8.2 Coordinates Systems

Quartz School for Well Site Supervisors 8.2. Well Planning & Azimuth Corrections Module – 8 Directional Drilling Section – 2 Coordinate Systems & Azimuth Corrections

C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections

Contents












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Introduction The Well Plan / Maps of Well Trajectory Geographic Coordinates Projection Maps Coordinate Systems UTM Coordinates Lambert Coordinates Legal Coordinates Local Coordinates Magnetic Declination Grid Convergence

8.2. Coordinates Systems & Azimuth Corrections Introduction Well Planning is the first step in the construction of any directional well from a surface location to a given down hole target. Well planner must work coordinated with the Drilling Engineer, Geologist and the Directional Driller assigned to the project. The operator generally provides surface coordinates and one or more down hole targets for well path control. Besides that, all relevant information from offset wells and possible limitations or restrictions that may affect the well trajectory design or execution C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps To design a well plan it is necessary to know the exact position of both the origin and the target on the earth surface and in the subsurface, respectively, as well as the desired well path, among other geological & boundaries information. Surface and subsurface locations of well must be represented on a MAP and located by means of their distances to the reference axis of a grid system superimposed over the Earth map, by using a given System of Coordinates. One map is a flat projection of the Earth’s surface which in turn is an oblate spheroid (a squashed sphere..!) C. Alvarez

8.2. Well Planning & Azimuth Corrections Maps of Well Trajectory

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8.2. Well Planning & Azimuth Corrections Maps of Well Trajectory

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8.2. Coordinates Systems & Azimuth Corrections Systems of Coordinates The System of Coordinates is a mathematical development that allows the location of a given point in the Earth on the flat map. It is obvious that any projection on a plane of the Earth’s spheroid surface will result in distortion. The grade of distortion depend on the selected projection map and the relative position of a given area in the projection. The solution to this problem is found in a special branch of Cartography called “Geodetics”

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In the next slides the problem of making Maps and the systems of Coordinates developed for locating points of Earth on them is analyzed

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems

Coordinates for point A are: Latitude 6° 40' 30” N & Longitude 17° 58' 45” E C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Several Coordinates systems have been proposed to locate a given position of the Earth’s surface on a grid map given the distances of its projection on the map to the Reference Lines selected, called Latitude and Longitude. The more known Coordinate Systems are: 1. 2. 3. 4. 5. C. Alvarez

Geographical Coordinates (N-S & E-W axis) Universal Transverse Mercator, UTM (Transverse Cylindrical Projector) Lambert Conical Projection Legal Coordinates Local Coordinates

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Geographical Coordinates System based on imaginary lines of Latitude and Longitude drawn on the Earth’s surface intersecting among them at square angles to form a grid pattern that allows the location of any position on Earth by given its distances to the “reference lines” also known as the pair (Latitude, Longitude), or “Geographical Coordinates” Latitude lines are circles around the Earth globe running parallel to the Equator, simply known as “Parallel” lines. They are equally distanced every grade from the Equator to the North and South poles Longitude lines are also circles around the Earth globe passing through both North and South poles and running perpendicular to the parallels. They are better known as “Meridian” lines. C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Geographical Coordinates

• • • •

Parallels: imaginary lines around the globe 180 Parallel lines drawn every 1° starting at Equator 90 Parallels to the North and 90 Parallels lines to the South Equator is the Reference Line with Latitude = 0°

• Meridians: imaginary lines around the globe • 360 Meridians passing through both poles • Meridians are drawn every 1° to cover the sphere • The Reference Meridian passes by Greenwich • Longitude at Greenwich Meridian = 0°

Every Parallel & Meridian line represents 1 grade. Every grade is further divided into 60 minutes and every minute in 60 seconds C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Geographical Coordinates

