistent with the 1980 Tables.
The This Standard provides general procedures for the conversion of input data to generate CTL, Fp, CPL, and
CTPL values at the user specified base temperature and pressure (Tb, Pb) a form that is consistent with the
computation procedures used to generate VCF values. This section is then followed by two sets of procedures for
computing volume correction factor, one set for data expressed in customary units (temperature in °F, pressure in
psig), the other for the metric system of units (temperature in °C, pressure in kPa or bar). In contrast to the 1980
Tables, the metric procedures require the procedure for customary units be used first to compute density at 60°F.
This value is then further corrected to give the metric output.
The procedure recognizes three distinct commodity groups: crude oil, refined products, and lubricating oils. A
special application category is also provided which provides volume correction based on the input of an
experimentally derived coefficient of thermal expansion.
11.1.3.3 Calculation of CTL and CPL Factors in This Standard
The specific equation forms for the temperature and pressure correction factors used in this Standard are:
{ }
CTL = exp −αT ( t − T ) ⎡⎣1 + 0.8αT ( t − T + δT ) ⎤⎦
(14)
= exp {−α Δt ⎡⎣1 + 0.8α
T T ( Δt + δT )⎤⎦}
1
C PL = . (15)
1 − FP ( P − Pe )
where α T is the thermal expansion coefficient at the base temperature T , Δt is the difference between the alternate
temperature and the base temperature, FP is the compressibility coefficient, and δT is a small base temperature
correction value.
In the 1980 Standard, α T was correlated to the density at a 60°F base temperature and 0 psig pressure, ρ* , and is
denoted as α 60 . The CTL equation was developed as a correction to 60°F density, so T = 60 and δT = 0 . FP was
1
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