By now it should be well known that apparent resistivity (R,) is quite different from the true formation resistivity (R,) in complex formation environments. Efforts have been made to apply inversion techniques to derive R, from R,. The advantages of using inversion are that the method automatically derives an R, model and that the inverted-model is consistent with the logs. Inversion improves bed boundary definition and the water saturation calculation, However, there are two bottlenecks to the method, i.e. the processing speed and solution uniqueness. Because of these problems, inversion still has not been routinely used in log interpretation. The major part of the processing time in a rigorous inversion algorithm is spent on calculating the Jacobian matrix that sets the direction of model adjustment. In this 1-D fast algorithm, the Jacobian matrix calculation is avoided. The fast algorithm first applies a shaping filter to the logs. Equivalently, to first order approximation, the shaping filter maximizes the diagonal elements of the Jacobian matrix as well as symmetrizes the Jacobian matrix. The shaping filter differs from the conventional focusing filters in that it has no resolution enhancement. It only ensures that for each log point of the reshaped log the largest sensitivity is from the formation at the same depth point. The inversion solution is then updated iteratively according to the difference between the filtered log and the calculated tool response (with the same shaping filter applied) of the predicted model. The stability of the inverse algorithm is achieved by using the fact that induction measurements have little sensitivity to a resistive layer with thickness smaller than the main coil spacing. A simple automatic adjustment in correction step length is built into the algorithm to avoid resistivity over-correction and consequently the instability in updating the model. The algorithm converges to a stable R, model typically after three to five iteration steps. Since there is no Jacobian matrix calculation, the total computation time is roughly equal to the cost of a single forward run multiplied by the number of iterations.
Pulsed neutron capture (PNC) logs have been routine use for decades for the measurement of formation capture cross section. The measurement is robust, accurate, and statistically precise. However, borehole and diffusion effects on the measurement are difficult to characterize and use since they require accurate knowledge of not only borehole size but also borehole capture cross section. This paper presents an innovative approach to correct pulsed neutron logs for borehole and diffusion effects without the knowledge of borehole capture cross section or water salinity. This is accomplished through the utilization of all the information available in the time decay spectra of both the near and far detectors. The correction to the apparent formation capture cross section of one of the detectors is described as a mathematical model of the relative counts in different gates of the time decay spectra of both detectors. The coefficients of the model are obtained from a nonlinear least-squares fit of the model to data from different borehole and formation conditions. The model was optimized using over 5000 data points generated from accurate Monte Carlo simulations covering a very large range of down-hole conditions. The accuracy of the new algorithm when tested on modeling data was found to be on the order of 0.5-1.0 cu over the entire range of formation and borehole capture cross sections.
An updated and enhanced version of LAS (Log ASCII Standard) is proposed. LAS 3.0 is a consistent approach that provides a more robust standard for digital data exchange and storage. This revision increases the applicability of LAS files by accotnmodating all types of digital log data, as well as non-log borehole data. We anticipate that the final specifications will achieve wide acceptance, and we are therefore requesting feedback and input on the proposed revisions from industry to ensure that LAS 3.0 meets the needs of users and data managers.
The apparent resistivity measured by a system of electrodes (whether operating in direct or alternating current mode) aligned parallel to the vertical resistivity component in an anisotropic medium is equal to the horizontal resistivity component. Historically, this phenomenon is described as the "paradox of anisotropy"; its existence thwarts efforts to detect the vertical resistivity component of an anisotropic medium. As mentioned, in the case of alternating current, even when the transmitters and the receivers are both vertical electric dipoles, the paradox of anisotropy is observed. However, the paradox can be circumvented by detecting the magnetic field of a vertical electric dipole transmitter using a toroidal receiver. The formulae which convert the resistive and reactive voltage signals into apparent horizontal and vertical conductivities are simple. In addition, when skin effect is small, an apparent anisotropy coefficient is estimated that is within a few percent of the actual anisotropy coefficient.