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Geographical Coordinates - Limitations Geographical Coordinates are not accurate enough in reason that the real distances from one latitude or longitude grade to another depend on the position of the points under consideration on the Earth’s surface. Besides that, the Earth itself is not a perfect sphere but an oblate spheroid. This means that relative distances in a given well or between wells cannot be exactly known by using the geographical coordinate system For that reason, other systems have been developed to increase the required grade of accuracy in directional drilling measurements. They are based on Projection Maps that will be discussed in the following slides: C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems A mathematical formula that convert the latitudelongitude position on the surface of a sphere into another method of positioning which can be plotted onto a flat map with some degree of controlled error and known accuracy. The projected map can be referred to a grid system superimposed that allows location of real points on the projected image, as can be seen in the next slides The most common grid map positioning method is the “X”, “Y” Cartesian Coordinates C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Imagine a light inside the transparent Earth Globe projecting the image of Earth surface on a flat screen. The resulting image depends the type of surface used for projecting the Earth spherical surface. In this case, the image was projected on a flat plane directly above the North pole which is located in the center of the projection. C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems

1. Cylindrical Projection 2. Conical Projection 3. Planar Projection

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Mercator Projections A. Standard Mercator Map Earth surface is projected on a tangent vertical cylinder producing an image that is distorted toward both poles and close to the real shape near the Equator.  Grid system is composed of Meridian and Parallel lines drawn on the Earth surface as explained above. On the projection the Meridians are equidistant between them but not the parallels which seem closer toward the poles.  The scale is more exact for those areas close to the Reference Lines (Equator and Greenwich) C. Alvarez 

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Mercator Projections B. Transverse Mercator Map, UTM Earth surface is projected on a tangent horizontal cylinder producing an image that is more accurate near the poles and distorted as approaches to the Equator.  Grid system is composed of Meridian and Parallel lines drawn on the Earth surface as explained above. On the projection Meridians and parallels are not equidistant.  The scale is more exact along the areas closer to the tangent meridian and to the Equator 

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Mercator Projections

1. Central Line (for Latitude Reference): Ecuador 2. Central Line for Longitude Reference: Greenwich C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Mercator Projections Properties:

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Standard Mercator causes distortion towards the poles

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Transverse Mercator minimizes distortion towards the poles

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UTM is preferred in ~ 60 countries

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Used in countries/areas that run primarily North - South

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Conical Projections C. Lambert Projection.  Earth surface is projected on a tangent or secant cone with its axis aligned with the N-S axis of Earth.  Less distortion is found when moving from Equator toward both poles.  Parallels are equidistant while the meridian lines converge to the pole

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Conical Projections C. Lambert Projection.

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Conical Projections C. Lambert Projection. Projection of the earth on to a cone. The cone axis coincides with the geographic poles axis of the earth. Introduced by Johann Heinrich Lambert 1772

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Conical Projections C. Lambert Projection.

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Projects globe onto a cone

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Used in countries / areas that run primarily from East → West

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Uses feet instead of meters

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Lambert Zone Number must be specified for proper location of a given point on Earth surface

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Conical Projections C. Lambert Projection.

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Lambert cone penetrates the earth along standard parallels

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Scale exact along standard parallel

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Scale constant E → W

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Scale changes N → S

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Conical Projections C. Lambert Projection for USA mapping

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Has been used to map all mainland USA states

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Standard parallels at 33°N and 45°N

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Scale error of 0.5% and 1% between 30.5°N and 47.5°N

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Maximum error of 2.5% in Florida

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Conical Projections

D. Planar Projection  Also known as Azimuthal Projection  Earth surface is projected onto a tangent plan passing by the North pole  Is accurate for areas at or near the center (North Pole)  Distortion increases when moving to the edges of map  Commonly used to map North and South poles areas C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Conical Projections D. Planar Projection = Azimuthal Projection

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Ellipsoid and Datum Geodetic The three projections discussed still present difficulties for the accurate location of a given point on the Earth surface in reason not only to the distortion resulting from the projection itself, but also in reason of the irregular shape of the Earth. To solve this new problem, several models of Ellipsoids have been proposed to represent the shape of Earth. There is not a unique ellipsoid used for map projections but there is a number of them applied to different regions of the Earth. Ellipsoids adjusted to Earth surface are part of a mathematical development called Geodetic Datum C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Ellipsoid and Datum Geodetic

