Radial Drainage Research Articles

Drainage, topographic, and gravity anomalies in the Lake Superior Region: Evidence for a 1100 Ma mantle plume

A topographic dome, radial drainage pattern, and regional negative gravity anomaly, all centered on Lake Superior, are vestiges of a 1100 Ma mantle plume that formed the Midcontinent Rift System of central North America. The topographic and gravimetric relations suggest that the dome is maintained isostatically by fundamental changes imprinted on the lithosphere by the plume, including magmatic underplating of the crust and depletion of the upper mantle. These changes occurred at distances of up to 500 km or more from the center of the plume, well beyond the margins of the rift.

Horizantal drainage during consolidation: insights gained from analyses of a simple problem

This paper analyses consolidation with radial drainage to concentric inner and outer fixed drainage boundaries. An analysis in which coupling between flow of pore water and effective stress change is ignored gives results that are not physically reasonable. An exact closed form solution can be developed to the equation of radial pore water diffusion in an elastic material and the results of this analysis are compared with a third, finite element analysis, using an elastic-plastic description of the soil. Elastic and elastic-plastic analyses are compared in terms of isochrones of pore pressure, radial displacement and stress change within the sample, and in terms of the strain and stress paths followed by different soil elements in the consolidating clay. Non-uniformities of effective stress state, and hence of soil stiffness, can develop during consolidation; the pattern of deformations that develops is completely dominated by the occurrence of plastic strains. The oedometer should not be regarded as a single element test. The results of the analyses are in principle specific to the boundary conditions assumed, but some general aspects of soil behaviour are identified and observations are made on the implications of the results for geotechnical design. L'article présente une analyse de la consolidation avec drainage radial jusqu'à des limites de drainage intérieure et extérieure fixes. Une analyse qui ignore le couplage entre l'écoulement de l'eau interstitielle et des changements dans la contrainte effective donnent des résultats qui ne sont pas physiquement raisonnable. L'équation de la diffusion radiale de l'eau interstitielle dans une matière élastique peut être résolue dans une forme fermée précise. Les résultats de cette analyse sont comparés avec une analyse à éléments finis employant une description élastico-plastique pour l'argile. Les analyses élastique et élastico-plastique sont comparées en ce qui concerne les isochrones de la pression de l'eau interstitielle, le déplacement radial, le changement des contraintes dans l'échantillon et aussi les chemins de contrainte et de déformation suivis par de différents éléments dans l'argile pendant la consolidation. Un état de contrainte effective et par conséquent de rigidité de sol qui est non-uniforme peut se développer au cours de la consolidation. Le système de déformations qui se développe est régi par la présence de contraintes plastiques. Il ne faut pas considérer l'oedomètre comme un essai à élément simple. En principe les résultats de l'analyse sont spécifiques pour les conditions limites, mais des aspects généraux du comportement des sols sont identifiés et des observations faites concernant les implications des résultats pour la construction géotechnique.

Settlement Response of Soft Soils Reinforced by Compacted Sand Columns

Stone/compacted sand columns is a technique of soil reinforcement that is frequently implemented in soft cohesive soils to increase the bearing capacity of the foundation soil, to reduce the settlement, and to accelerate the consolidation of the surrounding saturated soft soil. The soil‐column interaction depends on several parameters, including the loading process and the loading rate, the replacement factor, the group effect, and the partial consolidation of the soft soil due to radial drainage through the column. This paper presents the results of a laboratory study that was conducted to investigate the effect of these various parameters on the settlement response of a soft foundation soil reinforced by compacted sand columns. Triaxial compression tests under different boundary conditions were performed on composite soil specimens made of annular silty soil samples with a central, compacted river‐sand column. These tests, performed in a specially modified triaxial cell, show that the group effect, the replacement factor, and the consolidation of the soft soil have a significant effect on the vertical stress concentration on the column and on the settlement reduction of the foundation soil.

