Landmark Compass培训材料

1、computerized planning etc. 高斯高斯-克吕格投影克吕格投影 1 高斯投影分带高斯投影分带 中央子午线以经度中央子午线以经度6将全球分为将全球分为60个带个带(6投影投影)。我国采用由。我国采用由 英国格林威治零子午线向东起算。我国境内最西部属第英国格林威治零子午线向东起算。我国境内最西部属第13投影带投影带 ，最东部为第，最东部为第23投影带，全国共投影带，全国共11个个 6带。带。 2 高斯平面直角坐标系高斯平面直角坐标系 高斯投影中，投影带的中央子午线作为纵坐标轴高斯投影中，投影带的中央子午线作为纵坐标轴(x轴轴)，赤道所形，赤道所形 成的直线作为横座标轴成的直线

2、作为横座标轴(y轴轴)。投影后互相垂直，其交点即为坐标。投影后互相垂直，其交点即为坐标 原点，构成了统一的平面直角坐标系。原点，构成了统一的平面直角坐标系。 3 坐标换算坐标换算 地质部门设计的坐标属于高斯平面直角坐标。地质部门设计的坐标属于高斯平面直角坐标。 gps(wgs84)与与bjz54坐标的换算需通过坐标的换算需通过wgs72坐标系统坐标系统 作为过渡。作为过渡。 13 23 常用坐标系常用坐标系 1 三个北极三个北极 地理北极、地磁北极、网格北极地理北极、地磁北极、网格北极 2 三个参数三个参数 子午线收敛角：高斯克吕格平面直角坐标纵线与地理坐标纵线子午线收敛角：高斯克吕格平面直角

3、坐标纵线与地理坐标纵线 之间的差角；之间的差角； 磁偏角：地理坐标纵线与地磁坐标纵线之间的夹角，当磁北方位磁偏角：地理坐标纵线与地磁坐标纵线之间的夹角，当磁北方位 线在正北方位线以东时，称为东磁偏角；在正北方位线以西称为线在正北方位线以东时，称为东磁偏角；在正北方位线以西称为 西磁偏角西磁偏角 地质设计的坐标地质设计的坐标(高斯克吕格坐标高斯克吕格坐标)：井口、靶点和井底坐标：井口、靶点和井底坐标 3 磁偏角校正磁偏角校正:真方位角磁方位角东磁偏角真方位角磁方位角东磁偏角 真方位角磁方位角西磁偏角真方位角磁方位角西磁偏角 true northmagnetic north true north

4、magnetic north compass - sign of magnetic declination - magnetic declination + magnetic declination e grid north magnetic north true north magnetic declination grid convergence northern hemisphere remember method: make true as basement lie in east is “ +” draw this before using grid, true and magnet

5、ic north e 误差模型误差模型(系统系统) 误差模型误差模型(系统系统) 如何计算井眼轨迹的不确定性如何计算井眼轨迹的不确定性 the error model defines how wellpath positional uncertainty is calculated. 锥形误差锥形误差 cone of error 系统椭圆误差系统椭圆误差 systematic ellipse 矢量误差矢量误差 iscwsa (井眼测量精度工业导向委员会井眼测量精度工业导向委员会) (the industry steering committee for wellbore survey accu

6、racy) 锥形误差锥形误差 cone of error 球体误差随深度变化球体误差随深度变化(误差表面是个锥体误差表面是个锥体) 现场和试验数据现场和试验数据 前一个球体半径前一个球体半径 + 井深变化量井深变化量 x 工具误差系数工具误差系数 / 1000. 工具误差系数工具误差系数 (常数或者随井斜的变化而变化常数或者随井斜的变化而变化) 起始误差起始误差=井口半径井口半径+井眼误差井眼误差 the starting error around the wellbore is the well error plus the top borehole radius (if defined).

