Denise E. Freed

Molecular Composition and Dynamics of Oils from Diffusion Measurements

We discuss examples and methods for using NMR diffusion measurements to obtain information about molecular sizes, their distributions, and dynamics. Scaling relationships between chain lengths and diffusion constants are derived and tested on diffusion measurements of many samples, including crude oils that are high in saturates. The diffusion constants of asphaltenes are also measured as a function of asphaltene concentration, indicating the formation of asphaltene aggregates at a concentration of approximately 0.2 g/L, and the sizes of the individual asphaltene molecules and aggregates are obtained. The examples and methods discussed in this paper can become the basis for in situ characterization of crude oils. Crude oils are complex mixtures of molecules encompassing a broad range of shapes and sizes.1−3 They include molecules ranging from alkanes, which are chain-like and relatively simple, to asphaltenes, which are complex and may interact strongly with one another.4 The composition determines the properties of crude oils, such as their viscosity and phase behavior. These properties are very important in the production of the oils. For example, the heavy oil components may precipitate and clog the formations and wells, depending on how oils are being lifted to the surface. There are several reasons why it is also important to characterize the composition of the oil in situ. First, many properties of the fluid depend critically on temperature and pressure, so it can be advantageous to make the measurements downhole. In some cases, oil samples even undergo irreversible changes as they are extracted from the well and transferred to the laboratory for analysis. Second, the fluid composition in a reservoir can exhibit large heterogeneity, and strong compositional gradients have been reported.5 Because downhole measurements

Interpretation of DFA Color Gradients in Oil Columns Using the Flory-Huggins Solubility Model

Downhole fluid analysis (DFA) has been successfully used to delineate reservoir attributes such as vertical and lateral connectivity and properties of the produced fluids. The new-generation DFA tools not only measure bulk fluid properties such as gas/oil ratio (GOR), density, and light-end compositions of CO2, C1, C2, C3–C5, and C6+ more accurately but also color (optical density) that is related to the heavy ends (asphaltenes and resins) in real time at downhole conditions. In addition, the color measurement is one of the most robust measurements in DFA. Therefore, color gradient analysis in oil columns becomes vital to discern reservoir complexities by means of integrating advanced asphaltene science with DFA Fluid Profiling. In this paper, a thermodynamic asphaltene grading model was developed to describe equilibrium distributions of heavy ends in oil columns using the multicomponent Flory-Huggins regular solution model combined with a gravitational contribution. The variations of oil properties such as molar volume, molar mass, solubility parameter, and density with depth were calculated by the equation of state (EOS). A three-parameter Gamma distribution function was employed to characterize asphaltene components. The primary factors governing asphaltene distribution in reservoirs are the gravitational term, which is determined in part by the size of the asphaltene molecular or colloidal particle, and the solubility term, which is determined in large part by the GOR. Consequently, it is critical to accurately measure both the fluid coloration and the GOR to understand the asphaltene distribution. The two field case studies showed that colored resins (asphaltene-like heavy resins) were molecularly dissolved in condensate oil columns whereas asphaltenes were dispersed as nanoaggregates in crude oils. The heavy ends (resins or asphaltenes) have a preference of going to the bottom of the oil column both because of gravity and the variation of the liquid-phase (live oil mixture) solubility parameter. The results obtained in this work were in accord with the observations in recent advances in asphaltene science. The asphaltene distributions were consistent with an equilibrium distribution implying reservoir connectivity. In both cases, the subsequent production data proved the reservoir connectivity and the methods developed herein were validated. This methodology establishes a new powerful approach for conducting DFA color and GOR gradient analyses by coupling advanced asphaltene science with DFA Fluid Profiling to address reservoir connectivity. Introduction In the past few decades, fluids in a hydrocarbon reservoir have been often assumed to be homogeneous in giant porous structures. However, there is now a growing awareness that fluids are frequently heterogeneous in different (small to large) hydrocarbonbearing sands. Reservoir fluids often demonstrate complexities in fluid compositions, properties, and phase behaviors owing to the impact of gravity, thermal gradients, biodegradation, active charging, water washing, leaky seals, and so on. Most of these mechanisms result in nonequilibrium or non-stationary state conditions in the reservoir and hence are very difficult to model. In addition, reservoir compartmentalization which is the biggest risk factor in deepwater oil production leads to discontinuous compositional and property distributions of hydrocarbon fluids. Thus compartments can be identified using downhole fluid analysis (DFA) and laboratory fluid analysis. Moreover, measurements of continuous and equilibrium distributions of reservoir fluids provide a new method to determine the connectivity of the reservoir. Because many of the processes acting on fluids are time-dependent, the existence of fluid gradients can yield understanding on relative rates of fluid movement in the reservoir, and