The Damage Discussion: Its Effect On Well Flow

Abstract Damage induced by hydraulic fracturing fluids has been a topic of concern in the oil and gas industry for the past several years. Better ways are now available to quality the consequences of this damage and therefore plan the best stimulation treatment for the well completion. Laboratory data, coupled with computer simulation, allows an examination of the more important damage mechanisms and their effect on a well's productivity. Using results from fluid compatibility and regained permeability core flow tests, it is possible to determine the effect of:permeability reduction by fluid invasion,invasion depth,relative permeability changes, andcapillary pressure changes in both radial and linear flow cases. This paper presents actual regained permeability data ranges and then uses this information in a reservoir simulator to assess the different damage mechanisms. Simulation results show that perceived "damage" problems are unrealistic, as even a very severe permeability reduction in the invaded zone does not significantly change well productivity. Introduction Hydraulic fracture treatments have become one of the most common and highly successful completion techniques used in western Canada. Much development work has been done on fracturing carrier fluids to avoid potential reservoir damage, though in reality, any fluid injected into a formation will do some damage. It is essential to understand basic reservoir mechanisms which control the flow from the reservoir into the wellbore. A step taken to understand and quantify this damage was made by Craft and Hawkinsw(1). They considered a concentric cylinder of altered permeability adjacent to the wellbore and the resulting well productivity in radially flowing wells. This altered permeability is now called "skin" and was defined by van Everdingen(2). The problem was then expanded by van Pollen(3) to include a vertical hydraulic fracture with a zone of altered permeability adjacent to the fracture face. Prats(4) extended van Pollen's analysis by considering the effect of finite conductivity fractures with fracture face damage in a radial drainage area. Well test theory provided a mathematical coupling of a vertical hydraulic fracture to a reservoir with wellbore storage and skin. Cinco Ley(5)) demonstrated the different flow regimes that were present in a fractured well. Linear flow was shown to exist in and adjacent to the fracture, while radial flow existed in the reservoir. Tannich(6) extended this work to include two phases in gas wells by the use of numerical simulation. Holditch(7) then included fracture face damage and capillary pressure effects for low-permeability gas wells. With these works as a foundation, this paper will first compare the effects of damage on productivity for radial and linear single-phase flow. The analysis will then consider the complex combination of relative permeability, capillary pressure and induced permanent damage when two-phase flow occurs. Laboratory Data The degree of permeability reduction from fracture fluid invasion can be placed into a realistic framework from actual regained permeability tests. Regained permeability tests are used to evaluate the fracturing fluids' compatibility and depth of invasion with a representative sample of the formation core.

Physics and Applications of DIP Coating and Spin Coating

ABSTRACTDip coating is a simple old way of depositing onto a substrate, especially small slabs and cylinders, a uniform thin film of liquid for solidification into a coating. The basic flow is steady, and in it film thickness is set by the competition among viscous force, capillary (surface tension) force and gravity. Thickness and uniformity can be sensitive to flow conditions in the liquid bath and gas overhead. The faster the substrate is withdrawn, the thicker the film deposited. This can be countered by using volatile solutes and combining rapid enough drying with the basic liquid flow. Then the physics grows more complicated, theoretical prediction of process performance more difficult, and control of the process more demanding. Outside product R&D labs it is far less often used in precision coating manufacture than a variety of premetered coating methods.Spin coating is a more recently developed way of getting onto piecemeal substrates, especially small flat disks, a uniform thin liquid film for the same end. The basic flow is unsteady radial drainage in which centrifugal and viscous forces so compete that ordinary (Newtonian) liquid of constant viscosity tends toward a uniform film that grows ever thinner ever more slowly. Volatile solvents are commonly used because conditions can often be found that adequately separate thinning by spin-off from later thinning and solidification by drying. Thickness and uniformity, today theoretically predictable, are sensitive to speed, gas conditions, and rheology of concentrating, solidifying liquid. For the rheology of photoresist coating in microelectronics, spin coating works well. For that of suspension coatings in magnetic disk technology the process demands more careful control; actually it is often modified.

Discussion: Non-uniformity of triaxial samples due to consolidation with radial drainage

Discussion: Non-uniformity of triaxial samples due to consolidation with radial drainage

Non-uniformity of triaxial samples due to consolidation with radial drainage. Technical note : Atkinson, J H; Evans, J S; Ho, E W L GeotechniqueV35, N3, Sept 1985, P353–355

Non-uniformity of triaxial samples due to consolidation with radial drainage. Technical note : Atkinson, J H; Evans, J S; Ho, E W L GeotechniqueV35, N3, Sept 1985, P353–355

Non-uniformity of triaxial samples due to consolidation with radial drainage

This note describes a limited series of tests in which 38 mm diameter triaxial samples of kaolin clay were consolidated isotropically with radial drainage and the variation in water content across the diameter of the sample was measured. The results showed that significant non-uniformities can occur during consolidation of soil samples in routine triaxial tests in which side drains are used. A consolidation increment of 200 kpa gave rise to non-uniform water contents which imply substantial variations in effective stress. The problem can be avoided by removing radial drainage or it can be minimized by slow drained loading if radial drainage is necessary. (TRRL)

