UNSTEADY-STATE SPHERICAL FLOW WITH STORAGE AND SKIN.

This paper presents short-time interpretation methods for radial-spherical (or radial-hemispherical) flow in homogeneous and isotropic reservoirs inclusive of wellbore storage, wellbore phase redistribution, and damage skin effects. New dimensionless groups are introduced to facilitate the classic transformation from radial flow in the sphere to linear flow in the rod. Analytical expressions, type curves (in log-log and semi log format), and tabulated solutions are presented, both in terms of pressure and rate, for all flow problems considered. A new empirical equation to estimate the duration of wellbore and near-wellbore effects under spherical flow is also proposed

Faber polynomials and poincare series

In this paper we consider weakly holomorphic modular forms (i.e., those meromorphic modular forms for which poles only possibly occur at the cusps) of weight 2−k∈2\Z for the full modular group \SL2(\Z). The space has a distinguished set of generators f2−k,m. Such weakly holomorphic modular forms have been classified in terms of finitely many Eisenstein series, the unique weight 12 newform Δ, and certain Faber polynomials in the modular invariant j(z), the Hauptmodul for \SL2(\Z). We employ the theory of harmonic weak Maass forms and (non-holomorphic) Maass–Poincaré series in order to obtain the asymptotic growth of the coefficients of these Faber polynomials. Along the way, we obtain an asymptotic formula for the partial derivatives of the Maass–Poincaré series with respect to y as well as extending an asymptotic for the growth of the ℓth repeated integral of the Gauss error function at x to include ℓ∈\R and a wider range of x.postprin

Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links.

Relationships to determine the probability that a weak link (WL)/strong link (SL) safety system will fail to function as intended in a fire environment are investigated. In the systems under study, failure of the WL system before failure of the SL system is intended to render the overall system inoperational and thus prevent the possible occurrence of accidents with potentially serious consequences. Formal developments of the probability that the WL system fails to deactivate the overall system before failure of the SL system (i.e., the probability of loss of assured safety, PLOAS) are presented for several WWSL configurations: (i) one WL, one SL, (ii) multiple WLs, multiple SLs with failure of any SL before any WL constituting failure of the safety system, (iii) multiple WLs, multiple SLs with failure of all SLs before any WL constituting failure of the safety system, and (iv) multiple WLs, multiple SLs and multiple sublinks in each SL with failure of any sublink constituting failure of the associated SL and failure of all SLs before failure of any WL constituting failure of the safety system. The indicated probabilities derive from time-dependent temperatures in the WL/SL system and variability (i.e., aleatory uncertainty) in the temperatures at which the individual components of this system fail and are formally defined as multidimensional integrals. Numerical procedures based on quadrature (i.e., trapezoidal rule, Simpson's rule) and also on Monte Carlo techniques (i.e., simple random sampling, importance sampling) are described and illustrated for the evaluation of these integrals. Example uncertainty and sensitivity analyses for PLOAS involving the representation of uncertainty (i.e., epistemic uncertainty) with probability theory and also with evidence theory are presented

Advancements in seismic tomography with application to tunnel detection and volcano imaging

Thesis (Ph.D.) University of Alaska Fairbanks, 1998Practical geotomography is an inverse problem with no unique solution. A priori information must be imposed for a stable solution to exist. Commonly used types of a priori information smooth and attenuate anomalies, resulting in 'blurred' tomographic images. Small or discrete anomalies, such as tunnels, magma conduits, or buried channels are extremely difficult imaging objectives. Composite distribution inversion (CDI) is introduced as a theory seeking physically simple, rather than distributionally simple, solutions of non-unique problems. Parameters are assumed to be members of a composite population, including both well-known and anomalous components. Discrete and large amplitude anomalies are allowed, while a well-conditioned inverse is maintained. Tunnel detection is demonstrated using CDI tomography and data collected near the northern border of South Korea. Accurate source and receiver location information is necessary. Borehole deviation corrections are estimated by minimizing the difference between empirical distributions of apparent parameter values as a function of location correction. Improved images result. Traveltime computation and raytracing are the most computationally intensive components of seismic tomography when imaging structurally complex media. Efficient, accurate, and robust raytracing is possible by first recovering approximate raypaths from traveltime fields, and then refining the raypaths to a desired accuracy level. Dynamically binned queuing is introduced. The approach optimizes graph-theoretic traveltime computation costs. Pseudo-bending is modified to efficiently refine raypaths in general media. Hypocentral location density functions and relative phase arrival population analysis are used to investigate the Spring, 1996, earthquake swarm at Akutan Volcano, Alaska. The main swarm is postulated to have been associated with a 0.2 km\sp3 intrusion at a depth of less than four kilometers. Decay sequence seismicity is postulated to be a passive response to the stress transient caused by the intrusion. Tomograms are computed for Mt. Spurr, Augustine, and Redoubt Volcanoes, Alaska. Relatively large amplitude, shallow anomalies explain most of the traveltime residual. No large amplitude anomalies are found at depth, and no magma storage areas are imaged. A large amplitude low-velocity anomaly is coincident with a previously proposed geothermal region on the southeast flank of Mt. Spurr. Mt. St. Augustine is found to have a high velocity core