Exact Time Evolution of Genuine Multipartite Correlations for N-Qubit Systems in a Common Thermal Reservoir

We investigate the dynamical evolution of genuine multipartite correlations for N-qubits in a common reservoir considering a non-dissipative qubits-reservoir model. We derive an exact expression for the time-evolved density matrix by modeling the reservoir as a set of infinite harmonic oscillators with a bilinear form of interaction Hamiltonian. Interestingly, we find that the choice of two-level systems corresponding to an initially correlated multipartite state plays a significant role in potential robustness against environmental decoherence. In particular, the generalized W-class Werner state shows robustness against the decoherence for an equivalent set of qubits, whereas a certain generalized GHZ-class Werner state shows robustness for inequivalent sets of qubits. It is shown that the genuine multipartite concurrence (GMC), a measure of multipartite entanglement of an initially correlated multipartite state, experiences an irreversible decay of correlations in the presence of a thermal reservoir. For the GHZ-class Werner state, the region of mixing parameters for which there exists GMC, shrinks with time and with increase in the temperature of the thermal reservoir. Furthermore, we study the dynamical evolution of the relative entropy of coherence and von-Neumann entropy for the W-class Werner state.

Finite-Element Modeling of Spontaneous Potential in an Axisymmetric Reservoir Model with Account of Its Shale Content

(1) This article is devoted to the development of a theoretical and algorithmic basis for numerical modeling of the spontaneous potential method (SP) as applied to the study of sandy-argillaceous reservoirs. (2) In terms of coupled flows, we consider a physical–mathematical model of SP signals from an electrochemical source, with regards to the case of fluid-saturated shaly sandstone. (3) An algorithm for 2D finite-element modeling of SP signals was developed and implemented in software, along with its internal and external testing with analytical solutions. The numerical SP modeling was carried out, determining the dependences on the reservoir thickness and porosity, the amount of argillaceous material and the type of minerals. We performed a comparative analysis of the simulated and field SP data, using the results of laboratory core examinations taken from wells in a number of fields in the Latitudinal Ob Region of Western Siberia. (4) The results of the study may be used either for the development of the existing SP techniques, by providing them with a consistent computational model, or for the design of new experimental approaches.

Reservoir Architecture Modeling at Sub-Seismic Scale for a Depleted Carbonate Reef Reservoir for CO2 Storage in Sarawak Basin, Offshore Malaysia

It is still a challenge to build a numerical static reservoir model, based on limited data, to characterize reservoir architecture that corresponds to the geological concept models. The numerical static reef reservoir model has been evolving from the oversimplified tank-like models, simple multi-layer models to the complex multi-layer models that are more realistic representations of complex reservoirs. A simple multi-layer model for the reef reservoir with proportional layering scheme was applied in the CO2 Storage Development Plan (SDP) study, as the most-likely scenario to match the geological complexity. Model refinement can be conducted during CO2 injection phase with Measurement, Monitoring and Verification (MMV) technologies for CO2 plume distribution tracking. The selected reservoir is a Middle to Late Miocene carbonate reef complex, with three phases of reef growth: 1) basal transgressive phase, 2) lower buildup phase, and 3) upper buildup phase. Three chronostratigraphic surfaces were identified on 3D seismic reflection data as the zone boundaries, which were then divided into sub-zones and layers. Four layering methods were compared, which are ‘proportional’, ’follow top’, ‘follow base’ and ‘follow top with reference surface’. The proportional layering method was selected for the base case of the 3D static reservoir model and the others were used in the uncertainty analysis. Based on the results of uncertainty and risk assessment, a risk mitigation for CO2 injection operation were modeled and three CO2 injection well locations were optimized. The reservoir architecture model would be updated and refined by the difference between the modeled CO2 plume patterns and The MMV results in the future.