Lowering the water table with radial drains

1. The method of lowering the water table by radial drains can be considered extremely promising. 2. The technology of opening deep shafts should be worked out with consideration given to the specific geologic conditions and available equipment. For this purpose, it is necessary to become extensively familiar with sectional reinforced-concrete sunken shafts. 3. Specialized construction organizations should be called upon to perfect the method of radial drainage; they can assist in working out standard technological flow charts for dewatering with radial drains. 4. For the widespread use of radial drains, it is necessary to adjust the series production of the ULB-130 rig and wire-frame filters.Z

Hydrodynamics of asymmetrical film thinning

AbstractThe thinning of the film beneath a liquid drop is often faster than predicted by radial drainage. This could be explained by asymmetrical drainage, but mathematical difficulties are then encountered. However, analytical solutions may be obtained for the two‐dimensional case and expressions are derived here for the asymmetric viscous drainage of films trapped between convex and concave wedges.Solutions for the symmetrical drainage beneath wedges and parabolae are also presented which are analogous to the three‐dimensional drainage beneath cones and paraboloids previously derived.

Evaporite diapirs in the La Popa basin, Nuevo León, Mexico

Reconnaissance mapping and stratigraphic work in the La Popa basin of Nuevo Leon, northern Mexico, has revealed two large structural features with cores of gypsum and anhydrite at the surface. These features are interpreted to be the surface expression of evaporite diapirs. They are exposed in folded sedimentary rocks belonging to the Potrerillos Formation of the Difunta Group of Maastrichtian age (Late Cretaceous). Sandstone units within the Potrerillos Formation pinch out toward the piercement features. Carbonate lentils composed of rudistid reefs and associated carbonate clastics flank the features and pinch out away from the features into marine shale members of the Potrerillos Formation. Most carbonate lentils occur in the immediate vicinity of the evaporite features and are interpreted to be genetically related to the diapirs. Syndiapiric sedimentary-facies patterns can be documented over 4,000 vertical feet (1,200 m) of section within the Potrerillos Formation. The large vertical extent of facies peculiarities near the piercement features indicates that the features were active for an extended period corresponding to at least two regressive-transgressive cycles during Maastrichtian time. A radial drainage pattern away from the northern feature indicates that the features are probably active today. A limestone inclusion from within one of the features has been dated as Kimmeridgian in age (Zuloaga or Smackover equivalent) and suggests that the evaporites are probably derived from the Jurassic Minas Viejas Formation. It is not known at present whether salt underlies the surface crust of gypsum and anhydrite. At the time that the first syndiapiric sediments of the Potrerillos Formation were deposited, the Minas Viejas Formation was buried at an estimated depth of 17,000 ft (5,200 m). The thick pre-Laramide cover, the pre-Laramide age of at least some of the syndiapiric sedimentary features, and the location of stocks away from major anticlines indicate that the emplacement of the diapirs is not related to Laramide compression. Geostatic loading is considered to be the most important mechanism for emplacement of the domes.

Embankments Through Cross River Swamp

The design, construction and performance of embankments across a deep clay flood plain are described, the construction involving a two-stage procedure with sand drains to aid consolidation. The Cross River was the major physical obstacle to the roadlink between Calabar and the mainland of Nigeria constructed between 1975 and 1977. The paper describes the investigation, alignment selection, design, construction and performance of embankments across the Cross River flood plain (Swanp), consisting of clays up to 30m deep. A two-stage construction procedure was employed, with sand hydraulically pumped up to 5km as embankment material. Sand drains were used for radial drainage and as relief wells to speed the consolidation and strengthening of the upper levels of the clay, prior to final embankment construction. Foundation performance was evaluated and strength increases measured. The embankments are performing satisfactorily, but they experienced large initial settlements during construction. (Author)

A laboratory study of efficiency of sand drains in relation to methods of installation and spacing

