Steady-state and dynamic thermal models for heat flow analysis of silicon-on-insulator MOSFETs

2004 ◽  
Vol 44 (3) ◽  
pp. 381-396 ◽  
Author(s):  
Ming-C. Cheng ◽  
Feixia Yu ◽  
Lin Jun ◽  
Min Shen ◽  
Goodarz Ahmadi
Keyword(s):  
Steady State ◽  
Heat Flow ◽  
Flow Analysis ◽  
Silicon On Insulator ◽  
Thermal Models

Steady-State Parametric Optimization and Transient Characterization of Heat Flow Regulation With Binary Diffusion

2020 ◽  
Vol 10 (12) ◽  
pp. 1996-2007
Author(s):  
Tanya Liu ◽  
James W. Palko ◽  
Joseph S. Katz ◽  
Feng Zhou ◽  
Ercan M. Dede ◽  
...  
Keyword(s):  
Steady State ◽  
Heat Flow ◽  
Parametric Optimization ◽  
Flow Regulation ◽  
Binary Diffusion

Formation-Rate-Analysis Technique: Combined Drawdown and Buildup Analysis for Wireline Formation Test Data

1999 ◽  
Vol 2 (03) ◽  
pp. 271-280 ◽  
Author(s):  
Ekrem Kasap ◽  
Kun Huang ◽  
Than Shwe ◽  
Dan Georgi
Keyword(s):  
Numerical Simulation ◽  
Steady State ◽  
Field Data ◽  
Formation Rate ◽  
Flow Analysis ◽  
Early Time ◽  
Late Time ◽  
Time Data ◽  
Analysis Techniques ◽  
Conventional Analysis

Summary The formation-rate-analysis (FRASM) technique is introduced. The technique is based on the calculated formation rate by correcting the piston rate with fluid compressibility. A geometric factor is used to account for irregular flow geometry caused by probe drawdown. The technique focuses on the flow from formation, is applicable to both drawdown and buildup data simultaneously, does not require long buildup periods, and can be implemented with a multilinear regression, from which near-wellbore permeability, p * and formation fluid compressibility are readily determined. The field data applications indicate that FRA is much less amenable to data quality because it utilizes the entire data set. Introduction A wireline formation test (WFT) is initiated when a probe from the tool is set against the formation. A measured volume of fluid is then withdrawn from the formation through the probe. The test continues with a buildup period until pressure in the tool reaches formation pressure. WFTs provide formation fluid samples and produce high-precision vertical pressure profiles, which, in turn, can be used to identify formation fluid types and locate fluid contacts. Wireline formation testing is much faster compared with the regular pressure transient testing. Total drawdown time for a formation test is just a few seconds and buildup times vary from less than a second (for permeability of hundreds of millidarcy) to half a minute (for permeability of less than 0.1 md), depending on system volume, drawdown rate, and formation permeability. Because WFT tested volume can be small (a few cubic centimeters), the details of reservoir heterogeneity on a fine scale are given with better spatial resolution than is possible with conventional pressure transient tests. Furthermore, WFTs may be preferable to laboratory core permeability measurements since WFTs are conducted at in-situ reservoir stress and temperature. Various conventional analysis techniques are used in the industry. Spherical-flow analysis utilizes early-time buildup data and usually gives permeability that is within an order of magnitude of the true permeability. For p* determination, cylindrical-flow analysis is preferred because it focuses on late-time buildup data. However, both the cylindrical- and spherical-flow analyses have their drawbacks. Early-time data in spherical-flow analysis results in erroneous p* estimation. Late-time data are obtained after long testing times, especially in low-permeability formations; however, long testing periods are not desirable because of potential tool "sticking" problems. Even after extended testing times, the cylindrical-flow period may not occur or may not be detectable on WFTs. When it does occur, permeability estimates derived from the cylindrical-flow period may be incorrect and their validity is difficult to judge. New concepts and analysis techniques, combined with 3-D numerical studies, have recently been reported in the literature.1–7 Three-dimensional numerical simulation studies1–6 have contributed to the diagnosis of WFT-related problems and the improved analysis of WFT data. The experimental studies7 showed that the geometric factor concept is valid for unsteady state probe pressure tests. This study presents the FRA technique8 that can be applied to the entire WFT where a plot for both drawdown and buildup periods renders straight lines with identical slopes. Numerical simulation studies were used to generate data to test both the conventional and the FRA techniques. The numerical simulation data are ideally suited for such studies because the correct answer is known (e.g., the input data). The new technique and the conventional analysis techniques are also applied to the field data and the results are compared. We first review the theory of conventional analysis techniques, then present the FRA technique for combined drawdown and buildup data. A discussion of the numerical results and the field data applications are followed by the conclusions. Analysis Techniques It has been industry practice to use three conventional techniques, i.e., pseudo-steady-state drawdown (PSSDD), spherical and cylindrical-flow analyses, to calculate permeability and p* Conventional Techniques Pseudo-Steady-State Drawdown (PSSDD). When drawdown data are analyzed, it is assumed that late in the drawdown period the pressure drop stabilizes and the system approaches to a pseudo-steady state when the formation flow rate is equal to the drawdown rate. PSSDD permeability is calculated from Darcy's equation with the stabilized (maximum) pressure drop and the flowrate resulting from the piston withdrawal:9–11 $$k {d}=1754.5\left({q\mu \over r {i}\Delta p {{\rm max}}}\right),\eqno ({\rm 1})$$where kd=PSSDD permeability, md. The other parameters are given in Nomenclature.