The Ellipsoid of Reference should have a surface close to sea level that mathematically fits well to the real surface of Earth in a given region. C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Ellipsoid and Datum Geodetic The Earth is not an exact ellipsoid For map projections, a constant ellipsoidal shape and size is used for different region Different reference ellipsoids are used for different regions of the Earth Over 50 ellipsoids in use today Approximately 15 ellipsoids cover 98% of the “oil country” areas of interest

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Ellipsoid and Datum Geodetic A geodetic datum is a mathematical surface that closely fits the mean sea level surface throughout the area of interest. It consists of : • An Ellipsoid of Reference • Orientation of the ellipsoid • Length unit • Region of the earth • Official Name

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Examples of Datum Geodetic The table below show some of the most commonly used Geodeic Datum for mapping and reference of well trajectories in Directional Drilling operations, covering almost all oil & gas regions:

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Projection Models and Grid Systems

The two projection models and its associated Grid Systems more commonly used are: 1. UTM Grid System • • •

Divides world into 60 equal longitudinal zones Each zone is 6 deg wide Distortion increases north & south of the equator

2. Lambert Conformal Conic Projection • •

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Parallels of latitude that are unequally spaced arcs of concentric circles Distortion increases toward the edges

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Universal Transverse Mercator System = UTM Coordinates System Widely used in Oil & Gas Industry, this Coordinates System is derived from the transversal projection of the Earth globe onto the surface of a horizontal cylinder tangent to the Earth in a given meridian. As a result, the axis of the cylinder is parallel to the Earth’s Equator. The projection has good accuracy along the central meridian tangent to the cylinder For that reason Coordinates UTM developed from the projection described are widely used for maps in areas having more North – South extension and less East – West extension.

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Universal Transverse Mercator System = UTM Coordinates System Characteristics: The world is divided into 60 UTM Zones Length is defined in meters UTM Grid Reference must include: − Zone Number − Hemisphere (N or S) Scale factor − Function of position in zone −Central Meridian has 0.9996 Scale Factor − Lines of true scale (1:1) lie ~180 km either side of central meridian C. Alvarez

Scale Factor (F) =

Grid Distance True Distance

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Universal Transverse Mercator System = UTM Coordinates System UTM Zones

• Earth Projection onto a horizontal Cylinder C. Alvarez

• World is divide in 60 zones of projection • Then each zone is 6° wide • Due to the high distortion toward the poles, zones go from 84° N to 80° S

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Universal Transverse Mercator System = UTM Coordinates System UTM Zones

Projection zones of UTM system are numbered from 1 to 60, starting at the left side of the map (Long 180° West). Greenwich Meridian (Central Meridian) is then located in the zone number 31.

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Universal Transverse Mercator System = UTM Coordinates System UTM Zones

 Each zone has its own central meridian which in turn the N-S Reference Line for the zone.  There is a transverse projection for each zone with the tangent cylinder in contact with the central meridian of the specific zone.  As a result, each zone is 6° wide and the whole globe has 60 zones to cover the 360° of the sphere  Projection of polar areas result with high distortion and are consequently discarded from the UTM model C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Universal Transverse Mercator System = UTM Coordinates System

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Universal Transverse Mercator System = UTM Coordinates System UTM Zones

UTM Zone

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Universal Transverse Mercator System = UTM Coordinates System UTM Zones  The origin of Coordinates for each UTM zone is the intersection between the central meridian of the zone and the Equator of Earth  On each zone the distortion increases when going away of the origin in any direction  The UTM Coordinates are given by:  The number of UTM zone  Coordinate East or West, commonly called “Easting”  Coordinate North or South, commonly called “Northing”

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Universal Transverse Mercator System = UTM Coordinates System

3°

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3°

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Equator runs East → West

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Central Meridian runs North → South

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Rectangular Grid system superimposed on zone for mapping purposes

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Allows UTM coordinates of points to be defined as “Northing” and “Easting”

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Grid Sectors are divided into squares of 100 x 100 kilometers and then further divided into squares of 10 x 10 kilometers

