AN UNSUPERVISED LEARNING ALGORITHM TO COMPUTE FLUID VOLUMES FROM NMR T1-T2 LOGS IN UNCONVENTIONAL RESERVOIRS

摘要

A key objective for formation evaluation in unconventional reservoirs is to estimate reservoir quality by quantifying the volumes of different fluid components. Spectroscopy-based tools can estimate the total organic carbon in a reservoir. Resistivity and dielectric tools are sensitive to the water-filled porosity. On the other hand, nuclear magnetic resonance (NMR) tools have the capability and sensitivity to further partition the hydrocarbon and water into fluid components based on their properties and geometry in the pore space.ğ‘‡_1−ğ‘‡_2 maps from NMR logging tools show uniquesignatures for hydrocarbons such as gas, bitumen, and producible and bound oil. Similarly, capillary and clay-bound water and water in larger pores have different signatures. These signatures depend on many factors: properties of the fluids (composition, viscosity), properties of the rock (pore geometry) and the geometrical configuration of fluid phases within the pore space. Unless the fluids have very distinct and non-overlapping signatures in the ğ‘‡_1−ğ‘‡_2 domain, it ischallenging to visually separate the contribution from different fluids and estimate fluid volumes from ğ‘‡_1−ğ‘‡_2 maps.This problem was addressed by an automated unsupervised learning algorithm called blind source separation (BSS), wherein the NMR ğ‘‡_1−ğ‘‡_2 maps of anentire logged interval are factorized into two matrices: the first matrix contains the ğ‘‡_1−ğ‘‡_2 signatures of thedifferent fluids and the second contains the corresponding volumes. This method has been shown to work well on multiple field data sets, where there was a sufficient dynamic range in the underlying volume fractions.In this paper, we address two well-known limitations in the BSS algorithm. First, the algorithm assumes a dynamic range in the volume fractions. For this reason, the entire logged interval is considered in the matrix factorization. However, doing so mixes the effects in ğ‘‡_1−ğ‘‡_2 maps due to changes in rock properties withchanges in fluid volumes. Second, it assumes that the number of sources (or fluids) is known a priori. This is a well-known ill-conditioned problem and is akin to model-order selection in the field of signal processing.In this paper, we propose several modifications in the algorithm to address the above two limitations. First, we leverage the information that the NMR signature of a fluid is expected to be connected in the ğ‘‡_1−ğ‘‡_2 domain.This expectation arises from the smoothness constraint imposed on the inversion algorithm used to compute the maps from the measured magnetization data as well as the underlying smooth distribution of the composition of crude oil. Second, we assume that each point in ğ‘‡_1−ğ‘‡_2 space corresponds at most to one fluid. Lastly, wepropose a quantitative metric to guide the analyst in selecting the number of components.The method consists of the following steps. First, we use the signal-to-noise ratio (SNR) in the data to obtain a rough estimate of the overall footprint of all the fluids. Second, a non-negative matrix factorization (NMF) technique is used to compute a footprint corresponding to the different fluids. A hierarchical clustering method is used to ensure that the footprint of each fluid is compact and connected in the ğ‘‡_1−ğ‘‡_2 domain.Subsampling of the maps is used to study the stability and compute the most likely number of fluids present. The last step consists of applying the mask corresponding to the different fluids to the measured ğ‘‡_1−ğ‘‡_2 maps to determine the fluid volumes.There are a few key advantages of this unsupervised learning method over other methods proposed in the literature. First, similar to BSS, it does not require predetermined information about cutoffs to distinguish fluids. Second, simulations show that the method does not require a wide variation in fluid volumes at different depths. This allows the petrophysicist to pick a relatively short depth interval consisting of one rock type to study ğ‘‡_1−ğ‘‡_2 map variations due to variations in fluidproperties. Last, it provides a metric to help guide the analyst in selecting the number of fluids in the underlying dataset. We demonstrate the application of this method on simulated datasets as well as field data sets from the Eagle Ford formation and Permian basin.