Effect of Proximity of Permeable and Impermeable Lenses on Well Performance

1964 ◽  
Vol 4 (04) ◽  
pp. 285-290
Author(s):  
Edward P. Miesch ◽  
Paul B. Crawford
Keyword(s):  
Electrical Resistivity ◽  
Steady State ◽  
Production Capacity ◽  
Oil Reservoirs ◽  
Reservoir Rock ◽  
Unsteady State ◽  
Mathematical Study ◽  
Thermal Models ◽  
State Data ◽  
Resistivity Model

Abstract A study was made of the effect of permeable and impermeable lenses in a reservoir on the production capacity of a well. Both steady-state and unsteady-state data were obtained. An electrical resistivity model was used to obtain the steady- state data and thermal models were constructed to obtain the unsteady-state data. The productivity of a well is affected very greatly only when the lenses are close to the well. The effect of circular lenses on the Productivity ratio can be correlated with the distance from the center of the lens to the center of the well divided by the radius of the lens. Then this dimensionless distance is equal to six or greater, the effect of the lenses on production capacity will be negligible. The pseudo steady-state productivity of a heterogeneous reservoir can be predicted using steady- state data. Introduction Many analytical solutions of reservoir behavior assume that reservoir rock is uniform and homogeneous. Although this assumption is used, all of the data from core analyses and well logging indicate that the reservoirs are heterogeneous. Very little work has been done on the performance of heterogeneous reservoirs. The work of Landrum, et al. showed that transient phenomena in oil reservoirs could be studied with thermal models. Pickering and Cotman used thermal models to study flow in stratified reservoirs and investigated the effect of inhomogeneities in oil reservoirs on transient flow performance. Loucks made a mathematical study of the pressure build-up in a system composed of two concentric regions of different permeability. Root, Silberberg and Pirson studied the effect of me growth of the flooded region on water influx predictions using a thermal model consisting of three concentric cylindrical regions of different thermal properties which simulated the aquifer, the flooded region and the unflooded portion of the original hydrocarbon region. Tomme, et al. made a mathematical study of vertical fractures. The object of this investigation was to study the effect of highly permeable and impermeable lenses in the vicinity of the wellbore on the pressure depletion history of the well. Steady- state data were obtained for both conductive and nonconductive lenses that completely penetrated the formation. The lenses were symmetrically located at various distances from the wellbore. The unsteady-state data were obtained on seven thermal models. EXPERIMENTAL EQUIPMENT AND PROCEDURE STEADY-STATE DATA The steady-state data were obtained from an electrical resistivity model 30 in. in diameter and approximately 1 1/2 in. deep. The outside of the model was lined with a 30-in. diameter copper strip, which served as the outer boundary of the reservoir. The bottom was covered with a sheet of plexiglass so that it would be nonconductive. The model was filled with a slightly saline solution. The well size was varied from an 0.064-in. diameter copper wire to a 10-in. diameter copper cylinder. Readings were taken with an impedance bridge using AC current to prevent polarization at the contacts. Copper and wax lenses were used to represent infinitely conductive and nonconductive lenses, respectively. The resistance was first measured for each well diameter with no lenses in the reservoir. Then the conductive and nonconductive lenses were spaced symmetrically at various distances from the well and the resistance read from each lens location. The diameters of the conductive lenses were 3, 1.022 and 0.624 in., and those of the nonconductive lenses were 3, 2.25 and 1.563 in. SPEJ P. 285ˆ

scholarly journals Reconstructing bottom water temperatures from measurements of temperature and thermal diffusivity in marine sediments