Mellin transform of CPMG data

This paper describes a new method for computing moments of the transverse relaxation time T(2) from measured CPMG data. This new method is based on Mellin transform of the measured data and its time-derivatives. The Mellin transform can also be used to compute the cumulant generating function of lnT(2). The moments of relaxation time T(2) and lnT(2) are related to petro-physical and fluid properties of hydrocarbons in porous media. The performance of the new algorithm is demonstrated on simulated data and compared to results from the traditional inverse Laplace transform. Analytical expressions are also derived for uncertainties in these moments in terms of the signal-to-noise ratio of the data.

The equivalence between off-resonance and on-resonance pulse sequences and its application to steady-state free precession with diffusion in inhomogeneous fields

We show that the spin dynamics of any pulse sequence with off-resonant pulses is identical to that of a modified sequence with on-resonant pulses, including relaxation and diffusion effects. This equivalence applies to pulse sequences with arbitrary offset frequency deltaomega(0) which may exceed the RF field strength omega(1). Using this approach, we examine steady-state free precession (SSFP) in grossly inhomogeneous fields. We show explicitly that the magnitude of the magnetization for each mode at an offset frequency deltaomega(0) is equal to that for SSFP with on-resonance pulses of rescaled amplitude, with the same dependence on relaxation times and diffusion coefficient. The rescaling depends on offset frequency and RF field strength. The theoretical results have been tested experimentally and excellent agreement is found.

Continuous moment estimation of CPMG data using Mellin transform

This paper provides a theoretical basis to directly estimate moments of transverse relaxation time T(2) from measured CPMG data in grossly inhomogeneous fields. These moments are obtained from Mellin transformation of the measured CPMG data. These moments are useful in computing petro-physical and fluid properties of hydrocarbons in porous media. Compared to the conventional method of estimating moments, the moments obtained from this method are more accurate and have a smaller variance. This method can also be used in other applications of NMR in inhomogeneous fields in characterizing fluids and porous media such as in the determination of hydrocarbon composition, estimation of model parameters describing relationship between fluid composition and measured NMR data, computation of error-bars on estimated parameters, as well as estimation of parameters and σ(lnT(2)) often used to characterize rocks. We demonstrate the performance of the method on simulated data.

ESTIMATION OF PETROPHYSICAL AND FLUID PROPERTIES USING INTEGRAL TRANSFORMS IN NUCLEAR MAGNETIC RESONANCE

In the past decade, low-field NMR relaxation and diffusion measurements in grossly inhomogeneous fields have been used to characterize properties of porous media, e.g., porosity and permeability. Pulse sequences such as CPMG, inversion and saturation recovery as well as diffusion editing have been used to estimate distribution functions of relaxation times and diffusion. Linear functionals of these distribution functions have been used to predict petro-physical and fluid properties like permeability, viscosity, fluid typing, etc. This paper describes an analysis method using integral transforms to directly compute linear functionals of the distributions of relaxation times and diffusion without first computing the distributions from the measured magnetization data. Different linear functionals of the distribution function can be obtained by choosing appropriate kernels in the integral transforms. There are two significant advantages of this approach over the traditional algorithm involving inversion of the distribution function from the measured data. First, it is a direct linear transform of the data. Thus, in contrast to the traditional analysis which involves inversion of an ill-conditioned, non-linear problem, the estimates from this new method are more accurate. Second, the uncertainty in the linear functional can be obtained in a straight-forward manner as a function of the signal-to-noise ratio (SNR) in the measured data. We demonstrate the performance of this method on simulated data.

