API MPMS Chapter 11.3.4 Miscellaneous Hydrocarbon ...ballots.api.org/copm/comq/ballots/docs/Ch11p3p4...

This document is not an API Standard; it is under consideration within an API technical committee but has not received all approvals required to become an API Standard. It shall not be reproduced or circulated or quoted, in whole or in part, outside of API committee activities except with the approval of the Chairman of the committee having jurisdiction and staff of the API Standards Dept. Copyright API. All rights reserved.

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API MPMS Chapter 11.3.4

Miscellaneous Hydrocarbon Properties – Denatured Ethanol and Gasoline Component Blend Densities and Volume Correction Factors

1 Forward – Boilerplate

2 Contents

1 Forward – Boilerplate ................................................................................................................ 1

2 Contents .................................................................................................................................... 1

3 Introduction ................................................................................................................................ 2

4 Scope ........................................................................................................................................ 2

5 Normative References .............................................................................................................. 3

6 Terms & Definitions ................................................................................................................... 3

6.1 Blend Volume Percent (BVP) .................................................................................................... 3

6.2 Blendstock for Oxygenate Blending (BOB) ............................................................................... 3

6.3 excess alpha ............................................................................................................................. 3

6.4 Excess Volume Fraction (EVF) ................................................................................................. 3

6.5 Ideal Fraction Ethanol (IFE) ...................................................................................................... 4

6.6 nominal ethanol content ............................................................................................................ 4

7 Symbols & Abbreviations .......................................................................................................... 4

7.1 Coefficients ................................................................................................................................ 4

7.2 Concentrations .......................................................................................................................... 4

7.3 Density ...................................................................................................................................... 4

7.4 Volume ...................................................................................................................................... 5

7.5 Temperature and Pressure ....................................................................................................... 5

7.6 Subscripts .................................................................................................................................. 5

8 Implementation Procedures ...................................................................................................... 5

8.1 Blends of Gasoline and Ethanol (bge) Volume and Density Correction ................................... 5

8.1.1 Background ............................................................................................................................... 5

8.1.2 Source of Excess Thermal Expansion and Excess Volume ..................................................... 6

8.1.3 Units of Measure ....................................................................................................................... 6

8.1.4 Functions Specific to Blends of Gasoline and Ethanol (bge) Blends ....................................... 6

8.2 Application of API 11.1 .............................................................................................................. 8

8.2.1 Pressure Correction of Denatured Ethanol to Base Conditions ................................................ 8

8.2.2 Temperature and Pressure Correction of Blends of Gasoline and Ethanol (bge) to Base Conditions 9



8.3 Correction to Other Standard Conditions .................................................................................. 9

8.4 Rounding ................................................................................................................................. 10

8.5 Calculation of Blending Scenarios .......................................................................................... 10

8.5.1 Definition of Scenario Inputs and Targets ............................................................................... 10

8.5.2 Scenario 1 Calculation of Blends of Gasoline and Ethanol (bge) V60 and Density from Blending Volumes and Densities ................................................................................................................ 11

8.5.3 Scenario 2 Blends of Gasoline and Ethanol (bge) and Denatured Ethanol Measured, BOB Volume Unmeasured .................................................................................................................................. 15

8.5.4 Scenario 3 Calculation of BOB Volume and BOB & Blends of Gasoline and Ethanol (bge) Densities, Ethanol and Blends of Gasoline and Ethanol (bge) Volumes Measured .................................. 22

8.5.5 Scenario 4 Calculation of Blends of Gasoline and Ethanol (bge) Volume at Base Conditions with Minimal Information ............................................................................................................................. 28

9 Precision Statement ................................................................................................................ 31

10 Bibliography ............................................................................................................................. 32

Annex A. Calculation of Alpha60 for Input to Blends of Gasoline and Ethanol (bge) CTPL – Worked Examples – Informative ............................................................................................................................... 33

Annex B. Calculation of Excess Volume Fraction – Worked Examples – Informative .......................... 35

Annex C. Calculation of Scenarios – Worked Examples – Informative .................................................. 38

Annex D. Convergence Acceleration – Informative ................................................................................ 45

Annex E. Measurement Field Descriptions for API MPMS 11.3.4 - Informative ........................................ 47

3 Introduction

4 Scope

1. General This standard covers density and volume correction factors for blends of denatured ethanol and gasoline blend components ranging from 0% to 95% denatured ethanol based upon calculation methods defined in API MPMS Chapter 11.1 and 11.3.3. Calculation of blends and denatured ethanol containing more than 95% ethanol should use the calculation procedures within API MPMS 11.3.3. The standard consists of correlations and algorithms for estimating the blend volume change at base conditions and for calculating volume correction factors of denatured ethanol and gasoline component blends. This standard also provides the algorithms to estimate certain blend properties in blending situations where some of the required parameters are not measured.

2. Range of applicability This standard is applicable to blends containing denatured ethanol and gasoline blend components with 60 °F densities ranging from 680 to 800 kg/m3 containing between 0% and 95% by volume denatured ethanol over the temperature range of 40°F to 120°F and pressure range of 0 to 1500 psig



5 Blends of Gasoline and Ethanol (bge) Normative References

The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document applies (including any addenda/errata).

Manual of Petroleum Measurement Standards, Chapter 11—Physical Properties Data, Section 1—Temperature and Pressure Volume Correction Factors for Generalized Crude Oils, Refined Products, and Lubricating Oils, Adjunct to: ASTM D 1250-04 and IP 200/04, MAY 2004 ADDENDUM 1, SEPTEMBER 2007

Manual of Petroleum Measurement Standards, Chapter 11.2.2 (R2012) Compressibility Factors for Hydrocarbons: 0.350-0.637 Relative Density (60 deg. F/60 deg. F) and -50 deg. F to 140 deg. F Metering Temperature

Manual of Petroleum Measurement Standards, Chapter 11.3.3 Miscellaneous Hydrocarbon Product Properties – Denatured Ethanol Density and Volume Correction Factors 2 ed., Sept 2015

6 Terms & Definitions

6.1 Blends of Gasoline and Ethanol (bge)

A Blend of denatured ethanol and gasoline blend components ranging from 0% to 95% denatured ethanol

6.2 Blend Volume Percent (BVP)

The concentration of ethanol in the mixture based on the ratio of the volume of denatured ethanol to the total observed volume of the mixture adjusted to base conditions times 100, expressed as a percentage. It is bounded by 0% and 100%.

6.3 Blendstock for Oxygenate Blending (BOB)

A refined product component consisting of unfinished gasoline to which denatured ethanol will be added to make a finished motor fuel.

6.4 Excess alpha

The incremental increase in the thermal expansion coefficient of the mixed liquid that exceeds the coefficient calculated from a volume proportional addition of the component alphas.

6.5 Excess Volume Fraction (EVF)

The incremental volume growth generated by mixing denatured ethanol and BOB. The excess volume is expressed as a fractional volume divided by the sum of the component volume so it is dimensionless. It is bounded by 0 and 1.



6.6 Ideal Fraction Ethanol (IFE)

Concentration of ethanol in the mixture expressed as the volume of denatured ethanol divided by the volume of a simple addition of the component volumes at base conditions. As a volume divided by volume measure, it is dimensionless. It is bounded by 0 and 1.

6.7 nominal ethanol content

The labeled denatured ethanol content of an ethanol-blended fuel. The actual ethanol content may vary from the nominal value due to labeling conventions and blending constraints.

7 Symbols & Abbreviations

Coefficients

60 Thermal expansion factor at 60°F (°F-1)

α60ε Excess alpha (°F-1)

aj Coefficients for the cubic equation that defines the thermal expansion coefficient, α60. There are 4 different coefficients; each will be identified by their subscript (j).

as1, as2, as3, as4, Coefficients used in the API 11.2.2 procedure to determine the scaled compressibility factor, Fs. Subscripts modified from 11.2.2 to avoid confusion with the thermal expansion coefficient coefficients.

A, AHC, B, n, Z Coefficients used in the excess volume fraction equation

CTPL Combined volume correction factor due to temperature and pressure

Fs Scaled compressibility factor (psi-1)

y Fit parameter for the equation (dimensionless)

Concentrations

φethanol Ideal Fraction Ethanol (dimensionless, Volume)

V%ethanol Blend Percent Denatured Ethanol (%)

bge Blends of Ethanol and Gasoline

Density

Density value (kg/m³)

60 Density at base conditions (60°F and 0 psig) (kg/m³)

t,p Density at alternate conditions (kg/m³)



Volume

V Observed volume at flowing conditions conditions (m3)

V60 Volume at base conditions (60F and 0 psig)

Vt ,P Volume at specified conditions (t and P)

Vε Excess volume fraction (dimensionless)

Temperature and Pressure

P Pressure value (psig)

T Temperature value (°F)

Subscripts

Subscripts may be added to any symbol to clarify the component to which a property is associated, to distinguish it from a similar property from a different calculation, or to specify an iteration number. In some cases, a comma may be used in a subscript to separate parts for greater visual distinction without further significance.

BOB Blendstock for Oxygenate Blending properties

CTPL Calculated using thermal expansion correlations

ethanol Denatured Ethanol properties

bge bge properties

i referring to the value of a specific iteration.

mass Calculated using mass balance

observed values measured at field conditions without adjustment to base conditions

8 Implementation Procedures

Blends of Gasoline and Ethanol (bge) Volume and Density Correction

Background

Experimental and field experience has demonstrated that blending denatured ethanol into gasoline blending stocks results in a mixture that exhibits apparent volume growth over that simple addition of the blended volumes. The mixture also shows an incremental increase in the coefficient of thermal expansion over that expected by volume proportional addition of the blend stock coefficients.

API gathered a series of laboratory density measurements at various temperatures, pressures, and concentrations for 4 BOB samples, 4 denatured ethanol samples, and their 8 possible combinations.



These laboratory results were evaluated to filter out outliers and procedural artifacts, and the remaining dataset of 1662 samples were used in regression studies. These studies determined the functions and parameters that best fit the “excess functions”. Combining these excess functions with the previously documented API 11.1 functions extends the range of API 11.1 to bge blends.

Source of Excess Thermal Expansion and Excess Volume

When BOB and denatured ethanol are mixed, the two fluids are infinitely soluble in each other and form a single liquid phase. The fluids are chemically different in that BOB is a hydrocarbon mixture consisting primarily of nonpolar and aromatic molecules and ethanol is polar. This difference leads to the fluids’ molecules interacting at a molecular level.

A simple construct that explains the observed effects on physical properties, is that the ethanol molecules interfere with the densest alignment of the BOB nonpolar molecules leading to a decrease in expected density or the creation of “excess volume”.

The same interaction causes the thermal expansion coefficient (α60) for the mixture to be larger than the coefficient expected for a hydrocarbon fluid of that density or for a volumetric average of the coefficients of the BOB and ethanol components.

Units of Measure

For this current standard, the approach was to develop functions and procedures that extend the functionality of existing API standards to cover ethanol-blended fuels. The primary standard for temperature and pressure adjustment to base conditions is API 11.1. API 11.1 accepts inputs and generates outputs in many units of measure, but all calculations go through an internal conversion to customary units for use in legacy correlations.

It is intended for the algorithms in this standard to be incorporated into 11.1 calculation engines. Therefore, all the calculations in this standard are based on the same units as used in the API 11.1 legacy correlations. This is primarily manifested in the exclusive use of °F for temperature and kg/m3 for density.

Volumes in the calculations shall use m3. This is necessary because several equations multiply density (kg/m3) by volume (m3), and require consistent units of measure.

Functions Specific to Blend of Gasoline and Ethanol (bge)The functions in this section are necessary components of the functions required to calculate excess volume fraction and excess α60.

Ideal Fraction Ethanol

Ideal Fraction Ethanol, φethanol, is the fraction of the mixture that would be ethanol assuming ideal mixing without excess volume effects. It is used in some of the calculations because it does not require knowledge of the volume expansion caused by the ethanol. It is calculated with the following equation.

,

, , (1)

Where

V60,ethanol and V60,BOB are the volumes at base conditions of denatured ethanol and BOB respectively.



Blend Volume Percent Denatured Ethanol

For some regulatory and commercial purposes, the concentration of denatured ethanol is stated on a volumetric percent basis referenced to the total volume of bge at base conditions. Since bge blends demonstrate an excess volume fraction, the ideal volume fraction ethanol, φethanol, and the Blend Volume Percent Denatured Ethanol, V%ethanol differs numerically from φethanol by the excess volume fraction term in the denominator and by a factor of 100.

% ,

,∗ 100 ,

, , ∗∗ 100 (2)

Where

Vε is the fraction excess volume

bge α60 for use in API 11.1

The thermal expansion coefficient at 60 °F (α60) of bge is calculated as the volume proportional alphas of the BOB and denatured ethanol blend stocks and an additional component, the Excess Alpha (α60ε).