7、 系统椭圆误差系统椭圆误差 systematic ellipse 工业标准工业标准 系统的内因和外因引起系统的内因和外因引起 发生在同一个矢量方向上发生在同一个矢量方向上 不考虑随机误差不考虑随机误差 测斜阅读误差较小或者可以取消测斜阅读误差较小或者可以取消 there are error sources that are random, but they are assumed to be small and tend to cancel out over a number of survey readings. 某些系数和加权数不适合现代定向测斜仪器某些系数和加权数不适合现代定向测斜仪器

8、六种误差系数六种误差系数 _ spe 9223， c.j.m. wolff & j.p. de wardt, jpt dec. 1981 不居中度不居中度 misalignment error 工具在井眼工具在井眼/套管中心的误差套管中心的误差(井斜和方位井斜和方位) 相对深度误差相对深度误差 relative depth error 钻具长度的丈量、拉伸和测斜电缆长度误差钻具长度的丈量、拉伸和测斜电缆长度误差 井斜误差井斜误差 true inclination error 测斜仪重力的影响以及仪器的井斜灵敏度测斜仪重力的影响以及仪器的井斜灵敏度 罗盘误差罗盘误差 compass refere

9、nce error 磁性工具的干扰和准性的误差磁性工具的干扰和准性的误差 陀螺参考方位误差陀螺参考方位误差 gyroscope azimuth error 支架倾斜支架倾斜(gimbal drift)造成的陀螺方位偏差造成的陀螺方位偏差 磁性方位误差磁性方位误差 magnetic azimuth error 钻具的磁性影响钻具的磁性影响 六种误差系数六种误差系数 six coefficients 井斜、方位误差表格井斜、方位误差表格 inclination azimuth error grid: 更精密的仪器更精密的仪器 (速率陀螺速率陀螺) 仪器厂家提供仪器厂家提供 矢量误差矢量误差 isc

10、wsa 固态磁性仪器固态磁性仪器 mwd & ems solid state magnetic instruments 描述动态误差项描述动态误差项 dynamic number of error terms 误差项名称、矢量方向、与误差项名称、矢量方向、与 误差源的连接方式、误差项误差源的连接方式、误差项 单位、误差计算公式单位、误差计算公式 _ spe 56702， h.williamson “ accuracy prediction for directional mwd 四种防碰扫描方法比较四种防碰扫描方法比较 三维最近距离扫描法三维最近距离扫描法 优点：中心点之间的最近距离优点：中心

11、点之间的最近距离 缺点：缺点： 水平扫描法水平扫描法 优点：易于理解优点：易于理解 缺点：不能用于水平井之间；缺点：不能用于水平井之间； 无法扫描水平段和垂直段；无法扫描水平段和垂直段； 不应用于非直井。不应用于非直井。 高边高边+方位角方位角 优点：能够区别参考井交优点：能够区别参考井交 叉直井叉直井 缺点：互成直角井眼防碰缺点：互成直角井眼防碰 数据缺失数据缺失 四种防碰四种防碰 扫描方法扫描方法 比较比较 法面法法面法 优点：钻头处最近点优点：钻头处最近点 缺点：易于混淆井深相缺点：易于混淆井深相 同时的距离；同时的距离； 难以区别参难以区别参 考井交叉直井考井交叉直井 运行环境：运行环

12、境：windows 95, windows 98 or windows nt 推荐推荐cpu：奔腾：奔腾ii 200mhz 安装要求硬盘：安装要求硬盘：30m 系统内存要求：系统内存要求：64m svga：800600 compass for windows version 98.7(32 bit) 井眼轨迹设计井眼轨迹设计 常规定向井常规定向井 水平井水平井 两维井两维井/三维井三维井 待钻井眼待钻井眼 井眼轨迹优化井眼轨迹优化 定向井设计内容定向井设计内容 (1) 靶点限制条件、井眼轨迹靶点限制条件、井眼轨迹 (2) 定向造斜方法及后续控制方法定向造斜方法及后续控制方法 (3) 测斜与计算

13、测斜与计算 (4) 井眼稳定环空携岩及井内波动压力井眼稳定环空携岩及井内波动压力 (5) 钻柱扭矩及阻力钻柱扭矩及阻力 定向井轨迹设计定向井轨迹设计 1 剖面类型剖面类型 三段制三段制(“ j” )剖面和五段制剖面和五段制(“ s” )等等 二维定向井、三维定向井二维定向井、三维定向井 2 设计原则设计原则 根据油田勘探、开发部署的要求，保证安全钻井根据油田勘探、开发部署的要求，保证安全钻井 要有利于提高油气产量和采收率要有利于提高油气产量和采收率 应有利于钻井、采油和修井作业应有利于钻井、采油和修井作业 应尽可能选择比较简单的剖面类型应尽可能选择比较简单的剖面类型 水平井轨迹设计水平井轨迹设

