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By S. Sarioglan

The bleaching of edible oils, industrial oils, and some chemicals may be achieved using natural and acid-activated clays. These materials remove impurities and pigments from the oils. In this work, a bentonite clay from Turkey (Somas bentonite) was activated with different concentration of H2SO4 and HCl at 70~90°C and 5~8 hours. Under these conditions several cations were removed from natural bentonite (Al, Mg, and Fe) and DTA-TGA, FT-IR curves of the solids obtained after acid treatment were examined. Treatment time and acid concentration increased the degree of destruction of the bentonite structure which was determined by ICP. Activated samples were tested in order to verify their capacity to bleach soybean oil and compared to standard commercial bleaching clays. The experimental results indicate that treated samples with H2SO4 have the same efficient in bleaching crude soybean oil with the standards and treated sample with HCl is more efficient in bleaching than the commercial products.

Jan 1, 2014

By Mohab Sabry

Pile foundations are used extensively around the world to support both inland and offshore structures, including important structures such as nuclear plants and oil drilling platforms. The limit of the pile depth is currently predicted during the pile deriving process, given no chance for the designer to predict accurately the capacity of these piles prior installation. Furthermore, after pile installation, designer may not be able to modify the pile group design by increasing the number of piles and or changing the geometry of the pile group. This paper presents a numerical model for the case of single piles driven in homogenous sand using finite element technique and the theory of cavity expansion. The model is capable of simulating all the construction stages of concrete piles up to the maximum depth, which can be driven in sand and accordingly the capacity, which can be attained by these piles. The program "PLAXIS" is used to perform the proposed analysis. This model simulates the process of pile driving in terms of the changes in the earth pressure and the overconsolidation ratio acting along the pile's shaft. Based on the results of the present investigation, these depths can be predicted based on the pile geometry and the sand properties. Charts are given to provide these depths for given pile/soil conditions.

Jan 1, 2006

By H. M. von Seebach, M. P. Trubeljal, L. G. Austin

Six US coals and a crystalline quartz were tested in an instrumented laboratory high-pressure grinding rolls machine equipped with 100-mm-diam. rolls. The machine was choke-fed to maximize the capacity. As expected, the specific capacity decreased with increased grinding pressure for each material tested. Among the six coals, there were significant differences in the critical angle of nip, the effective feed porosity and the variation of strain at the gap relative to the grinding pressure. Although a precise correlation was not obtained, the overall effect of these factors was that, at a given grinding pressure, the specific capacity increased as the Hardgrove grindability index of the coal increased. The relationship between the specific capacity and the grinding pressure for a given coal was independent of feed size down to 150 µm. However, smaller feed sizes produced anomalous results, and the flow within the feed hopper was restricted.

Jan 1, 1996

By Howard A. Perko, Melinda J. Hummel

"Hydraulically jacked piles, herein referred to as jacked piles, are commonly used for underpinning existing structures to arrest settlement or augment an existing foundation for higher loads. They consist of steel pipe segments coupled together and jacked into the ground using a hydraulic ram. Pipe sections can vary in size from 3"" diameter to 18"" diameter or larger. Jacking resistance is typically provided by dead loads of existing structures. This type of piling system has been utilized for foundation underpinning, repair, and augmentation for more than 120 years, yet little has been published on the capacity, installation standards, and reliability of these systems. Pile load tests from a number of projects are presented and analysed. The data show that previous methods of jacked pile capacity and depth prediction are crude at best. Empirical relationships between capacity, depth, soil type, and standard penetration resistance blow count contain a high degree of scatter. Scatter in the data indicate capacity prediction for jacked piles needs further research and refinement.INTRODUCTIONPush pier, resistance pile, steel pier, and jacked pile are some of the names often applied to hydraulically jacked piles used for underpinning. The term ‘jacked pile’ is more common in building codes and will be used herein. Although jacked piles can be installed for new construction, this paper is focused on piles used for support of existing structures.Jacked piles consist of short segments of pipe or structural steel tube that are coupled together and forced into the ground using a hydraulic ram fastened to or beneath a footing, stem wall, or grade beam of an existing structure. In this way, the weight of the structure provides the resistance necessary to force the pile into the ground. A factor of safety can be achieved in design by redundancy, which is consecutively installing more than one jacked pile to support the same portion of foundation. Installing jacked piles consecutively using the same dead load and then releasing the load after each pile installation allows one to continue adding piles to the same general area until a total aggregate capacity is achieved to account for anticipated dead plus live loads and a desired factor of safety for that area.An engineering schematic of an example jacked pile connected to a footing foundation is shown in Figure 1. Modern jacked piles typically incorporate a steel bracket. There are many sizes and styles of brackets available. Some categories include plate brackets that bolt to the outside of an existing foundation wall, wide and narrow angle brackets that extend under existing footings, pin brackets for attachment to structural steel, and reverse angle brackets for attachment to footing and wall. Table 1 lists example brackets and their benefits."

