Because of the importance of chemical flooding operations, the mechanisms of chemical dispersion and adsorption in porous media are of increasing interest to the petroleum industry. This paper presents a mathematical model for simulating presents a mathematical model for simulating chemical transport phenomena in porous rocks; these phenomena include dispersion and either Langmuir phenomena include dispersion and either Langmuir equilibrium or rate-controlled adsorption. The accuracy of this numerical model was verified by comparing the calculated results with those obtained by analytical solutions for a number of limiting cases. The effects of dimensionless dispersion, adsorptive capacity, flow rate, and kinetic rate groups controlling dispersion/adsorption mechanisms were investigated. The utility of the model was demonstrated further by matching experimental results. When adsorption of a chemical is rate-controlled or time-dependent, core flood data obtained at times much shorter than reservoir residence times can lead to a serious underestimation of chemical requirements for the field projects. Introduction Chemical dispersion and adsorption in porous media are of increasing interest to the petroleum industry because of the increasing importance of chemical flooding operations. While dispersion causes mixing and dissipation of a chemical slug, adsorption can result in a real chemical loss to the reservoir; the ultimate success of a chemical recovery process is controlled by the nature and magnitude of the loss. Although diffusion and dispersion have been studied extensively during the past two decades, publications on the adsorption of chemical recovery publications on the adsorption of chemical recovery agents have been limited. The relatively simple case of adsorption of a gas on a clean, homogeneous, solid surface illustrates the complexity of the adsorption phenomenon. The adsorption can be purely physical, purely chemisorption, a combination of physical, purely chemisorption, a combination of both, or an intermediate type. The adsorption of polymer and surfactant solutions on porous rocks is polymer and surfactant solutions on porous rocks is complicated by the physiochemical properties of the solutions and rocks and by the nature of the pore structure of the rock matrix. Nevertheless, adsorption from dilute aqueous-phase solutions can be described by the Langmuir equilibrium isotherm for a variety of chemicals, including many surfactants and polymers. These chemicals can sometimes exhibit adsorptions that are significantly rate-controlled or time-dependent rather than instantaneous. The classical model for rate-controlled adsorption was proposed by Langmuir. This paper presents numerical solutions to the transport equations for dispersion and adsorption in porous media, considering Langmuir equilibrium porous media, considering Langmuir equilibrium adsorption as well as Langmuir rate-controlled adsorption. The effects of various process parameters on adsorption also were investigated. parameters on adsorption also were investigated. Model Development Transport Equations A chemical transport equation chacterizing dispersion and adsorption of a chemical solution flowing through a porous medium can be derived by a mass balance as follows. 2C q C C 1- CrD ----- - ---- --- = ----- + ---- pr -----.x2 A x t t...................................(1) The dispersion coefficient, D, can be expressed as qD= (---)= u.................................(2)A SPEJ P. 129
Shales are important constituents of petroleum systems, and it is necessary to study their petrophysical properties as both reservoir components and as seals. Nuclear magnetic resonance has proven to be a good technique for measuring the reservoir engineering properties of rocks. This paper presents measurements of NMR relaxation in shales. It establishes that shale petrophysical information is accessible using standard NMR lab techniques employed in the oil industry. Even for good seals, shale porosity and pseudo-capillary pressure curves can be derived from NMR relaxation data. This opens the question as to whether NMR logging can be used to ascertain seal quality for oil and gas storage reservoirs and for CO2 disposal reservoirs. NMR measurements were performed in a low field spectrometer primarily on shales characterizing seals. Multiexponential T2 and T1 relaxation rates were determined from CPMG and inversion recovery experiments, respectively. Mean log T2 values of the undersaturated samples were about 0.4 ms. The T2 relaxation times increased after the shales were saturated but remained below 2 ms. Porosity for each sample was derived from the T2 magnetization and calibrated against a standard. Since NMR detects total porosity, the porosity was generally larger than that determined from laboratory gas flow-saturation techniques. The T2 relaxation rate distributions were normalized using the total magnetization calibration and integrated from the larger times to yield pseudo-capillary pressure curves. Introduction This study focuses on the applicability of the NMR to derive petrophysical properties to shales. Shales can be found in any of the constituents of the petroleum systems as seals, in reservoir rocks, or as source rocks. In any of these scenarios, it is fundamental to estimate porosity, permeability, fluid saturations, or capillary pressure. Common logging tools, such as resistivity, neutron and density logs, are sensitive to the presence of shales; therefore, NMR can be a valuable tool to study their properties1. A secondary objective of this investigation is to evaluate the capabilities of NMR in estimating seal quality of shales, which is fundamental to any exploratory or production study, as well as in environmental investigations, as for example the search of a well-sealed disposal aquifer for use in CO2 sequestration of residual gas from power plants. A more long-range objective might be to develop the ability to assess shale fabric while drilling by using a measurement-while-drilling NMR tool.
The thermal force on a sphere of insulating material centered between parallel plates has been measured in the three monatomic gases He, Ne, and Ar and the two diatomic gases N2 and HD over a broad range of mean free paths. These measurements are on a finite system, an apparatus where the sphere radius and the plate spacing are of the same order of magnitude. Behavior near the observed maximum of the thermal force is stressed. The translational heat flux characterizes the dependence of the thermal force on the gas. Comparison with existing theories is made for the three basic Knudsen regimes, and the data are compared to previous measurements of the thermal force on aerosols.
The characterization of surfactant candidates for a given reservoir can be improved by the use of linear coreflood residual-oil-saturation profiles measured along the core after chemical flooding. A surfactant formulation's functional relation of oil recovery to slug size can be calculated from a single coreflood with the assumption of a relaxed scaling law. A volumetric linear scaling approach is developed from laboratory coreflood data. Residual-oil-saturation profiles measured in reservoir material with a microwave absorption instrument support this approximate scaling relation. Analysis of 32 linear surfactant-slug corefloods is presented as additional verification. The limits of this scaling law are defined, with emphasis on the role of mixing and dispersion. The procedure for using saturation profiles to calculate oil recovery as a function of slug size is developed and a test case is presented. A recovery relation derived from a single coreflood saturation profile is compared with that determined by multiple conventional corefloods. Introduction Many techniques and instruments are now available for noninvasive measurement of oil/brine saturations along linear cores during secondary and tertiary displacement experiments, these are reviewed briefly in Ref. 1. The most popular recent method is based on the microwave absorption properties of water. Such saturation- profile measurements provide much more information on a given chemical-flood experiment than can be collected merely from effluent material balance. This abundance of data can be used in two ways: to determine relations that would otherwise have to be developed laboriously from many separate conventional corefloods and to develop predictive capability for estimating surfactant- flood performance in new situations. Both applications are possible as an outgrowth of the concept of volumetric linear scaling for chemical flooding proposed by Parsons and Jones. This relaxed scaling technique is supported by the data of Ref. 6 and a wide variety of conventional and scanned corefloods presented in this work. A process can be defined as volumetrically linearly scalable if the fluid compositions and saturations at any point in the matrix at any time are functions only of the PV of fluids injected relative to that point with respect to the injection point. This can be stated simply for a single slug of surfactant: a given-PV slug of surfactant will produce the same compositions and saturation distributions in a core of any physical shape and size. Moreover, a 0. 10-PV slug injected into a 2-m core will produce the same composition and saturation distribution in the first meter of that core as would be produced over the entire length of a 1-m core that had seen a 0.20-PV slug. This is a trivial-but not an obvious-view of the recovery process. Limitations to this relative-sizing concept are discussed in the following paragraph. SPEJ P. 511^
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