Apparatus and method for determining inclination and orientation of a downhole tool using pressure measurements

An apparatus for use in a wellbore for estimating one of inclination and orientation of a downhole tool in the wellbore, comprising:

• a plurality of pressure sensors, wherein a first pressure sensor in the plurality of pressure sensors is vertically displaced from at least one of other pressure sensors, and the pressure sensors measure pressure of a non-compressible liquid filled volume disposed within a sphere, wherein the sphere contains the non-compressible liquid filled volume and a thermal expansion volume configured to allow the non-compressible liquid filled volume to expand to occupy substantially an entire volume of the sphere at a downhole temperature;
• a circuit configured to provide signals corresponding to pressure measured by the plurality of pressure sensors when the downhole tool is in a non-vertical position in the wellbore;
• and
• a processor configured to estimate the one of inclination and orientation of the downhole tool using pressure measurements, wherein the processor is further configured to estimate the one of inclination and orientation using pressure values computed as ρgh, where ρ is density of the substantially non-compressible liquid, g is the acceleration of gravity, and h is immersion depth of each pressure sensor within the substantially non-compressible liquid.

An apparatus for estimating at least one of inclination and orientation of a tool in a wellbore, comprising:

• a spherical body containing a non-compressible liquid filled volume and a thermal expansion volume configured to allow the non-compressible liquid filled volume to expand to occupy substantially an entire volume of the spherical body at a downhole temperature;
• a plurality of pressure sensors arranged in the spherical body configured to provide pressure measurements of the non-compressible liquid filled volume, wherein a pressure sensor in the plurality of pressure sensors is vertically disposed from at least one other pressure sensor in the plurality of pressure sensors;
• and
• a processor configured to estimate the one of inclination and orientation of the tool using pressure measurements, wherein the processor is further configured to estimate the one of inclination and orientation using pressure values computed as ρgh, where ρ is density of the substantially non-compressible liquid, g is the acceleration of gravity, and h is immersion depth of each pressure sensor within the substantially non-compressible liquid.