Changes

* Analysis of log responses

* Analysis of log responses

The methods to determine the occurrence of difficult lithologies from the first six sources just listed are not covered in this article. (For information on these sources, see “[[Mudlogging: drill cuttings analysis]]” and “[[Mudlogging: the mudlog]]”; also see “[[Core description]]”.)

The methods to determine the occurrence of difficult lithologies from the first six sources just listed are not covered in this article. (For information on these sources, see [[Mudlogging: drill cuttings analysis]] and [[Mudlogging: the mudlog]]; also see [[Core description]].)

Identifying the occurrence of difficult lithologies from logs can be formidable. Two crossplot techniques are commonly used to identify the occurrence of mineralogies: (1) the M-N crossplot and (2) the MID crossplot.

Identifying the occurrence of difficult lithologies from logs can be formidable. Two crossplot techniques are commonly used to identify the occurrence of mineralogies: (1) the M-N crossplot and (2) the MID crossplot.

===M-N crossplot===

===M-N crossplot===

The M-N crossplot uses the density, compensated neutron, and compressional sonic logs to identify binary and ternary mixtures of minerals. The terms ''M'' and ''N'' are defined as follows:

The M-N crossplot uses the density, [[Basic open hole tools#Compensated neutron|compensated neutron]], and compressional [[Basic open hole tools#Sonic|sonic]] logs to identify binary and ternary mixtures of minerals. The terms ''M'' and ''N'' are defined as follows:

:<math>M  = \frac{\Delta t_{\rm fl} - \Delta t_{\rm log}}{\rho_{\rm b} - \rho_{\rm fl}} \times 0.01</math>

:<math>M  = \frac{\Delta t_{\rm fl} - \Delta t_{\rm log}}{\rho_{\rm b} - \rho_{\rm fl}} \times 0.01</math>

The MID or ''m''atrix ''id''entification crossplot uses the apparent volumetric cross section (UMAA) and the apparent matrix grain density (RHOMAA) to identify minerals. UMAA represents the projection of the volumetric photoelectric absorption index, U (the product of Pe and electronic density), to the value at zero porosity. RHOMAA results from a mathematical projection of the bulk density of an interval to its value at zero porosity. These projections to zero porosity effectively eliminate variance due to porosity, resulting in a variance mainly due to lithology.

The MID or ''m''atrix ''id''entification crossplot uses the apparent volumetric cross section (UMAA) and the apparent matrix grain density (RHOMAA) to identify minerals. UMAA represents the projection of the volumetric photoelectric absorption index, U (the product of Pe and electronic density), to the value at zero porosity. RHOMAA results from a mathematical projection of the bulk density of an interval to its value at zero porosity. These projections to zero porosity effectively eliminate variance due to porosity, resulting in a variance mainly due to lithology.

This method requires that an estimate of total porosity be determined first. Typically, this can be done from a density-neutron crossplot (see “[[Standard interpretation]]”). Using this porosity, an apparent matrix density is determined from the following equation:

This method requires that an estimate of total porosity be determined first. Typically, this can be done from a density-neutron crossplot (see [[Standard interpretation]]). Using this porosity, an apparent matrix density is determined from the following equation:

:<math>\mbox{RHOMAA} = \frac{\rho_{\rm log} - \phi \cdot \rho_{\rm fl}}{1.0 - \phi}</math>

:<math>\mbox{RHOMAA} = \frac{\rho_{\rm log} - \phi \cdot \rho_{\rm fl}}{1.0 - \phi}</math>

Each logging measurement can be expressed in a response equation that relates the recorded log to the volumetric components of lithology and fluids. (For these response equations expressed in their most basic configuration, see [[Standard interpretation]].) These basic equations can be expanded to include any number of mineralogies and fluids.

Each logging measurement can be expressed in a response equation that relates the recorded log to the volumetric components of lithology and fluids. (For these response equations expressed in their most basic configuration, see [[Standard interpretation]].) These basic equations can be expanded to include any number of mineralogies and fluids.

All the logging response equations can then be set up for each measurement, such as the density, neutron, and sonic. The unknowns must be less than or equal to the number of equations for a unique solution to be obtained. A paramount fact that must be kept in mind is that the number of variables that are being computed cannot exceed the number of equations. For example, if the density, neutron, and sonic logs are being used, the total number of equations that can be set up is four—one for each of the measured logs and the fourth for the material balance equation (exemplifying that the sum of all constituents equals 100% of the volume of the rock). Thus, in this case, only four variables can be computed. Assumptions and local knowledge can be used to constrain the problem by reducing the amount of unknown knowledge.

All the logging response equations can then be set up for each measurement, such as the [[Basic open hole tools#Density|density]], [[Basic open hole tools#Compensated neutron|neutron]], and [[Basic open hole tools#Sonic|sonic]]. The unknowns must be less than or equal to the number of equations for a unique solution to be obtained. A paramount fact that must be kept in mind is that the number of variables that are being computed cannot exceed the number of equations. For example, if the density, neutron, and sonic logs are being used, the total number of equations that can be set up is four—one for each of the measured logs and the fourth for the material balance equation (exemplifying that the sum of all constituents equals 100% of the volume of the rock). Thus, in this case, only four variables can be computed. Assumptions and local knowledge can be used to constrain the problem by reducing the amount of unknown knowledge.

Once these logging relationships are established for the difficult lithology being addressed, a number of methods are available to solve these equations effectively for a solution. The more commonly used methods are

Once these logging relationships are established for the difficult lithology being addressed, a number of methods are available to solve these equations effectively for a solution. The more commonly used methods are