Adjoint formulation and constraint handling for gradient-based optimization of compositional reservoir flow

An adjoint formulation for the gradient-based optimization of oil–gas compositional reservoir simulation problems is presented. The method is implemented within an automatic differentiation-based compositional flow simulator (Stanford’s Automatic Differentiation-based General Purpose Research Simulator, AD-GPRS). The development of adjoint procedures for general compositional problems is much more challenging than for oil–water problems due to the increased complexity of the code and the underlying physics. The treatment of nonlinear constraints, an example of which is a maximum gas rate specification in injection or production wells, when the control variables are well bottom-hole pressures, poses a particular challenge. Two approaches for handling these constraints are presented—a formal treatment within the optimizer and a simpler heuristic treatment in the forward model. The relationship between discrete and continuous adjoint formulations is also elucidated. Results for four example cases of increasing complexity are presented. Improvements in the objective function (cumulative oil produced) relative to reference solutions range from 4.2 to 11.6 %. The heuristic treatment of nonlinear constraints is shown to offer a cost-effective means for obtaining feasible solutions, which are, in some cases, better than those obtained using the formal constraint handling procedure.     

Behaviour of deep immersed tunnel under combined normal fault rupture deformation and subsequent seismic shaking

Immersed tunnels are particularly sensitive to tensile and compressive deformations such as those imposed by a normal seismogenic fault rupturing underneath, and those generated by the dynamic response due to seismic waves. The paper investigates the response of a future 70 m deep immersed tunnel to the consecutive action of a major normal fault rupturing in an earthquake occurring in the basement rock underneath the tunnel, and a subsequent strong excitation from a different large-magnitude seismic event that may occur years later. Non-linear finite elements model the quasi-static fault rupture propagation through the thick soil deposit overlying the bedrock and the ensuing interaction of the rupture with the immersed tunnel. It is shown that despite imposed bedrock offset of 2 m, net tension or excessive compression between tunnel segments could be avoided with a suitable design of the joint gaskets. Then, the already deformed (“injured”) structure is subjected to strong asynchronous seismic shaking. The thick-walled tunnel is modelled as a 3-D massive flexural beam connected to the soil through properly-calibrated nonlinear interaction springs and dashpots, the supports of which are subjected to the free-field acceleration time histories. The latter, obtained with 1-D wave propagation analysis, are then modified to account for wave passage effects. The joints between tunnel segments are modeled with special non-linear hyper-elastic elements, properly accounting for their 7-bar longitudinal hydrostatic pre-stressing. Sliding is captured with special gap elements. The effect of segment length and joint properties is explored parametrically. A fascinating conclusion emerges in all analysed cases for the joints between segments that were differentially deformed after the quasi-static fault rupture: upon subsequent very strong seismic shaking, overstressed joints de-compress and understressed joints re-compress—a “healing” process that leads to a more uniform deformation profile along the tunnel. This is particularly beneficial for the precariously de-compressed joint gaskets. Hence, the safety of the immersed tunnel improves with “subsequent” strong seismic shaking!     

Seismic response of single-column bent on pile: evidence of beneficial role of pile and soil inelasticity

While seismic codes do not allow plastic deformation of piles, the Kobe earthquake has shown that limited structural yielding and cracking of piles may not be always detrimental. As a first attempt to investigate the consequences of pile yielding in the response of a pile-column supported bridge structure, this paper explores the soil–pile-bridge pier interaction to seismic loading, with emphasis on structural nonlinearity. The pile–soil interaction is modeled through distributed nonlinear Winkler-type springs and dashpots. Numerical analysis is performed with a constitutive model (Gerolymos and Gazetas 2005a, Soils Found 45(3):147–159, Gerolymos and Gazetas 2005b, Soils Found 45(4):119–132, Gerolymos and Gazetas 2006a, Soil Dyn Earthq Eng 26(5):363–376) materialized in the OpenSees finite element code (Mazzoni et al. 2005, OpenSees command language manual, p 375) which can simulate: the nonlinear behaviour of both pile and soil; the possible separation and gapping between pile and soil; radiation damping; loss of stiffness and strength in pile and soil. The model is applied to the analysis of pile-column supported bridge structures, focusing on the influence of soil compliance, intensity of seismic excitation, pile diameter, above-ground height of the pile, and above or below ground development of plastic hinge, on key performance measures of the pier as is: the displacement (global) and curvature (local) ductility demands and the maximum drift ratio. It is shown that kinematic expressions for performance measure parameters may lead to erroneous results when soil-structure interaction is considered.     

