Well placement optimization subject to realistic field development constraints

This work considers the well placement problem in reservoir management and field development optimization. In particular, it emphasizes embedding realistic and practical constraints into a mathematical optimization formulation. Such constraints are a prerequisite for the wider use of mathematical optimization techniques in well placement problems, since constraints are a way to incorporate reservoir engineering knowledge into the problem formulation. There are important design limitations that are used by the field development team when treating the well placement problem, and these limitations need to be articulated and eventually formalized within the problem before conducting the search for optimal well placements. In addition, these design limitations may be explicit or implicit. In this work, various design limitations pertaining to well locations have been developed in close collaboration with a field operator on the Norwegian Continental Shelf. Moreover, this work focuses on developing constraint-handling capability to enforce these various considerations during optimization. In particular, the Particle Swarm Optimization (PSO) algorithm is applied to optimize for the well locations, and various practical well placement constraints are incorporated into the PSO algorithm using two different constraint-handling techniques: a decoder procedure and the penalty method. The decoder procedure maps the feasible search space onto a cube and has the advantage of not requiring parameter tuning. The penalty method converts the constrained optimization problem into an unconstrained one by introducing an additional term, which is called a penalty function, to the objective function. In contrast to the penalty method, only feasible solutions are evaluated in the decoder method. Through numerical simulations, a comparison between the penalty method and the decoder technique is performed for two cases. We show that the decoder technique can easily be implemented for the well placement problem, and furthermore, that it performs better than the penalty method in most of the cases.     

Climatic deterioration and the end of the Gortian Interglacial in sediments from Derrynadivva and Burren Townland,near Castlebar,County Mayo,Ireland

Pollen and macrofossil analyses of two sequences of organic sediment in western Ireland have allowed the recognition of the latter parts of the Gortian Interglacial, a Middle Pleistocene temperate stage. The palaeobotanical information from the two sites identifies the preservation of partial sequences from the Gortian Interglacial (believed to be the equivalent of the Hoxnian Stage of Britain and the Holsteinian of Europe). The pollen and macrofossil data from one of the sites, Derrynadivva, span the middle and latter parts of the temperate stage. The results show that fire influenced the vegetation throughout the middle part of the temperate stage, and the termination of the organic depositional sequence appears to have been due to environmental deterioration. The former is identified through the abundant occurrence of charcoal in the sediments, whereas the latter is apparent in the sediment sequence and in the reworking of thermophilous pollen types into the upper part of the deposit. The second site, Burren Townland, records only part of the later zones of the interglacial, but the ericaceous assemblages of the latter part of the Gortian Interglacial are well developed and well preserved. Macrofossil analyses and scanning electron microscopy work on the pollen at the latter site has allowed the recognition of Rhododendron ponticum, adding to previous records of this species, which now has a very disjunct European distribution.     

Geochemical and Isotopic Evolution of Loihi Volcano, Hawaii

The Publishers wish to apologise for the incorrect representationof figure 10 which accompanied this paper. The correct figureis reproduced below.     