This Paper is concerned with an experimental study of the inward radial drainage of remoulded kaolinete clay to a central model sand drain and has been undertaken primarily to assess the effects of the various methods of installation and spacing on the consolidation characteristics of the soil. An experimental programme has been designed and implemented using three sizes of Rowe consolidation cells (76, 152 and 254 mm dia.). Geometrical models of various methods of forming the drains were used for the three sample sizes consolidated under three levels of loading. A development incorporating the concept of non-circular cross-section for the drain former has been similarly assessed. Vertical flow consolidation tests were also conducted to compare the results with those from the radial drainage. These were done to assess the reliability of the commonly used method of deployment of vertical flow consolidation coefficient in the sand drain design procedure. The results indicate that there are marked differences in the performance of the methods, and that the effects of the method of installation of sand drains on the in situ characteristics of the soil are critically important in evaluating the design assumptions and cost of construction for any given project. Cet article se rapporte à une étude expérimentale du drainage radial vers l'intérieur argile à kaolinite remaniée, en direction d'un drain de sable modèle central; cette étude a été entreprise principalement en vue d'évaluer les effets de différentes méthodes d'installation et d'espacement sur les caractéristiques de consolidation du sol. Un programme expérimental faisant appel à des cellules de consolidation Rowe de 3 tailles différentes (76 mm, 152 mm et 254 mm de diamètre) a été concu et mis en oeuvre. Des modeles géométriques de différentes méthodes de formation de formation de drains ont été utilisés pour les trois tailles d'échantillons consolidés sous trois phases de chargement. Le concept d'une forme de drain à section non-circulaire a fait l'objet d'une étude analogue. Des essais de consolidation du type á écoulement vertical ont également été menés en vue de comparer les résultats avec ceux fournis par le drainage radial. Ces essais avaient pour but d'évaluer la fiabilité de la méthode très courante de déploiement des coefficients de consolidation par écoulement vertical dans les projets de drains de sable. Les résultats font apparaitre des différences très nettes de performance entre les méthodes, et montrent que les effets de la méthode d'installation des drains de sable sur les caractéristiques in situ du sol jouent un rôle important pour I'évaluation des hypothèses de calcul et du coût de construction de tout projet donné.

Consolidation of a clay cylinder with external radial drainage : YOSHIKUNI, H NAKANODO, H SOILS FOUND, V15, N1, 1975, P17–28

Consolidation of a clay cylinder with external radial drainage : YOSHIKUNI, H NAKANODO, H SOILS FOUND, V15, N1, 1975, P17–28

Distribution, trophic relationships and breeding habits of the fish populations in a tropical lake basin (Lake Bosumtwi‐Ghana)

In the meteoritic crater lake—L. Bosumtwi—and its inflowing streams there are 11 species of fish of which four are cichlids and one of these is endemic. The zonal distribution, feeding and reproductive habits, as well as morphological adaptations of the fish are described. The species show a remarkable zonation from the upper reaches of the permanent streams to the limnetic zone of the lake, with each species occupying a well defined habitat. The cichlid populations dominate the lacustrine environments, while the non‐cichlids predominate in the riverine situations. This distribution pattern is related to the distribution of food resources, the availability of breeding sites and also to the possession of suitable body form or some behavioural characteristics. Despite the presence of two mouth brooding planktonic feeders in the lake, the need to spawn on a firm substrate, together with the surface feeding habit of the juvenile cichlids, makes none of the fish completely independent of the shallows. Cohabiting species show well marked differences in their feeding habits and the near rigidity of these feeding habits throughout the year may be attributed to the stability of the environment.SummaryThe fish populations in a natural tropical lake basin—Lake Bosumtwi, Ghana were studied over a period of 14 months. The basin has a radial drainage pattern with 37 inflowing streams, five of which are permanent, and has no outflow. This situation has produced, over the geological history of the lake, two very different chemical environments: fairly dilute inflowing streams and a relatively concentrated soda lake.A combination of fishing methods was employed, and these included the use of gill nets, cast nets, hand nets, basket net traps, and hook and line fishing. The fish captured were identified, counted and their total lengths and maximum depths measured. The percentage composition of the food was estimated by a points scheme, and by the number method. Eleven species of fish recorded were from the lake basin. Three of these—Roloffia petersii, Epiplatys chaperi and Amphilius atesuensis—have not been recorded from this basin before.The distribution of Aufwuchs, phytoplankton, aquatic macrophytes, zooplankton, benthos and allochthonous fauna and plant debris—(the major food items of the fish)—were found to be zoned in the lake basin, with autochthonously produced food items predominating in the lacustrine zones, whilst the allochthonously produced items predominate in the riverine zones.The distribution of the fish populations was found to be related to the distribution of their food items, with the non‐cichlid populations, which feed on allochthonous food resources, predominating in the riverine zones, whilst the cichlid populations, which feed on autochthonously produced food items, predominate in the lacustrine zones.The juvenile and adult populations offish species investigated rely on very different food resources. The exception to this is Chromidotilapia güntheri.The fish populations occupying any of the riverine or lacustrine zones, show well marked differences in not only the level at which they feed, but also in their food preferences, especially where two or more co‐habitating species occupy the same feeding level. Conversely it was found that species with very similar feeding habits do not occur in the same zone.Of the five cichlid fishes in the lake two, Sarotherodon multifasciatus and Chromidotilapia güntheri are mouth brooders, whilst the remaining species, Tilapia discolor, T. busumana, and Hemichromis fasciatus are substratum brooders.The zonal distribution of the fish in the lake basin was found to be related not only to the distribution of their food items, but also to their body form, the behaviour of the fish, availability of breeding sites, and possibly the chemistry of the water.

