We construct an innovative static-dynamic integrated workflow capable of bridging the gap between input geological data, inherent to a lacustrine carbonate outcrop containing karst geobodies, and the description of the flow patterns and quantification of the multi-well productivity index (MWPI) for a particular well configuration in the outcrop. The workflow incorporates additional features stemming from the use of Machine Learning-based methods to mitigate lack of data in the locations away from the sections of input signals, along with the construction of new upscaling methods to assess the MWPI matrix. The ML-enhanced geostatic model hinges upon shallow surface geophysical data collected using Ground-Penetrating Radar (GPR) techniques. Furthermore, by discretizing the flow equations and adopting a flow-based upscaling method, we construct correlations between well flow rates and pressure drawdown in a typical five-spot well configuration. In this setting, we analyze the sensitivity of each well productivity with respect to heterogeneity distribution and correlations in the karst system within the outcrop. Computational simulations illustrate the ability of the integrated workflow proposed herein to improve prediction of hydraulic-connectivity between well pairs, which appear manifested in the entries of the MWPI matrix, whose magnitude aims at quantifying the effects of the karst geobodies upon geofluid production.

We propose a new computational model for two-phase immiscible flow in a poroelastic medium overlain by a saline formation displaying creep behavior with viscous strain ruled by a nonlinear dependence of power-law type on the deviatoric stress. Within the framework of the fixed-stress split algorithm, hinged upon freezing the total mean stress in the flow equations, hydrodynamics and geomechanics subsystems are solved by mixed finite element methods whereas the hyperbolic equation for the water saturation is formulated in terms of the Lagrangian porosity and solved adopting an operator splitting fractional-step method combined with a higher-order non-oscillatory finite volume central scheme. Within this typical multi-physics setting, the sequential formulation allows greater flexibility in the choice of the meshes for the subsystems, particularly for the geomechanics module, which can be solved in the extended domain including the adjacent impervious formations (over-, under- and side-burdens). Considering the upper interface of the rock salt dictated by the profile of saline dome geobodies, whose impermeability property precludes hydraulic communication between adjacent formations, the initial in situ undrained state is also modeled by invoking Skempton’s coefficient along with the characterization of the undrained bulk and shear modulus. By constructing a robust evolving algorithm between the discrete counterparts of the three subsystems in the reservoir, in conjunction with an iterative scheme underlying the mixed method for the nonlinear creep problem in the rock salt, numerical simulations of a water-flooding problem in secondary oil recovery are performed for different realizations of the input random fields. Numerical results illustrate the influence of viscoelastic effects in the cap rock upon subsidence, reservoir compaction, finger grow and breakthrough curves. Comparisons with the performance of traditional one-way formulation are also presented.

We develop a new three-scale (micro/meso/macro) computational model based on a reiterated homogenization procedure to describe flow in carbonate rocks containing complex geological structures, such as fractures and solution-collapse breccias in the sense of Loucks (AAPG Bull. 83(11), 1795–1834, 1999). In this setting, we construct a hierarchical karst-fracture model wherein the larger geological objects are incorporated explicitly whereas the higher density microscopic structures are homogenized and replaced by equivalent continua with properties computed from self-consistent homogenization schemes. In the upscaling method, we subdivide the different clastic arrangements in the breccia into crackle, mosaic, and chaotic substructures where equivalent permeability and elastic constants are assigned to each layer within the breccia. After reconstructing the mesoscopic coefficients, we adopt a flow-based upscaling to the macroscale, where the characteristic length is associated with a typical coarse grid cell of a reservoir simulator. The mesoscopic flow equations are constructed based on the discrete fracture model (DFM) and discretized by a robust computationally scheme with the ability to handle strong heterogeneity induced by the collapse breccia and pressure jumps across flow barriers. In addition to the scenario wherein the collapse breccia network is composed of disconnected objects (isolated chambers), we also develop a reduced model for the case of connected karst facies playing the role of a network of enlarged fractures. Numerical results, with input data extracted from outcrops drone images, are presented illustrating the influence of different settings on flow patterns and their effect upon the magnitude of macroscopic properties.

