Dan Xiao

Two-dimensional T2 distribution mapping in rock core plugs with optimal k-space sampling.

Spin-echo single point imaging has been employed for 1D T(2) distribution mapping, but a simple extension to 2D is challenging since the time increase is n fold, where n is the number of pixels in the second dimension. Nevertheless 2D T(2) mapping in fluid saturated rock core plugs is highly desirable because the bedding plane structure in rocks often results in different pore properties within the sample. The acquisition time can be improved by undersampling k-space. The cylindrical shape of rock core plugs yields well defined intensity distributions in k-space that may be efficiently determined by new k-space sampling patterns that are developed in this work. These patterns acquire 22.2% and 11.7% of the k-space data points. Companion density images may be employed, in a keyhole imaging sense, to improve image quality. T(2) weighted images are fit to extract T(2) distributions, pixel by pixel, employing an inverse Laplace transform. Images reconstructed with compressed sensing, with similar acceleration factors, are also presented. The results show that restricted k-space sampling, in this application, provides high quality results.

Velocity field measurements in sedimentary rock cores by magnetization prepared 3D SPRITE

A time-efficient MRI method suitable for quantitative mapping of 3-D velocity fields in sedimentary rock cores, and granular samples is discussed. The method combines the 13-interval Alternating-Pulsed-Gradient Stimulated-Echo (APGSTE) scheme and three-dimensional Single Point Ramped Imaging with T(1) Enhancement (SPRITE). Collecting a few samples near the q-space origin and employing restricted k-space sampling dramatically improves the performance of the imaging method. The APGSTE-SPRITE method is illustrated through mapping of 3-D velocity field in a macroscopic bead pack and heterogeneous sandstone and limestone core plugs. The observed flow patterns are consistent with a general trend for permeability to increase with the porosity. Domains of low permeability obstruct the flow within the core volume. Water tends to flow along macroscopic zones of higher porosity and across zones of lower porosity.

Restricted k-space sampling in pure phase encode MRI of rock core plugs.

In the study of rock core plugs with multidimensional MRI, the samples are of a regular cylindrical shape that yields well defined intensity distributions in reciprocal space. The high intensity k-space points are concentrated in the central region and in specific peripheral regions. A large proportion of the k-space points have signal intensities that are below the noise level. These points can be zero-filled instead of being collected experimentally. k-space sampling patterns that collect regions of high intensity signal while neglecting low intensity regions can be naturally applied to a wide variety of pure phase encoding measurements, such as T2 mapping SESPI, hybrid-SESPI and SPRITE, since all imaging dimensions can be under-sampled. With a shorter acquisition time, as fewer experimental data points are required, the RF and gradient duty cycles are reduced, while the image SNR is improved.

Mapping three-dimensional oil distribution with π-EPI MRI measurements at low magnetic field.

Magnetic resonance imaging (MRI) is a robust tool to image oil saturation distribution in rock cores during oil displacement processes. However, a lengthy measurement time for 3D measurements at low magnetic field can hinder monitoring the displacement. 1D and 2D MRI measurements are instead often undertaken to monitor the oil displacement since they are faster. However, 1D and 2D images may not completely reflect the oil distribution in heterogeneous rock cores. In this work, a high-speed 3D MRI technique, π Echo Planar Imaging (π-EPI), was employed at 0.2T to monitor oil displacement. Centric scan interleaved sampling with view sharing in k-t space was employed to improve the temporal resolution of the π-EPI measurements. A D2O brine was employed to distinguish the hydrocarbon and water phases. A relatively homogenous glass bead pack and a heterogeneous Spynie core plug were employed to show different oil displacement behaviors. High quality 3D images were acquired with π-EPI MRI measurements. Fluid quantification with π-EPI compared favorably with FID, CPMG, 1D-DHK-SPRITE, 3D Fast Spin Echo (FSE) and 3D Conical SPRITE measurements. π-EPI greatly reduced the gradient duty cycle and improved sensitivity, compared to FSE and Conical SPRITE measurements, enabling dynamic monitoring of oil displacement processes. For core plug samples with sufficiently long lived T2, T2(∗), π-EPI is an ideal method for rapid 3D saturation imaging.

π Echo-Planar Imaging with concomitant field compensation for porous media MRI.

The π Echo Planar Imaging (PEPI) method was modified to compensate for concomitant magnetic fields by waveform symmetrization. Samples with very short T2(∗) (a few hundred microseconds) and short T2 (tens of milliseconds to hundreds of milliseconds) were investigated. Echo spacings as short as 1.2 ms were achieved with the gradient pre-equalization method, enabling rapid 3D imaging of short relaxation time species with sub-millimeter resolution. The PEPI method yields superior quality images, compared to the Fast Spin Echo (FSE) method, with significantly reduced gradient duty cycle. Accelerated PEPI measurements with a variable number of centric interleaves are presented. Restricted k-space sampling was demonstrated for specific sample geometries, notably a Locharbriggs sandstone core plug, with the acquisition time further reduced. These methods generate proton density weighted images considering the echo time to sample T2 ratio. These methods are principally designed for 3D studies of fluid saturation in rock core plugs, evolving in time due to some manner of external perturbation, such as water flooding.

k-t acceleration in pure phase encode MRI to monitor dynamic flooding processes in rock core plugs.

