Flow in Heterogeneous Porous Media

1961 ◽  
Vol 1 (03) ◽  
pp. 153-169 ◽  
Author(s):  
J.E. Warren ◽  
H.S. Price
Keyword(s):  
Effective Permeability ◽  
Transient Flow ◽  
Spatial Configuration ◽  
Geometric Mean ◽  
Laboratory Data ◽  
Heterogeneous Porous Media ◽  
Physical Models ◽  
Core Analysis ◽  
Specific Distribution ◽  
The Individual

Abstract Techniques for studying the performance characteristics of heterogeneous reservoirs have been developed. The effect of permeability variation on both the steady-state and the transient flow of a single fluid has been investigated. Limited comparisons with field and laboratory data have been made. The physical models studied consist of random three-dimensional arrays of homogeneous porous blocks. The permeabilities of the individual elements are assigned according to a specific distribution function; uniform anisotropy is introduced by varying the relative dimensions of the blocks. A particular model is perturbed simply by re-arranging its elements at random. The behavior of a physical model is determined by digitally solving its numerical analogue. Based on computational experiments, subject to the restrictions implied by the assumptions that were made, the following general conclusions have been drawn.The most probable behavior of a heterogeneous system approaches that of a homogeneous system with a permeability equal to the geometric mean of the individual permeabilities.The effects of flow geometry and anisotropy on the most probable value of the effective permeability of a heterogeneous medium are finite but not significant.The permeability determined from a pressure build-up curve for a heterogeneous reservoir gives a reasonable value for the effective permeability of the drainage area.A qualitative measure of the degree of heterogeneity and its spatial configuration are obtained from a comparative study of core analysis and pressure build-up data. It has been indicated that these conclusions are predicated on the assumption that the core analysis and the pressure build-up data represent true reservoir characteristics. Common sources of error in these data have been discussed. Introduction One of the most significant problems of reservoir engineering is that of determining the nature and the disposition of the heterogeneities that inevitably occur in petroliferous formations. It is with this problem that this paper is concerned.

A Vertical Permeability Study

1972 ◽  
Vol 12 (03) ◽  
pp. 199-205 ◽  
Author(s):  
G.R. Hollabaugh ◽  
R.A. Slotboom
Keyword(s):  
Effective Permeability ◽  
Geometric Mean ◽  
Water Injection ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Analysis Data ◽  
Area Ratio ◽  
Core Analysis ◽  
Vertical Permeability ◽  
Permeability Study

Abstract A vertical permeability study was performed on three Rainbow field cores to examine the effect of crossflow on vertical permeability and to determine the best method for averaging vertical permeabilities. The study consisted essentially of a series of permeability measurements that were made as whole cores were progressively cut into smaller pieces. Results show that crossflow does contribute to vertical permeability. Further, the effect of crossflow varies inversely with the length-to-area ratio of the cores and is a very important factor to consider when determining a formation vertical permeability. Formation vertical permeabilities determined from the usual core analysis results are probably low because crossflow bas been minimized by using cores with a relatively high length-to-area ratio. For this reason, a more representative formation vertical permeability can be obtained by using a greater number of shorter permeability samples. As expected, the harmonic average of a series of core vertical permeabilities was found to best approximate the core permeability itself. The geometric average of the same permeabilities was found to be more representative of the formation where crossflow contributes to the vertical permeability. Introduction The Rainbow field was discovered in northwestern Alberta in 1965 and is presently comprised of some 50 separate reef reservoirs. Production is primarily from the Middle Devonian Keg River formation that lies at a depth of about 6,000 ft. Most of these reefs have high-vertical-relief (up to 600 ft) oil-bearing zones that usually are underlain by an aquifer and are sometimes capped by an initial gas cap. The production mechanism in these reservoirs, whether it be primary depletion or pressure maintenance by gas, solvent, or water injection, will therefore be gravity controlled and drainage will be predominantly in a vertical direction. Under these conditions, the vertical permeability of the reservoir will be a major factor in determining recovery efficiencies. Knowledge of the representative vertical permeability of the reservoir is therefore important to predict recovery efficiencies. Like other limestone reef formations, the Keg River is very heterogeneous, containing vugs, caverns, stylolites, and fractures. Because of the heterogeneities, it is difficult to determine the representative formation vertical permeability value from core analysis data. This paper deals with an attempt to determine the degree of contribution of crossflow to vertical permeability and to determine the best method for averaging vertical permeabilities. Some work in the same broad category has been done in the past. Cardwell and Parsons indicated that the effective permeability in a radial system of heterogeneous sands lies between an upper and lower limit approximated by the arithmetic and harmonic averages, respectively. Warren and Price concluded from computational experiments that the most probable effective permeability value of a heterogeneous system can be approximated by the geometric mean. More recently, Lishman arrived at several of our conclusions in his computer study simulating a three-dimensional random arrangement of isotropic permeability cells. LABORATORY STUDY PROCEDURE Routine whole-core analyses had been performed on a number of cores from the Rainbow field. Based on the permeability values obtained from these analyses, three cores were selected to give as great a range of permeability values as possible. To ensure thorough cleanliness, the cores were flushed with various solvents until the effluent was no longer discolored. The samples were then dried in an oven for several days at a temperature of 130 degrees F. The permeability to nitrogen was then determined for each sample. For this measurement and all subsequent measurements, a Hassler sleeve-type core holder was used to hold and seal the cores while making permeability determinations. SPEJ P. 199ˆ

