Measurement uncertainty volume measuring

The general list of factors influencing the uncertainty in the gross rock volume included the shape of structure, dip of flanks, position of bounding faults, position of internal faults, and depth of fluid contacts (in this case the OWC). In the above example, the owe is penetrated by two wells, and the dip of the structure can be determined from the measurements made in the wells which in turn will allow calibration of fhe 3D seismic. 

Reservoir engineers describe the relationship between the volume of fluids produced, the compressibility of the fluids and the reservoir pressure using material balance techniques. This approach treats the reservoir system like a tank, filled with oil, water, gas, and reservoir rock in the appropriate volumes, but without regard to the distribution of the fluids (i.e. the detailed movement of fluids inside the system). Material balance uses the PVT properties of the fluids described in Section 5.2.6, and accounts for the variations of fluid properties with pressure. The technique is firstly useful in predicting how reservoir pressure will respond to production. Secondly, material balance can be used to reduce uncertainty in volumetries by measuring reservoir pressure and cumulative production during the producing phase of the field life. An example of the simplest material balance equation for an oil reservoir above the bubble point will be shown In the next section. 

There are a few basic numerical and experimental tools with which you must be familiar. Fundamental measurements in analytical chemistry, such as mass and volume, use base SI units, such as the kilogram (kg) and the liter (L). Other units, such as power, are defined in terms of these base units. When reporting measurements, we must be careful to include only those digits that are significant and to maintain the uncertainty implied by these significant figures when transforming measurements into results. 

Suppose that you need to add a reagent to a flask by several successive transfers using a class A 10-mL pipet. By calibrating the pipet (see Table 4.8), you know that it delivers a volume of 9.992 mL with a standard deviation of 0.006 mL. Since the pipet is calibrated, we can use the standard deviation as a measure of uncertainty. This uncertainty tells us that when we use the pipet to repetitively deliver 10 mL of solution, the volumes actually delivered are randomly scattered around the mean of 9.992 mL. 

A standard solution of Mn + was prepared by dissolving 0.250 g of Mn in 10 ml of concentrated HNO3 (measured with a graduated cylinder). The resulting solution was quantitatively transferred to a 100-mL volumetric flask and diluted to volume with distilled water. A 10-mL aliquot of the solution was pipeted into a 500-mL volumetric flask and diluted to volume, (a) Express the concentration of Mn in parts per million, and estimate uncertainty by a propagation of uncertainty calculation, (b) Would the uncertainty in the solution s concentration be improved... 

Reduced Equations of State. A simple modification to the cubic van der Waals equation, developed in 1946 (72), uses a term called the ideal or pseudocritical volume, to avoid the uncertainty in the measurement of volume at the critical point. 

It is conventional to take as the activation volume the value of AV when P = 0, namely —bRT. (This is essentially equal to the value at atmospheric pressure.) Pressure has usually been measured in kilobars (kbar), or 10 dyn cm 1 kbar = 986.92 atm. The currently preferred unit is the pascal (Pa), which is 1 N m 1 kbar = 0.1 GPa. Measurements of AV usually require pressures in the range 0-10 kbar. The units of AV are cubic centimeters per mole most AV values are in the range —30 to +30 cm moP, and the typical uncertainty is 1 cm moP. Rate constant measurements should be in pressure-independent units (mole fraction or molality), not molarity. ... 

Anyone making a measurement has a responsibility to indicate the uncertainty associated with it. Such information is vital to someone who wants to repeat the experiment or judge its precision. The three volume measurements referred to earlier could be reported as... 

The experimental data in Table l-II show that decreasing the volume by one-half doubles the pressure (within the uncertainty of the measurements). How does the particle model correlate with this observation We picture particles of oxygen bounding back and forth between the walls of the container. The pressure is determined by the push each collision gives to the wall and by the frequency of collisions. If the volume is halved without changing the number of particles, then there must be twice as many particles per liter. With twice as many particles per liter, the frequency of wall collisions will be doubled. Doubling the wall collisions will double the pressure. Hence, our model is consistent with observation Halving the volume doubles the pressure. 

In a recent study, Huan et al. [25] performed NM R experiments in vibrofluidized beds of mustard seeds in which the small sample volume allowed pulses short enough that displacements in the ballistic phase were distinguishable from those in the diffusion phase. In this case, the average collision frequency is measured directly, bypassing the uncertainty of the multiplicative factor mentioned above. These workers also measured the height dependence of the granular temperature profile. 

The flatness of the computed curves in Fig. 6 shows that in the case of spheres in contact F is insensitive to rather large changes in V (or / ). Mason and Clark (M3) have measured the pendular bonding force as a function of the separation distance and bridge volume. Considering the experimental uncertainty involved, their results follow the expected trend quite satisfactorily. 

We have a second standard uncertainty for the volume of the volumetric flask. This estimate was obtained by making replicate measurements of the volume. The two standard uncertainties relating to the volume must be combined to produce a single value. This is achieved by a straightforward application of equation (6.12) ... 

Similarly, the overall precision of the volume measurement is obtained. An allowance for the uncertainty in the colour change observation at the end point must be included (e.g. 0.03 cm3... 

Since V = (2.1)2x 5.3 cm3, the estimate of the volume is 73 8 cm3-a surprisingly high uncertainty, given the relatively small uncertainties in the measurement of height and radius. This shows the cumulative properties of errors. 

The theory behind every measurement method can be generalised by Eq (1) [1]. Some quantity (or quantities, measurands) is measured, which has a specific relationship to the sought quantity. The measurand can be regarded to be a stochastic variable associated with an uncertainty, which implies that the sought quantity is also a random variable. The mathematical relationship depends on the physical model, that is, the model of the physical phenomenon of interest, for example temperature, pressure, and volume flow. The physical model always includes limitations, which implies that the measurement method has restrictions that is, it will only function in a certain measuring range and according to the assumption of the model. 

Attempts have been made, using helium, to measure the density of the adsorbed phase 108-110) to try to find out whether the films are to be thought of as gaslike or liquidlike. The volume of the adsorbent was determined before adsorption, and then after a known amount of gas had been adsorbed. It was concluded 109) that the adsorption of helium, although small, was finite, introducing uncertainty in the results. Furthermore, while the concept of density is useful when multilayers are considered, it is not necessarily so at coverages less than unity. 

For the specification of the measurand we need a statement of what we want to measure and at the same time a formula for the result which contains all relevant uncertainty sources. The example in the shde describes the calculation of the result of a determination of the amount of cadmium released from ceramic ware under certain conditions. The result depends on the content of Cd in the extraction solution Co, the volume of the leachate Vl, the surface area ay that is extracted and possibly a dilution factor. These parameters are used to calculate the result. But we also have to consider that the acid concentration, the extraction time and the temperature are influencing the result. Since they are not directly involved in the calculation of the result, we add factors with the value 1. But we assume that this value 1 will have an uncertainty as well. 

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