The alpha of BOB is computed from the generalized refined product commodity group procedures in API 11.1.6.1 or the fluid-specific procedures in 11.1.5.2, which are not repeated in detail here. API 11.3.3 sets a value of 0.000603 °F-1 at 60°F for the α60 of denatured ethanol.

The α60 of a bgebge shall be calculated by first calculating the excess alpha:

1.8 ∗ ∗ 1 ∗ . . ∗ . ∗ . ∗

Followed by calculating the proportional contributions of denatured ethanol, BOB, and the excess alpha.

, 1 ∗ , ∗ , (4)

Where:

α60ε = additional alpha to be added to the alpha proportionately contributed by the BOB and denatured ethanol components. φethanol ideal volume fraction denatured ethanol e Euler's number, 2.718281828…) α60,ethanol = 0.000603 °F-1

When using a user-input α60 in the API 11.1.6.1 procedure, definition of the density is not required. A table of worked examples of the α60 for bgebge of different denatured ethanol concentrations and BOB densities is shown in Annex A.

Excess Volume Fraction

The calculation of excess volume fraction involves 2 equations to calculate a fitting parameter and the excess volume fraction equation. The dimensionless fitting parameter is:



∗

∗ (5)

Where

φethanol is the volume fraction of denatured ethanol, Z is a fit parameter shown in Table 1.

The resulting y is substituted into the excess volume fraction equation:

1 60, /100 (6)

Where

Vε is the fraction of the sum of the component volumes not accounted for by simple addition A, AHC, B, n are fit parameters shown in Table 1 ρ60,BOB is the BOB density at 60 °F

If the excess volume fraction function returns a negative value, set the value to zero. Some combinations of high ethanol (>95%) and high BOB density (>785 kg/m3) can lead to a negative calculated value due to limitations of the fitted equation. Since these are commercially non-existent cases, the simplicity of the current equation is preferred over eliminating the artifacts.

Table 1 - Excess Volume Fraction Equation Parameters

Fit Parameter Value A 8.624574 AHC -0.010160136B -0.73742 n 5.411871 Z 2.00855

The user shall note that the required density input to calculate the α60ε calculation is the BOB density, NOT the bge density.

Application of API 11.1

Pressure Correction of Denatured Ethanol to Base Conditions

Denatured ethanol can be corrected to base conditions of 60°F, 0 psig using the method of API 11.2.2 with a coefficient, Fs, derived from literature data for the thermodynamic properties of ethanol. The multiplier 10-5 in the equation is to scale the result to the same basis as the Hydrocarbon Fs used in API 11.1.6.1.

, ∗ ∗ ∗ 10 (7)

Where:

Fs,ethanol = scaled compressibility factor, psi-1



as1 = 3.98002E-6 as2 = 1.92284E-3 as3 = 563.134E-3

There is insufficient data at this time to justify a modified equation for the pressure correction for bge.

Temperature and Pressure Correction of Blends of Gasoline and Ethanol (bge) to Base Conditions

Bge of any concentration shall be corrected to base conditions using the method of API 11.1 (and API 11.2.2). bge shall not use the Generalized Refined Product Commodity group approach, but rather uses a user-supplied alpha as calculated in section 0. In the situation where the user does not have the fluid-specific α60 for the BOB, the user may use the generic refined product equation in API 11.1 to calculate the BOB α60, then apply that α60 in the equation in section 0. The α60 from 0 shall be used in the 11.1 CTPL calculation.

Pressure correction shall be done using the procedure in API 11.1 or API 11.2.2 entering the procedure with the volume proportional Fs from the equation:

∗ , 1 ∗ , (8)

Where

Fs is the bge scaled compressibility factor (psi-1) Fs,ethanol is the ethanol scaled compressibility factor (psi-1)as calculated in section 0 Fs,BOB is the BOB scaled compressibility factor (psi-1)as calculated per API 11.1

Correction to Other Standard Conditions

The implementation procedure for correcting a volume from an observed temperature to another standard temperature (e.g. 15 °C or 20 °C) is a three step process. Calculations shall be carried at full machine precision.

Step 1 Calculate the CTPL from observed conditions to 60 °F Base conditions using the equations in Section 8.1 to determine the input parameters for API 11.1.6.2.

Step 2 Calculate the CTPL from the standard conditions to 60 °F (15.556 °C) using the same input parameters and methods.

Step 3 Multiply the observed volume times the CTPL (observed to 60) divided by the CTPL (other standard to 60) as described in the equation below.

∗ °

° (9)

Density can also be corrected in Step 3 with the formula

∗ (10)

Following this procedure an observed volume of 99.926 m3 of bge at 57 °F, 30 psig, 781 kg/m3 BOB, 0.492 ideal fraction ethanol as described in Scenario 1 Example, would be converted to alternate base temperatures :



15 °C Base Temperature

, ∗ , °

°99.926 ∗

1.00211251.0007638

100.061

∗ ° 783.368 ∗ 1.0007638 783.967

20 °C Base Temperature

° , ∗ , °

° °99.926 ∗

1.00211250.9728734

102.929 3

∗ ° 783.368 ∗ 0.9728734 762.118

Rounding

The implementation procedures shall be performed with no rounding or truncation of input, intermediate, or output values. Rounding of values is a topic addressed by other API standards. Within this standard, any apparent rounding in printed or tabulated values is solely for editorial convenience. Calculations within the examples were performed using full machine precision.

Calculation of Blending Scenarios

Definition of Scenario Inputs and Targets

In each of the scenarios, a hypothetical blending scenario requires calculation of the V60 of the bge with varying levels of information. Each of the scenarios is shown below in Table 2 –Available and Target Scenario Parameters. The parameters are classified into either “available” which is known and used in the calculation, “find” which is the objective of the calculation, and “ – “ which only designates that it is neither an objective nor required for the calculation.

In the example calculations, the m3 unit of volume measurement is indicated. Only one unit of volume measurement shall be used within the calculations. If another unit of volume measurement is required as an input or output, the user must convert the input value to m3 using the methods of API MPMS Ch.15 prior to entering these calculations.

Each example shown in this section is based on the same input values and has the same expected outputs, except each scenario is constrained by a different set of unknowns in the inputs.



Table 2 –Available and Target Scenario Parameters

Input Value Scenarios 1, 2, & 3 Examples

Units Scenario 1 Scenario 2 Scenario 3 Scenario 4 (Example

Input Values)

VBOB 50.603 m3 Available Find Find ‐‐

TObserved,BOB 53.0 °F Available Available Available ‐‐

PObserved,BOB 36.0 psig Available Available Available ‐‐

ρ60,BOB 781.000 kg/m3 Available Available Find ‐‐

V60,BOB ‐‐ m3 Find Find Find ‐‐

Nominal Ethanol Content ‐‐ ‐‐ ‐‐ Available(10%)

Vobserved,ethanol 49.644 m3 Available Available Available ‐‐

Tobserved,ethanol 76.0 °F Available Available Available ‐‐

Pobserved,ethanol 54.0 psig Available Available Available ‐‐

ρ60,ethanol 788.000 kg/m3 Available Available Available Available (788.0)

V60,ethanol ‐‐ m3 Find Find Find ‐‐

V observed,bge 99.926 m3 ‐‐ Available Available Available(99.613)

T observed,bge 57.0 °F Available Available Available Available(53.0)

P observed,bge 30.0 psig Available Available Available Available(75.0)

ρ60,bge ‐‐ kg/m3 Find Find Find Available(753.0)

ρobserved,bge 785.023 kg/m3 Find ‐‐ Available ‐‐

V60,bge ‐‐ m3Find Find Find Find

Scenario 1 Calculation of bgeBge V60 and Density from Blending Volumes and Densities

Calculation Method

In situations where the volumetric flow and density of the BOB and denatured ethanol streams are known, the density and V60 of the bge can be calculated directly without iteration.

If the flowing density of the bge is measured, the CTPL shall be calculated from the used to correct the flowing density to base conditions. If the flowing density is not measured, the BOB and denatured ethanol properties may be used to calculate a ρ60, bge.



Following the generic formula for each step is a worked example using the inputs listed in the Table 2.

Step 1 Calculate Ethanol CTPL

Using the α60 for denatured ethanol (95-99% purity) from API 11.3.3 and the Fs for ethanol from API 11.3.xx1, calculate the CTPL to correct the denatured ethanol volume from observed to base conditions.

CTPL ethanol = 0.990713

Step 2 Determine V60,ethanol

Using the CTPL from Step 1, adjust the ethanol volume to base conditions.

, , ∗

, 0.990713 ∗ 49.644 49.183

Step 3 Calculate CTPL for BOB

Using the calculation procedure in API 11.1 for either the specified α60 or the Generalized Method, calculate the CTPL to correct the VBOB to base conditions.

, 1.004229 usingtheGeneralizedRefinedProductsMethod

Step 4 Determine V60,BOB

Convert the BOB volume to base conditions

, ∗

, 1.004229 ∗ 50.603 50.817

Step 5 Calculate Ideal Ethanol Fraction

Use the formula from section 0

,

, ,

1 waiting for committee to supply reference for new ethanol pressure correction



49.18349.183 50.817

0.492

Step 6 Calculate Excess Volume

Using section 0:

∗1 ∗ 1

Then continuing to calculate excess volume:

1 60,BOB

0.492 ∗1 0.492 ∗ 1

0.001372

Where

φethanol is the ideal volume fraction of denatured ethanol from Step 5 Z, A, AHC, B, n are fit parameters from Table 1

Step 7 Calculate CTPL for bge

Using the α60 algorithm in 0 in API 11.1 as described in section 0

CTPL bge = 1.002112

Step 8 Calculate V60,bge from CTPL

Correct the observed bgebge volume to base conditions

, ∗

, 1.002112 ∗ 99.926 100.137

Step 9 Calculate Blend Volume Percent Ethanol

Using the V60 values from Step 2 and 8, calculate the blend volume percent ethanol.



% ,

,

49.183100.137

∗ 100 49.116%

Step 10 Calculate bge ρ60

bge density shall be calculated in either of two ways in this procedure:

1. If the flowing density is measured, use the CTPL calculated in Step7 to adjust the measured density to base conditions, or

2. If the density is unknown, use the following equations to calculate the ρ60.

Bge density is expected to be the volumetrically proportional combination of the BOB and ethanol densities, adjusted for the excess volume increase in bge volume

,

1 %100 ∗ 1 ∗ ,

%100 ∗ 1 ∗ ,

1

,

149.116100 ∗ 1 0.001372 ∗ 781.0

49.116100 ∗ 1 0.001372 ∗ 788.0

1 0.001372

, 783.368

Step 11 Calculate bge Flowing Density

If useful, calculate the bge flowing density using CTPL calculated in Step 7:

, ∗ , 785.023

Outputting results

The results to be reported for this scenario are:



Table 3 - Scenario 1 Output Values

Output Value From Step

Value

V60,ethanol 2 49.183 m3

V60,BOB 4 50.817 m3

V60,bge 8 100.137 m3

V%ethanol 9 49.116%

ρ60,bge 10 783.368 kg/m3

All results are outputted without rounding.

Scenario 2 Bge and Denatured Ethanol Measured, BOB Volume Unmeasured

In this scenario, the bge and denatured ethanol flowing volumes are measured, but the BOB volume is not available. It is assumed that the BOB density is available from laboratory data, such as the Certificate of Analyses. This case is similar to the previous scenario but adds another unknown.

Calculation Method

The calculation approach to solving this scenario is to assume a V60 for BOB, which enables the calculation of the V60 and ρ60 of the bge using their mixing and thermal expansion properties. The bge properties are then used to find the BOB V60 by mass balance. The mass balance solution is substituted back into the bge calculations iteratively until the V60, BOB changes less than the specified tolerance within an iteration.


Using the α60 for denatured ethanol (95-99% purity) from API 11.3.3 and the Fs for ethanol from API 11.3.xx2, calculate the CTPL to correct the denatured ethanol volume from observed to base conditions.

CTPL,ethanol = 0.990713

2 waiting for citation from committee




Using the CTPL from Step 1

, , ∗

, 0.990713 ∗ 49.644 49.183

Step 3 Make first estimate for V60,BOB (first step of iterative sequence)

The following steps form an iterative loop. The equations are shown for the iterations use the subscript “i”; the worked example calculations within each step are only for the first iteration and show the specific subscript “1”.

For the second and subsequent iterations use the value of V60,BOB from Step 10 of the previous iteration.

To initialize the first iteration, assume that the thermal expansion of bge is similar to that of BOB to estimate the V60 of the bge, and subtract the V60 of the ethanol, ignoring the excess volume contribution.

, , ∗ ,

Where CTPL is the CTPL determined for a generic refined product with a density equal to that of the BOB component. This approximation has only a minor effect on subsequent iteration convergence.