scholarly journals When Resources Are Scarce - Feasibility of Emergency Ventilation of Two Patients With One Ventilator

2020 ◽  
Author(s):  
Peter C. Reinacher ◽  
Thomas E. Schlaepfer ◽  
Martin A. Schick ◽  
Jürgen Beck ◽  
Hartmut Bürkle ◽  
...  
Keyword(s):  
Tidal Volume ◽  
Respiratory System ◽  
Breathing Circuit ◽  
Absolute Error ◽  
Physical Models ◽  
Respiratory System Mechanics ◽  
Emergency Ventilation ◽  
Artificial Lungs ◽  
Circuit Components ◽  
The Individual

AbstractA potential shortage of intensive care ventilators has led to the idea to ventilate more than one patient with a single ventilator. Besides other problems, this is associated with the lack of knowledge concerning distribution of tidal volume and the patients’ individual respiratory system mechanics.In this study we used two simple hand-manufactured adaptors to connect physical models of two adult respiratory systems to one ventilator. The artificial lungs were ventilated in the pressure-controlled mode and we investigated if disconnecting one lung from the ventilation circuit for several breaths would allow to determine reliably the other lung’s tidal volume and compliance.Compliances and volumes were measured both with the ventilator and external sensors corresponded well. However, tidal volumes measured via the ventilator were smaller compared to the tidal volumes measured via the external sensors with an absolute error of 5.3 ± 2.5%. The tidal volumes of the individual artificial lungs were distributed in proportion to the compliances and did not differ relevantly when both artificial lungs were connected to when one was disconnected.We conclude that in case of emergency, ventilation of two patients with one ventilator requires two simple hand-crafted tubes as adaptors and available standard breathing circuit components. In such a setting, respiratory system mechanics and tidal volume of each individual patient can be reliably measured during short term clamping of the tracheal tube of the respective other patient.

New evidence for the life habit of graptoloids from physical modelling

Paleobiology ◽  
1989 ◽  
Vol 15 (4) ◽  
pp. 402-413 ◽  
Author(s):  
Susan Rigby ◽  
Barrie Rickards
Keyword(s):  
Narrow Band ◽  
Physical Modelling ◽  
Physical Models ◽  
Life Habit ◽  
Passive Rotation ◽  
Directional Motion ◽  
Mode Of Life ◽  
The Individual ◽  
New Evidence ◽  
Colony Shape

