Estimating T2-diffusion probability density functions from nuclear magnetic resonance diffusion modulated amplitude measurements

A nuclear magnetic resonance system, including:

• a downhole tool;
• acquisition logic included in the downhole tool to acquire data representing a plurality of nuclear magnetic resonance (NMR) echo trains associated with a material;
• and
• processing logic to invert a model of at least one of the plurality of NMR echo trains to provide an estimated distribution of transverse relaxation time constants, to invert models of selected ones of the plurality of NMR echo trains using the estimated distribution of transverse relaxation time constants to provide an estimated diffusion distribution, and to invert a model of selected ones of the plurality of NMR echo trains, using quadratic form regularization and the estimated distributions of transverse relaxation time constants and diffusion, to provide at least one of an apparent or an intrinsic probability density function to identify fluid types in the material.

A method of using a nuclear magnetic resonance apparatus, including;

• acquiring data representing a plurality of nuclear magnetic resonance (NMR) echo trains associated with a material;
• inverting a model of at least one of the plurality of NMR echo trains to provide an estimated distribution of transverse relaxation time constants;
• inverting models of selected ones of the plurality of NMR echo trains using the estimated distribution of transverse relaxation time constants to provide an estimated diffusion distribution;
• and
• inverting a model of selected ones of the plurality of NMR echo trains, using quadratic form regularization and the estimated distributions of transverse relaxation time constants and diffusion, to provide at least one of an apparent or an intrinsic probability density function to identify fluid types in the material.

A non-transitory computer readable medium having instructions stored thereon which, when executed by a computer, cause the computer to perform a method of using a nuclear magnetic resonance apparatus, comprising:

• acquiring data for a plurality of nuclear magnetic resonance (NMR) echo trains associated with a material;
• inverting a model of at least one of the plurality of NMR echo trains to provide an estimated distribution of transverse relaxation time constants;
• inverting models of selected ones of the plurality of NMR echo trains using the estimated distribution of transverse relaxation time constants to provide an estimated diffusion distribution;
• and
• inverting a model of selected ones of the plurality of NMR echo trains, using quadratic form regularization and the estimated distributions of transverse relaxation time constants and diffusion, to provide at least one of an apparent or an intrinsic probability density function to identify fluid types in the material.