The Rate of Decolorization of a Radical Ion Reagent Was Used to Determine the Phenolic Content of Various Food Extracts

Polyphenols are among the most valuable and widely studied food components. In the laboratory, they are readily extractable with aqueous alcohol. An aliquot rapidly decolorizes a measured portion of ABTS, a stable deep blue radical ion. The semilog plot of light absorption versus time is typically a straight line, and an immediately evident slope provides rapid classification in terms of gallic acid equivalents. Experimental data are presented to show general agreement with the literature. The disproportionate concentration of antioxidant in the skins and peels of fruits, vegetables, and nuts is given special attention.

Uncertainties in Standard Analyses of Boundary Effects in Buildup Data

Summary Boundary effects are often observed in buildup data—or at least that is the conclusion frequently drawn from an observed increase in derivative on a log-log plot or an increase in slope on a semilog plot. Furthermore, if (for instance) it is concluded that the effects of a sealing fault are seen in a given data set, then simple line methods or direct analytical-modeling efforts are normally used to determine the distance to the boundary. A sealing fault is the normal choice of boundary model if a doubling is observed in derivative or semilog slope. If a four-fold increase in derivative is observed, then a model with the well placed somewhere between two sealing faults forming a right angle would be a normal choice. But what if the two faults are not sealing? If the flow capacity on the other side of the faults is only one-third of the value on the well side, what will be the derivative characteristics? Problems like these are addressed in detail in this paper, with a series of simple rules given for possible combinations that will generate buildup data of a specific type (i.e., with specific "familiar characteristics"). The rules can be used to list alternative interpretations without running separate analyses. For instance, it is shown that the derivative characteristics of any sector model bounded by sealing faults correspond to an infinite number of two-zone sector models with an angle between the boundaries and permeability contrast satisfying a single equation. Other pairs of models with similar characteristics are models with partially sealing faults and specific three-zone sector models, and either of these types of models and radial composite models. This clearly complicates analyses. Also addressed are problems related to possible differences in the boundary effects observed in drawdown and buildup data for certain models. As one example, U-shaped and sector models can have identical buildup characteristics over a wide time range, although drawdown data from the models have distinctly different boundary characteristics. Radial composite and composite sector models are also of this type, with potentially significant differences between drawdown and buildup data. The reason for bringing up such cases is to emphasize the importance of attempting to collect high-quality drawdown data in addition to buildup data to limit the range of possible interpretation models. For completeness, effects of uncertainties in basic input parameters on the final analyses are also covered in the paper. Introduction It is well known that buildup data from a well near a sealing fault might exhibit a doubling of derivatives on a log-log diagnostic plot, as illustrated in Fig. 1. This doubling of derivatives corresponds to a doubling of slope on a semilog plot, as shown by Horner, and refers to a change between early and late data requiring storage effects to become negligible and radial flow to be reached before the onset of boundary effects. For this behavior to occur, it is also necessary for the flow period before shut-in to be long enough to be fully or almost fully affected by the boundary effect.

Effect of Flow Time Duration on Buildup Pattern for Reservoirs With Heterogeneous Properties

For a heterogeneous reservoir, the shape of a buildup curve is strongly dependent on the length of the preceding flow period. Therefore, in exploration well testing, where the flow period is usually short, modification of the pressure buildup pattern caused by insufficient flow time can lead to erroneous interpretation of well behavior. Buildup pattern, as a function of flow time, is discussed here for various types of pattern, as a function of flow time, is discussed here for various types of ideal heterogeneities such as linear reservoir discontinuities, natural fractures, vertical stratification, pressure support, and lateral permeability loss. A relationship is provided for the dimensionless flow permeability loss. A relationship is provided for the dimensionless flow time required to produce a certain buildup pattern. The effect of flow time on quantitative assessment of reservoir parameters is determined aswell. Introduction Well test analysis traditionally has been based on techniques developed for either drawdown calculations or buildup calculations after long flow periods. In exploration well testing, however, flow times prior to buildup periods. In exploration well testing, however, flow times prior to buildup tests are usually short. For a well in a reservoir with homogeneous properties and of infinite extent, the shape of neither the drawdown curve properties and of infinite extent, the shape of neither the drawdown curve nor the ensuing buildup curve is affected by flow time duration. Both are straight lines of a certain slope on a semilog plot of pressure vs. time. However, this is not the case for a reservoir with heterogeneous properties. For a heterogeneous reservoir in which a well shows a drawdown properties. For a heterogeneous reservoir in which a well shows a drawdown curve with multiple slopes on a semilog plot as production progresses, the drawdown as well as the buildup patterns become essentially dependent or the producing time. Moreover, for a given flow time, the drawdown curve and the following buildup curve may have different shapes. In well test analyses where the shape of pressure curves is used to evaluate reservoir properties, recognition of the pressure pattern alterations caused by properties, recognition of the pressure pattern alterations caused by insufficient flow time becomes important. In the case of a linear discontinuity such as a sealing fault, for example, it has been found that the buildup data on a Homer plot would show the second, double-slope straight-line characteristic of the fault only if the radius of investigation, before the well is shut in exceeds at least four times the distance, to the fault, = . Even this criterion is optimistic from a practical point of view. All buildup data exhibiting this characteristic double slope will be at relatively long shut-in times for which the Homer time ratio ( + ) is less than1.5. Since actual data seldom extend into this range, longer flow time swill be necessary. In what follows, the modification of buildup pattern caused by insufficient flow time is considered along with the specification of both the flow time and buildup time necessary to recognize a heterogeneity from its characteristic buildup pattern . The heterogeneities considered aresingle no-flow and constant pressure boundaries,single boundary with permeability and storage contrasts,multiple boundaries,radial loss in permeability,vertical stratification, andnatural fractures. Reservoir Limited by One or More Boundaries Linear No-Flow Boundary. Drawdown at a well producing a reservoir limited by an impermeable barrier, such as a sealing fault, according to the method of images that duplicates such a boundary mathematically, is and ............................(1) where ( ) is the exponential integral function, is the distance from the well to the fault, and = is the dimensionless flow lime. The characteristic drawdown pattern for a well near a sealing boundary, described by Eq. 1 and illustrated by the insert in Fig. 1, depicts on a semilog plot a curve consisting of two straight lines joined by a smooth transition. The first straight line represents the well response before the fault exerts any influence. The slope of this straightline, is inversely proportional to the reservoir transmissibility. This line is referred to as the middle-time region (MTR) line. The second straight line, formed after a smooth transitional period, represents the well behavior as affected by the fault. Its slope is twice that of the first straight line. The intersection of the two straight lines occurs at a nondimensional time ............................(2) The transition region between these two straight lines lasts, however, for more than one log cycle. The slope of the drawdown curve, ............................(3) SPEJ p. 294

Predicting When Children with Progressive Renal Disease May Reach High Serum Creatinine Levels

A method for predicting when children with progressive renal disease may reach high levels of serum creatinine (SC) was recently described in this journal.1 The authors did not seem to be aware that the same technique, ie, plotting the reciprocal (1/SC) or the logarithm (log SC) vs time has been tested in two slightly larger series of pediatric patients and was published some time ago.2,3 I agree that the reciprocal plot (1/SC vs time) is, in general, more appropriate than the semilog plot in predicting when a critical concentration of SC, say 10 mg/100 ml, may be reached.