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Universal Transverse Mercator System = UTM Coordinates System To avoid negative Eastings the Central Meridian is assigned a false Easting of 500,000m At the Equator the zone is ~600,000m wide Range of Eastings are: ~200,000m → ~800,000m Range of Eastings is maximum at Equator and narrows towards the poles

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Universal Transverse Mercator System = UTM Coordinates System •Northing Points North of Equator − Range from zero at the equator increasing to the north •Northing Points South of Equator − Just for SH:Range from 10,000,000m at the equator decreasing to the south −Just for NH:Range from Zero at the equator increasing to the North − avoids negative numbers similar to Eastings •UTM zone is cropped at 84°N and 80°S C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Universal Transverse Mercator System = UTM Coordinates System Example of Coordinates UTM for a given zone (Easting)  Location A is on Zone 13. It is 704,250 meters to the East of the reference line. It is also valid to say that point A is to the East of central meridian of the zone Then, the E-W Coordinate for point “A” or “Easting” is “704,250 m, East”  Location B is also on Zone 13. It is 400,000 meters to the East of reference line, which means that is to the left side of the central meridian which “Easting” is 500,000 as known. Then, the E-W coordinate or “Easting” for location B is “400,000 m, E” C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Universal Transverse Mercator System = UTM Coordinates System Example of Coordinates UTM for a given zone (Northing) Location A is inside zone 13. The UTM North – South Coordinate for point A is 6,391,520 meters The point is located above the Equator Location B is also in zone 13 The UTM North – South Coordinate for B is: 5,005,000 meters N Point B is located above the Equator C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Universal Transverse Mercator System = UTM Coordinates System Example of Coordinates UTM for a given zone (Northing)  To avoid negative values for North Coordinate of a point located in the South hemisphere, the value of 10,000,000 meters is assigned as UTM Coordinate to the Equator  The UTM South Coordinate for a point in the South Hemisphere is calculated by subtracting its distance in meters to the Equator from 10,000,000  The UTM Coordinate for the point C located to the South, is 10,000,000 – 5,000,100 = 4,999,900 meters to the South C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Lambert Coordinates System

 Is derived from the Conical Projection of Earth onto a plane surface. The systems works well in those areas with little distortion.  Latitude lines are arcs of concentric circles not evenly spaced.  Longitude lines are represented by straight lines converging in the central point of map separated by equidistant radii intersecting the latitude lines C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Lambert Coordinates System  The scale works well inside two standard lines of latitude. The pole in the same hemisphere of the Standard Parallel is one point; the other pole represents the infinitum  Lambert Coordinates are used in countries or regions where distances East – West are predominant In the USA the system has been used with a maximum error of 5%.

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems LEGAL Coordinates System  Legal Coordinates of a Directional Plan are based on a “Legal” Coordinate system defined by a national or regional authority with the objective that all local or regional coordinates have a unique National Geodetic Datum  The system divides the region or country in zones and can assign different coordinates systems to the different zones, depending on their N-S or E-W extension  In the USA some zones with predominant N-S extension use the UTM system while other rectangular zones with predominant E-W extension use the Lambert Coordinates system C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems LOCAL Coordinates System  In well planning “Local” Coordinates are always used  Local Coordinates are derived from a Local System which, in turn, is related to a “Legal” Coordinates system and also referred to an specific Geodetic Datum  The axis of a Local Coordinates system are parallel to the respective axis of the Legal Coordinates system of reference

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems LOCAL Coordinates System

 The coordinates in a LOCAL system are derived from distances measured to a point of “origin” located in the corresponding “Legal” Coordinates System of reference  The “origin” or reference point in the LOCAL system has its own coordinates in the LEGAL system (x, y)  The “origin” in the LOCAL system has coordinates (0,0)  To measure the well depth it is necessary to previously define one “Geodetic Datum”, called “Vertical Reference Datum”, such as “Ground Level”, “Mean Sea Level”, “Mud Line”, etc.