14、计 1 水平井剖面类型水平井剖面类型 小、中、大曲率半径水平井小、中、大曲率半径水平井 2 水平井剖面形状水平井剖面形状 双增剖面、变曲率剖面、圆弧单增剖面等双增剖面、变曲率剖面、圆弧单增剖面等 3 设计依据设计依据 钻井目的及采用的钻井方式钻井目的及采用的钻井方式 工艺装备工艺装备 条件及技术水平条件及技术水平 目的层的厚度、产状目的层的厚度、产状 设计井的基本设计数据设计井的基本设计数据 水平井分类水平井分类 分类 造斜率( /100ft) 半径(ft) 长半径 2to8 2865to716 中半径 8to30 716to191 过渡 30to60 191to95 短半径 60to200

15、95to28 分类 to mdto tvd to inclination to direction dogleg / toolface curves on line by tvd (calc. dogleg & toolface) tvd, lat & dep (calc. dogleg & toolface) tangent to point align by inclination to md to tvd tangent to a to point point (calc. build & turn) on line by tvd (calc. build & turn) build /

16、 turn curves to azimuth to inclination align by inclination optimise trajectory design kop dogleg torque/drag wellbore planner pickit here plan it here share it with the drilling share it with the drilling engineerengineer 井眼轨迹测量计算井眼轨迹测量计算 landmark 井眼轨迹控制概念井眼轨迹控制概念 井眼轨迹控制井眼轨迹控制：采用合理的措施采用合理的措施(包括包括bh

17、a、 操作参数及测控系统等操作参数及测控系统等), 强制钻头沿预制轨道强制钻头沿预制轨道 破碎地层而钻进的过程。破碎地层而钻进的过程。 控制井眼轨迹：控制井眼轨迹： 需要研制专门的井下工具和测斜系统需要研制专门的井下工具和测斜系统(硬件硬件) 必须开发井眼轨迹预测和控制软件必须开发井眼轨迹预测和控制软件(软件软件) 计算参数计算参数 基本参数：基本参数：井深、井斜、方位井深、井斜、方位 计算参数：计算参数：垂深、垂深、n和和e坐标、水平投影长度、坐标、水平投影长度、 垂直分量、井眼曲率（狗腿严重度）、闭合方垂直分量、井眼曲率（狗腿严重度）、闭合方 位、闭合距位、闭合距 井眼轨迹的测量与计算井眼

18、轨迹的测量与计算 测斜方法测斜方法 1 单点测斜单点测斜:一次下井只能测一个井深的参数一次下井只能测一个井深的参数 2 多点测斜仪多点测斜仪:一次下井可记录井眼轨迹上多个井一次下井可记录井眼轨迹上多个井 深处的井眼轨迹参数深处的井眼轨迹参数 3 随钻测斜仪随钻测斜仪:随同钻柱一同下入井内，在钻进过随同钻柱一同下入井内，在钻进过 程中连续测量，并实时将测量数据传至地面程中连续测量，并实时将测量数据传至地面 测量误差的形成测量误差的形成 1 由于井眼轨迹的理想假设，导致了与真实井眼由于井眼轨迹的理想假设，导致了与真实井眼 轨迹的偏差轨迹的偏差 2 测量数据在每次测量过程中存在着不同程度的测量数据在

19、每次测量过程中存在着不同程度的 误差，导致由此计算出来的井眼轨迹与实际轨误差，导致由此计算出来的井眼轨迹与实际轨 迹不符迹不符 3 由于测点间存在间距由于测点间存在间距(一般一般30m)，造成井眼轨造成井眼轨 迹误差迹误差 测量数据的处理测量数据的处理 1 不确定椭圆随着井深的增加而加大不确定椭圆随着井深的增加而加大 2 要用陀螺测量资料校正要用陀螺测量资料校正“ 不确定椭园区不确定椭园区” 3 compass提供三种误差分析方法：提供三种误差分析方法： cone of error systematic ellipse iscwsa vertical section view in boreh

20、ole azimuth plan view tvd east v.section tvd north vertical lateral high side h.minor min.azi depth lateral high side x borehole plane = perpendicular to wellpath vector at depth of interest 3 dimensional view compass error ellipse report x borehole x borehole depth 测量仪器误差值测量仪器误差值 误差分类误差分类 ：1，系统误差系统