CTPL for generalized refined product with t = 57°F, p = 30psig, ρ60 = 781.0 kg/m3 is 1.00191.

, , 99.926 ∗ 1.00191 49.183 50.933

Subsequent iterations use the V60,BOB,i determined in the previous iteration’s Step 10 as stated above.


Using the values from Step 2 and 3

,

, , ,

49.18349.183 50.933

0.491



Step 5 Calculate Excess Volume Fraction (EV)

Using section 0:

∗1 ∗ 1

, 1 60, /100

0.491 ∗1 0.491 ∗ 1

,1 0.001373


By the definition of Blend Volume Percent Ethanol

% ,

, ,

Since: , , , ∗ 1

Therefore also:

% ,

, , , , ∗ 1 ,

% 49.183

50.933 49.183 ∗ 1 0.001373∗ 100 49.059%

Step 7 Find bge Density

bge density is expected to be the volumetrically proportional combination of the BOB and ethanol densities, adjusted for the excess volume fraction increase in bge volume



, ,

1 %

100 ∗ 1 , ∗ ,%

100 ∗ 1 , ∗ ,

1 ,

, ,

149.059100 ∗ 1 0.001373 ∗ 781.0

49.059100 ∗ 1 0.001373 ∗ 788.0

1 0.001373

, , 783.363


Using the method shown previously in Section 11.3.4.0, calculate the CTPL for bge using the values from the current iteration.

CTPL,bge,1 = 1.002113

Step 9 Correct bge to V60

Using the CTPL from Step 8

, , , , ∗

, , 1.002113 ∗ 99.926 100.137

Step 10 Calculate V60,BOB,mass,i from Mass

Using the mass of the bge and ethanol, calculated by multiplying density times volume

, , , ,, , ∗ , , , ∗ ,

, ,

, , , ,. ∗ . . ∗ .

.50.816



Step 11 Calculate V60,BOB,i Convergence

BOB V60 was input in Step 3 and calculated by mass balance from a CTPL-calculated V60,bge in Step 10. The values of V60,BOB and ρ60,bge for the unmeasured parameters are determined when both the principle of conservation of mass and the known correlation of thermal expansion yield a consistent set of results.

absolute , , , , , , ,

, , , ,

absolute50.934 50.816

50.8162.3 ∗ 10

Convergence shall be considered sufficient when the absolute value of the convergence criteria is less than 10-7. Three to four iterations are usually sufficient. Convergence accelerators are not advantageous for this application.

Conducting the next iteration

If the convergence criteria is not met, the value of V60,BOB obtained in Step 10 shall be used as the starting value in Step 3. The iterative calculation loop, Steps 3 through Step 11, are repeated until the convergence criteria are met.

Step 12 Calculate Flowing VBOB

The value of the flowing volume of BOB may be calculated if the convergence criteria is met, calculate the observed volume, VBOB using the converged value of V60,BOB and the methods of API 11.1.6.1. If the iteration has not converged, it is not necessary to calculate VBOB because it is not used within the iteration loop.

VBOB = 50.603 m3

Outputting results

After the final iteration, i, the results to be reported are from the final iteration:


Output Value Iteration Symbol Step Value V60,ethanol V60,ethanol 2 49.183 m3 V%ethanol V%ethanol,i 6 49.116 %



ρ60,bge ρ60,bge,i 7 783.368 kg/m3 V60,bge V60,bge,i 9 100.137 m3 V60,BOB V60,BOB,mass,i 10 50.817 m3 VBOB VBOB 12 50.603 m3

All results shall be outputted without rounding.



Continuation of Scenario 2 Example

The following table contains the initial iteration results shown for illustration in the above scenario procedure, with the subsequent iterations included. Following the convergence criteria, 3 iterations would have been sufficient, but an additional iteration is included to provide another calculation example for the user.

Table 5 - Scenario 2 Example Iteration Results

Step Action Iteration 1 Iteration 2 Iteration 3

1 Calculate Ethanol CTPL 0.990713

2 Determine Vol60_ethanol 49.183

3 Make first guess for Vol60 BOB 50.933 50.816 50.817

4 Calculate Ideal Ethanol Fraction 0.491 0.492 0.492

5

Calculate Excess Volume Fraction (EV) 0.001373 0.001372 0.001372

6 Calculate V%ethanol 49.059% 49.116% 49.116%

7 Make guess for bge Density 783.363 783.368 783.368

8 Calculate CTPL for bge 1.002113 1.002112 1.002112

9 Correct bge to V60 100.137 100.137 100.137

10 Calculate V60 BOB from Mass 50.816 50.817 50.817

11 Calculate V60 BOB Convergence 2.3E-03 1.3E-05 7.9E-08

12 Calculate Flowing Vol_BOB 50.603



Scenario 3 Calculation of BOB Volume and BOB & bge Densities, Ethanol and bge Volumes Measured

This scenario details the property determination in a situation where the BOB volume is not measured, nor is the density of the BOB known. Without the volume and density of the BOB component, the measurements of the bge at flowing conditions cannot be corrected to base conditions. It does assume that the volume and density of the bge is measured at flowing conditions.

Note: This scenario does require that the flowing bge density be known.

Calculation Method

The approach used to estimate the necessary BOB parameters and calculate the volume of bge by both mass balance and volume expansion equations. At the correct BOB volume and density, the difference between the V60,bge by mass balance and CTPL methods will approach zero.

This does require an iterative approach. The convergence of the method is usually sufficient by direct substitution of the results of the previous trial, but any convergence accelerator may also be used within the method.


As in the previous scenario, calculate the CTPL and V60 of the denatured ethanol component.

CTPL ethanol = 0.990713


, ∗

, 0.990713 ∗ 49.644 49.183

Step 3 ρ60, bge (Beginning of iterative portion)

The following steps form an iterative loop. The equations are shown for the iterations use the subscript “i”; the worked example calculations within each step are only for the first iteration and show the specific subscript “1”.

The first estimate of ρ60 for the bge may be made by any means but the suggested method is by using the method of API 11.1 type II calculation assuming the bge is a generalized refined product. This is not technically correct, but as an approximation is usually sufficient to initialize the iterations. There can be



convergence problems if the BOB portion is less than 1% and the observed temperature is significantly different from the base temperature.

For:

Temp_Obs_bge 57.0 psig_Obs_bge 30.0 Rho_Flowing_bge 785.023289 Commodity Group “B” ρ60,bge,1 = 783.569 kg/m3

For second and subsequent iterations, the ρ60,bge,CTPL,i shall be determined by mass balance (Step 13) or by a convergence accelerator using the results of Step 13 as an input.

Step 4 Find V60, bge from Mass

Using the measured flowing properties of the bge and the estimate of ρ60,bge,i, calculate the trial V60,bge,mass,i by mass balance.

, , ,∗

, ,

, , ,

99.926 ∗ 785.023

783.569100.112

Step 5 Estimate Ideal Ethanol Fraction (for First Iteration Only)

If this is not the first iteration, skip this step. For the first trial iteration only, an approximation to the ideal fraction ethanol is made ignoring the contribution made by the excess volume effect. Subsequent iterations shall use previously determined V60BOB.

,

, ,

49.183100.112

0.491


Using the V60,ethanol from Step 2 and the V60,bge,mass,i from Step 4

% ,

, , ,∗ 100



% 49.183100.112

∗ 100 49.129%

Step 7 Estimate ρ60,BOB (for First Iteration Only)

If this is not the first iteration, skip this step. This step is only required to develop the necessary input to calculate an initial value of excess volume fraction and CTPL for bge.

, ,

,%

100 ∗ ,

1 %

100

, ,

783.56949.129%100 ∗ 788.0

149.129%100

779.289

At low concentrations of BOB and large bge temperature offsets from 60°F, the calculated density can return unreasonable values that lead to later convergence problems. If the calculated ρ60,BOB,i is outside the range of 700 to 800 kg/m3, a value of 750 kg/m3 shall be used instead of the calculated value.


Calculate the excess volume fraction Vεi.. For iteration 1 the values approximated in iteration 1, Step 5, φethanol1, and Step 7, ρ60,BOB,1, shall be used. For subsequent iterations, the values calculated in Steps 10 and 11 of the previous iteration (φethanol,i-1 and ρ60,BOB,i-1) shall be used.

,1 0.001412

Step 9 Calculate V60,BOB

, ,,,

1 ,,

, ,100.1121 0.001412

49.183 50.787

Step 10 ρ60,BOB from Mass

Using the iteration-calculated V60,BOB from Step 9 and the expected mass of BOB, calculate a value of ρ60,BOB. The flowing properties of bge, ρbge and Vbge, are measured inputs, ρ60,ethanol is a given input, and V60,ethanol is that determined in Step 2.



, , ,∗ , ∗ ,

, ,

, , ,

785.023 ∗ 99.926 788.0 ∗ 49.183

50.787781.5

If the volume of BOB is very small relative to the bge volume, slight errors in the measured density of the bge or ethanol can lead to either a physically impossible calculated negative mass for BOB or an unreasonable value for the expected density. If the numerator is negative, end the calculation and return an error code, the case cannot converge. If the calculated ρ60,BOB,mass,i is outside the range of 700 to 800 kg/m3, the user shall set the ρ60,BOB,mass,i to 750 kg/m3 and continue another iteration; these cases may not converge.


Calculate the ideal fraction ethanol using the iteration-calculated V60,BOB,i from Step 9.

,

, , ,

49.18349.183 50.787

0.492


The ρ60,BOB,mass,i from Step 10 and the φethanol,i from Step 11 are used to calculate an α60 for the bge (section 0) which is used according to API 11.1.6.1 to determine a CTPL,i for bge.

, , 1.002108

Step 13 Calculate ρ60 for bge from CTPL

Using the CTPL from the previous step

, , ,, ,

, , ,

785.023

1.002108783.372

Step 14 Calculate V60 for bge from CTPL

Using the CTPL from Step 12 calculate the bge volume at base conditions



, , , , , ∗

, , , 1.002108 ∗ 99.926 100.137

Step 15 Check Iteration Convergence of bge Volume Calculated By Mass and CTPL

bge V60 was calculated by mass in Step 4 and by CTPL in Step 14. The values of ρ60 and V60 for the unknown BOB component are determined when both the principle of conservation of mass and the known correlation of thermal expansion yield a consistent set of results.

absolute , , , , , , , ,

, , , ,

absolute100.112 100.137

100.137 2.51 ∗ 10

Convergence is achieved when the absolute value of the convergence is less than 10-7. This typically happens within 4 iterations.

If used in a convergence accelerator method, the sign is necessary and a similar equation may be used without the absolute value function. However, the convergence criteria remains the same. Convergence acceleration is of limited value in this application.

If more than a few iterations are performed without checking for convergence, some cases can fail because the difference diminishes below the machine tolerance for zero and the equations in some intermediate steps generate a “divide-by-zero” error.

Step 16 Calculate VBOB

If the iteration has satisfactorily converged, calculate the observed volume of BOB using the V60,BOB,i from Step 9 and the ρ60,BOB,i from Step 10 of the final iteration in the API 11.1.6.5 method to find the CTPL and apply the following equation.

, ,

If the iteration has not converged, it is not necessary to calculate VBOB as it is not used in the iteration sequence.

Conducting the next iteration

If the convergence criteria is not met, the value of ρ60,bge obtained in Step 13 shall be used as the starting value in Step 3 for the next iteration.

This implementation is based on direct substitution and does not recommend convergence acceleration. If an acceleration method is used, the method should return a value of ρ60,bge to use in Step 3. There does not appear to be significant value in accelerating the convergence of additional variables.



Outputting results

After the final iteration, i, the following results shall be reported from the specified step of the final iteration:


Output Value Iteration Symbol Step Value V60,ethanol V60,ethanol 2 49.183 m3 V%ethanol V%ethanol,i 6 49.116% V60,BOB V60,BOB,i 9 50.817 m3 ρ60,BOB ρ60,BOB,i 10 781.000 kg/m3 ρ60,bge ρ60,bge,i 13 783.368 kg/m3 V60,bge V60,bge,CTPL,i 14 100.137 m3 VBOB VBOB 16 50.603 m3

All results are outputted without rounding.

Continuation of Scenario 3 Example

The following table contains the initial iteration results shown for illustration in the above scenario procedure, with the subsequent iterations included. Following the specified convergence criteria, 3 iterations would be sufficient.




