![]() There are two very special cases of the logarithm which have unique notation: the natural logarithm and the logarithm with base 10.For example:Īnd for those who prefer symbols instead of bunnies, here's the formal definition of a logarithm:īefore we expand the logarithmic expressions and see the formulas, let's mention a few essential facts concerning logs: However, as opposed to logarithms, roots return the exponent base, not the exponent itself (in the above language: they return the size of a single litter, not the number of generations that have to pass). Note that taking a root is also considered an inverse operation to taking a power. Observe that the little 6 corresponds to the size of a single litter. Our animal example corresponds to wondering how many generations have to pass before we get a fixed number of little ones. The logarithm is the inverse operation to an exponent. Therefore, if each of a couple's kids got another 6 small ones later in life (with an outside partner, of course), and the same for their kids, and their kids, then we can calculate how big the fourth generation is with a new mathematical tool: exponents: Obviously, the next generation has similar interests to their parents. Therefore, if, for instance, we had 4 couples and each got 6 younglings, we describe the overall number of little ones using multiplication: ![]() The meeting of two such animals (of the opposite sex, of course) leads to more rabbits. From the very moment two rabbits met each other and decided to prolong the existence of their species, all they had in mind was mathematics, even if they didn't quite know it.Īpart from raising the probability of their survival (which, as we know, was very successful), the rabbits managed to become a symbol of multiplication. The reservoir discussed in this paper is high pressure (>20,000 psi), which limits logging tool availability and evaluation techniques.Some of you may disagree, but deep down, we all know that mathematics lies at the bottom of it all. All logging tools have a borehole signature which must be removed before formation salinity can be estimated. Some of these measurements have a very shallow depth of investigation and their interpretation can become very complicated when OBM invasion occurs. Logs that can be used for evaluation of salinity are 2D NMR, NMR antenna gain, NMR antenna "Q" factor, and neutron-gamma spectroscopy. Some log measurements contain a signature of salinity, brine composition or brine volume in the reservoir. These few drops are sufficient to obtain ambient conditions measurement of water resistivity and complete chemical analyses if sample handling and analysis protocol is strictly followed. Ultra centrifuging core samples may only produce a few drops of brine, particularly if the core is high on structure and water saturations are at or near irreducible. ![]() If clays are present, clay-bound water corrections may be required. Correctly calculating formation brine salinity from Dean Stark crush-and-leach protocol requires corrections for additional anion and cation produced by mineral dissolution and mineral reactions. These core-based methods include extracting salts (Dean Stark crush-and-leach) or by expelling formation brine by ultra centrifuging the samples. These techniques are not new but are often conducted incorrectly. When conventional core is cut with oil-based mud (OBM) it is possible to estimate salinity directly. ![]() Obtaining formation water resistivity directly from the hydrocarbon-bearing interval is not as simple. Aquifer water resistivity can also be indirectly estimated using Picket plots. In water legs, salinity can be determined directly using two techniques produced water samples, or by centrifuging free water out of conventional core cut with oil-based mud. Cores and specialized logs can be used to obtain more representative formation water-resistivity values, which will improve water saturation calculations in hydrocarbon-bearing intervals. The assumption that water properties in the water leg are the same as those in the hydrocarbon leg needs to be proved, not assumed. Water saturation in exploration, appraisal and early development wells is usually computed from resistivity logs.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |