Tim J. Gunner
Consultant
West Sussex, U.K.Malcolm J. Drury
Consultant
Surrey, U.K.
Crude oil volume correction factors, during custody transfer, need to account for phase separation phenomena of waxy crude. As an alternative a mass calculation could be made.
Throughout the 1980s and the early 1990s research addressed the complications of phase separation within paraffinic crude oils when transported by sea at lower temperatures. One objective was to identify the critical temperature at which phase separation occurred and to determine a method for obtaining the critical temperature onboard a vessel.
Various correlations were produced based on analysis with different criteria/parameters' but it remained necessary for a vessel to establish this parameter with a simple test procedure. This resulted in determining the density for various crude oils over an expected carriage temperature range to determine whether this procedure would accurately detect the phase separation temperature.
WAXY CRUDES
At certain cooler temperatures, paraffinic crude oils develop a third phase' as distinct from the two commonly associated phases, namely liquid and vapor. This phase is usually found as a partially solidified phase with its associated oils.
This third phase can be detected by variations in the linearity of a density-vs.-temperature plot, such as Fig. 1a(109772 bytes). At the points where non-linearity exists, analysis shows that paraffinic waxes are phase separating from their ,'mother" liquid crude oil.
Studies of density-vs.temperature plots showed that thermal expansion coefficients of a paraffinic crude oil could vary greatly over limited temperature ranges and especially over the critical phase separation temperature range.
Based on sample preparation procedures for the various crude oils used for developing the Petroleum Measurement Tables,' phase separation influence was greatly reduced by removing the wax phase together with sampling the top of the original sample. This procedure supplied the data for calculating the oil coefficient of expansion in the tables.
The example data when plotted shows an inflection point such as at about 150 C. in Fig. 1b(109772 bytes). Nevertheless, the rest of the plot shows linearity. However, as shown by Fig. 1a,(109772 bytes) such linear behavior is not typical for a paraffinic crude oil and inflections occur at varying temperatures depending on the specific crude.
The consequence of the sample preparation procedure, adopted to avoid the influence of suspended water on the density determinations,5 is that the density-vs.-temperature behavior for the "generalized" crude oil bears limited similarity to the actual behavior of paraffinic crude oil densities over a carriage/custody transfer temperature range.
If the temperature intervals between the density determinations are large, the curve would lack definition as simulated in 1c(109772 bytes) for the same crude oil as in Fig. 1a.(109772 bytes)
With regard to the samples used for developing the petroleum tables, it should be noted that no "wax-rich" crude oils were included, although many such oils now exist and are regularly traded.
THERMAL EXPANSION
The development of the current Petroleum Measurement Tables required two best fit equations using the density data as supplied by the U.S. National Bureau of Standards. The Tables contain coefficients (volume correction factors) for reducing a volume at an observed temperature to a standard temperature of either 150 C. or 600 F.
These coefficients depend on determining a mean or "generalized" thermal expansion coefficient (a) for crude oil. The a, as required by the tables, is determined at "base" or standard. temperature. However, the pour-point temperature for a significant number of paraffinic crude oils exceeds the standard "base" temperature or 150 C. and therefore a at 150 C. is irrelevant for these oils. Similarly, determination
of the reference density, at 150 C. from the relevant table is also irrelevant because of the change in state of the original liquid phase of the crude oil caused by phase separation.
The thesis then follows that the coefficient of expansion at the base temperature is a constant throughout the prescribed temperature range, i.e., a function of the linearity of the observed density-vs.-temperature curve. Therefore, this required a generalized equation that would best represent all the varying coefficients of expansion at the base temperature for the crude oil tested.
A generalized a needed to be determined before developing the generalized function for the volume correction factor. At about 150 C. (base temperature), a generalized or mean expansion coefficient at base temperature for the crude oil samples resulted in the following equations for all crude oils:
[SEE FORMULA]
where:
aT = Expansion coefficient at base temperature.
Ko = A function of nonlinear regression of the observed expansion coefficients at base temperature-in this case recorded as 613.9723 for crude oils.
K, = A function of nonlinear regression of the observed expansion coefficients at base temperature-in this case recorded as 0.00 for crude oils
PT = Density at the base temperature of 150 C.
Because of the nonlinear behavior of a paraffinic crude oil density-vs.-temperature curve, particularly with the wax-phase precipitation as seen in Figs. 1a and 1c,(109772 bytes) a generalized a would be difficult to achieve.