Design of bridges against large tectonic deformation

The engineering community has devoted much effort to understanding the response of soil-structure systems to seismic ground motions, but little attention to the effects of an outcropping fault offset. The 1999 earthquakes of Turkey and Taiwan, offering a variety of case histories of structural damage due to faulting, have （re）fueled the interest on the subject. This paper presents a methodology for design of bridges against tectonic deformation. The problem is decoupled in two analysis steps： the first （at the local level） deals with the response of a single pier and its foundation to fault rupture propagating through the soil, and the superstructure is modeled in a simplified manner; and the second （at the global level） investigates detailed models of the superstructure subjected to the support （differential） displacements of Step 1. A parametric study investigates typical models of viaduct and overpass bridges, founded on piles or caissons. Fixed-head piled foundations are shown to be rather vulnerable to faulting-dnduced deformation. End-bearing piles in particular are unable to survive bedrock offsets exceeding 10 cm. Floating piles perform better, and if combined with hinged pile-to-cap connections, they could survive much larger offsets. Soil resilience is beneficial in reducing pile distress. Caisson foundations are almost invariably successful. Statically-indeterminate superstructures are quite vulnerable, while statically-determinate are insensitive （allowing differential displacements and rotations without suffering any distress）. For large-span cantilever-construction bridges, where a statically determinate system is hardly an option, inserting resilient seismic isolation bearings is advantageous as long as ample seating can prevent the deck from falling off the supports. An actual application of the developed method is presented for a major bridge, demonstrating the feasibility of design against tectonic deformation.     

Macrobenthic community structure over the continental margin of Crete (South Aegean Sea, NE Mediterranean)

Macrobenthic faunal composition, abundance, biomass and diversity together with a suite of sedimentary environmental parameters were investigated on a seasonal basis in order to determine factors regulating faunal distribution over the oligotrophic continental margin of the island of Crete (South Aegean Sea, North Eastern Mediterranean). Macrofaunal species composition was similar to that of the western Mediterranean and the neighboring Atlantic having several common dominant species. Mean benthic biomass, abundance and diversity decreased with depth, with a major transition zone occurring at 540 m, beyond which values declined sharply. At comparable depths biomass and abundance values were considerably lower to those found in the Atlantic, high-lighting the extreme oligotrophy of the area. The continental margin of Crete was characterised by a high diversity upper continental shelf environment (dominated by surface deposit feeding polychaetes) and a very low diversity slope and deep-basin environment (dominated by carnivorous and filter feeding polychaetes). Classification and ordination analyses revealed the existence of four principle clusters divided by a faunal boundary between 200 and 540 m, as well as beyond 940 m depth. Significant correlations between macrofauna and sediment parameters led to the conclusion that besides depth, food availability (as manifested by the concentration of chloroplastic pigments) is the principle regulating factor in the system. Such being the case, the prevailing hydrographic features that structure the pelagic food web and are directly responsible for the propagation of organic matter to the benthos also affect its community structure.     

Shaking table testing of multidrum columns and portals

A common type of ancient monuments around the Mediterranean is the ancient Greek temple. Unfortunately, very few remain intact; most of them surviving in the form of free‐standing multidrum columns. Composed of stones resting on top of each other without any connection, such columns are considered vulnerable to earthquakes. The paper presents an experimental study of such structures, aiming to explore their seismic vulnerability and derive insights on the key factors affecting their response. Reduced scale models of a single multidrum column and of a portal were tested at the shaking table of the National Technical University of Athens Laboratory of Soil Mechanics. The models, constructed of marble just as the originals, were excited by idealized Ricker pulses and real seismic records. Single columns exhibit a remarkable earthquake resistance. Subjected to the strongest motions ever recorded in Greece, where many such monuments are situated, the columns hardly suffered any permanent deformation. Collapse is probable only for extremely harsh directivity‐affected seismic motions. Portals proved even more robust, surviving extreme seismic excitations. Their superior performance is related to the beneficial role of the epistyle, which adds energy dissipation and restoring force to the system. Their performance is very sensitive to minor changes in geometry or input motion. The complexity increases exponentially with the number of drums, being directly associated with the number of drum‐to‐drum interfaces and the increased probability of interface imperfections. In contrast to PGA, the maximum spectral displacement SD_max and the length scale L_p have turned out to be effective intensity measures. Copyright © 2014 John Wiley & Sons, Ltd.