21、误差 2，随机误差，随机误差 3，过失误差，过失误差 深度误差深度误差 (1/1000) 线性误差线性误差 (degree) 角度误差角度误差 (degree) 基准误差基准误差 (degree) 钻具磁性误钻具磁性误 差差 (degree) 陀螺误差陀螺误差 (degree) goog gyro0.50.030.20.1-0.5 poor gyro2.00.20.51.0-2.5 good mag.1.00.10.51.50.25- poor mag.2.00.31.01.55.0+5.0- weighting11sin isin isin i sin a(cos i)-1 井眼轨迹计算方法

22、井眼轨迹计算方法 中国钻井行业：中国钻井行业：手工计算时采用平均角手工计算时采用平均角 法，计算机计算时采用最小曲率法，计算机计算时采用最小曲率 compass：最小曲率法、曲率半径法、平：最小曲率法、曲率半径法、平 均角法、平衡正切法均角法、平衡正切法 定向井、水平井设计图例定向井、水平井设计图例 丛式井丛式井 防碰扫描技术防碰扫描技术 目的目的 在丛式井设计和施工中，不仅要求中靶，在丛式井设计和施工中，不仅要求中靶， 而且要求防止两井交叉相碰而且要求防止两井交叉相碰 进行邻井距离扫描有助于两井任一井深时进行邻井距离扫描有助于两井任一井深时 的相对位置，以便采取相应的措施的相对位置，以便采取

23、相应的措施 邻井距离扫描方法邻井距离扫描方法 3d最近距离扫描法最近距离扫描法 法面法法面法(traveling cylinder) 平面法平面法(horizontal plan) 高边方位角法高边方位角法(highside+azimuth) 常用扫描方法介绍常用扫描方法介绍 最近距离扫描：最近距离扫描：可以确定参考井井眼轴线上可以确定参考井井眼轴线上 任一点到比较井井眼轴线的最近距离和最近距任一点到比较井井眼轴线的最近距离和最近距 离扫描图离扫描图 法面距离扫描：法面距离扫描：可以确定参考点切线的法面可以确定参考点切线的法面 与扫描点的交点，同时求出两点间的距离及相与扫描点的交点，同时求出两

24、点间的距离及相 对方位，进而在极坐标平面上画出法面距离扫对方位，进而在极坐标平面上画出法面距离扫 描图描图 扫描方法的选用扫描方法的选用 1 指导定向井施工或确定剖面符合率时，指导定向井施工或确定剖面符合率时， 优先使用法面距离扫描优先使用法面距离扫描 2 遇到丛式井防碰问题时，宜使用最近距遇到丛式井防碰问题时，宜使用最近距 离扫描图离扫描图 3 在要求很高的定向井在要求很高的定向井(如救援井如救援井)施工中，施工中， 应同时使用法面距离扫描图和最近距离应同时使用法面距离扫描图和最近距离 扫描图扫描图 平台优选技术平台优选技术 井口排列方式井口排列方式 平台位置平台位置 丛式井设计丛式井设计

25、优化丛式井设计，可以提高油田开发的综优化丛式井设计，可以提高油田开发的综 合效益和加快投资回收速度。合效益和加快投资回收速度。 1 优化地面井口的排列方式优化地面井口的排列方式 2 优选平台位置优选平台位置 优选地面井口排列方式优选地面井口排列方式 根据每一个平台上井数的多少选择平台内根据每一个平台上井数的多少选择平台内 地面井口的排列方式地面井口的排列方式 1 矩形排列：适合于一个丛式井打多口井矩形排列：适合于一个丛式井打多口井 2 环状排列：适用于在陆地或浅海人工岛环状排列：适用于在陆地或浅海人工岛 钻丛式井，在一个丛式井平台上钻几十钻丛式井，在一个丛式井平台上钻几十 口井口井 优选平台位

26、置优选平台位置 根据每个平台上各井井底位置根据每个平台上各井井底位置(目标点目标点)和和 地面条件等因素优选，优选平台位置。地面条件等因素优选，优选平台位置。 优选平台位置可按照平台位置的优选原则优选平台位置可按照平台位置的优选原则 进行优选进行优选 用户报告用户报告 表格 图形 打印机 绘图仪 技术支持技术支持010-84864819 ? start 课程安排课程安排 using on-line helpgetting help from compass data structurehierarchical data structure site optimise