2.5D modelling, inversion and angle migration in anisotropic elastic media

2.5D modelling approximates 3D wave propagation in the dip‐direction of a 2D geological model. Attention is restricted to raypaths for waves propagating in a plane. In this way, fast inversion or migration can be performed. For velocity analysis, this reduction of the problem is particularly useful. We review 2.5D modelling for Born volume scattering and Born–Helmholtz surface scattering. The amplitudes are corrected for 3D wave propagation, taking into account both in‐plane and out‐of‐plane geometrical spreading. We also derive some new inversion/migration results. An AVA‐compensated migration routine is presented that is simplified compared with earlier results. This formula can be used to create common‐image gathers for use in velocity analysis by studying the residual moveout. We also give a migration formula for the energy‐flux‐normalized plane‐wave reflection coefficient that models large contrast in the medium parameters not treated by the Born and the Born–Helmholtz equation results. All results are derived using the generalized Radon transform (GRT) directly in the natural coordinate system characterized by scattering angle and migration dip. Consequently, no Jacobians are needed in their calculation. Inversion and migration in an orthorhombic medium or a transversely isotropic (TI) medium with tilted symmetry axis are the lowest symmetries for practical purposes (symmetry axis is in the plane). We give an analysis, using derived methods, of the parameters for these two types of media used in velocity analysis, inversion and migration. The kinematics of the two media involve the same parameters, hence there is no distinction when carrying out velocity analysis. The in‐plane scattering coefficient, used in the inversion and migration, also depends on the same parameters for both media. The out‐of‐plane geometrical spreading, necessary for amplitude‐preserving computations, for the TI medium is dependent on the same parameters that govern in‐plane kinematics. For orthorhombic media, information on additional parameters is required that is not needed for in‐plane kinematics and the scattering coefficients. Resolution analysis of the scattering coefficient suggests that direct inversion by GRT yields unreliable parameter estimates. A more practical approach to inversion is amplitude‐preserving migration followed by AVA analysis. SYMBOLS AND NOTATION A list of symbols and notation is given in Appendix D .     

Graphical methods for rapid vector analysis of demagnetization data

Summary. Working graphs are presented which, when used in conjunction with a stereographic projection, enable (a) magnitude and direction of the difference between two vectors to be estimated, and (b) a vector to be resolved into two or three components of prescribed directions. Applications of the methods to multicomponent natural remanent magnetizations are illustrated.     

Using stratiform magnetic anomalies to map near-surface architecture: insights from the Amadeus Basin

The Amadeus Basin displays subtle magnetic anomalies that trace strata for considerable distance, highlighting complex folding patterns. Magnetic modelling techniques can be utilised on these stratiform anomalies to extrapolate the near-surface structure of the basin. However, because of the mathematical trade-off between the dip and magnetisation of bodies, the dips of the bodies cannot be known unless the magnetisation is also known. Normally it would be optimal to measure the magnetisation, but this is not always possible or feasible. In this study, we investigate the relationships between dip and magnetisation using an approach that would generally be considered a little backward, i.e. constraining magnetisation direction using geological data. Three study areas were chosen to investigate a number of stratigraphic horizons, the Waterhouse Range, Glen Helen and Ross River areas. Modelling results suggest that some layers primarily retain induced magnetisation, remanence is dominant in others, but both are present in most. Remanence is mainly associated with relatively oxidised units that contain only hematite (e.g. Arumbera Sandstone), and we have demonstrated that these magnetisations predate folding of the Ross River Syncline. In some cases, the anomalies represent redox zonation within units, e.g. the Pertatataka Formation near Glen Helen, where discrete magnetic layers correspond to thin grey (reduced, magnetite-rich) horizons interbedded with more prevalent red (oxidised, hematite-rich) horizons. We also found that where magnetised units are relatively thin and occur near the surface, their magnetic response is sharp, and in aeromagnetic data such adjacent anomalies commonly overlap to form a single anomaly, thus misrepresenting the magnetic field, and mis-mapping the actual magnetic horizons. While the magnetic properties of the causative bodies are variable, we have demonstrated that a better understanding of the magnetic properties of these magnetised horizons can be used to provide insights into the structure and tectonic history of the Amadeus Basin.     

Nonlinear output constraints handling for production optimization of oil reservoirs

Adjoint-based gradient computations for oil reservoirs have been increasingly used in closed-loop reservoir management optimizations. Most constraints in the optimizations are for the control input, which may either be bound constraints or equality constraints. This paper addresses output constraints for both state and control variables. We propose to use a (interior) barrier function approach, where the output constraints are added as a barrier term to the objective function. As we assume there always exist feasible initial control inputs, the method maintains the feasibility of the constraints. Three case examples are presented. The results show that the proposed method is able to preserve the computational efficiency of the adjoint methods.