Step Action Iteration 1 Iteration 2 Iteration 3

1 Calculate ethanol CTPL

0.990713

2 Determine Vol60_ethanol

49.183

3 Rho60 bge from CTPL (11.1 Tab5 to start)

783.569 783.372 783.368

4 Find V60 bge from Mass

100.112 100.137 100.137

5 Estimate Ideal Ethanol Fraction

0.491 -- --

6 Calculate Blend Volume Percent Ethanol

49.129% 49.116% 49.116%

7 First Estimate ρ60,BOB

779.289 -- --

8 Calculate Excess Volume Fraction (EV)

0.001412 0.001361 0.001372

9 Calculate V60_BOB

50.787 50.817 50.817

10 ρ60,BOB from Mass_BOB

781.5 781.0 781.0

11 Calculate Ideal Ethanol Fraction

0.492 0.492 0.492

13 Calculate CTPL for bge

1.002108 1.002113 1.002112

12 Calculate ρ60,bge from CTPL

783.372 783.368 783.368

14 Calculate V60_bge from CTPL

100.137 100.137 100.137

15

Check convergence V60_bge by CTPL and Mass

2.51E-04 4.61E-06 9.80E-08

16 Calculate Vol_Flowing_BOB

50.603

Scenario 4 Calculation of bge Volume at Base Conditions with Minimal Information

This scenario is presented for the limited scope of determining the CTPL and density of delivered cargos of ethanol-blended fuels for the use in verification calculations. It is not suitable for generating properties for custody transfer quantities. This scenario uses a very limited number of input parameters that are likely to be available to the receiver of a shipment. The values derived from this calculation are expected to be sufficiently accurate to form the basis for a commercial discussion of the delivered volume.

The complication in calculating the CTPL for bge cargos is that the excess alpha portion of the calculation requires the ideal fraction ethanol φethanol which in turn requires the ρ60,BOB, which in this scenario is unknown.



This scenario may not converge reliably for blend ethanol percentages over 20% unless the actual concentration of the ethanol is close to the labeled quantity or unless the actual BOB density is available (not assumed). Though it is within its scope, the calculation may not be useful for E85 blends.

Table 8 - Scenario 4 Available Input Values

Parameter Value Assumed Source V60,bge FindNominal Ethanol Content 10 % Bill of Lading ρ60,ethanol 788.000 kg/m3 Blenderρ60,bge 753.0 kg/m3 BlenderTobserved,bge 53.0 °F Measurement Pobserved,bge 75.0 psig Measurement Vobserved,bge 99.613 m3 Measurement

Calculation Method

This implementation procedure uses an estimate of the BOB properties to calculate the expected blend density and then iterates to improve the estimate until it matches the expected value.

Step 1 Blend Volume Percent Ethanol from Certificate of Analysis

Obtain the nominal percent denatured ethanol from the Certificate of Analysis or other documentation. The actual concentration of ethanol may be different within bounds specified by regulation.

Step 2 Estimate Ideal Ethanol Fraction

Estimate the ideal fraction ethanol for the first iteration as the nominal ethanol blend percentage divided by 100.

, %

100

, 10%100

0.1

Since the actual blended ethanol concentration is not known, this value cannot be improved over the original estimate and is not included in the iteration.

Step 3 Estimate ρBOB (Start of iterative loop)

As a first estimate, assume the density of the BOB component is the same as that listed for the bge on the Certificate of Analysis or other documentation. For the second and subsequent iterations use the value of ρ60,BOB,i‐1 determined in the previous iteration Step 6.

, , ,

, , 753.0




Using the equations in section 0, calculate the excess volume fraction (Vε) with the ϕethanol from Step 1 and the ρ60,BOB,i from Step 3. Vε,1 = 0.001453

Step 5 Adjust the Blend Density for the Excess Volume Expansion

Adjust the bge density to remove the effect of excess volume. This value has no significance outside this scenario calculation.

, , ∗ 1 ,

, 753.0 ∗ 1 0.001453 754.094

Step 6 Calculate ρ60,BOB

Calculate an estimated density (mass of 1 m3) for the BOB component by subtracting the mass of the ethanol from the mass of the bge and normalizing the BOB fraction to 1 m3.

, , , ∗ ,

1

, ,

754.094 0.1 ∗ 788.000

1 0.1750.327

Step 7 Convergence Criteria

The calculation shall be considered converged when the difference of ρ60,BOB in Step 3 and ρ60,BOB calculated in Step 6 divided by ρ60,BOB calculated in Step 6 of an iteration are less than 10-7 according to the equation

, , , , , ,

, , ,

753.0 750.327

750.3273.56 ∗ 10

If the convergence criteria is greater than the specified level, the iteration shall be repeated using the Step 6 calculated value as the starting point in Step 3.


After the case has converged, use the calculated density of BOB from Step 6 and the observed temperature and pressure, calculate the CTPL according to the method in section 0.



CTPL = 1.005517

Step 9 Calculate V60,bge from CTPL

Calculate the volume of bge at base conditions using the CTPL

, , ∗ ,

, , 1.005517 ∗ 99.613 100.163

Scenario 4 Output Values

The only output for this implementation procedure is the V60,bge calculated in Step 6 of the last iteration. The other values are not to be used as output.

Continuation of Scenario 4 Iteration Example

The values calculated in each of the example’s iterations are shown in the table below.


Step Action Iteration 1 Iteration 2 Iteration 3 Iteration 41 Blend Volume Percent Ethanol from CoA 10.00% 2 Estimate Ideal Ethanol Fraction 0.100 3 Estimate ρ60,BOB 753.000 750.327 750.360 750.3604 Calculate Excess Volume Fraction (Vε) 0.001453 0.001493 0.001493 0.0014935 Calculate Adjusted Blend Density 754.094 754.124 754.124 754.1246 Calculate ρ60,BOB 750.327 750.360 750.360 750.3607 Convergence Criteria 3.56E‐03 4.52E‐05 5.73E‐07 7.26E‐098 Calculate Ctpl for bge 1.0055179 Calculate V60,bge from Ctpl 100.163

9 Precision Statement

The unweighted uncertainty of the bge volume, density, and CTPL calculations is believed to be 0.17% at the 95% level, based on a back calculation of 942 experimental density data points gathered in an API-sponsored laboratory project.

The uncertainty of primary output parameters of the blending scenario calculations are calculated on a weighted basis and are described in Table 10. These uncertainties were derived by Monte Carlo simulation of the scenario calculation procedures. These uncertainties include the underlying uncertainty of the CTPL equations themselves.

The P50 Error represents the difference between the calculated value with uncertainty and “expected” without uncertainty at the 50% probability level. There is an equal chance of having an error less or greater than this value. The source of this small error is the weighting of the scenario uncertainties. The function correlations are carried out across the entire breath of the experimental results, while the scenarios focus on a more limited range of conditions.

The P50 can differ from the mean for distributions that are not symmetrical such as log functions.



The uncertainty of Scenario 4 is 0.16% for nominal ethanol concentrations less than E85. V60 for E85 mixtures cannot be calculated using this procedure as case will not converge. The E20 cases and less have been demonstrated to converge.

Table 10 - Scenario Uncertainties

All values are Percent Scenario 1 Scenario 2 Scenario 3 Scenario 4 V60 bge

P 50 Error 0.02 0.02 0.02 0.02 Uncertainty 95% 0.12 0.19 0.31 0.16

Rho60 bge

P 50 Error 0.00 0.00 -0.02 -- Uncertainty 95% 0.01 0.01 0.30 --

V60 BOB

P 50 Error -- 0.00 0.00 -- Uncertainty 95% -- 0.26 0.48 --

10 Bibliography

Ethanol/Gasoline VCF, CTL-α60ε, Data and Modeling Research Report Gasoline and Denatured Ethanol Blends, STCS, Jeffrey L. Savidge, PhD, July 2015



Annex A. Calculation of Alpha60 for Input to bge CTPL – Worked Examples – Informative

Table A-1 - Calculation of Alpha60 for Input to bge CTPL - Worked Examples Inputs Alpha60 *1E6 °F-1

Case Denatured Ethanol Percent

Rho60 BOB kg/m3

BOB Ethanol Alpha Excess

Combined

1 31 784 554.2 603.0 63.3 632.6 2 25 720 709.9 604.0 65.3 748.7 3 50 750 667.2 605.0 50.4 686.5 4 91 721 708.4 606.0 9.0 624.2 5 88 762 651.4 607.0 12.3 624.6 6 6 722 706.9 608.0 40.2 741.2 7 91 756 659.2 609.0 9.0 622.5 8 57 748 669.9 610.0 44.4 680.2 9 75 743 676.7 611.0 26.6 654.0 10 12 726 700.9 612.0 57.9 748.2 11 33 736 686.5 613.0 62.3 724.5 12 54 740 680.9 614.0 47.1 691.8 13 62 786 541.9 615.0 39.8 627.0 14 93 767 645.0 616.0 6.9 624.9 15 82 731 693.7 617.0 18.9 649.7 16 97 748 669.9 618.0 2.8 622.4 17 21 732 692.2 619.0 65.5 742.3 18 69 773 623.6 620.0 32.9 654.0 19 2 747 671.3 621.0 17.0 687.3 20 0 744 675.4 622.0 0.0 675.4 21 93 752 664.5 623.0 6.9 632.8 22 71 723 705.4 624.0 30.8 678.4 23 69 760 654.0 625.0 32.9 666.9 24 46 746 672.6 626.0 53.6 704.7 25 92 750 667.2 627.0 8.0 638.2 26 35 762 651.4 628.0 61.1 704.3 27 17 747 671.3 629.0 63.9 727.9 28 54 732 692.2 630.0 47.1 705.7 29 70 734 689.4 631.0 31.9 680.4 30 80 723 705.4 632.0 21.1 667.8 31 18 773 623.6 633.0 64.5 689.8 32 19 752 664.5 634.0 64.9 723.6 33 66 733 690.8 635.0 35.9 689.9 34 26 770 641.2 636.0 65.1 705.0 35 79 726 700.9 637.0 22.2 672.6 36 23 785 548.0 638.0 65.6 634.3 37 0 742 678.1 639.0 0.0 678.1 38 40 772 630.1 640.0 57.9 692.0 39 87 783 560.4 641.0 13.4 643.9 40 45 725 702.4 642.0 54.3 729.6 41 49 766 646.3 643.0 51.2 695.9



Table A-1 - Calculation of Alpha60 for Input to bge CTPL - Worked Examples Inputs Alpha60 *1E6 °F-1

Case Denatured Ethanol Percent

Rho60 BOB kg/m3

BOB Ethanol Alpha Excess

Combined

42 62 777 598.0 644.0 39.8 666.3 43 96 735 687.9 645.0 3.8 650.6 44 30 773 623.6 646.0 63.7 694.1 45 29 734 689.4 647.0 64.1 741.2 46 93 766 646.3 648.0 6.9 654.8 47 49 772 630.1 649.0 51.2 690.6 48 15 745 674.0 650.0 62.1 732.5 49 86 778 591.7 651.0 14.5 657.2 50 26 730 695.1 652.0 65.1 749.0 51 89 787 535.8 653.0 11.2 651.3 52 35 776 604.4 654.0 61.1 682.9 53 55 726 700.9 655.0 46.2 721.9 54 63 752 664.5 656.0 38.9 698.0 55 96 747 671.3 657.0 3.8 661.4 56 91 723 705.4 658.0 9.0 671.3 57 57 723 705.4 659.0 44.4 723.4 58 85 754 661.9 660.0 15.6 675.8 59 2 735 687.9 661.0 17.0 704.4 60 76 734 689.4 662.0 25.5 694.0 61 89 757 657.9 663.0 11.2 673.6 62 81 736 686.5 664.0 20.0 688.3 63 40 762 651.4 665.0 57.9 714.8 64 10 722 706.9 666.0 53.7 756.4 65 7 736 686.5 667.0 44.3 729.5 66 37 723 705.4 668.0 59.9 751.5 67 49 766 646.3 669.0 51.2 708.6 68 75 783 560.4 670.0 26.6 669.2 69 86 743 676.7 671.0 14.5 686.3 70 51 740 680.9 672.0 49.6 725.9 71 16 790 529.2 673.0 63.1 615.3 72 81 735 687.9 674.0 20.0 696.6 73 99 741 679.5 675.0 0.9 676.0 74 9 741 679.5 676.0 51.0 730.2 75 99 730 695.1 677.0 0.9 678.1


Annex B. Calculation of Excess Volume Fraction – Worked Examples – Informative

The following table contains calculated values following the excess volume fraction method in 0. The input values are randomized and shown to their full significant figures. The excess volume fraction is shown to 7 decimal places for editorial convenience.