27、rbest site location to drill targets template editorcalculate template co-ordinates planningdesign shape of wellpath survey compute shape of wellpath anti-collisionseparation between wellpaths anti-collisioncombined exercise wall plotsediting profile and plan plots 数据结构数据结构 data structure company (公

28、司公司) field (油田油田) site (井场井场) well (井井) wellpath (井眼轨迹井眼轨迹) plan and survey (设计和测斜设计和测斜) compass has a hierarchical data structure . . starting at the lowest level. measured depth inclination direction or for inclination only md, inclination or for inertial tvd, n/s, e/w survey observation survey a

29、survey is a series of observations made in a section of wellbore with the same survey tool on the same tool run. measured depth inclination direction or for inclination only md, inclination or for inertial tvd, n/s, e/w survey observation survey a survey is a series of observations made in a section

30、 of wellbore with the same survey tool on the same tool run. the survey tool can be traditional (md, inc, azi), inclination only (md, inc), or inertial (tvd, n/s, e/w). measured depth inclination direction or for inclination only md, inclination or for inertial tvd, n/s, e/w survey observation surve

31、y a survey is a series of observations made in a section of wellbore with the same survey tool on the same tool run. the survey tool can be traditional (md, inc, azi), inclination only (md, inc), or inertial (tvd, n/s, e/w). each survey tool is assigned an error model for calculating positional unce

32、rtainty. company field site well wellpath plan and survey wellpath plans a wellpath may have many plans . wellpath plans a wellpath may have many plans . .but only one principal plan wellpath plans a wellpath may have many plans . .but only one principal plan a wellpath may also have many surveys su

33、rveys a wellpath may have many surveys a wellpath may have many plans . .but only one principal plan a wellpath will have a definitive wellpath wellpath definitive wellpath plans surveys a wellpath may have many surveys a wellpath may have many plans . .but only one principal plan a wellpath may hav

34、e a definitive wellpath at the planning stage, the definitive wellpath may the principal plan . wellpath definitive wellpath plans surveys wellpath definitive wellpath plans a wellpath may have many surveys a wellpath may have many plans . .but only one principal plan a wellpath may have a definitiv

35、e wellpath at the planning stage, the definitive wellpath may be the principal plan but while drilling, it would be a combination of the most accurate surveys surveys wellpath a wellpath will also have its own local magnetic field calculated using the geomagnetic model defined at the field level geo

36、magnetic field igrf wellpath a wellpath will also have its own local magnetic field calculated using the geomagnetic model defined at the field level this local field is calculated using an appropriate date of operations when surveys were being recorded and the wellpath location geomagnetic field ig

37、rf survey date: 20/04/2000 loc: 51 5 45” n 3 15 33” e company field site well wellpath plan and survey well a well is a surface location referenced from the site local co-ordinate system 0.0 n/s 0.0 e/w well a well is a surface location referenced from the site local coordinate system it may have on

38、e or more wellpaths referenced to it 0.0 n/s 0.0 e/w well a well is a surface location referenced from the site local coordinate system it may have one or more wellpaths referenced to it if required, a well can have a well reference point which defines a permanent point upon which vertical depths ca

39、n be displayed, stored and referenced. 0.0 n/s 0.0 e/w well reference point company field site well wellpath plan and survey a site is a collection of wells. 0.0 n/s 0.0 e/w site a site is a collection of wells. the site centre may given map or geodetic co- ordinates. 0.0 n/s 0.0 e/w site 0.0 n/s 0.

40、0 e/w site a site is a collection of wells. the site centre may given map or geodetic co- ordinates. and an elevation above a system or field datum. 0.0 n/s 0.0 e/w site drilling targets a site is a collection of wells. the site centre may given map or geodetic co-ordinates. and an elevation above a

41、 system or field datum. the site coordinate system can be aligned to either true north or grid north n 0.0 n/s 0.0 e/w site drilling targets a site is a collection of wells referenced by the same local coordinate system. the site centre may given map or geographic co-ordinates. and a elevation above

42、 a system or field datum. the site coordinate system can be aligned to either true north or grid north sites can have drilling targets. n 0.0 n/s 0.0 e/w site drilling targets n a site is a collection of wells referenced by the same local coordinate system. the site centre may given map or geographi

