Barbara Anderson

An efficient solution for the response of electrical well logging tools in a complex environment

A symmetrical form of the solution for an electrical source in a multibed well-logging environment is derived. The method uses local reflection and transmission operators of a single-bed boundary and a general recursive algorithm to derive generalized reflection and transmission operators. Using this method, the computation time scales linearly as N, where N is the number of beds in the environment. A computer program was developed to implement the solution. The program is robust and generates accurate results from 20 kHz to 25 MHz. >

Electrical anisotropy due to gas hydrate-filled fractures

In 2006, the Indian National Gas Hydrate Program Expedition01,orNGHP-01,discoveredgashydrateasfillinnearvertical fractures in unconsolidated sediments at several drillingsitesontheIndiancontinentalmargins.Thesegashydrate-filled fractures were identified on logging-while-drilling resistivity images. The gas hydrate-filled fracture intervals coincide with high measured resistivity at the NGHP-01 sites. High measured resistivity translates into high hydrate saturationsviaArchie’sequation;however,thesehighsaturations contradict lower gas hydrate saturations determined from pressure core and chlorinity measurements.Also, in intervalswithnear-verticalgashydrate-filledfractures,thereis considerable separation between phase shift and attenuation resistivity logs, with 2-MHz resistivity measurements being significantly higher than 400-kHz resistivity measurements. We modeled the sensitivity of the propagation resistivity measurements in the gas hydrate-filled fracture intervals at NGHP-01 Sites 5 and 10. Near-vertical hydrate-filled fracturescancausetheabnormallyhighresistivitymeasurements in vertical holes due to electrical anisotropy. The model suggests the gas hydrate saturations in situ are usually significantlylowerthanthosecalculatedfromArchie’sequation.In addition, these modeled gas hydrate saturations generally agree with the lower gas hydrate saturations obtained from pressure core and chlorinity measurements at NGHP-01 Sites5and10.

Simulation of induction logging by the finite-element method

The response of an electromagnetic induction logging tool passing through many invaded thin beds is simulated by the finite‐element method. This simulation has achieved high accuracy by using a difference potential which enables the transmitter‐receiver mutual coupling to be treated analytically. Consequently the removal of the mutual coupling from the induction tool response has no numerical ill effects. The finite‐element model is truncated at a very large distance with a zero field outside the model. In order to achieve both accuracy and computational efficiency, the grid is projected to the truncation surface by gradually increasing its size according to an estimated error analysis of the finite‐element method. The numerical results were verified against analytical solutions for limiting cases and excellent agreement was obtained. In the presence of skin effect, which is beyond Doll’s analysis by geometrical factory theory, the finite‐element solution conveniently provides a way to check and improve t...

A Formative Evaluation of Shared Family Mealtime for Parents of Toddlers and Young Children

Shared family mealtime offers numerous health benefits for young children. Unfortunately, only a few studies examine the benefits and barriers to eating together as a family. The present study seeks to fill this gap in the literature by applying the health belief model to understand parents perceptions about the challenges of preparing and executing family mealtime for toddlers and young children. Six focus groups were conducted with parents of toddlers and/or young children (nu2009=u200924). Results revealed that parents identified several benefits to shared family mealtime, including good teaching moments for their children, enhanced family connectedness, and encouraging nutritious meals. Parents also identified barriers to eating together as a family, including child behavioral issues, scheduling difficulties, and ill-prepared husbands. The risks associated with not eating together as a family were seldom mentioned; however, parents highlighted several issues related to self-efficacy, such as difficulty in selecting meals and challenges with cooking. Potential cues to action include print materials encouraging parents by emphasizing the benefits of eating together as a family. Results are discussed with an emphasis on message design strategies for health practitioners interested in advocating this important yet under-studied phenomenon.