Table B-1 Excess Volume Fraction Worked Examples

Case Number

Ideal Ethanol Fraction

Density BOB

kg/m3


Ve 1 0.6362 782.0 0.0008440 2 0.7857 743.0 0.0007425 3 0.7816 794.0 0.0002070 4 0.5255 700.0 0.0030244 5 0.0932 706.0 0.0020587 6 0.0703 793.0 0.0006497 7 0.4107 718.0 0.0031348 8 0.4031 753.0 0.0022886 9 0.2080 765.0 0.0019211

10 0.5366 741.0 0.0020806 11 0.9123 719.0 0.0003255 12 0.2195 749.0 0.0023336 13 0.7228 718.0 0.0014043 14 0.1285 706.0 0.0025583 15 0.1454 701.0 0.0028509 16 0.2060 795.0 0.0012275 17 0.2046 785.0 0.0014525 18 0.1979 742.0 0.0024014 19 0.8516 713.0 0.0006687 20 0.1246 797.0 0.0009107 21 0.8611 706.0 0.0006648 22 0.3391 710.0 0.0034795 23 0.8074 762.0 0.0004562 24 0.9557 781.0 0.0000083 25 0.2406 728.0 0.0029078 26 0.3944 798.0 0.0011852 27 0.6738 759.0 0.0010702 28 0.0156 716.0 0.0004036 29 0.7857 761.0 0.0005500 30 0.0122 776.0 0.0001749 31 0.8114 734.0 0.0007059 32 0.0227 753.0 0.0004148 33 0.5399 730.0 0.0022984 34 0.5476 788.0 0.0010410 35 0.5980 701.0 0.0025321 36 0.2891 736.0 0.0028135 37 0.3883 782.0 0.0015944 38 0.9668 772.0 0.0000179 39 0.1512 705.0 0.0028357 40 0.2967 703.0 0.0036527 41 0.8364 728.0 0.0006324 42 0.0374 794.0 0.0003743 43 0.4403 741.0 0.0024781 44 0.0483 795.0 0.0004594 45 0.0191 777.0 0.0002645 46 0.8333 733.0 0.0006063 47 0.1085 762.0 0.0013929 48 0.8478 748.0 0.0004224


Case Number


Density BOB

kg/m3


Ve 49 0.9670 798.0 0.0000000 50 0.0992 735.0 0.0017158 51 0.1589 759.0 0.0018193 52 0.7432 800.0 0.0002306 53 0.1838 739.0 0.0023908 54 0.8175 754.0 0.0004924 55 0.7970 755.0 0.0005665 56 0.4783 725.0 0.0027095 57 0.0584 782.0 0.0006692 58 0.7315 795.0 0.0003265 59 0.5616 753.0 0.0017116 60 0.7074 776.0 0.0006693 61 0.2794 795.0 0.0013262 62 0.1343 767.0 0.0015060 63 0.9505 741.0 0.0001118 64 0.0079 745.0 0.0001635 65 0.9539 764.0 0.0000491 66 0.2420 724.0 0.0030092 67 0.1789 754.0 0.0020383 68 0.1635 790.0 0.0012091 69 0.1770 726.0 0.0026274 70 0.0538 764.0 0.0007932 71 0.5906 800.0 0.0006643 72 0.6702 721.0 0.0016974 73 0.2928 792.0 0.0014067 74 0.9997 769.0 0.0000001 75 0.1647 748.0 0.0020808 76 0.0017 796.0 0.0000182 77 0.2223 750.0 0.0023201 78 0.7186 715.0 0.0014730 79 0.9031 770.0 0.0001179 80 0.8965 786.0 0.0000482 81 0.4419 735.0 0.0026173 82 0.8511 707.0 0.0007165 83 0.2453 757.0 0.0022189 84 0.4245 739.0 0.0025767 85 0.9539 766.0 0.0000444 86 0.3707 762.0 0.0021243 87 0.8797 764.0 0.0002065 88 0.5946 704.0 0.0024978 89 0.5421 794.0 0.0009318 90 0.3917 718.0 0.0031879 91 0.4868 783.0 0.0013409 92 0.7210 797.0 0.0003288 93 0.4864 758.0 0.0019157 94 0.5575 787.0 0.0010291 95 0.6306 772.0 0.0010425 96 0.9173 716.0 0.0003159



Case Number


Density BOB

kg/m3


Ve 97 0.8420 752.0 0.0004137 98 0.4351 736.0 0.0026162 99 0.1174 772.0 0.0012991 100 0.4853 756.0 0.0019656 101 0.9901 744.0 0.0000171 102 0.6008 726.0 0.0020384 103 0.9205 708.0 0.0003336 104 0.3208 757.0 0.0022943 105 0.0595 792.0 0.0005779 106 0.1965 732.0 0.0026188 107 0.4695 768.0 0.0017412 108 0.6974 710.0 0.0016873 109 0.4799 723.0 0.0027486 110 0.8600 722.0 0.0005585 111 0.0233 721.0 0.0005669 112 0.5775 789.0 0.0009216 113 0.7237 704.0 0.0015894 114 0.0816 705.0 0.0018783 115 0.5923 772.0 0.0012000 116 0.3733 751.0 0.0023976 117 0.2851 732.0 0.0029094 118 0.0303 702.0 0.0008291 119 0.3460 778.0 0.0017474 120 0.4838 730.0 0.0025697 121 0.4838 706.0 0.0031221 122 0.5931 790.0 0.0008497 123 0.5237 792.0 0.0010299 124 0.8243 703.0 0.0009149 125 0.4807 759.0 0.0019131 126 0.5750 709.0 0.0025283 127 0.5042 778.0 0.0014003 128 0.1324 746.0 0.0018761 129 0.6335 730.0 0.0017713 130 0.1611 751.0 0.0019958 131 0.8731 741.0 0.0003717 132 0.1170 768.0 0.0013637 133 0.2737 754.0 0.0023445 134 0.8716 784.0 0.0000995 135 0.7566 753.0 0.0007663 136 0.0146 799.0 0.0001422 137 0.8950 745.0 0.0002674 138 0.3790 780.0 0.0016589 139 0.6128 766.0 0.0012271 140 0.2130 795.0 0.0012426 141 0.8440 705.0 0.0007746 142 0.7879 765.0 0.0004989 143 0.7538 761.0 0.0006814 144 0.7378 784.0 0.0004518 145 0.9974 767.0 0.0000013 146 0.3618 755.0 0.0023136 147 0.5437 708.0 0.0027431 148 0.7931 786.0 0.0002624 149 0.9528 774.0 0.0000269 150 0.3279 745.0 0.0025969 151 0.7052 738.0 0.0012282 152 0.3078 784.0 0.0016108


Case Number


Density BOB

kg/m3


Ve 153 0.4381 757.0 0.0020987 154 0.0773 728.0 0.0015139 155 0.4244 726.0 0.0028948 156 0.8134 700.0 0.0010136 157 0.0307 797.0 0.0002963 158 0.4315 723.0 0.0029439 159 0.6672 778.0 0.0007936 160 0.2720 720.0 0.0031882 161 0.3573 779.0 0.0017115 162 0.4088 790.0 0.0013602 163 0.9293 730.0 0.0002126 164 0.4956 770.0 0.0016094 165 0.8465 713.0 0.0006976 166 0.6892 746.0 0.0011959 167 0.5238 791.0 0.0010514 168 0.5805 729.0 0.0020977 169 0.2419 739.0 0.0026461 170 0.8223 753.0 0.0004822 171 0.6430 703.0 0.0021805 172 0.6679 723.0 0.0016797 173 0.7531 735.0 0.0010031 174 0.2470 739.0 0.0026606 175 0.9939 797.0 0.0000000 176 0.7918 743.0 0.0007131 177 0.1601 733.0 0.0023555 178 0.0268 710.0 0.0007007 179 0.6740 747.0 0.0012600 180 0.0871 738.0 0.0015201 181 0.9040 800.0 0.0000000 182 0.6762 754.0 0.0011379 183 0.5904 711.0 0.0023904 184 0.3360 750.0 0.0024658 185 0.3647 778.0 0.0017284 186 0.3977 755.0 0.0022509 187 0.6515 744.0 0.0014282 188 0.5466 788.0 0.0010443 189 0.7136 724.0 0.0013790 190 0.4321 799.0 0.0010956 191 0.3481 717.0 0.0032932 192 0.6290 716.0 0.0020475 193 0.6773 729.0 0.0015261 194 0.4879 714.0 0.0029179 195 0.4743 765.0 0.0017958 196 0.7531 770.0 0.0005741 197 0.2843 768.0 0.0020056 198 0.4528 706.0 0.0032692 199 0.3705 765.0 0.0020490 200 0.1389 704.0 0.0027197 201 0.9122 770.0 0.0000999 202 0.6094 724.0 0.0020245 203 0.5869 703.0 0.0025690 204 0.5445 708.0 0.0027383 205 0.3233 704.0 0.0036394 206 0.8424 746.0 0.0004597 207 0.3099 738.0 0.0027761 208 0.3084 741.0 0.0026997



Case Number


Density BOB

kg/m3


Ve 209 0.2027 792.0 0.0012881 210 0.8693 792.0 0.0000511 211 0.2716 723.0 0.0031128 212 0.5883 799.0 0.0006906 213 0.2650 731.0 0.0029007 214 0.3052 724.0 0.0031288 215 0.5471 779.0 0.0012316 216 0.7412 729.0 0.0011457 217 0.9976 720.0 0.0000069 218 0.2648 716.0 0.0032715 219 0.1920 772.0 0.0017044 220 0.6283 734.0 0.0017306 221 0.7834 733.0 0.0008618 222 0.4476 710.0 0.0031959 223 0.7705 793.0 0.0002459 224 0.6269 770.0 0.0010937 225 0.4329 755.0 0.0021622 226 0.7363 773.0 0.0006002 227 0.5280 736.0 0.0022297 228 0.6929 724.0 0.0015076 229 0.0926 715.0 0.0019199 230 0.4263 723.0 0.0029618 231 0.2543 756.0 0.0022627 232 0.9572 726.0 0.0001265 233 0.2827 771.0 0.0019291 234 0.3582 726.0 0.0030524 235 0.9886 715.0 0.0000366 236 0.8641 792.0 0.0000588 237 0.6605 754.0 0.0012152 238 0.4134 754.0 0.0022391 239 0.6678 782.0 0.0007266 240 0.5805 752.0 0.0016430 241 0.3345 737.0 0.0027969 242 0.9623 783.0 0.0000009 243 0.9252 708.0 0.0003108 244 0.3307 701.0 0.0037133 245 0.3196 751.0 0.0024468 246 0.5100 731.0 0.0024264 247 0.3308 797.0 0.0012749 248 0.6011 794.0 0.0007469 249 0.6405 764.0 0.0011402 250 0.5229 741.0 0.0021453 251 0.7444 726.0 0.0011650 252 0.9334 727.0 0.0002079 253 0.6520 763.0 0.0011053 254 0.8340 759.0 0.0003862


Case Number


Density BOB

kg/m3


Ve 255 0.2163 709.0 0.0032542 256 0.7714 799.0 0.0001753 257 0.8323 746.0 0.0005017 258 0.8057 701.0 0.0010557 259 0.9520 744.0 0.0001005 260 0.2191 756.0 0.0021682 261 0.9832 735.0 0.0000378 262 0.7697 734.0 0.0009244 263 0.9669 750.0 0.0000546 264 0.3781 737.0 0.0027416 265 0.7009 716.0 0.0015753 266 0.6992 767.0 0.0008336 267 0.7622 754.0 0.0007288 268 0.8330 774.0 0.0002640 269 0.0503 724.0 0.0011025 270 0.3302 722.0 0.0031802 271 0.7577 762.0 0.0006529 272 0.6660 763.0 0.0010419 273 0.7600 766.0 0.0005956 274 0.8565 759.0 0.0003092 275 0.8166 764.0 0.0004041 276 0.0432 769.0 0.0006186 277 0.5167 732.0 0.0023720 278 0.6747 718.0 0.0017163 279 0.2268 727.0 0.0028805 280 0.2606 787.0 0.0015102 281 0.3575 785.0 0.0015593 282 0.7973 792.0 0.0001903 283 0.3709 740.0 0.0026789 284 0.0459 781.0 0.0005540 285 0.2688 791.0 0.0014190 286 0.1183 796.0 0.0008979 287 0.7038 797.0 0.0003775 288 0.7042 704.0 0.0017279 289 0.9060 704.0 0.0004252 290 0.1069 737.0 0.0017757 291 0.0913 720.0 0.0018293 292 0.8140 713.0 0.0008885 293 0.6507 710.0 0.0020074 294 0.1172 738.0 0.0018718 295 0.0002 708.0 0.0000057 296 0.9386 753.0 0.0001081 297 0.0035 727.0 0.0000861 298 0.9445 776.0 0.0000302 299 0.3313 789.0 0.0014778 300 0.4480 714.0 0.0030985


Annex C. Calculation of Scenarios – Worked Examples – Informative

This Annex contains example cases for each of the scenarios intended to assist the user in understanding the calculations. The number of significant figures shown is arbitrarily set for printing, this standard specifies no rounding of inputs, intermediate values, or final results. The input values for each case are the same and based on Table C.1. Table C.2 contains input values required for Scenarios 2 and 3 that must be calculated so as to correctly return the values from the other scenarios. Table C.3 is the output results for Scenario 1, Table C.4 covers Scenario 2, and Table C.5 covers Scenario 3.

