Gaseous unsteady-state radial flow behavior from the calculated results of Bruce et al

1999 ◽  
pp. 231-285
Author(s):  
E.J. Hoffman
1985 ◽  
Vol 25 (06) ◽  
pp. 804-822 ◽  
Author(s):  
Jeffrey A. Joseph ◽  
Leonard F. Koederitz

Abstract This paper presents short-time interpretation methods for radial-spherical (or radial-hemispherical) flow in homogeneous and isotropic reservoirs inclusive of wellbore storage, wellbore phase redistribution, and damage skin effects. New dimensionless groups are introduced to facilitate the classic transformation from radial flow in the sphere to linear flow in the rod. Analytical expressions, type curves (in log-log and semilog format), and tabulated solutions are presented, both in terms of pressure and rate, for all flow problems considered. A new empirical equation to estimate the duration of wellbore and near-wellbore effects under spherical flow is also proposed. Introduction The majority of the reported research on unsteady-state flow theory applicable to well testing usually assumes a cylindrical (typically a radial-cylindrical) flow profile because this condition is valid for many test situations. Certain well tests, however, are better modeled by assuming a spherical flow symmetry (e.g., wireline formation testing, vertical interference testing, and perhaps even some tests conducted in wellbores that do not fully penetrate the productive horizon or are selectively penetrate the productive horizon or are selectively completed). Plugged perforations or blockage of a large part of an openhole interval may also promote spherical flow. Numerous solutions are available in the literature for almost every conceivable cylindrical flow problem; unfortunately, the companion spherical problem has not received as much attention, and comparatively few papers have been published on this topic. papers have been published on this topic. The most common inner boundary condition in well test analysis is that of a constant production rate. But with the advent of downhole tools capable of the simultaneous measurement of pressures and flow rates, this idealized inner boundary condition has been refined and more sophisticated models have been proposed. Therefore, similar methods must be developed for spherical flow analysis, especially for short-time interpretations. This general problem has recently been addressed elsewhere. Theory The fundamental linear partial differential equation (PDE) describing fluid flow in an infinite medium characterized by a radial-spherical symmetry is (1) The assumptions incorporated into this diffusion equation are similar to those imposed on the radial-cylindrical diffusivity equation and are discussed at length in Ref. 9. In solving Eq. 1, the classic approach is illustrated by Carslaw and Jaeger (later used by Chatas, and Brigham et al.). According to Carslaw and Jaeger, mapping b=pr will always reduce the problem of radial flow in the sphere (Eq. 1) to an equivalent problem of linear flow in the rod for which general solutions are usually known. (For example, see Ref. 17 for particular solutions in petroleum applications.) Note that in this study, we assumed that the medium is spherically isotropic; hence k in Eq. 1 is the constant spherical permeability. This assumption, however, does not preclude analysis in systems possessing simple anisotropy (i.e., uniform but unequal horizontal and vertical permeability components). In this case, k as used in this paper should be replaced by k, an equivalent or average (but constant) spherical permeability. Chatas presented a suitable expression (his Eq. 10) obtained presented a suitable expression (his Eq. 10) obtained from a volume integral. It is desirable to transform Eq. 1 to a nondimensional form, thereby rendering its applicability universal. The following new, dimensionless groups accomplish this and have the added feature that solutions are obtained directly in terms of the dimensionless pressure drop, PD, not the usual b (or bD) groups. ......................(2) .......................(3) .........................(4) The quantity rsw is an equivalent or pseudospherical wellbore radius used to represent the actual cylindrical sink (or source) of radius rw. SPEJ p. 804


1976 ◽  
Author(s):  
Heber Cinco L. ◽  
F. Samaniego V. ◽  
N. Dominguez A.

Author(s):  
F. J. Wallace ◽  
G. P. Blair

The study of the pulsating-flow behavior of small inward radial-flow turbines as used in automotive type turbosuperchargers is of great importance in relation to the mode of operation of such units in conjunction with internal-combustion engines. In complete engine-turbocharger systems detailed analysis of turbine behavior is handicapped by the complex interaction of engine and turbocharger, with resultant interdependence of operating variables. In the present investigation the use of a rotary valve driven at various predetermined speeds and discharging cold air under critical conditions ensures close control of the pressure pulses constituting the turbine-energy input. It has therefore been possible to investigate systematically the influence of the most important parameters, viz., (a) pulse frequency, (b) pulse form, (c) pulse amplitude, (d) pipe length, (e) pipe diameter, and (f) turbine speed.