Jan 1, 2017

By S. X. Liang

In China, the bearing capacity predictions of the pile with Stress-Wave Theory have been developed rapidly in recent years. This paper recommended a DZH-3 Pile Driving Analyzer and its relevant computer programs. Taking Qinghai Hotel Project for example, it gave their applications in the dynamic tests of large diameter cast-in-place piles.

Jan 1, 2010

By M. Mets

Pile foundations have been used in Estonia since the beginning of 1960's. To evaluate the capacity of piles nearly 2,500 pile tests and 1,800 pile loading tests Have been carried out. The pile foundations of nearly 150 houses are under settlement observations.

Jan 1, 2000

By J. Wennerstrand

Slender steel piles have found an increased use in Sweden in resent years. These piles are often driven throw soft normally consolidated clay to refusal in till or at the rock surface. In contrast to most other piles the bearing capacity with regard to failure of the shaft is in many cases smaller than the bearing capacity with regard to failure of the soil or rock at the lower end of the pile. Imperfections such as deviations from a straight line of the pile centerline and residual stresses in rolled and welded profiles are important for the capacity of the pile shaft. Even thow the second order moment caused by initial deviations in piles is only half of that in a column with the same slenderness, imperfections can and should be accounted for in much the same way as for columns.

Jan 1, 1989

By Fábio Heiji Yamada, Marcelo Koiti Fugihara, Ruano Fonseca Araujo

Conception the simulation and optimization technologies for industrial processes applied in the mining environment: tools and methodologies. Clarifications provided about the differences of these techniques when compared with static analysis (intuition, use of static spreadsheets, etc.). Presentation of practical cases at several big mining companies in Brazil. These projects will be presented and illustrated through dynamic simulation models developed at those companies, each one with its set of objectives, scope and results (for example: sizing the number of equipment, silo, piles related to the mining processing, logistics, ROM transportation, mine operations plan, etc.).

Oct 3, 2019

By Emad Farouz

This paper compares the predicted axial capacity of driven Pre-cast Pre-stressed Concrete (PPC) piles for the Lake Gaston Water Treatment Plant (LGWTP) using several design methodologies versus the axial capacity measured from dynamic and static load testing. The LGWTP site is located in Chesapeake, Virginia and is part of the Great Dismal Swamp. The subsurface investigation included soil borings, in-situ dilatometer (DMT) tests, and in-situ piezocone (CPTu) tests. The axial capacity predictions of the PPC piles were performed using the computer programs DRIVEN and FB-DEEP which are based on SPT N-values. Additionally, an empirical method proposed by Martin, et al. (1987) based on local experience with PPC pile design in the Yorktown formation in the Tidewater area of Virginia was also evaluated. Finally, the ?Laboratoire Central des Ponts et Chausées (LCPC)? method developed by Bustamante and Gianeselli (1982) based on CPT measurements was also used to develop the axial pile capacity of the piles. This paper shows that the FB-DEEP computer program and the LCPC method provided a reasonably good prediction of the pile axial capacity measured from PDA, CAPWAP, and Static Load Tests in comparison with the other design methods used. The soils in this area develop significant setup over time and it was found that FB-DEEP and the LCPC method are capable of incorporating this setup in the prediction of the long-term axial capacity of driven piles in this area.