Permeability measurements taken with the probe permeameter in carbonates can be highly variable and very sensitive to small changes of location and/or tip dimensions. These problems are associated with the measurement volume of the probe permeameter, which is very small (1-9x w7m3) and is illustrated in this paper. The problem of measurement volume (which is also the statistical support volume) is usually avoided by taking larger (whole core) samples. However, with whole core samples, it is not possible to assess the support by measuring an adjacent lateral sample. The variability of adjacent measurements is analogous to the variability of an average at different locations (which is statistical stationarity). This paper shows how the probe permeameter can be used to assess permeability support and stationarity in a variety of carbonate pore types. A published method is applied here-multisupport probe (MSP) permeametry-to provide speedy, nondestructive sampling at high density (close spacing) and at multiple volumes. The key feature of the MSP is the use of different tip sizes to measure the permeability at different sample support volumes. Through use of the MSP permeameter, the permeability data are screened to assess whether they are appropriate for upscaling or modeling. The use of MSP permeameter as a screening device for petrophysical measurement in carbonates is recommended. A numerical model of the unsteady state probe permeameter is described. This has been used to understand the tool response in a very heterogeneous carbonate rock sample. The results show that the device is sensitive to the ratio between the size of the vugs and the probe tip dimensions and can be used as a qualitative measure of vug connectivity. An experiment is also described to demonstrate the ability of this method to quantify the upscaling process. To obtain the required averaging method in carbonate rock, an upscaling experiment has been performed on cubic samples. The averaging method for the probescale data is quantified by comparison between the probe and cube data. In a carbonate with isolated vugs, the cube data are best estimated by the hamionic or geometric averages, an outcome that is in accord with the connectivity of the pore system.
With the rapid expansion of horizontal drilling, the interpretation of logs, especially resistivity logs, has become an increasingly complex problem. The proximity of shale layers or of water legs can seriously affect deep resistivity logs, and invasion can strongly affect shallow resistivity logs. The current state of affairs is that determining R, in a horizontal or very high angle well is often impossible. Modeling techniques are now available for solving the full 3D problem necessary for deviated well interpretation. This paper describes a 3D modeling code and applies it to improve the interpretation of multiarray induction tool response. The code uses the Lanczos spectral-decomposition method to solve Maxwell''s equations on a staggered finite-difference grid. The finite-difference code has been benchmarked against analytical solutions for subsets of the 3D geometry, and agreement is within three percent. Fifty ft of 3D log can be generated in under half an hour on a modern workstation or high-end PC. The code takes into account dipping beds and unsymmetrical invasion at the same time, as well as resistivity anisotropy. Several horizontal well interpretation problems are investigated with the code. One is the case of axisymmetric cylindrical invasion in a permeable zone below a cap shale interface. In this case modeling shows that for shallow invasion, the deepest Array Induction Imager tool (AIT) curves can be used to infer R, and proximity to the shale cap, while the shallowest curve indicates R,,. If deeper invasion is modeled, only the deepest induction curve indicates R,, while several of the shallow curves read R,,. The code is also used to analyze non-circular invasion fronts caused by either permeability anisotropy or buoyancy segregation typical in highly deviated wells. Both cases are characterized by a considerable quantity of filtrate shunted away from the well in preferential directions, resulting in less invading fluid near the wellbore. As a consequence, there is an increase of the influence of R, on the shallow AIT logs. These cases indicate ihai induction logs in complex formations still have geometrical interpretations, but that they are different than interpretations used in vertical wells. A log example illustrates the power of 3D modeling in interpreting multiarray induction logs in difficult wells. In a horizontal well with moderately salty invasion, modeling shows that a large separation between the deepest induction curves is caused by a combination of invasion effects and polarization horns near a cap shale. In addition, an annulus is present to complicate interpretation.
