Observation data

Once production commences, data such as reservoir pressure, cumulative production, GOR, water cut and fluid contact movement are collected, and may be used to history match the simulation model. This entails adjusting the reservoir model to fit the observed data. The updated model may then be used for a more accurate prediction of future performance. This procedure is cyclic, and a full field reservoir simulation model will be updated whenever a significant amount of new data becomes available (say, every two to five years). 

This paper is structured as follows in section 2, we recall the statement of the forward problem. We remind the numerical model which relates the contrast function with the observed data. Then, we compare the measurements performed with the experimental probe with predictive data which come from the model. This comparison is used, firstly, to validate the forward problem. In section 4, the solution of the associated inverse problem is described through a Bayesian approach. We derive, in particular, an appropriate criteria which must be optimized in order to reconstruct simulated flaws. Some results of flaw reconstructions from simulated data are presented. These results confirm the capability of the inversion method. The section 5 ends with giving some tasks we have already thought of. 

What is addressed by these sources is the ontology of quantal description. Wave functions (and other related quantities, like Green functions or density matrices), far from being mere compendia or short-hand listings of observational data, obtained in the domain of real numbers, possess an actuality of tbeir own. From a knowledge of the wave functions for real values of the variables and by relying on their analytical behavior for complex values, new properties come to the open, in a way that one can perhaps view, echoing the quotations above, as miraculous. ... 

Later in this section, we shall specify the analytic properties of the functions involved and obtain exact formulas similar to Eqs. (9) and (10), but less simple and harder to apply to observational data of, say, moduli. 

In the nonclassical ion controversy discussed in Chapter 9, there was never any question on either side of the debate about the validity of the observed data, only about their interpretation. Had any of the experimental data been questioned or found to be incorrect, this would have been soon found out because so many people repeated and rechecked the data. This is the strength of science (in contrast to politics, economics, etc.), i.e., that we deal with reproducible experimental observation and data. Nevertheless, interpretation can still result in heated discussions or controversies, but science eventually will sort these out based on new results and data. 

I. Under the null hypothesis, it is assumed that the respective two samples have come from populations with equal proportions pi = po. Under this hypothesis, the sampling distribution of the corresponding Z statistic is known. On the basis of the observed data, if the resultant sample value of Z represents an unusual outcome, that is, if it falls within the critical region, this would cast doubt on the assumption of equal proportions. Therefore, it will have been demonstrated statistically that the population proportions are in fact not equal. The various hypotheses can be stated ... 

Pauli spin susceptibility for the aligned CNTs has been measured and it is reported that the aligned CNTs are also metallic or semimetallic [30]. The temperature dependence of gn and gx s plotted in Fig. 5(a). Both values increase with decreasing temperature down to 40 K. A similar increase is observed for graphite. The g-value dependence on the angle 0 at 300 K is shown in Fig. 5(b) (inset). The g-value varies between gn = 2.0137 and gx= 2.0103 while the direction of magnetic fields changes from parallel to perpendicular to the tubes. These observed data fit well as... 

Observation Observation/Data Collection from instruments Unjustified Assumptions/Familiar Associations... 

With so many variables, expressions for convective heat flow cannot be as simple as those for conduction. The interpretation of observed data has been made possible by the use of a number of groups which combine the variables and which can then be used to estimate convective heat flow. 

How do we know that the carbocation mechanism for electrophilic addition reactions of alkenes is correct The answer is that we don t know it s correct at least we don t know with complete certainty. Although an incorrect reaction mechanism can be disproved by demonstrating that it doesn t account for observed data, a correct reaction mechanism can never be entirely proved. The best we can do is to show that a proposed mechanism is consistent with all known facts. If enough facts are accounted for, the mechanism is probably correct. 

Models can resolve apparent conflicts in observed data and can be used to optimally design experiments. 

Both Eq. (144) and Eq. (145) give values higher than the observed data, in particular for water-glycerol systems containing lower concentrations of glycerol. It should be mentioned that, in this comparison with experiment, the assumption is made that the suspended bubbles entrained by the fluid, which describe complicated trajectories in the fluid, are moving relative to the... 

Fig. 16. Graphical representation of Arrhenius parameters for the low temperature decomposition of ammonium perchlorate (pelleted, orthorhombic, o, and cubic, , forms). Compensation behaviour is observed. Data from Jacobs and Ng [452]. N = nucleation, B = branching, G = growth processes.

The evidence presented so far excludes the formation of dissociated ions as the principal precursor to sulfone, since such a mechanism would yield a mixture of two isomeric sulfones. Similarly, in the case of optically active ester a racemic product should be formed. The observed data are consistent with either an ion-pair mechanism or a more concerted cyclic intramolecular mechanism involving little change between the polarity of the ground state and transition state. Support for the second alternative was found from measurements of the substituent and solvent effects on the rate of reaction. 

The vibrational relaxation of simple molecular ions M+ in the M+-M collision (where M = 02, N2, and CO) is studied using the method of distorted waves with the interaction potential constructed from the inverse power and the polarization energy. For M-M collisions the calculated values of the collision number required to de-excite a quantum of vibrational energy are consistently smaller than the observed data by a factor of 5 over a wide temperature range. For M+-M collisions, the vibrational relaxation times of M+ (r+) are estimated from 300° to 3000°K. In both N2 and CO, t + s are smaller than ts by 1-2 orders of magnitude whereas in O r + is smaller than t less than 1 order of magnitude except at low temperatures. 

It is physically realistic to introduce a steric factor larger than unity, but to do so can be fairly arbitrary. In our study, the calculated Z values are consistently smaller than the observed data by a factor of 5 therefore, if a steric factor is introduced, it could best be assumed as 5. 

In general, the result of measurement is only an approximation or estimate of the value of the specific quantity subject to measurement, and thus the result is complete only when accompanied by a quantitative statement of its uncertainty. Because the reliability of evaluations of components of uncertainty depends on the quality of the information available, it is recommended that all parameters upon which the measurand depends be varied to the fullest extent practicable so that the evaluations are based as much as possible on observed data. 

Statistically speaking we are seeking the most likely set of basis coefficients given our observed data. Mathematically this can be written as,... 

Again an approach that chooses the displacement a to maximize the probability of obtaining the received data appears reasonable. This is illustrated in Fig. 4, where the two possible locations of the positioning of the pdf in Fig. 4(a) is clearly more consistent with the observed data than Fig. 4(b). Let us assume an ideal detector, one with a large number of pixels and with the only noise resulting from the discrete nature of photons. The probability of D photons in a pixel is given by... 

Figure 4. The estimation of the pdf from the observed data where (a) the pdf is consistent with the data, and (b) the pdf is inconsistent with the data.

To formulate a model is to put together pieces of knowledge about a particular system into a consistent pattern that can form the basis for (1) interpretation of the past history of the system and (2) prediction of the future of the system. To be credible and useful, any model of a physical, chemical or biological system must rely on both scientific fundamentals and observations of the world around us. High-quality observational data are the basis upon which our understanding of the environment rests. However, observations themselves are not very useful unless the results can be interpreted in some kind of model. Thus observations and modeling go hand in hand. 

Some historical data, meaningful in the experience of early scientists, might not be meaningful or accessible to modem students. For example, observational data about planetary motion (or even the nature of planetary motion itself) is not something which easily eonneets with the everyday experienee of students today. 

Keeling, C.D., Bacastow, R.B., Carter, A.F., Piper, S.C., Whorf T.P, Heimann, M., Mook, W.G. and Roeloffzen, H. 1989 A three-dimensional model of atmospheric COj transport based on observed winds 1. Analysis of observational data. Geophysical Monographs 55 165-236. 

---