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Abstract 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.
To estimate the static bottom hole temperature in wells where the geothermal gradient is not known, this paper proposes a novel method based on the ratio of shallow to deep resistivity measurements from an array induction log and the continuous mud temperature survey that is usually available with it. This ratio in shales is practically a straight line decreasing from values higher than one at the bottom of the well to values less than one close to surface, reflecting the variation of the radial temperature gradient between mud and formation as a function of depth. The depth at which the ratio is one is where mud and formation temperature are the same. From the mud temperature at this depth and the yearly average surface temperature, the static bottom hole temperature is extrapolated assuming a linear temperature gradient. The method has been successfully tested in several wells of the San Jorge and Neuquen basins by comparing the results with the temperature estimated from the known geothermal gradient.
It is important to determine downhole temperature as accurately as possible as it can affect the functioning of logging tools and has an important effect on rock and fluid properties. For example, mud conductivity increases with temperature, increasing the conductivity of shallow resistivity devices. Quantitative log analysis parameters, such as formation water and clay conductivity also increase with temperature. Gas density and oil viscosity are a function of temperature. Oil composition variations in a reservoir can be partly due to temperature effects1.
Downhole temperature can be calculated from the surface temperature and the geothermal gradient, which is assumed to be linear2. If the mean surface temperature for a given area is not known, data from the closest location can be used. However, differences in altitude, for example, can produce large differences in temperature between the well site and the closest location. For reference, Table 1 lists the mean annual temperature of several oil field locations in Latin America. Offshore, the sea bottom temperature is mainly a function of water depth. In the Atlantic Ocean the sea bottom temperature ranges between 9°C (48°F) at 600 meters and 2°C (36°F) at 2000 meters. In shallow water the bottom hole temperature depends mainly on the geographical location and sea currents.
For log analysis, the geothermal gradient is usually calculated from the mean surface temperature and the bottom hole temperature measured during logging operations. But because of the cooling of formations while circulating mud, the recorded bottom hole temperature can be 20°F to 40°F lower than the actual (static) formation temperature2,3. For this reason it is more accurate to use the geothermal gradient computed from cased-hole temperature measurement in several wells during completion or workover operations. This information is usually available in development fields. An example of gradient determination is shown in Fig. 1 for a field in the Neuquen basin in Argentina. In this case the computed gradient is 0.065°F/m, and the extrapolated surface temperature is 58°F, in agreement with the mean annual temperature of the city of Neuquen (see Table 1).
When the geothermal gradient is not known, for example in exploration wells, the static (i.e., undisturbed by mud circulation) bottom hole temperature has to be estimated from some other method. If several logging runs are made in the well, and the bottom hole temperature is measured in each run, the static bottom hole temperature can be estimated with a Horner-type plot of temperature vs. time4. This method is seldom used today, as modern logging tools can acquire a complete set of logs in a single run into the hole and therefore only one bottom hole temperature is available.
Reliable values of static temperature are important for a number of reasons. For example, they are required in designing deep-well cementing programs and in analyzing reservoir fluid properties. Though many engineers hate discouraged the use of recorded log temperatures, these log temperatures can be used to predict static temperature.
Static formation temperature should be determined as accurately as possible for a number of reasons. In-situ sauration distributions computed from resistivity logs require accurate formation water resistivities that depend on temperature. Reliable estimates of bottom-hole temperatures are important in designing deep-well cementing programs and in evaluating reservoir-fluid formation volume factors. Also, the determination of static temperature is necessary for establishing geothermal gradients that can be used to estimate the temperatures of deeper zones. More recently, new exploration techniques have used temperature as a mappable proximity parameter. proximity parameter. Unfortunately, the temperatures recorded during logging operations frequently are not static temperatures. The recorded values are too low. These low temperatures result because the circulating mud temperature frequently is much less than the formation temperature. Schoeppel and Gilarranz reported that early investigators had discouraged the use of bottom-hole temperatures obtained from logs under the assumption that the temperatures would not be correct because the mud and the formation were not in thermal equilibrium.
More recently, however, Timko and Fertl suggested that the temperatures recorded while running a series of logs can be interpreted to estimate static formation temperature. They recommend use of a Horner temperature plot, similar to the conventional pressure buildup method, plot, similar to the conventional pressure buildup method, for estimating static formation temperature. Timko and Fertl demonstrate the apparent applicability of the technique with an example. Significantly, we have been unable to find any theoretical justification for an analysis of this type. However, we have seen field cases where the technique gives satisfactory results. The accuracy of this analysis was especially surprising when it was concluded that the two methods - pressure build-up and temperature buildup - are not completely analogous. Thus, the chief objective of the present study was to determine under what conditions the Horner temperature plot can be used to estimate static temperature.
Comparison of Temperature And Pressure Buildup
Pressure Buildup Pressure Buildup The equation that describes pressure behavior at each point at any time in the well drainage area is point at any time in the well drainage area is 2p 1 p c p ----- + ---- ---- = ------ ------ ...........(1) r2 r r k t
Eq. 1 frequently and referred to as the "diffusivity" equation because of its similarity to the diffusivity equation in the heat-transfer literature. Subject to the constraints of an initial condition and a set of boundary conditions, Eq. 1 can be solved.
Consider the case of a well producing at a constant rate and located in an infinitely large reservoir.