1977 ◽  
Vol 17 (04) ◽  
pp. 271-280 ◽  
Author(s):  
A.S. Odeh

Abstract An analytic solution for pseudosteady-state flow of an oil well with limited entry and with an altered zone is derived. Wells that are open to flow along a traction of their productive interval, and that have a wellbore surrounded by a zone whose physical characteristics have been altered because of damage or improvement, are termed wells with limited entry and an altered zone. The finite cosine transform was used to solve the partial differential equations that describe the behavior of the physical system. The solution was programmed for the CDC 6400 computer, and many programmed for the CDC 6400 computer, and many computer runs covering a wide range of variables were made. The results were used to reduce the complicated analytical solution to a simple approximate solution that permits the engineer to account easily for the combined effect of limited entry and altered zone on the pseudosteady-state flow behavior of an oil well. Introduction This paper reports the derivation of an analytical relation between drawdown and flow rate for a well producing under pseudosteady-state flow with producing under pseudosteady-state flow with restricted entry to flow and with an altered zone around the wellbore. "Altered zone" refers to a zone whose permeability and/or porosity values have been changed because of mud damage, acidizing, or sand consolidation, for example. The effect of an altered zone around the wellbore on the calculation of the productive capacity of a well is normally accounted for by introducing a skin factor, s, in the proper flow equations. Hawkins developed an algebraic expression relating the wellbore radius, the altered-zone radius and permeability, and the reservoir permeability to s. Hawkins' equation assumes radial flow into the wellbore. This implies that the well is open to flow along the total length of the productive interval. Flow into the wellbore when only a fraction of the productive interval is open to flow, with or without an altered zone, is not radial. The common practice of using Hawkins' equation in such cases practice of using Hawkins' equation in such cases to calculate s could lead to highly erroneous results. For example, the flow rate calculated for a well producing under pseudosteady state, with restricted producing under pseudosteady state, with restricted entry and with an altered zone and using a skin factor calculated by Hawkins' equation, can be too high by more than 100 percent. Rowland and Jones and Watts introduced a correction factor into Hawkins' equation to account for the effect of nonradial flow behavior around the wellbore. Hawkins' skin value is multiplied by ht/hp, where ht is the total thickness of the productive interval and hp is the length of the productive interval and hp is the length of the interval open to flow at the wellbore. The ht/hp correction factor is based on the assumption that the flow into the wellbore is radial in the altered zone opposite the open interval. This implies that the nonradial components of flow into the wellbore are negligible. Using model studies, Jones and Watts showed that the error introduced in the calculated skin values by neglecting the nonradial components of flow is less than 20 percent in the worst case. Furthermore, they proposed a modified equation to eliminate this error. The suitability of the radial flow assumption upon which the factor ht/hp is based depends on the values of many variables such as the radius of the altered zone and its permeability, and the length of the open interval. Because of their discretized nature, numerical models at times do not accurately represent the physical flow pattern around the wellbore. Most models assume the flow to be radial between the wellbore and the adjacent cells, regardless of whether part or all of the productive interval is open to flow. Therefore, results from model studies may not be adequate to define the limits of applicability of the modification to the radial flow formula, such as the ht/hp correction factor. One purpose of the work reported in this paper is to define these limits. paper is to define these limits. The analytic solution is very complex and is not suited for engineering work. Because of this, it was programmed for the CDC 6400 computer, and many computer runs were made. SPEJ P. 271


2006 ◽  
Vol 2006.12 (0) ◽  
pp. 343-344
Author(s):  
Ippei SUZUKI ◽  
Kazuma SATO ◽  
Yoshitaka MUKAI ◽  
Kazumi TSUNODA
Keyword(s):  

Author(s):  
Dewasish BISWAS ◽  
Hiroyuki YAMASAKI ◽  
Takao MATSUI ◽  
Yoshinori SAITO ◽  
Susumu SHIODA
Keyword(s):  

2014 ◽  
Vol 12 (1) ◽  
pp. 497-512 ◽  
Author(s):  
Fang-Zhi Xiao ◽  
Zheng-Hong Luo

Abstract Based on a complete CFD Eulerian–Eulerian two-fluid approach, a comprehensive three-dimensional (3D) two-phase reactor model was suggested to describe the flow behavior in radial flow moving-bed reactors (RFMBRs). A porous media model was incorporated into the reactor model in order to describe the flow resistance provided by the porous walls of the center and annular pipes. Compared with these previous reactor models, the reactor model considers the solid-phase movement instead of immobilization, which benefits for predicting the formation of cavity practically. The simulation results are agreement with the published experimental data. By employing the verified model, the flow field parameters in the reactors such as pressure drop and flow velocity were obtained. Besides, the simulations were then carried out to investigate the effect of the bed voidage on the flow behavior and to understand the phenomenon of cavity in the RFMBRs. The simulation results showed that both the centripetal and the centrifugal flow configurations have the inhomogeneous flow distribution and the phenomenon of cavity. Furthermore, the inhomogeneous distribution increases with the increase of the bed voidage, whereas the phenomenon of cavity is more obvious with the increase of gas inlet velocity. As a whole, this work provided a realistic modeling and a useful approach for the understanding of RFMBRs.


Author(s):  
J. P. Feser ◽  
A. K. Prasad ◽  
S. Advani

A radial flow device was fabricated to experimentally characterize the in-plane flow behavior of gas diffusion layers (GDL). Radial flow of gas and liquid through the GDL result in the same permeability values. Finally, four types of commercially available GDL are characterized at various levels of compression.


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