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems LOCAL Coordinates System

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8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Example of Well Plan Proposal with Coordinates System used

Canon 10 Plan Proposal Report Date: Client: Field: Structure / Slot: Well: Borehole: UWI/API#: Survey Name / Date: Tort / AHD / DDI / ERD ratio: Grid Coordinate System: Location Lat/Long: Location Grid N/E Y/X: Grid Convergence Angle: Grid Scale Factor:

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November 13, 2004 Pemex Exploracion y Produccion Canon Field Canon 10 / Canon 10 Canon 10 Canon 10 Canon 10 Plan / November 12, 2004 40.000° / 1575.89 ft / 4.811 / 0.160 NAD27 UTM Zone 14N N 26 8 28.039, W 98 28 19.018 N 2891256.240 m, E 552784.190 m +0.23265583° 0.99963440

Survey / DLS Computation Method: Vertical Section Azimuth: Vertical Section Origin: TVD Reference Datum: TVD Reference Elevation: Sea Bed / Ground Level Elevation: Magnetic Declination: Total Field Strength: Magnetic Dip: Declination Date: Magnetic Declination Model: North Reference: Total Corr Mag North -> True North: Local Coordinates Referenced To:

Minimum Curvature / Lubinski 16.260° N 0.000 ft, E 0.000 ft RKB 133.1 ft relative to MSL 118.110 ft relative to MSL 5.977° 46224.017 nT 55.296° April 25, 2002 BGGM 2004 True North +5.977° Well Head

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems Summary: 1. To locate a point of the Earth on a Map it is necessary one Coordinates System 2. There are available five well known Coordinates Systems: Geographic Coordinates, UTM, Lambert, Legal and Local 3. There are three Projection Methods widely used of the Earth onto plane surfaces: Mercator’s Cylinder, Lambert’s Conical, and Planar. 4. Each projection has areas with low and high distortion C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Projection Maps & Coordinates Systems

Summary: 5. 6. 7. 8.

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The use of a Geodetic Datum allows higher accuracy to the allocation of a given point on the Earth. The UTM system is widely used in zones with predominant N-S extensions Lambert’s Conical system of Coordinates is preferred in zones with predominant E-W extensions Legal Coordinates are developed for regional control of maps, have their own Geodetic Datum and can use different projection / coordinates systems, depending on the extension predominant Local system is the one used for well planning and is referred to a Legal system

8.2. Coordinates Systems & Azimuth Corrections Magnetic Declination “Magnetic” North and “True” North Locations True North Location Magnetic North Location: Latitude: 75.5N Longitude: 100.5W

X X

Location of Magnetic North changes over time Location of Magnetic North is updated often Can be displayed on maps or computer databases C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Magnetic Declination Magnetic North and True North Locations

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8.2. Coordinates Systems & Azimuth Corrections Magnetic Declination Magnetic Survey Corrections 1. 2. 3. 4. 5. 6.

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The Geographic North of the Earth is also called “True” North or “Grid” North All Projection Maps are constructed referred to the Geographic North (axis of the Earth ellipsoid = “True’ North = “Map” North) “Magnetic” North is the axis of the magnetic field of Earth or “Compass” North Surveys taken with magnetic measuring devices are referred to the “Magnetic” North of Earth The separation between the two axis is measured by an angle called “declination magnetic” To have the right direction of a well at a given survey station, the azimuth recorded with magnetic instruments must be corrected and referred to the “True” North by adding or subtracting the “magnetic declination”

8.2. Coordinates Systems & Azimuth Corrections Magnetic Declination Definition: 1. The angle between True North and Magnetic North as TN measured going from True North to Magnetic North. 2. 3.

If that movement is clockwise, the Magnetic Declination is to the East and is positive If on the contrary, the movement from one North to the other is counterclockwise, the Magnetic Declination is negative

4.

Magnetic Declination is added to Magnetic Azimuth

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MN

EAST

8.2. Coordinates Systems & Azimuth Corrections Grid Convergence Definition: 1. 2.

The angle between True North and Grid North as measured going from True North to Grid North.

GN TN

If that movement is clockwise, the Convergence is to the East and is positive WEST

3.

If on the contrary, the movement from one North to the other is counterclockwise, the Convergence is negative

4.