Physical models of graptolites have been constructed for a range of morphologies, with emphasis on planar, multiramous forms. The models are life size and have the density of a living graptolite, based on the now-established collagenous nature of the periderm and unavoidable assumptions about the amount of extrathecal tissue present in the living colony. These models have been used to test the two main hypotheses of graptolite life habit developed by Bulman, Rickards, Kirk, and others. Testing of graptoloid models in water suggests that many rhabdosome shapes were designed for passive rotation within the water column. This is caused in the models by a variety of modifications, including changes in thecal and stipe orientation, alterations of colony shape and the addition of vanes and hooks. Rotation would only have been useful when the rhabdosome was in directional motion and the frequency of such modifications seems anomalous if no such movement occurred. Thus movement by some means is required, either passively, by changes in buoyancy, or by automobility. Spiralling action would increase the harvesting path of an individual living on a planar, multiramous colony, making this a theoretically advantageous mode of life for the morphology. It would prevent the individual zooids of scandent biserial and uniserial colonies from feeding from the same narrow band of water.

Evaluation of the Pertussis Components of Diphtheria-Tetanus-Pertussis Vaccine

PEDIATRICS ◽  
1983 ◽  
Vol 71 (2) ◽  
pp. 200-205
Author(s):  
M. Dianne Murphy ◽  
Jeane Rasnack ◽  
Harold D. Dickson ◽  
Marc Dietch ◽  
Philip A. Brunell
Keyword(s):  
Pertussis Vaccine ◽  
Geometric Mean ◽  
Aluminum Phosphate ◽  
The United States ◽  
Geometric Mean Titer ◽  
Whole Cell ◽  
Pertussis Antigen ◽  
Dtp Vaccine ◽  
Local Reactions ◽  
The Individual

The adjuvant and antigen components of the pertussis fraction of diphtheria-tetanus-pertussis (DTP) vaccine were evaluated. Four preparations of DTP vaccine composed of either whole cell (Wc) or extracted (E) pertussis antigen combined with either an aluminum phosphate (Ph) or alum (Al) adjuvant were compared. Local reactions were similar in all four vaccines after the first two immunizations but were significantly increased in incidence and severity following the third immunization with vaccine WcPh. This appeared to be due to the Ph adjuvant rather than the antigen component. Febrile reactions were experienced more often (P = .0009) and with higher temperatures (P = .0001) with the WcPh vaccine following the first immunization. This appeared to be due to the Wc component. Comparing the pooled Wc groups with the pooled E groups revealed a greater febrile response in the Wc group after both the first (P = .0008) and the second (P = .03) immunization. Local reactions appear temporally and etiologically to be distinct from febrile reactions. The pooled Wc antigen group produced a higher geometric mean titer than the pooled E antigen group (P = .05). Serologic responses, with respect to geometric mean titer, were not significantly different among the individual vaccines. This study suggests that the combination of whole cell and aluminum phosphate, which is currently in use in the United States, is probably not the optimal formulation for pertussis vaccine.

scholarly journals Splenomegaly in relation to Schistosoma mansoni egg counts: a population based study

1986 ◽  
Vol 28 (6) ◽  
pp. 389-394 ◽  
Author(s):  
Maria Fernanda Furtado de Lima e Costa ◽  
R. S. Bocha ◽  
Naftale Katz
Keyword(s):  
Geometric Mean ◽  
Age Groups ◽  
Individual Case ◽  
Population Based ◽  
Control Analysis ◽  
Ecological Data ◽  
Cross Sectional Survey ◽  
Cross Sectional ◽  
Individual Analysis ◽  
The Individual

A cross: sectional survey on schistosomiasis was done in Comercinho (Minas Gerais State, Brazil), a town with 1474 inhabitants. Stool (Kato-Katz method) and physical examinations were done on 90% of the population and on 84% of the individuals over 2 years of age, respectively. The ecological and individual (case-control) analysis were used to investigate the relation between splenomegaly and S. mansoni egg counts in different age groups. In the ecological analysis there was a clearly correspondence between higher geometric mean of eggs and higher percentage of splenomegaly in the age groups 5-9 and 10-12 years. In the individual analysis it was found that only in the youngest individuals (5-8 or 5-9 years old) the splenomegaly was related with higher mean egg counts in the feces, having been a tendency to the decrease of excretion of eggs in patients with splenomegaly as the age increased. These results strongly suggest that the ecological data are' better indicator of the severity of schistosomiasis in endemic areas, as the decrease of the egg excretion in patients with splenomegaly may be a confounding variable for the individual analysis.