Jan 1, 2007

By Nahiri Hirsh

El programa de fortalecimiento de capacidades Capas y Capaces impulsa el trabajo articulado de las instituciones educativas Nuestra Señora de La Merced, Rafael Loayza Guevara y Dos de Mayo, organizaciones de base, Yanacocha y la Dirección Regional de Educación, para el desarrollo sostenible de las comunidades. Se trabaja en el desarrollo y mejora de capacidades técnicas en estudiantes de 3°, 4° y 5° año de secundaria, así como de padres y madres de Cajamarca, con el objetivo de prepararlos para la vida y desterrar la dependencia económica. La capacitación se realiza con métodos innovadores (haciendo uso de laboratorios, equipos y maquinaria moderna) que han logrado convertir al programa en referente del Ministerio de Educación para la educación técnica en instituciones públicas a nivel nacional.

Sep 20, 2019

By J. G. Martin, J. C. Campbell

THE VICTORIA JUNCTION 31,4-million-ton coal preparation complex went into operation in October 1976."' It is designed to produce a metallurgical coking coal by lowering the sulphur and ash content of the raw coal using a heavy-media cycloning process to treat deslimed crushed coal, with scavenging of fine coal by flotation from the primary minus-28-mesh screen product. A secondary H-M cyclone scavenges a thermal-grade coal from the primary H-M cyclone tailing.

Jan 1, 1985

By Dan Currie, Tom Lamb, J. Coady Marsh, Gary Landry

"This paper describes the Cape Breton Development Corporation's experience with the Lovat M-300 tunnel-boring machine at the Donkin-Morien Mine. Between January 3 and December 21, 1984, the 7.6 m (25 It) diameter TBM advanced 3350 m (10 990 ft) . The authors will describe experiences with the machine and highlight the implications of tunnelling machines to underground coal mine development in Canada. IntroductionThe Cape Breton Development Corporation (CBDC) has recently completed the drivage of a 7.6 m (25 ft) diameter tunnel, 3.5 km (2.2 miles) in length , to access the Harbour Coal Seam at the Donkin-Morien Project. The tunnel was successfully driven with the first Canadian rock tunnel-boring machine (RTBM or TBM), designed and built by Lovat Tunnel Equipment, Inc. The initial mine development consists of the drivage of two tunnels to the first major coal seam. Future plans are proposed for the development of a 4 million tonne-per-year mine (Marsh et al., 1983, Gillman, 1982), which will require the drivage of a further two tunnels and could access up to four coal seams. The tunnel cross-sectional areas were designed to provide sufficient ventilation area and access for a production of 4 million tonnes per year."

Jan 1, 1986

By J. Kochhar, Robert G. Cooper

"The Cape Breton Development Corporation is a federal Crown corporation which was formed in 1968. Initially, the Corporation had two divisions - the Industrial Development Division, whose purpose was to stimulate Cape Breton Island's economy, and the Coal Division with a mandate to phase out the operating coal mines. However, that strategy changed in the early 1970s with the Middle East oil crisis. As a result of that crisis, Nova Scotia Power Corporation adopted an ""off oil"" policy. Today, approximately 700/0 of Nova Scotia power needs are met by generation of electricity from coal. Therefore, since the early 1970s, emphasis has been on the rehabilitation of the Cape Breton coal mining business with the opening of three new mines.Today, Devco is solely a coal mining company which employs 3300 people.Physical DescriptionThe mines operate in the Sydney coal field which is located on the eastern tip of Cape Breton. The Corporation leases the deposit from the province of Nova Scotia and its leases cover all coal from the outcrop to the 4000 ft depth. The seams outcrop along the shoreline and dip beneath the ocean floor at dips varying between 5% and 100%.There are eleven seams, of which three - the Harbour, Phalen, and Hub - have been extensively mined."