Table C.1 Independent Input Values for Scenarios 1, 2, and 3

Case

INPT

Vol60

BOB

INPT Temp

Obs BOB

INPT psig

Obs

BOB

INPT Rho

60 BOB

INPT

Vol60

DEtOH

INPT

Temp Obs

DEtOH

INPT psig

Obs

DEtOH

INPT

Rho60

DEtOH

INPT Temp

Obs bge

INPT psig

Obs bge

1 59.5 139.0 44. 756.0 40.5 111.0 313.0 790.0 83.0 347.

2 14.7 72.0 107. 779.0 85.3 ‐4.0 314.0 789.0 ‐34.0 80.

3 13.8 48.0 254. 750.0 86.2 39.0 94.0 795.0 83.0 153.

4 68.9 117.0 283. 759.0 31.1 ‐12.0 324.0 795.0 24.0 162.

5 18.2 47.0 223. 788.0 81.8 67.0 40.0 795.0 2.0 286.

6 43.1 14.0 366. 791.0 56.9 ‐2.0 327.0 794.0 ‐5.0 236.

7 59.6 ‐2.0 146. 782.0 40.4 39.0 263.0 793.0 54.0 337.

8 39.1 59.0 164. 763.0 60.9 30.0 103.0 795.0 ‐18.0 250.

9 20.7 ‐30.0 183. 735.0 79.3 31.0 40.0 789.0 ‐23.0 289.

10 77.0 ‐5.0 124. 734.0 23.0 90.0 316.0 791.0 117.0 93.

11 37.4 82.0 109. 791.0 62.6 98.0 239.0 793.0 85.0 359.

12 24.8 77.0 318. 746.0 75.2 ‐23.0 396.0 788.0 ‐17.0 211.

13 26.7 ‐5.0 173. 733.0 73.3 103.0 248.0 794.0 84.0 163.

14 31.2 51.0 120. 786.0 68.8 ‐16.0 141.0 795.0 59.0 121.

15 64.1 96.0 34. 779.0 35.9 69.0 305.0 792.0 87.0 272.

16 51.3 ‐32.0 7.0 735.0 48.7 ‐11.0 117.0 788.0 66.0 158.

17 68.7 80.0 324. 784.0 31.3 31.0 106.0 793.0 90.0 344.

18 41.0 88.0 194. 799.0 59.0 23.0 89.0 793.0 67.0 223.

19 41.9 16.0 326. 796.0 58.1 ‐23.0 295.0 790.0 ‐5.0 333.

20 35.2 48.0 176. 795.0 64.8 73.0 205.0 794.0 113.0 204.

21 10.1 67.0 255. 732.0 89.9 42.0 396.0 791.0 ‐15.0 216.

22 28.2 132.0 133. 800.0 71.8 27.0 126.0 789.0 6.0 391.

23 70.2 ‐9.0 240. 757.0 29.8 ‐24.0 151.0 796.0 83.0 292.

24 4.0 76.0 51. 755.0 96.0 23.0 99.0 789.0 24.0 344.

25 83.7 ‐7.0 279. 748.0 16.3 115.0 38.0 793.0 31.0 167.

26 63.7 34.0 368. 733.0 36.3 ‐36.0 109.0 789.0 104.0 219.

27 48.0 112.0 286. 760.0 52.0 99.0 166.0 788.0 ‐30.0 20.

28 80.2 44.0 158. 750.0 19.8 49.0 93.0 794.0 89.0 254.

29 51.8 80.0 91. 797.0 48.2 54.0 216.0 788.0 70.0 337.

30 19.3 ‐2.0 394. 791.0 80.7 ‐2.0 240.0 793.0 ‐31.0 376.

31 36.0 75.0 399. 732.0 64.0 88.0 380.0 796.0 ‐3.0 62.

32 72.1 123.0 200. 753.0 27.9 45.0 350.0 791.0 62.0 76.

33 60.9 73.0 183. 782.0 39.1 ‐28.0 252.0 796.0 42.0 54.

34 38.3 132.0 60. 743.0 61.7 ‐21.0 386.0 788.0 104.0 330.

35 69.9 ‐38.0 277. 788.0 30.1 ‐9.0 125.0 788.0 ‐13.0 173.

36 25.8 122.0 66. 756.0 74.2 ‐18.0 228.0 788.0 ‐23.0 113.

37 19.8 107.0 341. 766.0 80.2 64.0 194.0 788.0 56.0 319.

38 53.9 ‐18.0 111. 731.0 46.1 ‐26.0 40.0 788.0 35.0 185.

39 2.2 3.0 147. 757.0 97.8 7.0 206.0 789.0 112.0 245.

40 26.3 ‐30.0 138. 794.0 73.7 20.0 260.0 788.0 42.0 251.

41 73.6 84.0 351. 766.0 26.4 ‐21.0 130.0 791.0 78.0 393.

42 85.2 1.0 270. 775.0 14.8 99.0 335.0 795.0 43.0 61.

43 11.2 ‐19.0 74. 797.0 88.8 ‐36.0 125.0 790.0 43.0 49.

44 66.4 8.0 168. 743.0 33.6 44.0 107.0 788.0 104.0 236.

45 65.5 ‐22.0 153. 758.0 34.5 90.0 241.0 794.0 ‐27.0 116.


Case

INPT

Vol60

BOB

INPT Temp

Obs BOB

INPT psig

Obs

BOB

INPT Rho

60 BOB

INPT

Vol60

DEtOH

INPT

Temp Obs

DEtOH

INPT psig

Obs

DEtOH

INPT

Rho60

DEtOH

INPT Temp

Obs bge

INPT psig

Obs bge

46 66.9 111.0 227. 731.0 33.1 ‐33.0 365.0 790.0 27.0 248.

47 26.3 12.0 152. 779.0 73.7 4.0 129.0 794.0 6.0 386.

48 15.0 62.0 58. 743.0 85.0 67.0 126.0 793.0 90.0 48.

49 56.2 104.0 284. 752.0 43.8 76.0 176.0 793.0 ‐11.0 234.

50 98.1 51.0 89. 756.0 1.9 ‐27.0 3.0 795.0 1.0 220.


