We present a new method that is designed for accurate formation resistivity Rt estimation using inversion of galvanic or induction array logs acquired in vertical and deviated wells. At the first step, the method generates a near-borehole resistivity structure of a fixed thickness using inversion of the shallow-reading log measurements. At this step, the method does not aim for accurate estimation of Rxo but determines the parameters of an equivalent near-borehole zone that enables explaining (or fitting) only the shallow measurements. At the second step, the method determines the virgin zone resistivity, Rt, using inversion of the deep-reading logs in the model, which includes an equivalent near-borehole zone determined at the previous step. Because at each step the method performs inversion for a single model parameter, it enables fast and stable reconstruction of the Rt. To illustrate how the method can be used in practice, we present two field examples using array induction (2D case) and array lateral log (3D case) data.
Introduction
Accurately interpreting modern array resistivity log data is critical to drilling, formation evaluation, and reservoir characterization. Multidimensional inversion-based array data interpretation techniques are required to optimize data information extraction to determine the resistivity of the hydrocarbon-bearing formation. However, application of an inversion-based interpretation technique may provide an incorrect (equivalent) solution, resulting in erroneous hydrocarbon (HC) estimates. Nonuniqueness of resistivity inversion is caused primarily due to an incorrect formation model parameterization.
Some of previously proposed methods for reducing or solving the nonuniqueness problem were based on better initial model determination 1–2 and sequential determination of the formation parameters using, for example, time-lapse logging measurements 3–4. In this paper, we propose a new method that offers fast and hands-off Rt estimation by using inversion of induction or galvanic array logs without attracting any additional measurements and information about the formation.
Method
To interpret array logs in vertical and deviated wells and perform accurate Rt estimation, we suggest using the following data-driven inversion-based algorithm.Estimate the near-borehole resistivity structure, Rxo, using inversion of the most shallow-reading array logs. At this step, the method does not aim accurate estimation of invaded zone parameters but generates an equivalent near-borehole resistivity structure of a fixed thickness.It is known that galvanic measurements can be represented by an equivalent series of resistivities, and induction measurements can be represented by equivalent parallel resistivities 5. Therefore, in order to estimate an Rxo, we assume that Rt>>1 in the case of array induction, and Rt<<1 in the case of array Laterolog, and run inversion for Rxo only.Determine the virgin zone resistivity, Rt, using inversion of the deep-reading logs in the model which includes an equivalent near-borehole zone. It should be noted that if at this step we can fit the deep measurements well (which is often the case), we do not need to re-estimate the parameters of the near-borehole zone. However, if the fit is not satisfactory, an inversion-based correction of Lxo or Rxo may be applied.
Because the formation model utilized by the method has a known cylindrical structure with a constant invasion thickness in each layer, one can use optimized radial grids for the forward modeling routines, which provides a significant acceleration of inversion calculations.
We tested the method on a simple theoretical cylindrical (1D) model. The model parameters were selected using the array induction case study formation presented in the following section. The model parameters are as follows: borehole diameter, Cal=8", mud resistivity, Rm=0.04 Ohm-m, depth of invasion, Lxo=24", resistivity of invasion, Rxo=2 Ohm-m, resistivity of the formation, Rt=20 Ohm-m.
