Modelització numèrica de flux compressible en medi Porós amb fractures

Tradicionalment, els reservoris d'Oil i Gas (O&G) s'han modelitzat des del punt de vista dels fluids en un medi porós d'esquelet sòlid indeformable i infinitament resistent. En temps recents però, s'està fent palès que sense modelar adequadament el comportament del medi geològic com a sòlid amb el seu comportament mecànic, les seves possibles discontinuitats, etc., difícilment es pot arribar a una bona representació global del comportament del reservori

A note on assignment games with the same nucleolus

We show that the family of assignment matrices which give rise to the same nucleolus forms a compact join-semilattice with one maximal element. The above family is in general not a convex set, but path-connected

A procedure to compute the nucleolus of the assignment game

The assignment game introduced by Shapley and Shubik (1972) is a model for a two-sided market where there is an exchange of indivisible goods for money and buyers or sellers demand or supply exactly one unit of the goods. We give a procedure to compute the nucleolus of any assignment game, based on the distribution of equal amounts to the agents, until the game is reduced to fewer agents

The nucleolus of the assignment game. Structure of the family

We show that the family of assignment matrices which give rise to the same nucleolus forms a compact join-semilattice with one maximal element. The above family is in general not a convex set, but path-connected

Insights into the nucleolus of the assignment game

We show that the family of assignment matrices which give rise to the same nucleolus form a compact join-semilattice with one maximal element, which is always a valuation. -see p.43, Topkis, 1998-. We give an explicit form of this valuation matrix. The above family is in general not a convex set, but path-connected, and we construct minimal elements of this family. We also analyze the conditions to ensure that a given vector is the nucleolus of some assignment game

Assortative multisided assignment games. The extreme core points [WP]

We analyze assortative multisided assignment games, following Sherstyuk (1999) and Martínez-de-Albéniz et al. (2019). In them players’ abilities are complementary across types (i.e. supermodular), and also the output of the essential coalitions is increasing depending on types. We study the extreme core points and show a simple mechanism to compute all of them. In this way we describe the whole core. This mechanism works from the original data array and the maximum number of extreme core points is obtained

Solving Becker's assortative assignments and extensions

We analyze assortative assignment games, introduced in Becker (1973) and Eriksson et al. (2000). We study the extreme core points and show an easy way to compute them. We find a natural solution for these games. It coincides with several well-known point solutions, the median stable utility solution (Schwarz and Yenmez, 2011) and the nucleolus (Schmeidler, 1969).We also analyze the behavior of the Shapley value. We finish with some extensions, where some hypotheses are relaxed

Further developments in stress initialization in geomechanics via FEM and a two-step procedure involving Airy functions

The in-situ stress field in rock masses is a key aspect when a numerical analysis of a rock mass is carried out in any area of geo-engineering, such as civil, mining, or Oil & Gas. A method for the numerical generation of the in-situ stress state in the FE context, based on Airy stress functions was previously introduced. It involves two steps: 1) an estimate of the stress state at each Gauss point is generated, and 2) global equilibrium is verified and re-balancing nodal forces are applied as needed. In this paper, new developments towards improving the accuracy of the stress proposal are discussed. A real application example has been used to illustrate the results achieved with the new implementation.Postprint (published version

Numerical stress initialization in geomechanics via the FEM and a two-step procedure

The knowledge of the in-situ stress field in rock masses is crucial in different areas of geo-engineering, such as mining or civil underground excavations, hydrocarbon extraction, CO2 storage, hydraulic fracture operations, etc. A method for the numerical generation of the in-situ stress state is described in this paper, which involves two steps: 1) an estimate of the stress state at each Gauss point is generated, and 2) global equilibrium is verified and re-balancing nodal forces are applied as needed. While the re-equilibration step is a closed procedure based only on statics, the first estimate of the stress state can be done in a variety of ways to incorporate all the information available. In this paper, the various options available are discussed and compared, and a new alternative procedure is presented which is based on the Airy stress function. The performance of the various procedures is illustrated with a real application example