2014 ◽  
Vol 11 (5) ◽  
pp. 2391-2422
Author(s):  
F. Miesner ◽  
A. Lechleiter ◽  
C. Müller
Keyword(s):  
Steady State ◽  
Heat Flow ◽  
Water Temperature ◽  
Marine Sediments ◽  
Bottom Water ◽  
Measured Data ◽  
Temperature History ◽  
Artificial Data ◽  
Bottom Water Temperature ◽  
Steady State Heat

Abstract. Temperature fields in marine sediments are studied for various purposes. Often, the target of research is the steady state heat flow as a (possible) source of energy but there are also studies attempting to reconstruct bottom water temperature variations to understand more about climate history. The bottom water temperature propagates into the sediment to different depths, depending on the amplitude and period of the deviation. The steady state heat flow can only be determined when the bottom water temperature is constant while the bottom water temperature history can only be reconstructed when the deviation has an amplitude large enough or the measurements are taken in great depths. In this work, the aim is to reconstruct recent bottom water temperature history such as the last two years. To this end, measurements to depths of up to 6 m shall be adequate and amplitudes smaller than 1 K should be reconstructable. First, a commonly used forward model is introduced and analyzed: knowing the bottom water temperature deviation in the last years and the thermal properties of the sediments, the forward model gives the sediment temperature field. Next, an inversion operator and two common inversion schemes are introduced. The analysis of the inversion operator and both algorithms is kept short, but sources for further reading are given. The algorithms are then tested for artificial data with different noise levels and for two example data sets, one from the German North Sea and one from the Davis Strait. Both algorithms show good and stable results for artificial data. The achieved results for measured data have low variances and match to the observed oceanographic settings. Lastly, the desired and obtained accuracy are discussed. For artificial data, the presented method yields satisfying results. However, for measured data the interpretation of the results is more difficult as the exact form of the bottom water deviation is not known. Nevertheless, the presented inversion method seems rather promising due to its accuracy and stability for artificial data. Continuing to work on the development of more sophisticated models for the bottom water temperature, we hope to cover more different oceanographic settings in the future.

scholarly journals Comparison of Solvers Performance for Load Flow Analysis

2019 ◽  
Vol 3 (1) ◽  
pp. 26 ◽  
Author(s):  
Vishnu Sidaarth Suresh
Keyword(s):  
Steady State ◽  
Power System ◽  
Reactive Power ◽  
Flow Analysis ◽  
Steady State Solution ◽  
Load Flow ◽  
State Solution ◽  
Computational Time ◽  
Load Flow Analysis ◽  
Active And Reactive Power

Load flow studies are carried out in order to find a steady state solution of a power system network. It is done to continuously monitor the system and decide upon future expansion of the system. The parameters of the system monitored are voltage magnitude, voltage angle, active and reactive power. This paper presents techniques used in order to obtain such parameters for a standard IEEE – 30 bus and IEEE-57 bus network and makes a comparison into the differences with regard to computational time and effectiveness of each solver

A mechanistic theory of ice lens formation in fine-grained soils

1980 ◽  
Vol 17 (4) ◽  
pp. 473-486 ◽  
Author(s):  
Jean-Marie Konrad ◽  
Norbert R. Morgenstern
Keyword(s):  
Steady State ◽  
Heat Flow ◽  
Freezing Temperature ◽  
Cold Side ◽  
Freezing Soil ◽  
Fine Grained ◽  
Mechanistic Theory ◽  
Two Parameters ◽  
Lens Formation

This study reveals that a freezing soil can be characterized by two parameters, the segregation-freezing temperature Ts and the overall permeability of the frozen fringe [Formula: see text]. During unsteady heat flow, the variation of these parameters with temperature produces rhythmic ice banding in fine-grained soils. At the onset of steady-state conditions, freezing tests conducted at a fixed warm end temperature showed that Ts was independent of the cold side step temperature. In addition, a model is presented that indicates how the overall permeability of the frozen fringe can be calculated without detailed measurements at the scale of the frozen fringe. It is also constant in the tests reported here.

Techniques to Create Compact Thermal Models — Steady State Problems

2014 ◽  
pp. 179-187
Author(s):  
Clemens Lasance ◽  
Mohammed-Nabil Sabry ◽  
Avram Bar-Cohen
Keyword(s):  
Steady State ◽  
Thermal Models
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