One of classic but still a controversial problem is the determination of reservoir descriptions by pressure decline or production history curves. The data available from gas or oil reservoirs during production are oil, gas and water production histories, pressure history and history of produced hydrocarbon compositions. These histories are affected by permeability, porosity, reservoir size, original gas and oil in place and initial pressure, so that it may be possible to determine these reservoir descriptions from the profile of the various histories. Some previous authors ran to such an extreme as to determine heterogeneous permeabilities of a reservoir dividing it into more than 6 or 7 blocks. Another author went too far in saying that they can determine rock compressibility and water influx constant in addition to gas in place and aquifer volume only from gas production and pressure histories. But is it always possible to determine so many reliable parameters from such little information though most of the field data and mathematical models include various errors? This paper answers a certain aspect of this question applying a systematical error analysis to a parameter determination problem for a gas reservoir whose production histories are known.
The simplicity and versatility of the Kalman sequential filter has establish it as a fundamental tool in the analysis and solution of linear estimation problems. Petroleum engineers recently recognized it as a potential tool for regression analysis and applied it to non-linear problems. However numerical experience has shown that the Kalman filter algorithm is sensitive to computer round-off and that numeric accuracy sometimes degrades to the point where the results cease to be meaningful. In order to avoid this trouble, Potter proposed to decompose the covariance matrix into a square root covariance matrix. In this paper, the Potter's linear algorithm is applied to two non-linear problems, one of which is non-recurrence type and the other is recurrence type. The linearization of the non-linear functions proposed in this paper appears to be proper to the respective type mathematical models. In addition, two other methods for parameter determination are tested in this paper, which are suitable to mathematical problems with discontinuous functions.
The petroleum geology in China has been reported by several authors and the outline of the geologic conditions of the oil and gas fields in China can be understood through the published papers. It was reported that more than 50% of the Chinese petroleum production was from the Ta-ch'ing oilfield in the Sung-liao basin, Northeast China, in which the non-marine sediments of the Mesozic and Tertiary ages were deposited. Thus, the non-marine sedimentary basins rated highest in petroleum production in China. However, it is considered by the present author that the marine and paralic sediments of the Paleozoic and Mesozoic ages are of importance to the future petroleum exploration in China, especially in the inland regions of the continent. From this standpoint, the geological and geochemical aspects on the following items are described. 1) 382 oilfield in Tibet. This oilfield is located on an elevation of about 4, 000 meters and some 300km north of Lasa. Petroleum has probably been produced from the marine sediments of the Paleozoic and Mesozoic ages or the Tertiary lacustrine sediments. 2) Newly discovered oil and gas reservoirs in the Southwest Tarim basin. In the new oilfield located in between Aksu and Kashgar, Sowthwest Tarim basin, petroleum is probably produced from the marine and paralic sediments of the Mesozoic and Tertiary ages. 3) Geologic horizons of oil and gas reservoirs in the Central-Eastern China. The commercial petroleum production in the Jen-ch'iu and Sheng-li South oilfields was reported from the marine Paleozoic reservoirs. In the Szechwan basin, hydrocarbons have been produced from the marine Permian and Triassic reservoirs and from the non-marine Jurassic ones. In the Ch'ien-chang oilfield in the Tung-t'ing basin, the petroleum production is from the Devonian and Carboniferous reserviors. Thus, in the sedimentary basins along Yang-tze River, the marine Paleozoic and Mesozoic sediments including carbonate rocks, sandstones and shales probably are of importance to hydrocarcon exploration, bec- ause, it was reported by the Chinese exploration geochemists that in China even the Sinian carbonate rocks still keep up the potential for petroleum generation. 4) Natural gas in the coastal areas along the East China Sea. Many gas producing locations were found in the area. In the sedimentary basin near Shang-hai, the thickness of sediments ranges from 4 to 6km or more. It is considered by the author that the marine Paleozoic and Mesozoic sediments, the probable continental and paralic Tertiary sediments and the paralic Quaternary sediments are the main targets for hydrocarbon exploration in the Shang-hai area. In addition to this, in the South-East China, small but many sedimentary basins filled with the Mesozoic lacustrine deposits of only from several ten to several hundred meters thick are the economic exploration targets. As a conclusion, it is supposed that the marine and paralic sediments of the Paleozoic and Mesozoic ages in China have higher potential in hydrocarbon resources than have been estimated.