The formation temperature affects numerous logging measurements including nuclear magnetic resonance (NMR) data. Obtaining NMR porosity requires the multiplication of the raw NMR signal by a factor that includes the temperature in the sensitive volume. Typically, the temperature of the mud is used as a proxy for the temperature in the sensitive volume. However, if the two temperatures are not equal, the temperature effect reduces the accuracy of the NMR porosities. In some environments (e.g., NMR logging while drilling in deep wells) the NMR temperature effect might as large as 10% of the total NMR porosity.
The main challenge in correcting the NMR porosity for temperature effect is the estimation of the temperature in the sensitive volume. By assuming that heat conduction is the main heat transfer mechanism, the formation temperature can be estimated by solving the heat equation in the proximity of the borehole. To reduce the computational time, a level-based approach is used, whereby the size of the model is controlled by the borehole size. Moreover, by assuming that the temperature in the axial direction is constant within the sensitive volume, the 3-D temperature distribution is reduced to a 1-D distribution (in the radial direction) that can be numerically computed by a finite-difference (FD) scheme.
The temperature distribution around the borehole depends on several parameters including the undisturbed temperature of the formation, the borehole size, the thermal diffusivity of the formation, the time since drilled, and the whole history of drilling mud temperatures. A level-by-level FD computation of the formation temperature is too slow for practical use. Fortunately, the FD computation can be fully replaced by a fast analytical computation based on two pre-computed maps. The maps contain dimensionless formation temperature as function of dimensionless time and dimensionless radius. The first map is for the continuous cooling case (mud temperature is constant and lower than formation temperature), while the second map is for a so-called impulse cooling case.
This paper presents the theoretical background of the NMR temperature correction, several FD schemes and the quasi-analytical approach used for the computation of the formation temperature, numerical examples illustrating the computation of the formation temperature for several cases (e.g., a logging-while-drilling run and a logging-after-drilling run), and a temperature correction workflow for NMR logging data.