Jan 1, 1990

By M Graham, R Brunning, C Andringa-Bate, S Westergren

In 2010, Rio Tinto Iron Ore’s operations commenced the planning and design of a sampling and analysis system for the new 50 Mt/a Cape Lambert Port B (CLB) facility. Current sampling systems at the ports consist of automated robotic, mass-based sampling protocols employed at Dampier, and semi-automated, time-based sampling systems operating at Cape Lambert Port A.The new sampling system at CLB has brought together a fully automated sampling and analysis system utilising time-based sampling, with the capacity to sample ore products of medium quality variation as defined in ISO 3082 (ISO, 2009). The CLB system is required to sample at shiploading rates from 6000 t/h to 13 440 t/h and provide full load-port analysis. The sampling approach is to proportionally extend primary increments (of varying mass relative to shiploading rate) to a standard length using variable speed aero-belt conveyor systems. This enables a fixed number of secondary cuts to be achieved for all primary increment masses and to be delivered to the automated cell. The cell is required to be capable of concurrently processing four individual shipments, each containing multiple cargoes.Achieving the target sampling precision for all export cargo sizes has culminated in the planning, design and construction of the largest automated iron ore port laboratory in the world. The CLB sampling and analysis cell was commissioned in Q3 and Q4 2013. This paper discusses the sampling philosophy and commissioning outcomes.CITATION:Brunning, R, Andringa-Bate, C, Graham, M and Westergren, S, 2014. Cape Lambert Port B shiploading, sampling and analysis, in Proceedings Sampling 2014 , pp 79–90 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Jul 29, 2014

By S Russell

The completion of the $1.1 B Cape Lambert Upgrade project is the second ‘pillar’ in Rio Tinto Iron Ore’s expansion program that has enabled Rio Tinto Iron Ore to effectively double iron ore shipping capacity from the Pilbara between 2003 and 2009 to 220 million tonnes per annum (Mt/a), following the successful completion of the Dampier Port upgrade project two years earlier.The Cape Lambert Upgrade has built on and enhanced many of the engineering achievements of the Dampier Port upgrade project, as well as developing innovative and unique engineering solutions for this complex ‘brownfields’ project that presented its own challenges, particularly in this distinctive open-water port environment.The project was implemented in two phases to achieve an increase in port shipping capacity from 55 to 80 Mt/a – an enhancement phase and an expansion phase.The initial enhancement phase, which provided an increase to shipping capacity from 55 to 60 Mt/a, focused on increasing the utilisation and effi ciency of existing plant and equipment with a relatively small capital expenditure.The expansion phase, which provided the increase in shipping capacity to 80 Mt/a, included extending the existing iron ore wharf by 256 m to create four shipping berths, a new shiploader, an expanded stockyard (including a new fourth bucket wheel reclaimer) and a new surge bin facility to maximise outloading tonnage rates.The Cape Lambert Upgrade project was implemented whilst the port remained fully operational and continued to ship record tonnages of iron ore throughout the project duration. This achievement required signifi cant upfront planning and sequencing of construction activities to support the operation of the port. Innovative design and construction techniques were used to mitigate the impact and enable construction activities in and around the operating plant.Throughout the project, new benchmarks in engineering design and construction practices were established, which have since been adopted for new iron ore port facilities currently in planning phases.

Jul 11, 2011

By S. Chilka, I. Maloney, J. Brady

"The purpose of this project was to design the Electrical Service Platform (ESP) for the Cape Wind Offshore Wind Farm. The ESP structure comprises two primary parts: the topside platform housing the electrical equipment and the two jacket substructures providing foundation support to the platform. The topside is supported only by the two inner legs of each jacket. The site water depth is relatively shallow and the seabed comprised of loose sediment subject to severe local scour up to 18 feet. The piles are designed for local scour, storm conditions, vessel impact, ice loads and pile installation fatigue. This paper focuses on the design and construction aspect of this project.PROJECT DESCRIPTIONBackgroundThe Cape Wind project will be located in Nantucket Sound between Cape Cod on the Massachusetts mainland (northeastern coast of the USA) and the Islands of Martha’s Vineyard and Nantucket (Fig. 1). The project is to be sited on Horseshoe Shoal, about equal distances from the mainland and the two islands. The project will produce 75% of the electricity used on Cape Cod and the Islands of Martha’s Vineyard and Nantucket with zero pollution emissions and resulting in the reduced operations, fuel consumption and pollution emissions from the fossil fuel power plants in the region. The wind farm, if constructed per plan, is expected to be America’s first offshore wind farm.The wind farm will consist of an array of 130 Siemens 3.6-megawatt offshore wind turbines with a combined production capacity of 468-megawatts. The offshore wind turbine towers will be bolted onto the transition pieces supported by monopile foundations driven into seabed. The power from the 130 wind turbine generators will be delivered to the Electrical Service Platform (ESP) by an array of up to 14 seabed conductors."