In the conventional approach to the interpretation of nuclear magnetic resonance (NMR) measurements on water-saturated reservoir rocks, it is assumed that the T, distribution and the pore size distribution are directly related. However, both laboratory and log data show that this relationship breaks down in many pore systems, especially carbonates, which consist of micro (,intragranular) and macro (intergranular) porosity. This breakdown limits our ability to predict permeability and movable fluid fractions. Physically, it is due to the diffusion of magnetization between the intraand intergranular pores. We present here three geometrical models that help clarify the relationship between NMR measurements and the underlying pore geometry. All of the models characterize this geometry in terms of four parameters: ( 1 ) the volume fraction of total porosity, $ (2) the volume fraction of intergranular porosity, fm ( 3 ) the pore volume to surface area ratio for the micropores, (4) the pore volume to surface area ratio for the macropores, Vsni In the first model, we apply random walk numerical simulations to an ordered cubic packing of consolidated microporous grains. For given values of the above parameters, the Tz distribution is evaluated as a function of surface relaxation parameter, p . In the second and third models, the microporous grains are treated as a continuum. For they values of greatest interest, roughly, 1.50 essentially identical results can be derived from a three-dimensional analytical model. In addition, for all values ofp, many features of the T, distribution can be represented in terms of a one-dimensional (1 D) model pore space.
For matching LWD and wireline resistivity logs, has been customary to include the effects of several factors such as invasion, dip, anisotropy and dielectric constant. Experimental results were obtained measuring the electrical resistivity of Berea sandstone, tight-gas-sand rocks and Ottawa sandbentonite mixtures saturated with NaCl brine solutions at frequencies between 10 Hz to 10 MHz. These results indicate that rock resistivity becomes dispersive at frequencies above 0.1 MHz for the various conditions of salinity, wettability, clay content, and degree of rock consolidation investigated. Therefore, an additional correction for frequency dependence has to be added for matching LWD and wireline sistivity logs. Similar conclusions have been reached by simulating shaly-sand resistivity using a generalized HanaiBruggeman model, and carbonate-rock resistivity ing the Complex Refractive Index model. Supporting well log examples were obtained in impermeable non-dipping shales in two Conoco test wells. A systematic trend of resistivity decrease with increasing frequency has been observed in these test wells with all the electromagnetic instruments operating in 20 KHz to 1 GHz frequency band.
One of the most controversial problems in formation evaluation in the Nubian Sandstone of the Zeit Bay Field, Gulf of Suez, is the shale effect in the reservoir rocks. An accurate determination of formation porosity and fluid saturation in shaly sand is subject to many uncertain parameters. It is necessary to integrate information from several different log responses using various interpretation models and local knowledge in order to accurately estimate the desired formation properties. This note illustrates that a conventional approach for handling the problem of shaly sand provides accurate values of shale volume from different shale indicator tools and thereafter a reliable effective porosity. Hydrocarbon saturation profiles have been calculated using a laminated shale model. The validity of petrophysical parameter values estimated by this integrated approach is confirmed by a comparison with petrophysical properties measured on core samples collected from shaly sand sections in the same wells.
A new processing algorithm for multiarray induction tools has been tailored for highly deviated wells. This algorithm provides the same interpretation for invasion that has been available in the past only in vertical wells. The new algorithm is based on maximum-entropy inversion of the raw, borehole-corrected array data through a fast 1D forward model. It allows interpretation of multiarray induction logs even in the presence of invasion. Tests on a wide range of invasion profiles computed with a 3D induction forward model code at relative dip angles as high as 85" show that the new inversion allows determination of R,,,, R,, and the invasion profile with similar accuracy to that determined in vertical wells. In theory the process works to 90"; however, the current parameterization requires that the wellbore cut all beds of interest. Studies of sensitivity to incorrect dip angle show that in most cases the relative dip must be known to *5'' to satisfy reasonable petrophysical requirements. Sensitivity studies to other sources of error, including coherent borehole noise, show that the new process has a sensitivity to these effects similar to the current field processing. Because the nonlinear response of induction arrays to conductivity is handled explicitly, and without approximation, the new process also handles large shoulder-bed contrasts without horns and overshoots at all apparent dip angles. Application to field logs at a variety of relative dip angles confirms that the results predicted from modeled data transfer to the real world, producing R, estimates that are fully corrected for dip effect.