Consolidation of a Clay Cylinder with External Radial Drainage

The rate of consolidation for a clay cylinder with external radial flow of water is usually analyzed by the solution, which is presented by I. Da Silveira as a solution of the consolidation equation of Terzaghi in radial case, independent of the deformation condition of a clay cylinder. However, it is well known from laboratory test results that the rate of K 0 -consolidation differs from that of isotropic consolidation. In this study, processes of consolidation for a clay cylinder with external radial drainage are investigated under four conditions as an application of the consolidation theory proposed by H. Yoshikuni. The prepared conditions for calculation of consolidation are as follows; 1) The K 0 -consolidation with the average vertical load kept constant. 2) The K 0 -consolidation with radial load kept constant. 3) The isotropic consolidation with load kept constant. 4) The no vertical strain consolidation with radial load kept constant.

OBSERVATIONS ON THE BEHAVIOUR OF A PILE-RAFT FOUNDATION ON LONDON CLAY.

The Paper adds greatly to the understanding of the behaviour of such complex foundations. However, the Author’s analysis is only a class B prediction. Has this method been used on projects to provide a class A prediction of settlements? 69. Close inspection of the chosen finite element mesh reveals points not covered in the Paper. Does the program allow a variation of soil properties across each element? The mesh appears excessively fine in view of the neglect of stress values distant from the raft, and many elements have poor aspect ratios. Would the Authoi comment on permissible distortions for this element? 70. The choice of the position and type of boundaries (i.e. smooth, rough, rigid or elastically restrained) at the sides and base of the model are of paramount importance to the settlement values. Indeed, the choice of boundaries may have as much influence on the computed settlements as may the choice of other factors normally considered of greater significance, such as the chosen value of Poisson’s ratio. 71. In this context the use of an undrained Poisson’s ratio of 0.47 is noted. Since the chosen element is capable of simulating much less compressible behaviour if a minimum integrating order is used would the Author comment on the choice of the low value? (In such a case one may not always trust nodal stresses, but that is rarely a great loss.) 72. In 27 it is suggested that shear tractions at the soil-raft interface are negligible. It is certainly obvious that in the model with its concentric cylindrical reinforcements (piles) shear strains are prevented, but it is equally as evident that this is not so in the prototype. The results of reference 10 are important in this context. 73. The Author’s final comments on the rate of settlement are also important. Does his settlement analysis take into account radial drainage? If not, it is hardly surprising that calculated settlement rates are inaccurate (even taking into account factors such as the true consolidation behaviour of the London Clay). It is probable that radial drainage has a greater influence with this geometric configuration than the influence of preferential horizontal drainage paths. Would a coupled (i.e. Biot) type of consolidation theory not provide a more elegant solution to this problem and would it yield the same undrained and drained settlements or would load transfers during the consolidation process lead to a different final settlement picture?