Table C.2 Calculated Inputs for Scenarios 1, 2, and 3

Case EXPT VolObs BOB EXPT RhoObs

BOB

EXPT VolObs

DEtOH

EXPT RhoObs

DEtOH EXPT Vol60 bge EXPT VolObs bge

EXPT RhoObs

bge

1 62.790812 716.378699 41.688942 767.469710 100.220981 101.584908 757.760195

2 14.793627 774.069831 82.024880 820.503487 100.017284 94.608383 832.410382

3 13.666806 757.309365 85.074516 805.517367 100.035385 101.386246 778.004938

4 71.424591 732.172203 29.771166 830.484782 100.224418 97.676599 788.516399

5 18.051603 794.477920 82.123979 791.863731 100.018024 96.488836 822.609158

6 42.006925 811.582855 54.772693 824.838028 100.090958 96.172100 824.258801

7 57.557480 809.750536 39.829144 804.365759 100.156716 99.558973 789.927797

8 39.031091 764.347064 59.785206 809.824086 100.129960 95.168292 822.215034

9 19.498246 780.300962 77.924563 802.926539 100.079007 94.953502 819.160942

10 73.690369 766.965897 23.369295 778.500180 100.272663 104.617657 714.133753

11 37.813716 782.345746 63.957492 776.168644 100.072047 101.376049 781.498201

12 25.024896 739.295783 71.524079 828.498605 100.087372 95.307518 815.868479

13 25.542794 766.208279 75.116688 774.797202 100.114089 101.590659 765.535933

14 31.026408 790.397646 65.778632 831.516230 100.059155 99.916687 792.852551

15 65.472399 762.670998 36.017681 789.412288 100.170965 101.774573 770.002741

16 48.305972 780.555658 46.697437 821.792430 100.244084 100.546917 756.672631

17 69.320248 776.985104 30.744408 807.330552 100.161052 101.855616 772.482689

18 41.552322 788.379536 57.689641 811.012154 100.068546 100.349121 792.692542

19 40.899298 815.476097 55.289043 830.164480 100.077162 96.128314 824.433474

20 34.945660 800.786136 65.216411 788.930254 100.057872 103.275261 769.160003

21 10.128351 729.950996 88.708746 801.622198 100.032009 95.525792 821.810513

22 29.270095 770.752538 70.352601 805.232484 100.029545 96.671721 819.373022

23 67.110073 791.854300 28.363845 836.304092 100.229114 101.663050 756.048535

24 4.041316 747.281423 93.862176 806.970426 100.005850 97.668311 806.443758

25 80.032542 782.276793 16.859289 766.693075 100.206969 98.058764 770.288113

26 62.422156 748.005245 34.331240 834.245999 100.286825 103.391984 728.613543

27 49.585007 735.706265 53.191305 770.351474 100.174221 94.528645 819.391838

28 79.270983 758.789633 19.657579 799.752609 100.222182 102.162596 742.651447

29 52.315545 789.145936 47.956096 792.007752 100.103185 100.494647 788.760422

30 18.659044 818.171613 77.720689 823.398513 100.017757 94.683385 837.120475

31 36.257430 726.802754 64.916338 784.763927 100.169811 96.114788 804.205070

32 75.142285 722.513294 27.586973 799.975397 100.237608 100.326138 761.119697

33 61.278418 777.170842 37.114600 838.581039 100.159003 98.990387 795.505528

34 40.264840 706.743160 58.751474 827.546902 100.163018 102.951963 748.664692

35 66.415555 829.341861 28.893372 820.907994 100.150918 95.813892 822.427708

36 26.896400 725.182549 70.830052 825.491422 100.079593 95.024741 820.569453

37 20.369043 744.600529 80.284692 787.168741 100.043685 99.575427 786.985328

38 51.148786 770.319356 43.855034 828.338204 100.264170 98.413272 769.486657

39 2.119677 785.685832 94.688113 814.930168 100.002618 103.078965 764.749625

40 25.118258 831.355417 71.864008 808.131933 100.032422 98.793341 799.221887

41 74.570252 756.033383 25.172152 829.583415 100.203306 101.196570 763.464608

42 82.155378 803.720971 15.118786 778.237069 100.143811 98.980052 785.976555

43 10.760147 829.579774 83.977165 835.369953 100.000000 98.953611 799.146176

44 64.103009 769.623781 33.256479 796.139607 100.264357 103.334135 733.658827

45 62.163056 798.689817 35.074167 781.002158 100.225586 94.532340 814.980356

46 69.223443 706.464425 31.315744 835.011310 100.295118 97.805728 767.367119

47 25.566757 801.341376 71.264896 821.130788 100.051945 96.603730 817.830736

48 15.013805 742.316812 85.284617 790.353552 100.045145 101.944313 770.518702

49 57.765875 731.615332 44.171113 786.337438 100.221981 95.475789 806.443188

50 97.463602 760.936377 1.806820 835.999290 100.034007 96.136550 787.152234


Table C.3 Calculated Outputs for Scenario 1 Examples

Case SC1 V60 BOB SC1 V60 DEtOH SC1 V60 bge SC1 Volume Pct

Ethanol SC1 Rho60 bge

SC1 V60 bge Error

%

1 59.50000031 40.50000000 100.22098065 0.40410700 768.07270792 ‐0.00000031

2 14.70000044 85.30000000 100.01728450 0.85285258 787.39390287 ‐0.00000044

3 13.80000023 86.20000000 100.03538523 0.86169509 788.51098350 ‐0.00000023

4 68.90000016 31.10000000 100.22441835 0.31030362 768.47140912 ‐0.00000016

5 18.20000000 81.80000000 100.01802396 0.81785259 793.58296491 0.00000000

6 43.10000014 56.90000000 100.09095770 0.56848292 791.98662718 ‐0.00000014

7 59.60000033 40.40000000 100.15671603 0.40336786 785.21344461 ‐0.00000033

8 39.09999977 60.90000000 100.12995967 0.60820957 781.47240107 0.00000023

9 20.70000016 79.30000000 100.07900738 0.79237396 777.20794833 ‐0.00000016

10 76.99999991 23.00000000 100.27266327 0.22937458 745.07844475 0.00000009

11 37.39999979 62.60000000 100.07204664 0.62554931 791.68161999 0.00000021

12 24.80000010 75.20000000 100.08737190 0.75134354 776.90520313 ‐0.00000010

13 26.70000033 73.30000000 100.11408872 0.73216468 776.82672814 ‐0.00000033

14 31.19999982 68.80000000 100.05915452 0.68759326 791.72365965 0.00000018

15 64.09999985 35.90000000 100.17096531 0.35838728 782.32948797 0.00000015

16 51.29999970 48.70000000 100.24408410 0.48581421 758.95850307 0.00000030

17 68.70000016 31.30000000 100.16105180 0.31249672 785.55185458 ‐0.00000016

18 41.00000044 59.00000000 100.06854558 0.58959586 794.91512081 ‐0.00000044

19 41.89999986 58.10000000 100.07716193 0.58055204 791.90295239 0.00000014

20 35.20000004 64.80000000 100.05787161 0.64762521 793.89256159 ‐0.00000004

21 10.09999987 89.90000000 100.03200937 0.89871233 784.78979380 0.00000013

22 28.20000000 71.80000000 100.02954513 0.71778793 791.86804154 0.00000000

23 70.19999980 29.80000000 100.22911388 0.29731880 766.86500588 0.00000021

24 4.00000049 96.00000000 100.00584970 0.95994384 787.59392796 ‐0.00000049

25 83.70000041 16.30000000 100.20696948 0.16266334 753.77491597 ‐0.00000041

26 63.70000009 36.30000000 100.28682489 0.36196180 751.17344757 ‐0.00000009

27 48.00000042 52.00000000 100.17422141 0.51909562 773.21289754 ‐0.00000042

28 80.20000016 19.80000000 100.22218225 0.19756105 757.03001365 ‐0.00000015

29 51.79999965 48.20000000 100.10318543 0.48150316 791.84493137 0.00000035

30 19.30000016 80.70000000 100.01775690 0.80685673 792.47328128 ‐0.00000016

31 35.99999998 64.00000000 100.16981067 0.63891505 771.64965654 0.00000002

32 72.09999976 27.90000000 100.23760759 0.27833865 761.79192463 0.00000024

33 60.89999964 39.10000000 100.15900313 0.39037929 786.22387947 0.00000036

34 38.30000035 61.70000000 100.16301848 0.61599581 769.51055546 ‐0.00000035

35 69.90000002 30.10000000 100.15091815 0.30054642 786.81255707 ‐0.00000002

36 25.79999988 74.20000000 100.07959252 0.74140989 779.12387568 0.00000012

37 19.80000026 80.20000000 100.04368470 0.80164980 783.30181692 ‐0.00000026

38 53.89999984 46.10000000 100.26417004 0.45978539 755.28177187 0.00000016

39 2.20000025 97.80000000 100.00261847 0.97797439 788.27535911 ‐0.00000025

40 26.29999980 73.70000000 100.03242208 0.73676113 789.32208532 0.00000020

41 73.59999986 26.40000000 100.20330600 0.26346436 771.03244481 0.00000014

42 85.20000027 14.80000000 100.14381126 0.14778746 776.84281253 ‐0.00000027

43 11.20000040 88.80000000 100.00000000 0.88800000 790.78400002 ‐0.00000040

44 66.40000026 33.60000000 100.26435685 0.33511410 756.12114193 ‐0.00000026

45 65.49999979 34.50000000 100.22558649 0.34422348 768.68594840 0.00000021

46 66.89999976 33.10000000 100.29511832 0.33002603 748.32056893 0.00000024

47 26.30000029 73.70000000 100.05194532 0.73661736 789.64481646 ‐0.00000029

48 14.99999982 85.00000000 100.04514514 0.84961644 785.14554502 0.00000018

49 56.19999976 43.80000000 100.22198131 0.43702988 768.25262282 0.00000024

50 98.10000031 1.90000000 100.03400679 0.01899354 756.48374413 ‐0.00000031



Case SC2 V60 DEtOH SC2 Volume Pct

DEtOH SC2 Rho60 bge SC2 V60 bge SC2 V60 BOB SC2 V BOB

1 40.50000000 0.40410701 768.07270833 100.22098065 59.50000005 62.79081173

2 85.30000000 0.85285259 787.39390290 100.01728450 14.70000000 14.79362655

3 86.20000000 0.86169499 788.51097897 100.03538519 13.79999934 13.66680512

4 31.10000000 0.31030362 768.47140915 100.22441835 68.90000000 71.42459084

5 81.80000000 0.81785259 793.58296489 100.01802396 18.20000000 18.05160300

6 56.90000000 0.56848292 791.98662718 100.09095770 43.10000000 42.00692486

7 40.40000000 0.40336784 785.21344441 100.15671603 59.59999997 57.55747966

8 60.90000000 0.60820958 781.47240111 100.12995967 39.10000001 39.03109124

9 79.30000000 0.79237439 777.20797308 100.07900674 20.70000269 19.49824839

10 23.00000000 0.22937459 745.07844515 100.27266328 77.00000006 73.69036915

11 62.60000000 0.62554931 791.68161998 100.07204664 37.40000000 37.81371621

12 75.20000000 0.75134364 776.90520764 100.08737178 24.80000047 25.02489638

13 73.30000000 0.73216478 776.82673448 100.11408877 26.70000089 25.54279454

14 68.80000000 0.68759326 791.72365964 100.05915452 31.20000000 31.02640818

15 35.90000000 0.35838728 782.32948797 100.17096531 64.10000000 65.47239915

16 48.70000000 0.48581427 758.95850675 100.24408410 51.30000052 48.30597277

17 31.30000000 0.31249670 785.55185443 100.16105180 68.69999998 69.32024782

18 59.00000000 0.58959585 794.91512081 100.06854558 41.00000000 41.55232156

19 58.10000000 0.58055206 791.90295232 100.07716193 41.89999999 40.89929813

20 64.80000000 0.64762519 793.89256157 100.05787161 35.20000000 34.94565996

21 89.90000000 0.89871351 784.78986665 100.03200776 10.10000824 10.12835939

22 71.80000000 0.71778793 791.86804152 100.02954513 28.20000000 29.27009500

23 29.80000000 0.29731881 766.86500601 100.22911388 70.20000002 67.11007322

24 96.00000000 0.95994396 787.59393199 100.00584964 4.00000045 4.04131596

25 16.30000000 0.16266333 753.77491569 100.20696948 83.69999996 80.03254157

26 36.30000000 0.36196185 751.17345017 100.28682492 63.70000038 62.42215629

27 52.00000000 0.51909563 773.21289789 100.17422140 48.00000003 49.58500659

28 19.80000000 0.19756106 757.03001370 100.22218225 80.20000001 79.27098285

29 48.20000000 0.48150314 791.84493148 100.10318543 51.80000001 52.31554537

30 80.70000000 0.80685673 792.47328128 100.01775690 19.30000000 18.65904384

31 64.00000000 0.63891532 771.64967446 100.16981038 36.00000215 36.25743219

32 27.90000000 0.27833865 761.79192467 100.23760759 72.10000001 75.14228526

33 39.10000000 0.39037928 786.22387936 100.15900313 60.89999999 61.27841835

34 61.70000000 0.61599590 769.51056006 100.16301855 38.30000068 40.26484034

35 30.10000000 0.30054642 786.81255707 100.15091815 69.90000000 66.41555498

36 74.20000000 0.74140992 779.12387646 100.07959249 25.80000008 26.89640020

37 80.20000000 0.80164981 783.30181712 100.04368470 19.80000002 20.36904275

38 46.10000000 0.45978544 755.28177489 100.26417002 53.90000040 51.14878653

39 97.80000000 0.97797404 788.27534754 100.00261819 2.19999816 2.11967499

40 73.70000000 0.73676114 789.32208527 100.03242208 26.29999999 25.11825818

41 26.40000000 0.26346436 771.03244482 100.20330600 73.60000000 74.57025214

42 14.80000000 0.14778746 776.84281252 100.14381126 85.20000000 82.15537774

43 88.80000000 0.88800000 790.78400000 100.00000000 11.20000000 10.76014662

44 33.60000000 0.33511412 756.12114274 100.26435686 66.40000011 64.10300886

45 34.50000000 0.34422348 768.68594834 100.22558649 65.50000000 62.16305620

46 33.10000000 0.33002604 748.32056950 100.29511832 66.90000008 69.22344333

47 73.70000000 0.73661736 789.64481645 100.05194532 26.29999999 25.56675671

48 85.00000000 0.84961620 785.14553224 100.04514501 14.99999815 15.01380333

49 43.80000000 0.43702988 768.25262284 100.22198131 56.20000001 57.76587525

50 1.90000000 0.01899354 756.48374413 100.03400679 98.10000000 97.46360169


Case SC3 V60 DEtOH

SC3 Pct DEtOH SC3 V60 BOB SC3 Rho60

BOB SC3 Rho60 bge SC3 V60 bge

SC3 Volume Flo wing BOB

1 40.50 0.40410702 59.49998957 756.00013253 768.07270673 100.22098081 62.79079975

2 85.30 0.85285029 14.70024373 778.98708423 787.39308494 100.01738840 14.79388589


3 86.20 0.86169508 13.80000316 749.99982807 788.51098416 100.03538516 13.66680885

4 31.10 0.31030362 68.89999977 759.00000255 768.47140920 100.22441834 71.42459058

5 81.80 0.81785256 18.20000120 787.99994822 793.58296430 100.01802404 18.05160417

6 56.90 0.56848291 43.10000071 790.99998697 791.98662680 100.09095775 42.00692552

7 40.40 0.40336788 59.59999971 782.00000379 785.21344471 100.15671602 57.55747949

8 60.90 0.60820958 39.09999949 763.00001004 781.47240134 100.12995963 39.03109072

9 79.30 0.79237403 20.69999527 735.00016784 777.20795191 100.07900692 19.49824179

10 23.00 0.22937458 76.99999868 734.00001262 745.07844413 100.27266335 73.69036791

11 62.60 0.62554931 37.40000293 790.99993804 791.68162044 100.07204658 37.81371923

12 75.20 0.75134356 24.79999813 746.00005616 776.90520439 100.08737174 25.02489400

13 73.30 0.73216468 26.70000176 732.99995168 776.82672863 100.11408868 25.54279526

14 68.80 0.68759323 31.19997917 786.00052483 791.72366080 100.05915438 31.02638840

15 35.90 0.35838727 64.10000350 778.99995741 782.32949154 100.17096485 65.47240338

16 48.70 0.48581420 51.30001425 734.99979583 758.95850324 100.24408406 48.30598454

17 31.30 0.31249670 68.70000547 783.99993760 785.55186068 100.16105102 69.32025386

18 59.00 0.58959582 41.00008449 798.99835341 794.91512309 100.06854529 41.55240938

19 58.10 0.58055203 41.90000019 795.99999644 791.90295229 100.07716194 40.89929831

20 64.80 0.64762523 35.19999511 795.00011052 793.89255949 100.05787187 34.94565518

21 89.90 0.89871233 10.09999966 732.00002489 784.78979396 100.03200934 10.12835079

22 71.80 0.71778791 28.20000075 799.99997877 791.86804120 100.02954518 29.27009584

23 29.80 0.29731881 70.19999003 757.00010748 766.86500461 100.22911404 67.11006431

24 96.00 0.95994385 3.99999996 755.00000716 787.59392814 100.00584970 4.04131547

25 16.30 0.16266334 83.69999947 748.00000474 753.77491612 100.20696946 80.03254113

26 36.30 0.36196179 63.70000596 732.99993145 751.17344951 100.28682463 62.42216155

27 52.00 0.51909563 47.99999965 760.00000560 773.21289784 100.17422138 49.58500618

28 19.80 0.19756107 80.19998644 750.00012682 757.03001130 100.22218257 79.27096970

29 48.20 0.48150316 51.79999535 797.00007152 791.84493122 100.10318545 52.31554057

30 80.70 0.80685665 19.30000556 790.99977204 792.47327716 100.01775742 18.65904886

31 64.00 0.63891506 35.99999970 732.00000609 771.64965669 100.16981065 36.25742972

32 27.90 0.27833865 72.09989755 753.00106995 761.79192440 100.23760761 75.14217204

33 39.10 0.39037930 60.89999833 782.00002142 786.22388060 100.15900298 61.27841658

34 61.70 0.61599580 38.30000418 742.99991891 769.51055688 100.16301831 40.26484437

35 30.10 0.30054643 69.89999756 788.00002754 786.81255848 100.15091797 66.41555289

36 74.20 0.74140990 25.79999957 756.00001271 779.12387594 100.07959249 26.89639964

37 80.20 0.80164981 19.80000137 765.99994704 783.30181685 100.04368471 20.36904419

38 46.10 0.45978535 53.89999948 731.00000699 755.28177195 100.26417003 51.14878570

39 97.80 0.97797437 2.20000418 756.99856225 788.27536099 100.00261825 2.11968056

40 73.70 0.73676114 26.30000101 793.99996965 789.32208515 100.03242211 25.11825906

41 26.40 0.26346436 73.59999629 766.00003866 771.03244455 100.20330603 74.57024832