Convergence is subtracted from the Corrected Magnetic Azimuth

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8.2. Coordinates Systems & Azimuth Corrections Total Correction (Declination and Convergence) TN MA

MN -10°

GN +6°

-4°

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The total correction converts the magnetic azimuth into Grid Azimuth in two steps: Apply Declination correction to the magnetic azimuth Apply Convergence correction to the corrected azimuth

Total Correction = Magnetic Declination - Grid Convergence C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Grid North & Convergence Corrections due to Convergence

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1.

Grid North lines are parallel

2.

True North lines converge on the Central Meridian

3.

Grid North and True North are only identical along UTM zone Central Meridian and the equator

4.

Grid Convergence: 1.

Angle from True North (TN) to Grid North(GN).

2.

+ve to the East

3.

-ve to the West

8.2. Coordinates Systems & Azimuth Corrections Grid Convergence Properties: 1.

Varies as the sine of the Latitude; 1. At the equator Grid Convergence = 0° 2. Theoretically at 90deg latitude North Grid Convergence = 90°

2.

Also varies with Longitudinal displacement from CM 1. At the CM Grid Convergence = 0° 2. At the edge of the Zone, Grid Convergence = SinLat x ?

3.

Standard formula; 1. Grid Convergence = Sin Latitude x (Longitude – CM) 2. This will give an accurate answer by calculator

4.

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What is the biggest Grid Convergence you can have?

8.2. Coordinates Systems & Azimuth Corrections UTM Convergence & Hemispheres UTM Convergence and Hemispheres:

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True North at any point aligns with the longitudinal line through that point

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In the Northern Hemisphere – True North points inwards to the Central Meridian

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In the Southern Hemisphere – True North points outward from the central Meridian

8.2. Coordinates Systems & Azimuth Corrections UTM Zone Exercise

Which quadrant contains the following point? 1

2

− Southern Hemisphere − Northing – 9,500,000m

3

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− Easting – 600,000m Is the convergence +ve or -ve?

8.2. Coordinates Systems & Azimuth Corrections Correction to Grid Azimuth Grid Convergence (Grid Con) 1. ONLY use this angle if Surveys are to be referenced to Grid North 2. Correcting for Grid Con will correct True North to Grid North 3. Measured from True North to Grid North 4. Declination West = -ve 5. Declination East = +ve Grid Azimuth = True North - Grid Con. C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Grid Convergence - Exercise What’s the North Reference? Grid Con. = 2.5°E TN Az. = 90° Grid Con. = -1.7° TN Az. = 195°

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8.2. Coordinates Systems & Azimuth Corrections Magnetic Declination - Exercise West Declination

East Declination True North

True North Magnetic North

D AMN

Bo re ho le

ATN

Az im ut h

Magnetic North

D AMN ATN r Bo

ol h e

e

h ut m i Az

True North (ATn) = Magnetic Azimuth(AMn) + Magnetic Declination(D) C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Magnetic Declination Practical North Reference Points Up Mag Dec. = 2.5°E MWD Az. = 90° Mag Dec. = -1.7° MWD Az. = 195° Mag Dec. = 6.7°W Gyro Az. = 265° C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Total Correction:

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8.2. Coordinates Systems & Azimuth Corrections Compass Quadrant Direction

The four quadrants are normally expressed as NE, SE, SW and NW. Originate the reading from north or south; then move toward the east or west in a positive or increasing angle. The graphic shows an example quadrant direction of S30°E. C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Azimuth Direction

The azimuth system uses directions ranging from 0° to 360°. The direction is reported from 0° in a positive or clockwise direction. A direction of 0° or 360° refers to north; 90° refers to east; 180° refers to south; and 270° refers to west. The graphic shows an example azimuth direction of 150° AZM. C. Alvarez

8.2. Coordinates Systems & Azimuth Corrections Compass Quadrant and Azimuth Relationships

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Quartz School. Module 8: Directional Drilling / Section 2

8.2. Coordinates Systems & Azimuth Corrections Polar and Rectangular Coordinates

The polar coordinate of a point is defined by a distance and a direction relative to North (azimuth). The rectangular coordinates of a point are given in feet or meters with a direction of North/South and East/West.

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