Jan 1, 2017

By W. R. Purcell

An apparatus is described whereby capillary pressure curves for porous media may be determined by a technique that involves forcing mercury under pressure into the evacuated pores of solids. The data so obtained are compared with capillary pressure curves determined by the porous diaphragm method, and the advantages of the mercury injection method are stated. Based upon a simplified working hypothesis, an equation is derived to show the relationship of the permeability of a porous medium to its porosity and capillary pressure curve, and experimental data are presented to support its validity. A procedure is outlined whereby an estimate of the permeability of drill cuttings may be made with sufficient acuracy to meet most engineering requirements. INTRODUCTION The nature of capillary pressures and the role they play in reservoir behavior have been lucidly discussed by Lev-rett', Hassler, Brunner, and Deah12, and others. As a result of these publications the value of determining capillary pressure curves for cores has come to be generally recognized within the oil industry. While considerable attention has been directed toward the subject in an effort to provide a reliable method of estimating percentages of connate water, it has been recognized that capillary pressure data may prove of value in other equally important applications. This paper describes a method and procedure for determining capillary pressure curves for porous media wherein mercury is forced under pressure into the evacuated pores of the solids. The pressure-volume relationships ob- tained are reasonably similar to capillary pressure curves determined by the generally accepted porous diaphragm method. The advantages of the method lie in the rapidity with which the experimental data can be obtained and in the fact that small, irregularly shaped samples, e.g., drill cuttings, can be handled in the same manner as larger pieces of regular shape such as cores or permeability plugs. Based upon a simplified working hypothesis, a theoretical equation will be derived which relates the capillary pressure curve to the porosity and permeability of a porous solid, and experimental data will be presented to support its validity. This relationship aplied to capillary pressure data obtained for drill cuttings by the procedure described provides a means for predicting the permeability of drill cuttings. METHODS FOR DETERMINING CAPILLARY PRESSURES Several techniques have so far been employed in determining capillary pressure curves and these fall into two principal categories: (1) Liquid is removed from, or imbibed by, the core through the medium of a high displacement pressure porous diaphragm (2) Liquid is removed from the core which is subjected to high centrifugal forces in a centrifuge4,'. There are? however, certain limitations inherent in both methods. The greatest capillary pressure which can be observed by method (I), above, is determined by the maximum displacement pressure procurable in a permeable diaphragm which at the present time appears to be less than 100 psi. An even more serious limitation of the diaphragm method is imposed hy the fact that several days may be required to reach saturation equilibrium at a given pressure; hence, the time re- quired to obtain a well-defined curve may be measured in terms of weeks. Furthermore, to date, no suitable technique for handling relatively small, irregularly shaped pieces of rock, such as drill cuttings, has been reported and, therefore, measurements must be made, in general, on cores, or portions thereof. The centrifuge method offers the distinct advantage over the porous diaphragm method of arriving at saturation equilibrium in a relatively short time by virtue of the elimination of the transfer medium for the liquid. The calculation of capillary pressures from centrifuge speeds is somewhat tediousa, however, and the equipment required is fairly elaborate. While there exists the possibility that this method might be adaptable to the determination of the capillary pressures of cuttings, this particular ramification has not been investigated, as far as is known. In view of the limitations of the two principal methods for determining capillary pressures, the apparatus described in the following sections has been devised in order that difficulties previously encountered might be circumvented. MERCURY INJECTION METHOD FOR DETERMINING CAPILLARY PRESSURES Theory The methods described above for determining capillary pressures are characterized by the fact that one of the fluids present within the pore spaces of the solid is a liquid which "wets" the solid, i.e., the contact angle which the liquid forms against the solid is less than 90" as measured through that phase. For these "wetting" liquids the action of surface forces is such that the fluid spontaneously fills the voids within the solid. These forces likewise oppose the withdrawal of the fluid from the pores of the solid.