43、c co-ordinates. and a elevation above a system or field datum. the site coordinate system can be aligned to either true north or grid north sites can have targets which can be selected by a wellpath 0.0 n/s 0.0 e/w site drilling targets n a site is a collection of wells referenced by the same local

44、coordinate system. the site centre may given map or geographic co-ordinates. and a elevation above a system or field datum. the site coordinate system can be aligned to either true north or grid north sites can have targets which can be selected by a single wellpath or selected by multiple wellpaths

45、 company field site well wellpath plan and survey field a field is a collection of sites. field a field is a collection of sites. within the same geodetic system. geodetic system field a field is a collection of sites. within the same geodetic system. sites within a field can be independently aligne

46、d to grid north or true north geodetic system g g t field a field is a collection of sites. within the same geodetic system. all sites within a field are independently aligned to grid north or true north a field has a system datum the name given to 0 tvd for the field e.g. mean sea level. geodetic s

47、ystem system datum e.g. msl g t g field a field is a collection of sites. within the same geodetic system. all sites within a field are independently aligned to either grid north or true north a field has a system datum, the name given to 0 tvd for the field data within the field can be referenced t

48、o the system datum geodetic system system datum e.g. msl field a field is a collection of sites. within the same geodetic system. all sites within a field are independently aligned to either grid north or true north a field has a system datum, the name given to 0 tvd for the field data within the fi

49、eld can be referenced to the system datum, wellpath datum geodetic system system datum e.g. msl wellpath datum e.g. rkb field a field is a collection of sites. within the same geodetic system. all sites within a field are independently aligned to either grid north or true north a field has a system

50、datum, the name given to 0 tvd for the field data within the field can be referenced to the system datum, wellpath datum or the well reference point geodetic system system datum e.g. msl well reference point e.g. ml wellpath datum e.g. rkb a field is a collection of sites. within the same geodetic s

51、ystem. all sites within a field are aligned to either grid north or true north a field has a system datum the name given to 0 tvd for the field data within the field can be referenced to the system datum, wellpath datum or the well reference point you can select a geomagnetic model to compute magnet

52、ic declination at any location and time within the field. fieldgeodetic system geomagnetic model system datum e.g. msl well reference point e.g. ml wellpath datum e.g. rkb company field site well wellpath plan and survey company a company may have several fields companies may have different policies

53、 on . company a company may have one or more fields companies may have different policies on . .anti-collision calculations . anti-collision preferences company d dmd cos(i) survey calculation method anti-collision preferences a company may have one or more fields companies may have different polici

54、es on . .anti-collision calculations . .survey calculation methods company survey tool errors errors intrinsic in wellbore surveying d dmd cos(i) survey calculation method anti-collision preferences a company may have one or more fields companies may have different policies on . .anti-collision calc

55、ulations . .survey calculation methods and .survey tool error parameters. survey history - the definitive path story definitve pathgyro 1 1st hole section cased mwd1 1st hole section open hole definitve pathdefinitve path gyro fs 2nd hole section cased - final survey gyro 2 mwd is the only data we h

56、ave so it becomes the definitive path mwd replaced by a gyro survey. the gyro survey becomes the definitive path mwd in next open hole section tied-on to gyro to form definitive path 2nd hole section open hole mwd2 gyro run from surface replaces all previous surveys to form the definitive path 大地坐标

57、company,field & site setup v.s.origin coordinate origin utm north references latitude departure lat /dep origin local cr slot vert sectn origin projected horizontal displacement slot local cr a utm zone grid north grid north 500,000 m equator 0 central meridian true north true north a utm zone grid

58、north grid north 500,000 m equator 0 central meridian true north true north local north from the field setup we know that the sites are aligned to grid north. a utm zone grid north grid north 500,000 m equator 0 central meridian true north true north local north . so we know know the site is east of

59、 the central meridian. east west a utm zone grid north 500,000 m equator 0 central meridian true north local north east grid convergence (the difference between true and grid north) is +0.68 +0.68 a utm zone grid north 500,000 m equator 0 central meridian true north local north east magnetic declination, the angle between true and magnetic north is -2.78 +0.68 magnetic north-2.78 a utm zone grid north 500,000 m equator 0 central meridian true north local north east a direction of 183 magnetic. +0.68 magnetic north-2.78 a utm zone grid north 500,000 m equator 0 central meridian true north loca