Monitoring the pore system in sedimentary rocks with MRI when fluids are introduced is very important in the study of petroleum reservoirs and enhanced oil recovery. However, the lengthy acquisition time of each image, with pure phase encode MRI, limits the temporal resolution. Spatiotemporal correlations can be exploited to undersample the k-t space data. The stacked frames/profiles can be well approximated by an image matrix with rank deficiency, which can be recovered by nonlinear nuclear norm minimization. Sparsity of the x-t image can also be exploited for nonlinear reconstruction. In this work the results of a low rank matrix completion technique were compared with k-t sparse compressed sensing. These methods are demonstrated with one dimensional SPRITE imaging of a Bentheimer rock core plug and SESPI imaging of a Berea rock core plug, but can be easily extended to higher dimensionality and/or other pure phase encode measurements. These ideas will enable higher dimensionality pure phase encode MRI studies of dynamic flooding processes in low magnetic field systems.

Monitoring oil displacement processes with k‐t accelerated spin echo SPI

Magnetic resonance imaging (MRI) is a robust tool to monitor oil displacement processes in porous media. Conventional MRI measurement times can be lengthy, which hinders monitoring time‐dependent displacements. Knowledge of the oil and water microscopic distribution is important because their pore scale behavior reflects the oil trapping mechanisms. The oil and water pore scale distribution is reflected in the magnetic resonance T2 signal lifetime distribution. In this work, a pure phase‐encoding MRI technique, spin echo SPI (SE‐SPI), was employed to monitor oil displacement during water flooding and polymer flooding. A k‐t acceleration method, with low‐rank matrix completion, was employed to improve the temporal resolution of the SE‐SPI MRI measurements. Comparison to conventional SE‐SPI T2 mapping measurements revealed that the k‐t accelerated measurement was more sensitive and provided higher‐quality results. It was demonstrated that the k‐t acceleration decreased the average measurement time from 66.7 to 20.3 min in this work. A perfluorinated oil, containing no 1H, and H2O brine were employed to distinguish oil and water phases in model flooding experiments. High‐quality 1D water saturation profiles were acquired from the k‐t accelerated SE‐SPI measurements. Spatially and temporally resolved T2 distributions were extracted from the profile data. The shift in the 1H T2 distribution of water in the pore space to longer lifetimes during water flooding and polymer flooding is consistent with increased water content in the pore space. Copyright

T2 selective π Echo-Planar Imaging for porous media MRI

The π Echo Planar Imaging (PEPI) method has recently been modified to permit proton density imaging of fluids in porous media with moderate T2 and short T2∗ signal components. In many applications, it is desirable to discriminate multiple T2 components within each image voxel. T2 selective imaging is explored in this paper through adiabatic inversion as a magnetization preparation with PEPI readout. When prior information of the sample relaxation times is known, responses of different species to broadband adiabatic inversion pulses can be predicted by Bloch equation simulation. Different relaxation components can be acquired by combining the images with and without inversion preparation pulses. T2 weighting can be easily introduced in the PEPI sequence by shifting the spatial encoding gradients based on its spin echo nature. T2 decay curves can be extracted for each image voxel from a series of T2 weighted images and spatially resolved T2 distributions can be generated. This method is reliable but slow. The two methods were implemented to image porous media samples with PEPI the common basis of spatial resolution. The results of both methods agree remarkably well.

Hybrid-SPRITE MRI.

In a FID based frequency encoding MRI experiment the central part of k-space is not generally accessible due to the probe dead time. This portion of k-space is however crucial for image reconstruction. SPRITE (Single Point Ramped Imaging with T1 Enhancement), SPI with a linearly ramped phase encode gradient, has been employed to image short relaxation time systems for many years with great success. It is a robust imaging method in significant measure because it provides acquisition of high quality k-space origin data. We propose a new sampling scheme, termed hybrid-SPRITE, combining phase and frequency encoding to ensure high quality images with reduced acquisition times, reduced gradient duty cycle and increased sensitivity. In hybrid-SPRITE, numerous time domain points are collected to assist image reconstruction. An Inverse Non-uniform Discrete Fourier Transform (INDFT) is employed in 1D applications. A pseudo-polar grid is exploited in 2D hybrid-SPRITE for rapid and accurate image reconstruction.