scholarly journals Estimates for the Effective Permeability of Intact Granite Obtained from the Eastern and Western Flanks of the Canadian Shield

Minerals ◽  
2020 ◽  
Vol 10 (8) ◽  
pp. 667
Author(s):  
A. P. S. Selvadurai ◽  
A. Blain-Coallier ◽  
P. A. Selvadurai
Keyword(s):  
Effective Permeability ◽  
Computational Models ◽  
Granitic Rock ◽  
Geometric Mean ◽  
Surface Region ◽  
Canadian Shield ◽  
Surface Permeability ◽  
Experimental Values ◽  
The One ◽  
High Level

Granitic rock from the western part of the Canadian Shield is considered as a potential host rock for the siting of a deep geological repository for the storage of heat-emitting high-level nuclear fuel waste. The research program focused on the use of surface permeability measurements conducted at 54 locations on a 300 mm cuboid of granite, obtained from the Lac du Bonnet region in Manitoba, to obtain an estimate for the effective permeability of the cuboid. Companion experiments are conducted on a 280 mm cuboid of granite obtained from Stanstead, Quebec, located in the eastern part of the Canadian Shield. The surface permeabilities for the cuboids of granite are developed from theoretical relationships applicable to experimental situations where steady flow is initiated at a sealed annular surface region with a pressurized central domain. The experimental values for the surface permeability are used with a kriging procedure to estimate the permeability variations within the cuboidal region. The spatial variations of permeability are implemented in computational models of the cuboidal regions to determine the one-dimensional permeabilities in three orthogonal directions. The effective permeability of the granite cuboids is estimated by appeal to the geometric mean. The research provides a non-destructive methodology for estimating the effective permeability of large specimens of rock and the experiments performed give estimates for the effective permeability of the two types of granitic rock obtained from the western and eastern flanks of the Canadian Shield.

scholarly journals Comprehensive Solution for Transient Flow in Heterogeneous Porous Media

2016 ◽  
Vol 113 (3) ◽  
pp. 549-566 ◽  
Author(s):  
Ricardo Hüntemann Deucher ◽  
Paulo Couto ◽  
Gustavo César Rachid Bodstein
Keyword(s):  
Porous Media ◽  
Transient Flow ◽  
Heterogeneous Porous Media

A phase I dose escalation and pharmacokinetic study of BIBF 1120 in combination with paclitaxel and carboplatin in patients with advanced gynecological malignancies

2007 ◽  
Vol 25 (18_suppl) ◽  
pp. 3561-3561 ◽  
Author(s):  
P. Harter ◽  
J. Huober ◽  
J. Pfisterer ◽  
P. Wimberger ◽  
S. Loibl ◽  
...  
Keyword(s):  
Phase I ◽  
Dose Escalation ◽  
Geometric Mean ◽  
Tumor Therapy ◽  
Plasma Concentrations ◽  
Hematological Toxicity ◽  
Gynecological Malignancies ◽  
Gynecologic Tumor ◽  
The Individual ◽  
Bibf 1120