Computation of transient electromagnetic waves in inhomogeneous media

A brief summary of the methods of solving transient electromagnetic wave problems in inhomogeneous media will be given. The two distinct general techniques, which are the inverse Fourier transformation of time-harmonic solutions and the direct time-domain formulation, will be illustrated by way of two examples. In the first example, an efficient numerical mode-matching method to obtain the response of an electromagnetic source in a two-dimensional cylindrical inhomogeneity is described. Using this method, the solution is first obtained in the frequency domain. The time-domain solution is then found by inverse Fourier transforming the frequency-domain solution. In the second method, a finite-difference scheme is used to find the transient response of a point source in a two-dimensional inhomogeneity. Two different methods are proposed to treat the source region singularity. Transmitting boundary conditions are applied on the walls of the finite difference grid so that a finite-sized box can be used to model an infinite region.

An integral transform solution to the fundamental problem in resistivity logging

This paper develops the analysis necessary for the computation of the response of a resistivity tool within a well bore as it traverses a thin‐invaded bed. The solution for the potential induced by a steady current source (point current electrode) is formulated in terms of both Fourier cosine and Fourier sine transforms with arbitrary coefficients. A suitable matching of the necessary boundary conditions results in a system of singular integral equations. An iterative solution (Neumann series) is obtained for these transform coefficients which, in turn, are used to determine the potential at an arbitrary point of measurement. The theory is applied to some typical focused resistivity tools, and the results are found to be in close agreement with similar results obtained via a resistor network (analog) solution.

Modeling low-frequency electrode-type resistivity tools in invaded thin beds

The authors formulate and implement a numerical mode-matching (NMM) method to model electrode-type resistivity tools in invaded thin beds. The authors derive the low-frequency approximation of the Maxwells equations to obtain the partial differential equation for the potential field. The new NMM program is validated by comparing the numerical results with those obtained from other dc programs. It is found that this new program is much faster than the program using the finite-element method (FEM), and hence is useful for routine interpretation of resistivity logs and for inversion. >

Transient response of some borehole mandrel tools

The response of transient mandrel tools in realistic well‐logging environments is simulated by first solving the problem analytically in the frequency domain using an efficient high‐speed computer model. Gaussian pulses of reasonable bandwidths are assumed. The geometry modeled includes a borehole, invasion layers, and bed boundaries. Both TE and TM type sources are considered. The resulting receiver voltages, displayed in variable‐density log (VDL) format, yield visually interpretable information regarding signal amplitude and attenuation. The speed and generality of the analytical model makes this approach practical for analyzing tool response in a wide variety of logging geometries. Preliminary results generated by this model demonstrate that transient electromagnetic logging tools have the potential to yield useful information for characterizing the conductivity and dielectric constant of beds penetrated by a wellbore. In the future, the model could be helpful in validating signal processing and data ...

A full wave analysis of wave propagation in multiregion, cylindrically stratified media

The wave scattering problem for a general multiregion, cylindrically stratified medium is formulated using the numerical mode matching method. The excitation of the wave is assumed to be axially symmetric and, hence, the field in the cylindrical structure will also have axial symmetry. A computer program has been developed for a general multiregion, vertically stratified medium, with arbitrarily many layers in both the vertical and the horizontal directions. Some numerical results are presented to demonstrate the use of this method. The efficiency of this method is about 100 times higher than that of the finite-element method. The computation time is linear in N, where N is the number of regions.<<ETX>>

Modeling low-frequency electrode-type resistivity tools in 2-D formations

Derives the low-frequency approximation of the Maxwells equations to obtain the partial differential equation for the potential field. The authors then formulate and implement a numerical mode-matching (NMM) method to solve this two-dimensional potential field in order to model electrode-type resistivity tools in invaded thin beds. The new NMM program is validated by comparing the numerical results with those obtained from other DC programs. It is found that this new program is much faster than the program using the finite-element method (FEM), and hence is useful for routine interpretation of resistivity logs. The authors illustrate one application of the NMM program with an inversion of multiple field logs.<<ETX>>