Formation compressibility has long been recognized as an important factor influencing production behavior from overpressured oil and gas reservoirs. However, formation compressibility data are not routinely collected and the use of formation compressibility in reservoir analysis and simulation is often oversimplified. This paper discusses more accurate methods to determine formation compressibility and introduces a new method for analyzing overpressured oil and gas reservoirs which utilizes the variability of formation compressibility with declining reservoir pressure. The newly developed method departs from earlier proposed methods in the use of variable rather than~formation compressibility by employing a "pore volume formation volume factor", Bt, that properly integrates pore volume compressibility effects over the full pressure range of investigation. Using the new concept of Bt, the material balance equation (MBE) can be modified to include the effects of pressure dependent formation compressibility.We find that the formation compressibility in highly overpressured unconsolidated reservoirs can be the same order of magnitude as gas compressibility and significantly higher than oil compressibility. In some types of reservoirs, an order of magnitude change in formation compressibility can occur during drawdown. We show that in many overpressured and/or unconsolidated reservoirs, proper integration of accurate formation compressibilities is important for reserve estimates, determination of drive energies, and overall reservoir development plans. For example, we find that the use of compressibility values in the MBE which are significantly lower than those which exist in the reservoir could suggest a strong water drive where one does not exist.

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<p style='text-indent:20px;'>The paper deals with global existence and blow-up results for a class of fourth-order wave equations with nonlinear damping term and superlinear source term with the coefficient depends on space and time variable. In the case the weak solution is global, we give information on the decay rate of the solution. In the case the weak solution blows up in finite time, estimate the lower bound and upper bound of the lifespan of the blow-up solution, and also estimate the blow-up rate. Finally, if our problem contains an external vertical load term, a sufficient condition is also established to obtain the global existence and general decay rate of weak solutions.</p>

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