42 14.80 0.14778747 85.19999737 775.00002395 776.84281424 100.14381104 82.15537591

43 88.80 0.88799999 11.20000065 796.99995411 790.78399991 100.00000001 10.76014719

44 33.60 0.33511409 66.40000534 742.99994022 756.12114364 100.26435663 64.10301363

45 34.50 0.34422350 65.49999530 758.00005441 768.68595135 100.22558610 62.16305208

46 33.10 0.33002604 66.89999961 731.00000421 748.32056900 100.29511831 69.22344283

47 73.70 0.73661742 26.29999297 779.00020823 789.64483089 100.05194349 25.56675143

48 85.00 0.84961641 15.00000693 742.99965651 785.14554684 100.04514490 15.01381213

49 43.80 0.43702988 56.19999909 752.00001215 768.25262328 100.22198124 57.76587427

50 1.90 0.01899354 98.09999914 756.00000664 756.48374451 100.03400674 97.46360084


Table C.6 Scenario 4 Examples for a Constant 1000 m3 Bge Observed Volume Information from Blender Locally Observed Calculated Unknown Inputs and Error for Comparison

Case Nominal Ethanol

Content %

Density Blend

Ethanol %

Density bge kg/m3

Temp Obs °F

Press Obs psig

Base Volume m3

True Ethanol Content

%

True BOB

Density kg/m3

True Base Volume m3

Error from True

Calculated Value

1 10 796 744 45 12 1010.960869 10.1 738 1010.964352 0.00 2 20 794 778 -12 2 1047.587172 17.7 774 1047.372805 0.02 3 20 792 748 21 10 1028.335552 15.7 740 1028.264278 0.01 4 30 792 750 74 25 989.997164 29.3 733 989.992078 0.00 5 30 795 778 68 6 994.574820 33.8 770 994.554218 0.00 6 10 792 765 84 0 983.139568 10.5 762 983.113017 0.00 7 85 792 778 108 25 969.282734 56.0 760 967.784147 0.15 8 85 793 773 42 17 1011.753433 63.0 739 1012.124352 -0.04 9 10 793 774 58 4 1001.377796 9.8 772 1001.376520 0.00

10 15 789 755 78 19 987.151818 13.8 749 987.173095 0.00 11 15 788 745 10 3 1036.204319 14.2 738 1036.167683 0.00 12 10 793 788 56 1 1002.374652 9.5 788 1002.368102 0.00 13 15 791 738 102 8 968.600342 10.6 732 968.870910 -0.03 14 15 796 747 11 18 1035.530783 10.9 741 1035.244908 0.03 15 10 793 773 82 11 984.997917 9.8 771 985.011989 0.00 16 10 791 782 51 20 1005.736653 9.8 781 1005.731095 0.00 17 15 791 782 66 9 996.236421 13.3 781 996.255838 0.00 18 20 789 762 88 2 979.961384 20.5 755 979.960595 0.00 19 20 790 751 60 7 1000.051262 16.3 743 1000.051034 0.00 20 10 795 761 75 7 989.448958 9.8 757 989.456064 0.00 21 5 788 748 66 16 995.889471 5.4 746 995.878412 0.00 22 10 793 769 -14 8 1050.533845 9.9 766 1050.517329 0.00 23 15 793 796 64 5 997.652356 15.0 796 997.652356 0.00 24 10 795 736 105 12 966.565357 10.0 730 966.565357 0.00 25 10 789 759 13 9 1032.901928 10.3 755 1032.932129 0.00 26 10 796 737 86 16 980.860569 9.7 731 980.879555 0.00 27 10 795 783 90 10 981.339270 9.9 782 981.349309 0.00 28 10 796 763 83 22 983.938058 10.4 759 983.917141 0.00 29 10 794 746 -4 13 1045.732671 10.5 740 1045.801744 -0.01 30 10 788 761 93 9 976.692725 9.6 758 976.723530 0.00 31 20 791 784 42 7 1011.358704 20.2 782 1011.362379 0.00 32 85 795 777 -2 11 1039.508407 67.0 739 1040.567414 -0.10 33 10 792 762 -15 12 1051.857468 9.8 759 1051.823948 0.00 34 10 789 756 0 22 1042.153371 10.3 752 1042.191682 0.00 35 85 788 791 8 22 1031.227513 62.0 797 1031.588277 -0.03 36 85 788 770 -18 19 1049.681130 61.0 742 1051.573380 -0.18 37 5 788 743 11 2 1034.456620 5.2 741 1034.501394 0.00 38 15 793 768 60 20 1000.135659 13.7 764 1000.135452 0.00 39 30 793 746 4 12 1040.538603 28.3 728 1040.579724 0.00 40 10 793 764 72 19 991.708561 10.5 761 991.695340 0.00 41 10 792 778 23 5 1023.902636 10.2 776 1023.924911 0.00 42 10 788 747 40 22 1014.531775 9.8 743 1014.522739 0.00 43 5 796 732 1 24 1042.442382 4.8 729 1042.385821 0.01 44 10 792 752 85 19 982.155382 9.8 748 982.167082 0.00 45 10 794 764 -4 13 1044.251802 9.6 761 1044.192645 0.01 46 10 796 750 72 9 991.415056 9.8 745 991.420775 0.00 47 10 792 769 12 20 1033.073131 10.2 766 1033.094251 0.00 48 10 795 784 59 9 1000.671627 10.3 783 1000.672622 0.00 49 10 796 739 52 5 1005.902476 10.3 733 1005.907996 0.00 50 15 790 772 68 17 994.526432 12.2 769 994.565296 0.00


Annex D. Convergence Acceleration – Informative

D.1 Convergence Acceleration

This standard does not specify a specific convergence accelerator procedure, nor does it prohibit the use of one in calculating the scenarios in section11.3.4.0. For the purposes of illustration, one accelerator approach is described briefly. Additional information on this approach and alternative approaches is available to the user on the internet.

D.2 Newton-Raphson Method using the Secant Approximation

The Newton-Raphson method of convergence acceleration is one of the more common approaches to optimization. It uses a tangent line to the function under study to identify a root solution. Unfortunately, it requires a first derivative of the function to project the slope of the tangent. For complex functions or rapidly converging functions, the work to determine the derivative may not be justified. Numerical approaches based on differences can approximate the derivative, but require solving the function at the original point and then at two points slightly offset on either side of the original point.

The Secant Method (NRS) approximates Newton-Raphson in that it uses the same underlying concepts, but it uses only two points, the current iteration value and the previous iteration value, both of which have already been calculated. The method supplies a suggested input for the third and subsequent iterations.

The formula for the NRS Method is:

In the context of the Scenario 3 example in section 11.3.4.0, the variables are:

Inputn = ρ60,bge,CTPL,i from Step 3 Inputn-1 = ρ60,bge,CTPL,i-1 from Step 3 f(Inputn) = Convergencei f(inputn-1) = Convergencei-1

Table D-1 Convergence for Cases With and Without Acceleration

w/o NRS w/NRS

Number of Cases 499 498

Non-Converged 2 3

Number of Trials in Converged Cases 1932 1908

Trials/Case 3.87 3.83


The results calculating the Scenario 3 example using the direct substitution described in this standard and using the secant method are shown in the accompanying table D-1. For this scenario calculation, the secant method offers no advantage in either speed of convergence or in ultimate convergence acceptability.

More information on the secant method can be found at https://en.wikipedia.org/wiki/Secant_method or in mathematics texts.


Annex E. Measurement Field Descriptions for API MPMS 11.3.4 - Informative

E.1 Purpose

The purpose of this Annex is to describe and illustrate the typical bge blending field measurement procedures and how they relate to the scenarios discussed in this standard. This Annex explains the application of the standard’s calculations to potential blending scenarios, under no circumstances shall it be understood to form requirements for measurement operations.

E.2 Background

There are several common terminal blending arrangements that are addressed by the standard. The design of the 11.3.4 calculations provide that regardless of the inputs provided, the user is able to generate a run ticket that contains the following information as illustrated in Table E.1:

Table E.1

Product Gross

Volume

(V unit)

Temperature

(T unit)

Density

(D unit) Net Volume (V unit)

bge Choice Choice Required Required Output BOB Choice Choice Required Required Output

Fuel Ethanol Required

Input Required

Input Required

Input Required Output

The choices for gross volume and temperature depend upon the metering scenario. For a given product both the gross volume and the temperature have to be selected together and both will be inputs to the volume correction algorithm. For a given application, data for the bge, the BOB, or both will have to be provided. If the gross volume and the temperature for a product are provided as input, the density must also be provided as input. If the gross volume is not input, the density of the product should be available for reporting as a calculated output. Input values may use any unit of measure required by users, but must be converted to the units used by this standard prior to entering the calculation sequence. Likewise, output values may be converted to any desired unit of measure after the calculations are converged and complete.

API MPMS Chapter 6.2A describes the following types of field blending.

E.3 Blending Operations

E.3.1 Splash blending: Splash blending is accomplished by manually loading individual components in the proper proportions according to the finished product recipe. Components are normally added one at a time through discrete product meters and loading arms.

Volumetric corrections are covered under Scenario 1, Calculation of bge V60 and Density from Blending Volumes and Densities. The user may choose either to measure the bge density and correct it to base conditions or to calculate a blended density from the component densities using Scenario 1.

E.3.2 Automatic sequential: Sequential blending is accomplished by loading individual components in the proper proportion according to the finished product recipe. This is accomplished by opening product line block valves one at a time through one meter/load arm position in a set sequence to complete the finished product.

Volumetric corrections are covered under Scenario 1, as in Splash Blending.


E.3.3 On rack ratio blending: On rack ratio blending is accomplished by simultaneously combining two or more products through dedicated unique meters in respective amounts and flow rates according to the finished product recipe. This is accomplished at the individual loading position while delivering into a truck or railcar. This process is typically automated.

Volumetric corrections are covered under Scenario 1.

E.3.4 Side stream blending: On rack side stream blending is accomplished by simultaneously combining a minor product flow through a dedicated flow meter and control valve upstream of the major products meter and control valve. The minor product flow is controlled based on the blended stream. This process is typically automated.


Volumetric corrections are covered under the Scenario 2, bge and Denatured Ethanol Measured, BOB Volume Unmeasured, assuming the BOB density is available from laboratory analyses. In this calculation method, the measured bge volume and density are used to back-calculate the BOB volume. If the BOB density is not available, Scenario 3 Calculation of BOB Volume and BOB & bge Densities, Ethanol and bge Volumes Measured is used. Scenario 3 back-calculates both the BOB volume and density at the expense of increased computational complexity and uncertainty.

E.3.5 Hybrid ratio: The blending is accomplished by simultaneously combining a ratio product with a sequential product stream through unique meters and control valves in respective amounts and flow rates according to the finished product recipe. This is accomplished at the individual loading position while delivering into a truck or railcar. This process is typically automated.

Volumetric corrections are covered under the Scenario 1, since the normal practice is that the ratio product is the hydrocarbon blend component of bge.

E.3.6 Hybrid side stream: The blending is accomplished by simultaneously combining a ratio/minor product through a dedicated meter and control valve with a sequentially blended product upstream of the final blend meter and control valve. The two respective streams are proportionally blended according to the finished product recipe. This is accomplished at the individual loading position while delivering into a truck or railcar. This process is typically automated.


Volumetric corrections are covered similar to Side Stream Blending under Scenario 2 or Scenario 3 depending on whether the BOB density is available.

E.3.7 Proportional blending: In this blending method, the flow of each component is controlled by the preset to ensure the final desired blend ratio is maintained throughout the entire loading process. The advantage is that the product being loaded is on specification throughout the entire course of the load.


E.3.8 Non-proportional blending: In this blending method, the flow of each component is controlled by the preset, similar to the proportional method; however, some components may be loaded at a fixed flow rate or sequentially rather than being loaded proportionally throughout the course of the load. The disadvantage is that the product being loaded may not meet final specification until the completion of the load.


E.4 Non-Blending Scenarios Covered

Calculation of the Base bge Volume without Blending Information

In receipt verification and storage tracking situations, a user may wish to calculate the volume of bge at base conditions without access to the blend component properties. It is assumed for this standard that the user only has access to the density of the bge and the blended denatured ethanol density and nominal content from the delivery papers as well as the properties that are known from on-site measurements, volume and temperature.

Volume correction calculations are performed using Scenario 4 Calculation of Bge Volume at Base Conditions with Minimal Information. The uncertainty of this scenario calculation is higher than other methods, so it is not recommended as an alternative to the other scenarios for custody transfer. This calculation method does not reliably converge for E85 blends unless the actual blend concentration is used instead of the nominal ethanol concentration.

API MPMS Chapter 11.3.4 Miscellaneous Hydrocarbon ...ballots.api.org/copm/comq/ballots/docs/Ch11p3p4...

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