Simple Graphical Procedure Research Articles

Use of Cumulative-Production Type Curves in Fracture Design

Summary When a fracture treatment is designed, the expected increase in productivity or production rate is usually considered. Because production rate varies with time, an economic evaluation based on a production rate increase at a given time can be misleading. A better method of economic evaluation would use the cumulative production after some time period. This can be determined by reservoir simulators that incorporate the effect of propped hydraulic fractures. These simulators are not readily accessible to everyone, however, and are time-consuming and expensive to run. Several authors have stated that cumulative-production type curves can be made with data generated by dimensionless-pressure type curves for a fractured well with infinite fracture conductivity. This paper shows how cumulative-production type curves for finite fracture conductivity can be generated from published dimensionless reciprocal-rate type curves or from reservoir simulators. A simple graphic procedure can then be used to give the combinations of fracture lengths and dimensionless fracture conductivity that will show the desired cumulative production or production rate at some particular time. Charts and simple equations also are given that will allow a quick estimate of the proppant volume required for the various fracture geometries needed for the desired production. This would form the basis for optimizing the fracture treatment. When used with methods to determine fracture fluid volumes for various fracture lengths, the minimum cost for any desired production can be made.

Water Quality Effects of Excavation and Diversion

Water quality data collected from Yellow Creek in northeast Mississippi before and during construction of the Divide Cut of the Tennessee‐Tombigbee Waterway provide information regarding the water quality effects of stream channelization and large‐scale construction projects. Simple graphical and statistical procedures for detecting changes in stream water quality are demonstrated. Data analysis was hindered by missing data, inconsistencies in the list of variables monitored, and changes in sampling frequency. Observed water quality changes were evidently due to increased inputs of sediment and reduced shade. Statistically significant changes in variances and means were observed for most grab‐sample variables. Mean values of specific conductance, turbidity, color, COD, and total alkalinity, hardness, ammonia, phosphorus, sulfate, iron, lead, and manganese were 50–100% greater during construction than before construction. Estimated average daily loadings of total metals, nutrients, and dissolved solids wer...

A method of stereotaxic localization adopted for conventional and digital radiography.

A method for the determination of stereotaxic coordinates in radiography, e.g. angiography, pneumoencephalography or digital vascular radiography, is described. A special localization frame containing radiopaque structures and scales defines a diagnostic coordinate system. This frame is fixed to the X-ray-table prior to the radiographic procedure and two projections are obtained at arbitrary angles to each other. The focus-film distances do not how to be fixed. The target coordinates are then determined either by a simple graphical procedure or with the use of a digitizing x-y-table, by a computer. With the computer method the films are placed on the digitizing table and the target and a few reference points are marked using a cursor. From the relative positions the computer calculates the coordinates. With the special head fixation system, coordinates of structures visualized in radiographic examinations can be transferred to various therapeutic or diagnostic stereotaxic devices.

A Simple Graphical Procedure for Rapid Estimation of Ash in Coal by X-Ray Back-Scattering

This paper describes a simple graphical calibration procedure for rapid determination of ash content in coal samples. The results obtained with this procedure are compared with those obtained earlier with the use of a regression equation. The two results are found to be in agreement.

Two-dimensional steady-state temperature distributions and heat flows in square corners

The Schwartz-Christoffel transformation is applied to the case of symmetrical and asymmetrical square corners, with solid walls and isothermal surfaces. The steady-state patterns of temperature distribution and of heat flow lines are shown. The distribution of heat flow intensity along the inside surfaces is illustrated for a range of wall thickness ratios. The Finite Element Method is applied to obtain the components of the maximum intensity occurring at the point where the two inside surfaces meet, and the results are tabulated for a range of wall thickness ratios. The total rate of heat flow for various cases is compared with that obtained from an analytical expression derived by Carslaw and Jaeger. ( Conduction of Heat in Solids, 2nd edn, p. 454). This is an approximate expression, asymptotically correct at points distant from the corner, but involving some error near to the corner. A simple graphical procedure is demonstrated, which now permits the total heat flow to be calculated at any distance from the inside corner. Additionally, a method is shown for finding the distance from the corner at which the analytical equation applies within a given error.

Comparison of optimization criteria for solar heating and some energy conservation measures

In this paper, the use of four different economic indices for optimal sizing of thermal insulation, recovery heat exchangers and solar heating systems is investigated. This results in two different optimum system sizes, the first corresponding to the maximum life-cycle savings and the second which gives the minimum payback period. For thermal insulation and the recovery heat exchanger, these optima may be obtained from non-dimensional charts. For solar heating, simple graphical procedures are obtained for the purpose of determining the optimum collector area.

