Akaike (1999) explains that "Time series analysis intends to grasp the characteristics of the temporal movement or the dynamics of an object,

and its final purpose is the realization of an adequate prediction." In this section, an innovative methodology introduced by Hayatdavoudi (1999) for interpretation of the production data by means of the Fourier series analysis is presented. Hayatdavoudi (1999) explains that "the Fourier periodiagram coefficients, frequency, and phase changes of the gas-water ratio of the monthly production data indicate a certain predictable precursor (signature) to the drop in oil production and formation damage prior to the onset of the real production decline." But, his applications have focused on the detection of the Fourier phase changes in the oil production data.

However, he points out that such a precursor may indicate the total skin as an integral contribution of the loss of the reservoir drive energy during flow through formation, perforations, well, and surface equipment. The changes in the produced gas-water ratio, which depends on the solubility of light gases (CH4, CO2, etc.) in the reservoir brine, is an important precursor to changes in oil production because dissolved gas liberation provides a significant source of the reservoir drive energy (Hayatdavoudi, 1999).

Hayatdavoudi (1999) considers the produced oil and gas data as a time series signal, oscillating with certain frequency and phase, which signals certain specific characteristics of the production regime, with an amplitude measured as pressure or the pressure and rate product. Hayatdavoudi (1999) analyzed the well production signals using the Fourier transform method.

To demonstrate the applications of the time series analysis, Hayatadavoudi (1999) considered two different wells:

Well No. 1 which could not be stimulated by acidizing, and

Well No. 2 that could be successfully stimulated by acidizing.

Hayatdavoudi (1999) shows the monthly production of the gas, oil and water, and the gas-water ratio for

Well No. 1. As can be seen, the oil production decreased gradually, and the gas and water productions increased gradually. Although, the well was acidized at the end of Month 156, no appreciable production increase was observed. Therefore, it was concluded that the acidizing did not stimulate the well. Hayatdavoudi (1999) shows the change of phase angle of the gas-water ratio, considered as a precursor to changes in oil production. The phase angle (pc} began widening at Month 32. Therefore, Month 32 is considered the onset time of the formation damage. Hayatdavoudi (1999) recommends a low-cost preventive workover at Month 32 to delay or eliminate the need for acidizing of this well.

Hayatdavoudi (1999) shows the production data for Well No. 2, for which the change in the phase angle and, therefore, the formation damage began at Month 33, as indicated Hayatdavoudi (1999). Notice the widening of the phase angle pattern

beginning with Month 33 through Month 156, at which time the well was acidized. Therefore, Hayatdavoudi (1999) recommends a low cost preventive workover at Month 33 for Well No. 2. Because this preventive workover has not been made, Well No. 2 had to be acidized at the end of Month 156, which was more costly. Notice the significant tightening of the phase angle pattern following Month 156, indicating that the acidizing successfully stimulated Well No. 2. The preceding exercises conducted by Hayatdavoudi (1999) indeed indicate that the change of the phase angle of the gas-water ratio is an effective precursor or signal for detection of the changes in the reservoir formation flow properties. This signal can be used to apply low-cost preventive measures at the onset of formation damage to avoid the need of costly stimulation treatments in the future.

Formation Damage Expert System

Development and application of knowledge and simulator-based expert systems for diagnosis, analysis, and mitigation of various formation damage and restoration processes are of continuing interest to the petroleum industry. Formation damage is a generic terminology, representing a large variety of adverse interactive processes causing flow impairment in petroleum reservoirs in a lumped manner. In a true sense, there is no fully computerized and capable formation damage expert system available today. This is because formation damage occurs by many processes in a complicated manner that are not yet fully understood.

Efforts are being made to understand and theoretically describe the governing processes. Quantitative determination of the various theoretical parameters at near in situ conditions will take a long time. As described in the previous chapters, modeling of various formation damage processes is an ongoing chore for the petroleum industry. Therefore, a truly useful formation damage advisor and expert program is a dream to accomplish in the future. However, companies and research institutions are developing proprietary expert systems with emphasis on certain specific applications. These systems capture the present state-of-the-knowledge in a systematic manner and make it available for analysis of specific types of formation damage problems.

Such computerized systems integrate various pertinent knowledge, including the rule-of-thumbs, guidelines, recipes, and mathematical models generated in particular areas of formation damage to apply to similar problems rapidly. The accuracy and capability of such expert systems are limited to the amount and quality of information available, which continually improves with research growth and experience with similar problems. Simulators, dressed-up with colorful high-resolution graphics software, may lack the theoretical rigor of the phenomenological equations and/or accurate properties and rate data necessary for accurate history matching and prediction of the formation damage scenarios. Development of a truly useful formation damage expert requires an interdisciplinary effort and will take a long time.


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