In Fig. 1d,(109772 bytes) the foregoing function showing the recorded and calculated a for internationally traded and recognized crude oils is plotted against their recorded densities at 150 C. The plot compares the scatter of the observed expansion coefficients at base temperatures with the calculated "mean" a plot from the previous equation.
The crude oils are scattered widely but one significant point is the varying gradients for the various crude oils. If a from the tables is greater than the calculated or generalized (mean) coefficient (Point A in Fig. 1d)(109772 bytes), then the gradient of the crude oil density plot at 150 C. is also greater than the mean or generalized density plot. This not only signifies the potential completion of a "solid" phase separation within the specific crude oil but also a larger expansion coefficient per degree of temperature increase for a limited temperature range than represented in the tables.
Further, if the real a of Point A is appropriate over the temperature range of 15201 C., then the mean coefficient from the tables for calculating the volume at 150 C. would be greater than the actual volume at 150 C. Point B has the opposite characteristic.
VOLUME CORRECTION
To obtain a generalized equation for the volume correction factors, a thesis was developed from observations of crude oil density data, namely that the crude oil expansion coefficient at temperature t may be represented by the equation:
[SEE FORMULA]
Where K is a temperature independent constant.
The constant 1.6 was assigned to K based on computer studies, the theoretical "curvature" of density/temperature curves, and a literature search' over a full temperature range from the tables.
This equation infers that the expansion coefficient at any temperature for any crude oil may be represented by a second order function of the expansion coefficient at base temperature. It is the root equation used to finally develop the standard volume correction factor (Y.C.F.) equation for the current Petroleum Measurement Tables.
To explore the applicability of this equation, Fig. 1e(109772 bytes) plots the density of two typical paraffinic crude and the calculated densities as derived from the Petroleum Measurement Tables.
As previously discussed, the slope of the density-vs.temperature curve is a closely associated function of the expansion coefficient. Fig. 1e(109772 bytes) indicates that the slope of the plot for the two crude oils varies on four occasions over the recorded temperature range. This is also reflected by a plot of the expansion coefficient-vs.-temperature of Crude A in Fig. 1f.(109772 bytes)
Between 10 and 150 C., the oil is expanding rapidly because the oil is changing in state from a solid to a liquid. Between 15 and 200 C., the oil expansion is reduced significantly because of changes in the nature of the precipitated wax phase compared to the liquid. Above 200 C., the oil is in a liquid phase and the expansion coefficients are reasonably uniform.
Jessup in 1930 reported similar behavior in the thermal expansion of lubricating oils.7 For three samples, he reported abnormally large expansion in the range of 0-750 C. Also these oils became cloudy when cooled to 00 C., indicating that wax began to freeze out. In general, Jessup's expansion coefficient deviation curves for his "waxy" lube-oil samples show a similar pattern to the curve in Fig. 1f.(109772 bytes)
From the foregoing discussion, it is evident that although the equation for a is suitable for most hydrocarbons it is not suitable for waxy paraffinic crude oils that have variations in behavior and precipitation of a solid phase. Various and sometimes large coefficients of expansion occur in an irregular fashion over a limited temperature range.
If the expansion coefficients were linear over the relevant temperature range (a linear density-vs-temperature plot) then Y.C.F. could be calculated using the simple function of:
Y.C.F. = p/pt
Where p is at the observed temperature.
This equation for determining Y.C.F. is regularly used for one wax-rich crude oil namely: Buattifel crude oil from Zuetina Libya.
The "Agip curve" is used to determine the Y.C.F. from p and PT. This simplified equation assumes a constant rate of density change with temperature over the required temperature range. The rate of change of density is independent of any generalized coefficients and is unique for the specific circumstances.
The final generalized Y.C.F. equation as developed from the primary equation and used for the volume correction factors in all the Petroleum Measurement Tables is:
Y.C.F. = exp[-aTAt (1 + 0.8aTAt)]
where:
aT = Thermal expansion coefficient at base temperature
At -- Difference in temperature between the observed temperature and the base or standard temperature
ERRORS
Because of the various types of crude oils and their differing qualities and physical behavior, it is difficult to stipulate the consequences of the errors from the present methods for all circumstances and temperature variations. However, as an example (see example box)(112127 bytes), the data for Crude B in Fig. 1e(109772 bytes) has been used to simulate the variations and systematic induced errors expected in a certain circumstance.