Economic designs for single-layer toroidal inductors

Maxwell's problem of winding the greatest possible inductance with a given length of wire is examined for single-layer toroids. Optimum designs are obtained when the turns are square or circular or the Shafranov D-shape. In each case the optimum number of turns is proportional to the square root of the wire length, and the best obtainable inductance increases approximately as the three-halves power of the wire length. A simple graphical procedure achieves the most economical design for a required inductance and current rating.

Exploring reliability data

AbstractDespite the recent revolution in statistical thinking and methodology. practical reliability analysis and assessment remains almost exclusively based on a black‐box approach employing parametric statistical techniques and significance tests. Such practice, which is largely automatic for the industrial practitioner, implicity involves a large number of physically unreasonable assumptions that in practice are rarely met. Extensive investigation of reliability source data indicates a variety of differing data structures, which contradict the assumptions implicit in the usual methodology. As well as these, lack of homogeneity in the data, due, for instance, to multiple failure modes or misdefinition of environment, is commonly overlooked by the standard methodology.In this paper we argue the case for exploring reliability data. The pattern revealed by such exploration of a data set provides intrinsic information which helps to reinforce and reinterpret the engineering knowledge about the physical nature of the technological system to which the data refers. Employed in this way, the data analyst and the reliability engineer are partners in an iterative process aimed towards the greater understanding of the system and the process of failure. Despite current standard practice, the authors believe it to be critical that the structure of data analysis must reflect the structure in the failure data. Although standard methodology provides an easy and repeatable analysis, the authors' experience indicates that it is rarely an appropriate one. It is ironic that whereas methods to analyse the data structures commonly found in reliability data have been available for some time, the insistence about the standard black‐box approach has prevented the identification of such ‘abnormal’ features in reliability data and the application of these approaches. We discuss simple graphical procedures to investigate the structure of reliability data, as well as more formal testing procedures which assist in decision‐making methodology. Partial reviews of such methods have appeared previously and a more detailed development of the exploration approach and of the appropriate analysis it implies will be dealt with elsewhere. Here, our aim is to argue the case for the reliability analyst to LOOK AT THE DATA. and to analyse it accordingly.

Analysis of equivalence for the Schlumberger resistivity methods using the RHO-R and RHO-C curves in the resistivity transform domain

The problem of equivalence in the resistivity methods is studied in the resistivity transform domain. The RHO-R and RHO-C curves, which are, respectively, determined by the transverse resistance and longitudinal conductance, are shown to define the asymptotes of the resistivity transform curve. Models which give almost identical asymptotes also give almost identical resistivity transform curves. Thus, equivalent models can be found by obtaining models which do not change the shape of these asymptotes. For a given layered model, a plot of the RHO-R, RHO-C, and resistivity transform curves graphically shows the range of equivalence of the model. Equivalent models can be obtained by changing either resistivity, thickness, or depth of the given model through a simple graphical procedure.

A Schmitt Trigger Design Technique for ‘Logic-Noise-Spike’ Elimination

A simple graphical procedure is introduced to optimise the design of a regenerative comparator (Schmitt trigger) capable of eliminating from a logic voltage waveform both positive-going ‘noise spikes’ contaminating the ‘0’ level (positive logic convention) and negative-going noise spikes contaminating the ‘1’ level.

Analysis of Equivalence for the Schlumberger Resistivity Methods Using the RHO-R and RHO-C curves in the Resistivity Transform Domain

The problem of equivalence in the resistivity methods is studied in the resistivity transform domain. The RHO-R and RHO-C curves, which are, respectively, determined by the transverse resistance and longitudinal conductance, are shown to define the asymptotes of the resistivity transform curve. Models which give almost identical asymptotes also give almost identical resistivity transform curves. Thus, equivalent models can be found by obtaining models which do not change the shape of these asymptotes. For a given layered model, a plot of the RHO-R, RHO-C, and resistivity transform curves graphically shows the range of equivalence of the model. Equivalent models can be obtained by changing either resistivity, thickness, or depth of the given model through a simple graphical procedure.

MAPPING SOLAR ACCESS IN HIGH RELIEF AREAS FOR REGIONAL ENERGY PLANNING∗

Access to the sun for space heating of structures is controlled, in part, by topographic shadowing in high-relief regions. A simple graphic procedure is presented for mapping shadows on topographic maps for any date and time of day. Comparisons of computed shadows and shadows measured from aerial photography confirm that the mapping procedure is reliable and accurate. Use of the procedure as a solar access inventory tool is illustrated in an area of the Green Mountains, VT.

