Chapter 1
Standard Formulas and Calculations

1.01 Abrasion Index

The abrasion index (sometimes referred to as the wear index) is a measure of equipment (such as drill bit) wear and deterioration. At first approximation, the wear is proportional to the rate of fuel flow in the third power and the maximum intensity of wear in millimeters) can be expressed:

dpl - maximum intensity of plate wear, mm.

a - abrasion index, mm s3/g h.

? - coefficient, determining the number of probable attacks on the plate surface.

k - concentration of fuel in flow, g/m3.

m - coefficient of wear resistance of metal;

w - velocity of fuel flow, meters/sec.

t - operation time, hours.

The resistance of materials and structures to abrasion can be measured by a variety of test methods (Table 1.1) which often use a specified abrasive or other controlled means of abrasion. Under the conditions of the test, the results can be reported or can be compared items subjected to similar tests. Theses standardized measurements can be employed to produce two sets of data: (1) the abrasion rate, which is the amount of mass lost per 1000 cycles of abrasion, and (2) the normalized abrasion rate, which is also called the abrasion resistance index and which is the ratio of the abrasion rate (i.e., mass lost per 1000 cycles of abrasion) with the known abrasion rate for some specific reference material.

Table 1.1 Examples of Selected ASTM Standard Test Method for Determining Abrasion*.

ASTM B611 Test Method for Abrasive Wear Resistance of Cemented Carbides ASTM C131 Standard Test Method for Resistance to Degradation of Small-Size Coarse Aggregate by Abrasion and Impact in the Los Angeles Machine ASTM C535 Standard Test Method for Resistance to Degradation of Large-Size Coarse Aggregate by Abrasion and Impact in the Los Angeles Machine ASTM C944 Standard Test Method for Abrasion Resistance of Concrete or Mortar Surfaces by the Rotating-Cutter Method ASTM C1353 Standard Test Method for Abrasion Resistance of Dimension Stone Subjected to Foot Traffic Using a Rotary Platform, Double-Head Abraser ASTM D 2228 Standard Test Method for Rubber Property - Relative Abrasion Resistance by the Pico Abrader Method ASTM D4158 Standard Guide for Abrasion Resistance of Textile Fabrics, see Martindale method ASTM D7428 Standard Test Method for Resistance of Fine Aggregate to Degradation by Abrasion in the Micro-Deval Apparatus ASTM G81 Standard Test Method for Jaw Crusher Gouging Abrasion Test ASTM G105 Standard Test Method for Conducting Wet Sand/Rubber Wheel Abrasion Tests ASTM G132 Standard Test Method for Pin Abrasion Testing ASTM G171 Standard Test Method for Scratch Hardness of Materials Using a Diamond Stylus ASTM G174 Standard Test Method for Measuring Abrasion Resistance of Materials by Abrasive Loop Contact

*ASTM International, West Conshohocken, Pennsylvania; test methods are also available from other standards organizations.

1.02 Acid Number

The acid number (acid value, neutralization number, acidity) is the mass of potassium hydroxide (KOH) in milligrams that is required to neutralize one gram of the substance (ASTM D664, ASTM D974).

Veq is the amount of titrant (ml) consumed by the crude oil sample and 1 ml spiking solution at the equivalent point, beq is the amount of titrant (ml) consumed by 1 ml spiking solution at the equivalent point, and 56.1 is the molecular weight of potassium hydroxide.

1.03 Acidity and Alkalinity

pH is given as the negative logarithm of [H+] or [OH-] and is a measurement of the acidity of a solution and can be compared by using the following:

[H+] or [OH-] are hydrogen and hydroxide ion concentrations, respectively, in moles/litter. Also, at room temperature, pH + pOH = 14. For other temperatures:

Kw is the ion product constant at that particular temperature. At room temperature, the ion product constant for water is 1.0 × 10-14 moles/litter (mol/L or M). A solution in which [H+=] > [OH-] is acidic, and a solution in which [H+=] < [OH-] is basic (Table 1.2).

Table 1.2 Ranges of Acidity and Alkalinity.

pH [H+] Property 7 >1.0 × 10-7 M Acid 7 1.0 × 10-7 M Neutral >7 <1.0 × 10-7 M Basic

1.04 Annular Velocity

Three main factors affecting annular velocity are size of hole (bigger ID), size of drill pipe (smaller OD) and pump rate. Thus:

For example, with a flow rate of 10 bbl/min and an annular capacity of 0.13 bbl/ft, the annular velocity is:

Other formulas include:

where Q is the flow rate in gpm, Dh is inside diameter of casing or hole size in inches, and Dp is outside diameter of pipe, tubing or collars in inch. Thus, for a flow rate of 800 gpm, a hole size of 10 inches, a drill pipe OD of 5 inches, the annular velocity is

Another formula used is:

Thus, for a flow rate equal to 13 bbl/min, a hole size of 10 inches, and a drill pipe OD of 5 inches, the annular velocity is:

1.05 Antoine Equation

The Antoine equation is a correlation used for describing the relation between vapor pressure and temperature for pure components. The Antoine constants A, B, and C (Table 1.3) are component specific constants for the Antoine equation:

Table 1.3 Example of the Antoine Constants.

  A B C Tmin, °C Tmax, °C Water 8.07131 1730.63 233.426 1 100 Water 8.14019 1810.94 244.485 99 374 Ethanol 8.20417 1642.89 230.3 -57 80 Ethanol 7.68117 1332.04 199.2 77 243

P is the vapor pressure, mm Hg, and T is the temperature, °C.

1.06 API Gravity - Kilograms per Liter/Pounds per Gallon

The American Petroleum Institute gravity (API gravity) is a measure of how heavy or light a petroleum liquid is compared to water: if the API gravity is greater than 10, it is lighter than water and floats on water. On the other hand, if the API gravity is less than 10, it is heavier than water and sinks. The formula to calculate API gravity from the specific gravity is:

Conversely, the specific gravity of petroleum liquids can be derived from their API gravity value by the equation:

Using the API gravity, it is possible to calculate the approximate number of of crude oil per metric ton. Thus:

The relationship between the API gravity of crude oil and kilograms per liter or pounds per gallon is presented in the table (Table 1.4) below.

Table 1.4 API Gravity Conversion to Kilograms per Liter/Pounds per Gallon

API gravity Specific gravity Kilograms per liter Pounds per...