3561 Background: BIBF 1120 is an oral triple angiokinase inhibitor targeting VEGFR, PDGFR, FGFR kinases which might be interesting targets for gynecologic tumor therapy. Therefore, we performed a phase I study to evaluate maximal tolerated dose (MTD), safety, and pharmacokinetics (PK) of twice daily BIBF 1120 in combination with carboplatin AUC 5 and paclitaxel 175 mg/m2 q21 (CP) in patients with advanced or recurrent gynecological malignancies. Methods: 6 courses of CP and escalating bid doses of BIBF 1120 (2x100 mg to 2x250 mg) on the days without i.v. chemotherapy were administered. A 3 + 3 dose escalation design was followed. An additional cohort of 6 pts was treated on the MTD level. Results: Twenty-three pts were enrolled and 21 pts were treated with at least one cycle of CP and BIBF 1120. At 2x250 mg of BIBF 1120, two pts developed reversible CTCAE °3 and °4 elevations of AST and ALT in the first treatment course. MTD was determined as 200 mg BIBF 1120 bid for the combination with CP. Within the other dose cohorts (2x100 mg, n= 3, 2x150 mg, n= 4, 2x200 mg, n= 13) no dose limiting toxicities were observed. There was no increase in hematological toxicity with the addition of BIBF 1120 compared to standard CP. Further non-hematological °3 toxicities were: diarrhea (n=4), ascites (n=1), dyspnoe (n=1), nausea (n=3).Thus far, the PK profiles of carboplatin, paclitaxel, and BIBF 1120 have been evaluated in seven pts (2x100 mg, n=3 and 2x150 mg, n=4). There was no significant change of the individual and geometric mean plasma concentrations of C and P before and after 3 weeks of continuous daily bid dosing with BIBF 1120. Conclusions: BIBF 1120 can be given safely at a dose of 200 mg bid together with standard doses of CP in pts with advanced gynecological malignancies. Preliminary PK analyses did not reveal any interaction of CP and BIBF 1120. [Table: see text]

ON THE GEOMETRY OF RADIO REFLECTIONS FROM AURORA

1960 ◽  
Vol 38 (5) ◽  
pp. 593-603 ◽  
Author(s):  
P. A. Forsyth
Keyword(s):  
Pulse Duration ◽  
Spatial Configuration ◽  
Beam Width ◽  
Volume Scattering ◽  
Antenna Beam ◽  
The Individual ◽  
Optical Evidence ◽  
Aspect Sensitivity

By assuming that auroral radio reflections are produced by volume scattering in clouds of ionization having the same spatial configuration as the visible auroral structures, and by taking into account the radar pulse duration and antenna beam width, it is possible to predict the probability of echo occurrence as a function of range and azimuth. This echo distribution is quite similar to that observed experimentally even when "aspect sensitivity" of the individual scatterer is neglected. Unfortunately, the optical evidence is not sufficiently extensive to permit precise calculations to be made, nor the radio evidence to permit detailed comparisons, but previous estimates of the shape of the scattering structures that have been based on the azimuthal echo distribution without regard to the factors discussed here are likely to be seriously in error.

A model for transient flow in porous media embedded with randomly distributed tree-shaped fractal networks

2015 ◽  
Vol 29 (19) ◽  
pp. 1550135 ◽  
Author(s):  
Xiao-Hua Tan ◽  
Xiao-Ping Li ◽  
Jian-Yi Liu ◽  
Lie-Hui Zhang ◽  
Jianchao Cai
Keyword(s):  
Porous Media ◽  
Transient Flow ◽  
Heterogeneous Porous Media ◽  
Flow In Porous Media ◽  
Inversion Method ◽  
Type Curves ◽  
Fractal Properties ◽  
Proposed Model ◽  
The Laplace Transform ◽  
Fractal Characteristics

A model for transient flow in porous media embedded with randomly distributed tree-shaped fractal networks was presented based on the fractal properties of tree-shaped capillaries and generalized Darcy's law. The dimensionless expression of flowing pressure was developed using the Laplace transform and Stehfest numerical inversion method. The bilogarithmic type curves were illustrated and the influences of different fractal factors on dimensionless flowing pressure were also discussed. The presented study indicated that the fractal characteristics for the tree-shaped fractal networks should be considered in analysis of transient flow in the heterogeneous porous media. The proposed model may be conducible to a better understanding of the mechanism for transient flow in the multi-porosity porous media.

Sign in / Sign up

Export Citation Format

Share Document