Single Crane Location Optimization

This paper involves the development of a mathematical prescriptive model to establish the optimal location of a crane within a construction site. The objective function of the model is the minimization of the total transportation cost between the crane and construction supportive facilities that are serviced by the crane. The technique developed considers radial and angular movement of construction materials. A simple graphical procedure is developed to facilitate the use of the model.

Determination of Michaelis parameters from differentials of progress curves.

First differentials of progress curves are easily obtainable in many enzyme assay systems. Such curves may be more readily applicable to kinetic analysis than are the usual progress curves. The theory for this approach is developed, and simple graphical procedures for the determination of Michaelis parameters are indicated. By using an electronic differentiator device the application of the method is demonstrated on the kinetics of three different serine proteinases with various synthetic substrates. Whenever the steady-state concentration of an intermediate of the reaction is proportional to the rate, the transition of this intermediate in substrate-depletion experiments may be analysed in similar terms. This is demonstrated with cytochrome c oxidase kinetics. A number of other possible applications are discussed.

A study on GRP skin/foam core sandwich structures

This paper presents a simple graphical procedure which allows a structural sandwich beam or panel to be designed from grp skin and foam core materials, so that the weight of the sandwich is a minimum. The method is based upon the well-known equations for bending rigidity, bending moment and weight of a sandwich beam.

A graphical solution for predicting the increase in strength of concrete slabs due to membrane action

Synopsis A simple graphical procedure for determining the effect of membrane action upon the load capacity of a rigid-perfectly-plastic reinforced concrete slab is presented. The load-enhancement-deflection curve is derived by asimple reflection of the yield criterion curve for the concrete section under axial force and moment. The method provides an immediate understandingof the effect of section design upon the load enhancement to be expected from membrane action.

Closure to “ Vadose Zone Permeability Tests: Unsteady Flow ” by D. B. Stephens and S. P. Neuman (May, 1982)

Saturated-unsaturated flow models are used to simulate transient conditions in four soils during constant head borehole infiltration tests in the vadose zone. Infiltration rate varies directly with saturated hydraulic conductivity and is also influenced by unsaturated soil properties, antecedent moisture conditions, anisotropy and borehole conditions. The method recommended by the U.S. Bureau of Reclamation to determine when to terminate a test may lead to overestimating saturated hydraulic conductivity. Simple graphical procedures are developed to overcome field problems associated with large water volume requirements or long time required to reach steady state by using early time date to estimate the steady infiltration rate.

Discrete cell model of pore‐mouth poisoning of fixed‐bed reactors

AbstractCatalyst deactivation in an isothermal fixed‐bed reactor under pore‐mouth poisoning conditions is investigated theoretically using a discrete mixing cell model. Two fundamental relationships which characterize the poisoning process in the reactor are identified and incorporated into the model to develop a simple graphical procedure for a quick, general insight into the problem. This graphical method is extended to design pellet impregnation profiles along the reactor which would give nondeteriorating reactor performance up to a given time. The effects of various system parameters on the lifetime and conversion performance of the reactor are also examined analytically, graphically and numerically.

Tri-axial ellipsoids as models for macromolecules in solution: Procedures for numerical inversion of the shape functions leading to a stable unique solution

Two FORTRAN IV algorithms are given for determining the two axial ratios of a macromolecule (as modelled by a tri-axial ellipsoid) from its hydrodynamic parameters. The first involves a simple graphical inversion procedure of the volume independent A and R functions but can only be applied to a restricted range of macromolecules. The second algorithm is more general and involves an R-function constrained non-linear least squares fit to birefringence decay data.

Exact computation of the reflectance of a surface layer of arbitrary refractive-index profile and an approximate solution of the inverse problem

The angular reflectance of a graded-index layer, of arbitrary refractive-index profile, on the surface of a uniform substrate is calculated exactly by direct numerical integration of the wave equation for both states of polarization of the incident light. A study of the results for a number of selected profiles shows that (1) oscillations in reflectance versus wave-number graphs have an almost constant period, and (2) the period, when plotted against angle of incidence, gives a curve that is quite sensitive to the shape of the refractive-index profile. This sensitivity is the basis of a simple graphical procedure by means of which the inverse problem (i.e., deducing the index profile from reflectance measurements) can be solved. The procedure is applied to published reflectance data to determine both the thickness of a graded-index surface layer and the refractive-index profile.