A NEW DIRECTIONAL PERMEABILITY MODEL COMBINING NMR AND DIRECTIONAL RESISTIVITY MEASUREMENTS FOR COMPLEX FORMATIONS

摘要

Conventional permeability models based on MercuryInjection Capillary Pressure (MICP) curves, such as theKatz-Thompson model, require estimation ofmicroscopic length parameters from core MICPexperiments. In wells lacking core data, these modelscannot be applied to estimate permeability. On the otherhand, conventional Nuclear Magnetic Resonance(NMR) permeability models can provide consecutivepermeability assessment along the wellbore, but theyare often unreliable in complex formations. We hereinpropose a new model for depth-by-depth directionalpermeability assessment in complex formations, bycombining borehole NMR and directional electricalresistivity measurements.The objectives of this paper are (a) to introduce a newNMR characteristic T_2 value to represent thecharacteristic length in real pore size distribution thatcontrols rock permeability, (b) to establish a newdirectional permeability model combining NMR anddirectional resistivity measurements, and (c) to test thereliability of the new model for permeabilityassessment in formations with multi-modal porosity(e.g. carbonate and tight sandstone formations).We numerically simulate the directional permeability,directional formation resistivity factor (FRF), and NMRT_2 relaxation curves, in 202 digital rock samples usingour state-of-the-art pore-scale simulation software. Thedigital rock samples are obtained by multi-scaleimaging on real rock samples, including dolostone,limestone, chalk, (tight) carbonate, (tight) sandstone,and sandpack samples. The simulated directionalpermeability is treated as the target reference for eachdigital rock sample.Next, we define a new NMR characteristic T_2 value torepresent the microscopic length parameter in real poresize distribution. The new NMR characteristic T_2 valueis minimally influenced by diffusional coupling effectthat distorts NMR T_2 distribution in multi-modal poresystems, and we numerically and theoreticallydemonstrate this property. Then we develop a newNMR-Resistivity model to estimate directionalpermeability by combining NMR characteristic T_2 anddirectional FRF. The new permeability model iscalibrated on 32 digital rock samples and successfullytested on the other 170 samples, with permeabilityranging from 8.4×10~(-5) mD to 48000 mD, spanning tenorders of magnitude. Results show that the modelestimatedpermeability is in good agreement with thetarget permeability for all rock types.Furthermore, we compare the model-predictedpermeability with lab permeability on 16 carbonate coresamples. We upscale the NMR characteristic T_2 andFRF from pore-scale to core-scale, and then estimatethe core-scale permeability by the proposed NMRResistivitymodel. Excellent agreement between themodel-estimated and lab permeability demonstrates thereliability of the new model on the core scale.Our proposed permeability model can be applied towells with NMR and directional resistivity logs,overcoming the requirement for core measurements. Itprovides accurate and consecutive directionalpermeability assessment along the wellbore. It alsoshows a potential in estimating relative permeability inhydrocarbon-bearing formations. The outcomes of thisresearch can significantly improve permeabilityassessment in complex reservoirs with multi-modalporosity, including carbonate, tight sandstone, andorganic-rich source rocks.