Jan 1, 1949

By W. R. Purcell

An apparatus is described whereby capillary pressure curves for porous media may be determined by a technique that involves forcing mercury under pressure into the evacuated pores of solids. The data so obtained are compared with capillary pressure curves determined by the porous diaphragm method, and the advantages of the mercury injection method are stated. Based upon a simplified working hypothesis, an equation is derived to show the relationship of the permeability of a porous medium to its porosity and capillary pressure curve, and experimental data are presented to support its validity. A procedure is outlined whereby an estimate of the permeability of drill cuttings may be made with sufficient acuracy to meet most engineering requirements. INTRODUCTION The nature of capillary pressures and the role they play in reservoir behavior have been lucidly discussed by Lev-rett', Hassler, Brunner, and Deah12, and others. As a result of these publications the value of determining capillary pressure curves for cores has come to be generally recognized within the oil industry. While considerable attention has been directed toward the subject in an effort to provide a reliable method of estimating percentages of connate water, it has been recognized that capillary pressure data may prove of value in other equally important applications. This paper describes a method and procedure for determining capillary pressure curves for porous media wherein mercury is forced under pressure into the evacuated pores of the solids. The pressure-volume relationships ob- tained are reasonably similar to capillary pressure curves determined by the generally accepted porous diaphragm method. The advantages of the method lie in the rapidity with which the experimental data can be obtained and in the fact that small, irregularly shaped samples, e.g., drill cuttings, can be handled in the same manner as larger pieces of regular shape such as cores or permeability plugs. Based upon a simplified working hypothesis, a theoretical equation will be derived which relates the capillary pressure curve to the porosity and permeability of a porous solid, and experimental data will be presented to support its validity. This relationship aplied to capillary pressure data obtained for drill cuttings by the procedure described provides a means for predicting the permeability of drill cuttings. METHODS FOR DETERMINING CAPILLARY PRESSURES Several techniques have so far been employed in determining capillary pressure curves and these fall into two principal categories: (1) Liquid is removed from, or imbibed by, the core through the medium of a high displacement pressure porous diaphragm (2) Liquid is removed from the core which is subjected to high centrifugal forces in a centrifuge4,'. There are? however, certain limitations inherent in both methods. The greatest capillary pressure which can be observed by method (I), above, is determined by the maximum displacement pressure procurable in a permeable diaphragm which at the present time appears to be less than 100 psi. An even more serious limitation of the diaphragm method is imposed hy the fact that several days may be required to reach saturation equilibrium at a given pressure; hence, the time re- quired to obtain a well-defined curve may be measured in terms of weeks. Furthermore, to date, no suitable technique for handling relatively small, irregularly shaped pieces of rock, such as drill cuttings, has been reported and, therefore, measurements must be made, in general, on cores, or portions thereof. The centrifuge method offers the distinct advantage over the porous diaphragm method of arriving at saturation equilibrium in a relatively short time by virtue of the elimination of the transfer medium for the liquid. The calculation of capillary pressures from centrifuge speeds is somewhat tediousa, however, and the equipment required is fairly elaborate. While there exists the possibility that this method might be adaptable to the determination of the capillary pressures of cuttings, this particular ramification has not been investigated, as far as is known. In view of the limitations of the two principal methods for determining capillary pressures, the apparatus described in the following sections has been devised in order that difficulties previously encountered might be circumvented. MERCURY INJECTION METHOD FOR DETERMINING CAPILLARY PRESSURES Theory The methods described above for determining capillary pressures are characterized by the fact that one of the fluids present within the pore spaces of the solid is a liquid which "wets" the solid, i.e., the contact angle which the liquid forms against the solid is less than 90" as measured through that phase. For these "wetting" liquids the action of surface forces is such that the fluid spontaneously fills the voids within the solid. These forces likewise oppose the withdrawal of the fluid from the pores of the solid.