Dispersion of T1 and T2 nuclear magnetic resonance relaxation in crude oils.

Crude oils, which are complex mixtures of hydrocarbons, can be characterized by nuclear magnetic resonance diffusion and relaxation methods to yield physical properties and chemical compositions. In particular, the field dependence, or dispersion, of T1 relaxation can be used to investigate the presence and dynamics of asphaltenes, the large molecules primarily responsible for the high viscosity in heavy crudes. However, the T2 relaxation dispersion of crude oils, which provides additional insight when measured alongside T1, has yet to be investigated systematically. Here we present the field dependence of T1-T2 correlations of several crude oils with disparate densities. While asphaltene and resin-containing crude oils exhibit significant T1 dispersion, minimal T2 dispersion is seen in all oils. This contrasting behavior between T1 and T2 cannot result from random molecular motions, and thus, we attribute our dispersion results to highly correlated molecular dynamics in asphaltene-containing crude oils.

The low-frequency dielectric response of charged oblate spheroidal particles immersed in an electrolyte

We study the low-frequency polarization response of a surface-charged oblate spheroidal particle immersed in an electrolyte solution. Because the charged spheroid attracts counterions which form the electric double layer around the particle, using usual boundary conditions at the interface between the particle and electrolyte can be quite complicated and challenging. Hence, we generalize Fixmans boundary conditions, originally derived for spherical particles, to the case of the charged oblate spheroid. Given two different counterion distributions in the thin electric double-layer limit, we obtain analytic expressions for the polarization coefficients to the first nontrivial order in frequency. We find that the polarization response normal to the symmetry axis depends on the total amount of charge carried by the oblate spheroid while that parallel to the symmetry axis is suppressed when there is less charge on the edge of the spheroid. We further study the overall dielectric response for a dilute suspension of charged spheroids. We find that the dielectric enhancement at low frequency, which is driven by the presence of a large ζ potential (surface charge), is suppressed by high ion concentrations in the electrolyte and depends on the size of the suspended particles. In addition, spheroids with higher aspect ratios will also lead to a stronger dielectric enhancement due to the combination of the electric double layer and textural effects. The characteristic frequency associated with the dielectric enhancement scales inversely with the square of the particle size, the major radius of the spheroid, and it has a weak dependence on the shape of spheroids.

A more accurate estimate of T2 distribution from direct analysis of NMR measurements.

In the past decade, low-field NMR relaxation and diffusion measurements in grossly inhomogeneous fields have been used to characterize pore size distribution of porous media. Estimation of these distributions from the measured magnetization data plays a central role in the inference of insitu petro-physical and fluid properties such as porosity, permeability, and hydrocarbon viscosity. In general, inversion of the relaxation and/or diffusion distribution from NMR data is a non-unique and ill-conditioned problem. It is often solved in the literature by finding the smoothest relaxation distribution that fits the measured data by use of regularization. In this paper, estimation of these distributions is further constrained by linear functionals of the measurement that can be directly estimated from the measured data. These linear functionals include Mellin, Fourier-Mellin, and exponential Haar transforms that provide moments, porosity, and tapered areas of the distribution, respectively. The addition of these linear constraints provides more accurate estimates of the distribution in terms of a reduction in bias and variance in the estimates. The resulting distribution is also more stable in that it is less sensitive to regularization. Benchmarking of this algorithm on simulated data sets shows a reduction of artefacts often seen in the distributions and, in some cases, there is an increase of resolution in the features of the T(2) distribution. This algorithm can be applied to data obtained from a variety of pulse sequences including CPMG, inversion and saturation recovery and diffusion editing, as well as pulse sequences often deployed down-hole.

A new approach for the estimation of the porosity in NMR

In this paper we describe a new approach for the estimation of the porosity and its uncertainty from Nuclear Magnetic Resonance relaxation measurements in porous media. The new approach is based on the Fourier transform of the measured data in √t domain. This approach was found to work reasonably well and had a smaller bias and variance in comparison to traditional methods of computing the porosity.