A three-scale model for flow in karst conduit networks in fractured carbonates is rigorously constructed based on a reiterated homogenization procedure. The first upscaling, performed from the high-fidelity flow model, is based on sequential partially and fully topological model reduction procedures considering two discrete networks of solution-enlarged fractures and conduits. The subsequent macroscopization procedure projects the reduced model into the cells of a coarse computational grid, where homogenized equivalent properties are numerically constructed. Such a two-level upscaling gives rise to a macroscopic flow model characterized by mass-transfer functions between the geological structures. A notable consequence of the approach proposed herein is the appearance of a new karst index concept, whose underlying physics relies on the generalization of the traditional Peaceman's theory of well index. Such a concept rules the mass exchange between conduits and matrix and can be extended to the general scenario of coupled flow in multi-branch karst conduit systems, displaying general noncircular cross sections and surrounding damage zones. The downscaling representation for the karst index can be further explored to improve accuracy of the exchange coefficient between the geological objects. Numerical experiments are carried-out showing the magnitude of the index for certain conduit and fracture arrangements, along with illustrating the impact upon flow patterns.

Abstract We construct a new numerical modeling for two-phase immiscible flow in a strongly heterogeneous deformable carbonate underneath a rock salt composed by halite and anhydrite displaying creep behavior with the viscous strain ruled by a nonlinear constitutive law of power-law type. Within the framework of the so-called iteratively coupled methods and fixed-stress split algorithm we develop mixed finite element methods for the flow and geomechanics subsystems which furnish locally conservative Darcy velocity and transient porosity input fields for the transport problem for the water saturation. Such transport equation is decomposed within an operator splitting technique based on a predictor-corrector scheme with the predictor step discretized by a higher-order non-oscillatory finite volume central scheme. Numerical simulations of a water-flooding problem in secondary oil recovery are presented for different realizations of the input random fields (permeability, Young modulus and initial porosity). Comparisons between the accuracies of the proposed approach and the traditional one-way coupled hydro-geomechanical formulation are presented. In addition, simulations including the viscoelastic behavior of the overburden rock salt are performed showing the effects of salt stiffness and irreversible deformation upon finger grow and breakthrough curves. A notable feature of the formulation proposed herein is the accurate prediction of the influence of geomechanical effects upon the unstable movement of the water front, whose evolution is dictated by carbonate heterogeneity, unfavorable viscosity ratio and geomechanical effects without deteriorating the local conservative character of the numerical schemes.

According to ASME B31.8 - Gas Transmission and Distribution Piping Systems, plain dents or dents on ductile welds of any depth are acceptable provided strain levels associated with the deformation do not exceed 6% and 4%, respectively. Appendix R of the Code presents a method for estimating strains in dents. In order to use this method, some technique is usually necessary to evaluate strains based on the pipe surface contour information captured from in-line inspection (ILI) tools or from direct measurement. In previous papers the authors have presented techniques based on B-spline curves or B-spline surfaces to evaluate the bending strains on dents which have a “well-behaved” topology or on dents having a complex shape, respectively. The B-splines are used to interpolate the geometry of the dent, to infer its radii of curvature and to calculate the bending strain components using a procedure similar to that suggested on the Appendix R of the ASME B31.8 Code. The strains are combined in order to obtain an equivalent strain field that does not take into account the effect of the membrane strains or include the effect of the longitudinal membrane component through an expression like that contained on the code. These techniques which were implemented in the DSE-B and the DSE-R programs, respectively, make the dent strain estimation based on data coming from in-line inspections (ILI) tools easier and automatic. This paper presents the DSE-T program, which uses the methodology implemented in the DSE-B program to calculate bending strains, and a dedicated finite element method to estimate membrane strains. Bending and membrane strains are combined to give the total strain fields on the inside and outside surfaces of the indented pipe. The program also enables the user to verify whether the dent is smooth or kinked and to simulate the effects of measuring the dent shape using “virtual” geometric tools with different degrees of resolution. Results obtained using the DSE-T are compared to results from nonlinear finite element analyses.