Jan 1, 1949

By M. King Hubbert

In 1856 Henry Darcy described in an appendix to his book, Les Fontaines Publiques de la Ville de Dijon, a series of experiments on the downward flow of water through filter sands, whereby it was established that the rate of flow is given by the equation: q= - K(h2- h2)/I1 in which q is the volume of water crossing unit area in unit time, I is the thickness of the sand, h1 and h2 the heights above a reference level of the water in manometers terminated above and below the sand, respectively, and K a factor of proportionality. This relationship, appropriately, soon became known as Darcy's law. Subsequently many separate attempts have been made to give Darcy's empirical expression a more general physical fornzulation, with the result that .so many mutually inconsistent expressions of what is purported to he Darcy's law have appeared in published literature that sight has often been lost of Darcy's own work and of its significance. In the present paper, therefore, it shall be our purpose to reinform ourselves upon what Darcy himself did, and then to determine the meaning of his results when expressed explicitly in terms of the pertinent physical variables involved. This will be done first by the empirical method used by Darcy himself, and then by direct derivation from the Navier-Stokes equation of motion of viscous fluids. We find in this manner that: q = (N4(p/p)[g - (l/p) gradPI = WE, is a physical expression for Darcy's law, which is valid for liquids generally, and for gases at pressures higher than about 20 atmospheres. Here N is a shape factor and d a characteristic length of the pore structure of the solid, p and IL are the density and viscosity of the fluid, a = (Nd2)(pip) is the volume conductivity of the system, and E = [g - (l/p) grad p] is the impelling force per unit mass acting upon the fluid. It is found also that Darcy's law is valid only for flow velocities such that the inertial forces are negligible as compared with those arising from viscosity. In general, three-dimensional space there exist two superposed physical fields: a field of force of charucteristic vector E, and a field of flow of vector q. The force field is more general than the flow field since it has values in all space capable of being occupied by the fluid. So long as the fluid density is constant or is a function of the pressure only, curl E = 0, E = - grad F where F = gz + dp/p The field of flow, independently of the force field, must satisfy the conservation of mom, leading to the equation of continuity div pq = — f ap/at , where f is the porosity, und t is the time. For steady rnotion ap/at = 0. and div pq = 0 .

Jan 1, 1957

By J. W. Marx

A method is given for predicting the complete gravity drainage characteristics of arbitrarily long columns from centrifuge drainage measurements on reconstituted core samples. Oil residuals corresponding to hundreds of years of normal gravity depletion can be obtained in a few hours on the centrifuge. The gravity flow rate at any stage of the depletion process may be determined from the time correlation derived, and experimentally checked, in this study. INTRODUCTION Apart from the original observations of Muskat et al1, research publications2,3,4 on the subject of gravity drainage have been largely concerned with establishing in detail the saturation, S as a function of the height, z, in a draining column at any given time, t. Some form of numerical integration must be employed to obtain production rates and cumulative production even when S(z, t) is known. Furthermore, the relevant experimental work has been concentrated on drainage of a single wetting liquid from unconsolidated media. Since oil production usually concerns the drainage of a partially wetting liquid from consolidated media, in the presence of connate water, and since it is unlikely that sufficient information exists to establish S(z, t) in detail for any natural reservoir, the published research work appears to be, at best, only qualitatively applicable to production problems. With this in mind, the present study was undertaken by the writer. Experiments were planned whose results would have two advantages over existing measurements: 1. Observations were to be made on specific reservoir rock, reconstituted with formation water and formation oil. This would reduce their generality, from the research viewpoint, but increase their utility for production purposes. 2. The measurements were to be self-integrating, i.e., the phenomena were to be described and interpreted in terms of cumulative results. THEORETICAL DEVELOPMENT It was commonly known that centrifuging a liquid bearing porous medium increases the drainage rates and minimizes capillary end effects. The specific problem lay in selecting an acceleration, a, such that the mean residual saturation of a model cylinder was equal to the residual saturation of an arbitrarily long prototype column when the latter was drained by earth gravity alone. The physical conditions required to permit a valid scaling of model drainage time, tm with prototype drainage time, t, may be stated as follows: (a) At t = tm = O, So = Smo; (b) At t = tm? 8 Sr. = Smr.; (c) For all intermediate values of t and dS/dt=dsm/dtm whenever S = Sm; (d) S(z) = Sm(z) = a constant when t = tm = 0. 1 Here S = T I S(z)dz, where h is the length of the « Jo cylindrical column being drained and the subscripts S,Sm, and refer to model, initial, and residual systems, respectively. The first three conditions mean, simply, that an 3 vs t plot will be numerically identical with an S, vs t, plot,

Jan 1, 1957