Related Fluid Flow Research Articles

Attenuation and dispersion of compressional waves in fluid‐filled porous rocks with partial gas saturation (White model)—Part II: Results

In this investigation, Biot’s (1962) theory for wave propagation in porous solids is applied to study the velocity and attenuation of compressional seismic waves in partially gas‐saturated porous rocks. The Physical model, proposed by White (1975), is solved rigorously by using Biot’s equations which describe the coupled solid‐fluid motion of a porous medium in a systematic way. The quantitative results presented here are based on the theory described in Dutta and Odé (1979, this issue). We removed several of White’s questioned approximations and examined their effects on the quantitative results. We studied the variation of the attenuation coefficient with frequency, gas saturation, and size of gas inclusions in an otherwise brine‐filled rock. Anomalously large absorption (as large as 8 dB/cycle) at the exploration seismic frequency band is predicted by this model for young, unconsolidated sandstones. For a given size of the gas pockets and their spacing, the attenuation coefficient (in dB/cycle) increases almost linearly with frequency f to a maximum value and then decreases approximately as 1/√f. A sizable velocity dispersion (of the order of 30 percent) is also predicted by this model. A low gas saturation (4–6 percent) is found to yield high absorption and dispersion. An analysis of all of the field variables (stresses and displacements) is presented in terms of Biot’s type I (the classical compressional) wave and type II (the diffusion) wave. It is pointed out that the dissipation of energy in this model is mainly due to the relative fluid flow from the type II wave. From our formulation, many of White’s equations can be derived as suitable approximations, and it is shown that the discontinuity in fluid pressure assumed by White at the gas‐water interface is the discontinuity in the fluid pressure contribution by the type II wave. Our quantitative results are in reasonably good agreement with White’s (1975) approximate theory. However, the phase velocities computed by White’s approximate treatment do not approach the correct zerofrequency limit (Gassmann‐Wood) when compared to the present theory. Most of these disagreements disappear if the corrections to White’s theory as suggested by Dutta and Seriff (1979, this issue) are incorporated.

Heat/Mass Transfer Characteristics for Flow in a Corrugated Wall Channel

Experiments based on the naphthalene sublimation technique were carried out to determine the local and average transfer characteristics for flow in a corrugated wall channel. The range of the experiments encompassed the laminar, transition, and low-Reynolds-number turbulent regimes. Local mass transfer measurements were made both in the spanwise (i.e., cross stream) and streamwise directions, and overall transfer rates were also determined. The experiments demonstrated the existence of a variety of complex transfer processes and related fluid flow phenomena. These included secondary flows and associated spanwise mass transfer variations, suppression of the secondary flow by counteracting centrifugal forces, and destruction of the secondary flow by the onset of turbulence. Flow separation on the leeward facets of the corrugated wall caused a sharp decrease in the local transfer rates, but relatively high transfer rates were in evidence in the reattachment region. In the laminar range, the average transfer coefficients for the corrugated wall channel were only moderately larger than those for a parallel-plate channel. On the other hand, in the low-Reynolds-number turbulent regime, the wall corrugations were responsible for an increase of nearly a factor of three in the average coefficient compared with the smooth wall channel.

Influence of lung inflation on respiratory control in neonates.

Influence of lung inflation on respiratory control in neonates.

Calculation of the Production Rate of a Thermally Stimulated Well

Abstract This paper presents a method for calculating the producing rate of a well as a function of time following steam stimulation. The calculations have proved valuable in both selecting wells for stimulation and in determining optimum treatment sizes. The heat transfer model accounts for cooling of the oil sand by both vertical and radial conduction. Heat losses for any number of productive sands separated by unproductive rock are calculated for the injection, shut-in and production phases of the cycle. The oil rate increase caused by viscosity reduction due to heating is calculated by steady-state radial flow equations. The response of successive cycles of steam injection can also be calculated with this method. Excellent agreement is shown between calculated and actual field results. Also included are the results of several reservoir and process variable studies. The method is best suited for wells producing from a multiplicity of thin sands where the bulk of the stimulated production comes from the unheated reservoir. The flow equations used neglect gravity drainage and saturation changes within the heated region. Introduction This paper presents a calculation method which can be used to predict the field performance of the cyclic steam stimulation process. The calculation method enables the engineer to select reservoirs that have favorable characteristics for steam stimulation and permits him to determine how much steam must be injected to achieve favorable stimulation. While the calculation represents a considerable simplification of physical reality and the results are subject to numerous assumptions which must be made about the reservoir, it has been found that realistic calculations can be made of individual well performance following steam injection. The duration of the stimulation effect will depend primarily on the rate at which the heated oil sand cools which, in turn, is determined by the rate at which energy is removed from the formation with the produced fluids and conducted from the heated oil sand to unproductive rock. A complete mathematical solution to this problem is a formidable task, and finite difference techniques would undoubtedly have to be used. The calculation method presented here utilizes analytic solutions of simple related heat transfer and fluid flow problems. The method is sufficiently simplified that it can be used as a hand calculation, although the calculations are somewhat lengthy and laborious. For that reason, the analysis was programmed for an IBM 7044 digital computer. Well responses observed at the Quiriquire field in eastern Venezuela have been matched using this program after making suitable approximations for reservoir and wellbore conditions. One of the most valuable uses of this calculation method is to assess the effect of reservoir and process variables on the stimulation response. This paper contains results of several studies made of key reservoir and process parameters. Among the most important of these is the influence of prior wellbore permeability damage. If a well is severely damaged prior to stimulation, a higher stimulation response will be observed than if it is undamaged. If a portion of this damage is removed, a permanent rate improvement will occur. THEORY DESCRIPTION OF CALCULATION METHOD The process of cyclic steam stimulation is essentially one of reducing oil viscosity around the wellbore by heating for a limited distance out into the formation through the injection of steam. Suitable modifications of the calculation technique presented here can be made so that stimulation of wells by hot gas injection or in situ combustion can also be calculated. A schematic drawing of the heat transfer and fluid flow considerations included in the calculation method is shown in Fig. 1. In brief, the calculation assumes that the oil sand is uniformly and radially invaded by injected steam. For wells producing from several sands, each sand is assumed to be invaded to the same distance radially. In calculating the radius heated r, energy losses from the wellbore and conduction to impermeable rock adjacent to the producing sands are taken into account. After steam injection is stopped, heat conduction continues and oil sands with r less than r cool as previously unheated shale and oil sand at r greater than r begin to warm. The effect of warming of oil sand out beyond r has little effect on the oil production rate compared to the effect of cooling of the oil sand nearer the wellbore than r. Thus, in computing the oil production rate, an idealized step function temperature distribution in the reservoir is assumed where the original temperature exists for r greater than r and where an average elevated temperature exists for r less than r . JPT P. 1613ˆ