Response of Streams to Structural Uplift: ABSTRACT

Drainage anomalies over structural uplifts in regions of low relief (less than about 150 ft local relief) and unconsolidated rocks are of 2 types--drainage pattern anomalies and single-channel anomalies. Field studies and model investigations have revealed certain basic stream responses to local uplift. In areas of generally uniform regional slope, local reversals or marked divergences of drainage pattern from the regional slope are structurally significant. Radial drainage patterns (full 360° radial patterns) are always anomalous. Concentric drainage is due to the exposure of beds of different resistance and may, or may not, be present. If the unconsolidated material is uniform or very poorly bedded, the local shifting or deflection of drainage is significant, but i well-bedded rocks it may be merely homoclinal shifting downdip. Marked local, opposed drainage deflections are apparently due to almost continuous uplift favoring continuous lateral shifting rather than accelerated incision. In unconsolidated rocks, the most important single-channel response to slight structural uplift is the local channel width-depth ratio. Changes in this ratio may be seen on aerial photographs. Such changes, however, may also be due to changes in lithology or in tributary streams. Decreases in gradient (such as upstream from a structure) result in increased channel width-depth ratio and increases in gradient decrease width-depth ratio. Meander compression or local changes in sinuosity may be due to structure or lithologic difference. Color aerial photography may aid in distinguishing structural and lithologic causes of single-channel features. End_of_Article - Last_Page 636------------

Volcanic and Glacial Landforms on Mount Giluwe, Territory of Papua and New Guinea

Mount Giluwe is a large extinct dome-shaped volcano built up mainly of thin flows of mafic lava rich in potassium. It rises from 2100 m to 4368 m above sea level. During the Pleistocene, it was covered by an ice cap which extended as low as the 3200 to 3500 m level. Although the volcano is dissected by a radial drainage system, cones, craters, lava mounds, lava flow surfaces, and volcanic debris, slopes are well-preserved below the glaciated area. Above this, the original volcanic landforms have been destroyed or modified by glacial activity, and well-preserved lateral moraines, groups of recessional moraines, glacial valleys, cirques, rock basins, and roches moutonnees are present. During the period of maximum glaciation, valley glaciers as thick as 400 m protruded from the edge of the ice cap down preexisting valleys and terminated at elevations between 2750 and 3000 m. On the northeastern side of the volcano, fluvioglacial deposits derived from the valley glaciers formed fans extending onto the Kaugel plain, which is incised 40 m by the present Kaugel River. This incision is almost entirely postglacial. Palagonitic breccia and scoria overlie, and are interlayered with, normal lava flows in the summit area of the volcano. They indicate that some subglacial volcanic activity took place and that there were probably at least two different periods of glaciation. The last glacial period (contemporaneous with the Wurm glaciation of Europe and the Wisconsin glaciation of North America) was the more extensive, covering about 190 km 2 . It was responsible for the development of the existing glacial landforms. Most of the volcanic landforms are older than this last glaciation.

Determining and Averaging Gas Reservoir Pressures

The results of this study indicate that the nearest fit to a linear gas material balance plot (the best estimate of initial gas in place) is obtained by correcting the estimated average well pressure for asymmetrical drainage effects, then weighting the individual average pressures by the pore volume drained by each well. A significant error may result in the estimated gas in place if geometric effects or asymmetrical drainage for the individual wells is not considered. This study is confined to one of the major Wilcox gas condensate sandstone reservoirs under the Sheridan field, Colorado County, Tex. Production is from 29 irregularly spaced wells located in the central two-thirds of the reservoir. The last one-fourth of the production period under consideration was influenced production period under consideration was influenced by transient drainage effects. Production acceleration caused a sustained period of transient pressure behavior that resulted in an erratic plot of the ratio of average pressure/gas deviation (P/Z) vs cumulative production. By contrast, the gas material balance curve should be linear for a volumetric reservoir and should not be affected by transient flow if average reservoir pressure can be determined accurately. The pressures used to prepare this performance curve were based on radial flow assumptions and rate weighting techniques. Similar material balance curves were prepared by estimating the pore volume and area for each well from the linear or semisteady-state portions of pressure-time plots. These data resulted in three pressure-time plots. These data resulted in threeadditional P/Z plots: geometrically corrected; pressure weighted by both Pore volume and production rates; and a pore volume weighted pressure based on radial drainage. Three indicators were used to measure the effectiveness of the four techniques: the magnitude of the standard deviation; a comparison of the extrapolated and actual initial pressure; and the shape of the performance curve in the anomalous region. The first performance curve in the anomalous region. The first two of these indicators are presented in Table 1 and the third is illustrated graphically in Fig. 1. It is apparent that volumetrically weighting the individual average well pressures is superior to rate weighting for either method of determining average pressure. This is to be expected since wells draining pressure. This is to be expected since wells draining this reservoir have different rates of pressure decline due to variable extent of formation damage and asymmetrical well drainage geometry. In addition, it is clear that smaller standard deviations result if the effects of asymmetrical (non-radial) drainage are considered. P. 249