Remarks on Selecting Length of Cylindrical Sample to Determine Magnetic Properties of its Material

When experimentally studying magnetic properties of the ferromagnetic materials, preferences are often given to a more convenient method involving the use of sufficiently long cylindrical samples with the L length and the D diameter placed in the solenoid field as an alternative to the method based on using classical samples of the toroidal shape (to exclude manifestations of the demagnetizing factor). Currently, required justification is practically missing for specific values of the relative L/D length, which would indicate such [L/D] values (for L/D ≥ [L/D]), at which magnetic properties of a sample (already long enough) correspond to magnetic properties of its material. While the existing recommendations such as [L/D] = 50 are postulated, let us note that relevant experimental studies of magnetic properties of the cylindrical samples with the L/D parameter targeted variation were not made. An attempt was made to fill this gap. For cylindrical steel samples with the different L/D values (from 1 to 50), families of the B magnetic induction and of the μ permeability field dependencies were obtained experimentally using the ballistic method. The sought [L/D] values were determined from the B and μ dependencies on the L/D by the junction abscissa of the ascending and self-similar branches. It was established that in the accepted field strength in the range of H = 0.94--54.2 kА/m magnetizing field, the [L/D] parameter is a variable substantially depending on H (and/or μ). It varies from [L/D] = 10--15 at H = 54.2 kA/m (μ = 30) to [L/D] = 50--60 at H = 4.7 kA/m (μ = 270). And at H < 4.7 kA/m, [L/D] > 50--60, i.e., more than is commonly believed. Thus, it was stated that the data on magnetic properties obtained when using even long samples (L/D = 50) and declared as data on the magnetic properties of the corresponding material, are only close to those with H < 4.7 kA/m. Phenomenological expressions were obtained for the [L/D] determination: exponential with the H argument and logarithmic with the μ argument

Identification of the permeability field for three-dimensional reservoir using the results of geophysical well survey

A model problem of the permeability field identification for a three-dimensional reservoir opened by a large number of wells in the conditions of stationary single-phase fluid filtration is considered. The permeability field is determined in the process of solving the inverse coefficient problem by on known values of bottomhole pressure. The solving problem algorithm is constructed so that the proportionality coefficients of the layers permeability on wells obtained from the results of geophysical well survey are preserved. The influence of various types of errors on the identification results is studied.

Numerical Study of Density-Driven Convection in Laminated Heterogeneous Porous Media

ABSTRACTIn the present study, we use direct numerical simulation to investigate the density-driven convection in a two-dimensional anisotropic heterogeneous porous media associated with significant laminated formation. At first, the heterogeneous porous media are randomly generated to represent laminated structure, in which the horizontal correlation length of permeability field is much longer than the vertical counterpart. Then, a highly accurate pseudo-spectral method and compact finite difference scheme with higher order of accuracy are employed to numerically reproduce the convection flow in the laminated porous media. The results show that the laminated structures restrict interactions among the downward plumes of heavier fluid. The plumes tend to descend more straightly in a laminated porous medium associated with a slower growth rate. As a result, the laminated distribution of permeability is considered having an inhibiting effect on the convection flow.

A New Object-Based Algorithm To Simulate Geometrical and Petrophysical Turbidite Channel Properties

Summary An object-based algorithm that models turbidite channels using training images, called skeleton-based simulation or SKESIM, is proposed in this study. These images are interpreted as a graph and used to extract the statistical distribution of parameters selected from the graph. From this information, a 3D model of turbidite channel systems was built. These channels were generated within the turbidite lobe, creating a simulated depositional system. After the geometry of the channels were simulated by SKESIM, the petrophysical properties were mapped by Gaussian-like distributions. Numerical simulations were used to fit the simulated permeability field to a reference case through an objective function. A commercial finite difference simulator was used to compare the reference data to the simulated data, and comparable results were obtained.

Injectivity of Multiple Slugs in Surfactant Alternating Gas Foam EOR: A CT Scan Study

Summary A surfactant alternating gas (SAG) process is often the injection method for foam, on the basis of its improved injectivity over direct foam injection. In a previous study, we reported coreflood experiments on liquid injectivity after foam flooding and liquid injectivity after injection of a gas slug following steady-state foam. Results showed that a period of gas injection is important for the subsequent liquid injectivity. However, the effects of multiple gas and liquid slugs were not explored. In this paper, we present a coreflood study of injectivities of multiple gas and liquid slugs in an SAG process in a field core. Nitrogen and surfactant solution are either coinjected or injected separately into the sandstone core sample. The experiments are conducted at an elevated temperature of 90°C with a backpressure of 40 bar. Differential pressures are measured to quantify gas and liquid injectivities. Computed tomography (CT) scanning is applied to relate water saturation to mobility. During the injection of a large gas slug following foam, a bank in which foam completely collapses or greatly weakens forms near the inlet and propagates slowly downstream. During the subsequent period of liquid injection, liquid flows through the collapsed-foam bank much more easily than further downstream. Beyond the collapsed-foam region, liquid first imbibes into the whole cross section. In this region, liquid flows mainly through a finger of high liquid saturation. Our CT results suggest a revision of our earlier interpretation; the process of gas dissolution does not merely follow fingering but is evidently directly involved in the fingering process. Our results suggest that, in radial flow, the small region of foam collapse very near the well greatly improves injectivity. The subsequent gas and liquid slugs behave near the wellbore, affecting injectivity, in a way similar to the first slugs. Thus, the behavior and modeling of the first gas slug and first subsequent liquid slug is representative of near-well behavior in an SAG process. The trends observed in our previous work are reproduced in a low-permeability field core.

Model Input and Output Dimension Reduction Using Karhunen–Loève Expansions With Application to Biotransport

We consider biotransport in tumors with uncertain heterogeneous material properties. Specifically, we focus on the elliptic partial differential equation (PDE) modeling the pressure field inside the tumor. The permeability field is modeled as a log-Gaussian random field with a prespecified covariance function. We numerically explore dimension reduction of the input parameter and model output. Specifically, truncated Karhunen–Loève (KL) expansions are used to decompose the log-permeability field, as well as the resulting random pressure field. We find that although very high-dimensional representations are needed to accurately represent the permeability field, especially in presence of small correlation lengths, the pressure field is not sensitive to high-order KL terms of the input parameter. Moreover, we find that the pressure field itself can be represented accurately using a KL expansion with a small number of terms. These observations are used to guide a reduced-order modeling approach to accelerate computational studies of biotransport in tumors.