Before considering the example, one should recall that the Y.C.F.s in the tables must, by definition, be completely accurate at the base temperature, i.e. 1.0000.
However, I.P. 207/71, "Relative Density and Density Measurements," advises that the appropriate Y.C.F. will be in error by an amount depending on how closely the cubical expansion coefficient of the oil in question approaches that for the oil for which the entry in the table has been computed.
Any error in the calculated weight caused by the errors described previously will be a maximum when the density is determined at standard temperature and a minimum when the property is determined at tank temperature. The difference between the minimum error and the maximum may be considerable.
The example box shows that because of the varying slopes of the density-vs.-temperature curve for Crude B, the Petroleum Measurement Tables, if used for the cargo quantification on loading or for the determination of the Bill of Lading quantities, would understate the calculated volume by 0.29%.
During the transportation and with the cooling of the cargo, different sections of the density-vs.-temperature curve become more relevant. The cargo temperature also approaches 150 C., where absolute calculation accuracy exists. Therefore, the understated Bill of Lading volume becomes evident by creating an apparent intransit gain. Had the cargo cooled to 150 C., then the full 0.29% of understated volume would be shown as an intransit gain.
This example depends on the varying slopes and the slope location on the density-vs.-temperature curve. It is entirely possible that with large coefficients of expansion over the relevant temperature range (larger than the "mean coefficient of expansion" used for the tables) that a Bill of Lading quantity could be overstated by the same amounts, (see Fig. 1d(109772 bytes) for the effect of varying a coefficients).
These errors are not taken into consideration in statistical reviews. Therefore it is dangerous to place great reliance upon statistical averages for losses or transit variations particularly for crude oil volumes.
To correct the potential errors associated with volumetric calculations using the current Petroleum Measurement Tables for paraffinic crude oils, one would almost need individual tables for each crude oil with its individual unique behavioral characteristics. This requirement is clearly impracticable and therefore an alternative technique, such as a mass calculation, should be explored.
MASS CALCULATION
A mass calculation is a possible alternative technique to quantify intermediate/high-paraffinic crude oils. This calculation may be most appropriate for an overall loss-control evaluation.
The number of crude oils that would benefit from such a method represent at least 20% of the world's traded crude oils and include such diverse geographic regional crudes as Iranian heavy, Flotta, G.S.M., Palanca, Lalang, Widuri, and Minas.
A suitable sample together with the primary parameters associated with a measurement of a crude oil (namely, oil temperature, T.O.V. and associated free water volume) the mass of the crude o may be easily and accurately calculated. T.O.V. is the tot observed volume (total Volume of oil and foreign matte at its observed temperature).
The density of the crude o sample can be obtained b using ASTM D4052-87 ("Density and Relative Density o Liquids by Digital Density Meter") over a range of typical carriage temperature at nine temperature intervals of 50 C The intervals may not b exactly 50 C. but the actual test temperature should be record ed to two decimal places for each density record.
The digital density mete should be equivalent to the Mettler/Paar model DMA50 so that the observed density is recorded to five decimal places in kg/I. These density observations should then b plotted graphically and the primary data together with the associated plot could form part of the oil Certificate of Quality for any financial/custody transfer transaction.
The mass of the oil may be calculated by multiplying the cubic meters of T.O.Y. less free water less sediment and water by the observed oil density at the specific temperature of the oil volume.
The density at the observed oil temperature may either be obtained directly from the graphical plot of density-vs.temperature or by linear interpolation between the analytically derived data points.
BENEFITS
Benefits of a mass calculation are as follows:
- Mass is a constant and not dependent upon temperature variation and is based upon a fundamental physical formula that would be unchallengeable and would unify all calculation procedure.
- For loss-control purposes mass measurement throughout oil transportation and refining will allow mass balances to more accurately reflect losses throughout the varying processes.
- The calculation method is simplified and removes almost all of the various factors and multiplications that could induce error.
- The density plot with its associated inflection (for wax-rich crude oils) shows the equivalent temperature for the wax-appearance temperature/cloud-point temperature of the oil and could guide the heating policy and cargo handling.
- A crude oil tonnage is currently required for the calculation of freight costs and therefore c.i.f. (cost, insurance and freight) costing would be standardized.
DISADVANTAGES
A mass calculation does have the following disadvantages:
- Elimination of standard volumes as a quantification concept and calculation will require retraining people.
- Crude oil prices will have to be converted to tons.