Workflow to Optimize Cluster Spacing Design of Horizontal Multistage Fractured Well in Unconventional Source Rock

Horizontal drilling and multistage hydraulic fracturing applied in unconventional reservoirs over the past decade to create a large fracture surface area to improve the well productivity. The combination of reservoir quality with perforation cluster spacing and fracture staging are keys to successful hydraulic fracturing treatment for horizontal wells. The objective of this work is to build and calibrate a dynamic model by integrating geologic, hydraulic fracture, and reservoir modeling to optimize the number of clusters and other completion parameters for a horizontal well drilled in the source rock reservoir using simulation and analytical models. The methodology adopted in this study covers the integration of geological, petrophysical, and production data analysis to evaluate reservoir and completion qualities and quantify the heterogeneity and the perforation clusters number required within a frac stage. Assuming all perforation clusters are uniformly distributed within a stage. The hydraulic planer fracture attributes assumed and the surface production measurement together with the production profile were used to calibrate the reservoir model. The properties of the Stimulated Reservoir Volume "SRV" were defined after the final calibration using reservoir model including hydraulic fractures. The calibrated reservoir model was used to carry out sensitivity analyses for cluster spacing optimization and other completion parameters considering the surface and reservoir constraints. An optimum cluster spacing was observed based on the Estimated Ultimate Recovery "EUR" of the subject well by reservoir properties. The final results based on 70% of perforation clusters contribution to production observed from PLT log, and the results of this study were implemented. Afterwards, another study has been undertaken to increasing the stimulation effectiveness and maximizing the number of perforation clusters contributing to productivity as an area for improvement to engineering the completion design. The methodology adopted in this study identifies the most important parameters of completion affecting well productivity for specific unconventional reservoirs. This study will help to engineer completion design, improve cluster efficiency, reduce cost and increase well EUR for the development phase.

Finite-Element Modeling of Spontaneous Potential in an Axisymmetric Reservoir Model with Account of Its Shale Content

(1) The article is devoted to the development of a theoretical and algorithmic basis for numerical modeling of the spontaneous potential method (SP) as applied to the study of sandy-argillaceous reservoirs. (2) In terms of coupled flows, we consider a physical-mathematical model of SP signals from an electrochemical source, with regard to the case of fluid-saturated shaly sandstone. (3) An algorithm for 2D finite-element modeling of SP signals was developed and implemented in software, along with its internal and external testing with analytical solutions. The numerical SP modeling was carried out, with determining the dependences on the reservoir thickness and porosity, the amount of argillaceous material and the type of minerals. We performed a comparative analysis of the simulated and field SP data, using the results of laboratory core examinations taken from wells in a number of fields in the Latitudinal Ob Region of Western Siberia. (4) The results of the study may be used either for the development of the existing SP techniques, by providing them with a consistent computational model, or for the design of new experimental approaches.

Hydrological Modeling of Karst Watershed Containing Subterranean River Using a Modified SWAT Model: A Case Study of the Daotian River Basin, Southwest China

Karst watershed refers to the total range of surface and underground recharge areas of rivers (including subterranean rivers and surface rivers) in karst areas. Karst water resources, as the primary source of domestic water supply in southwest China, are vital for the social and economic development of these regions. These resources are greatly significant for guiding water resources management in karst areas to establish a high-precision hydrological model of karst watersheds. Choosing the Daotian river basin in the Wumeng Mountains of Southwest China as the study area, this paper proposed a method for simplifying karst subterranean rivers into surface rivers by modifying the digital elevation model (DEM) based on a field survey and tracer test. This method aims to solve the inconsistency between the topographical drainage divides and actual catchment boundaries in karst areas. The Soil and Water Assessment Tool (SWAT) model was modified by replacing the single-reservoir model in the groundwater module with a three-reservoir model to depict the constraints of multiple media on groundwater discharge in the karst system. The results show that the catchment areas beyond topographic watershed were effectively identified after simplifying subterranean rivers to surface rivers based on the modified DEM data, which ensured the accuracy of the basic model. For the calibration and two validation periods, the Nash–Sutcliffe efficiencies (NSE) of the modified SWAT model were 0.87, 0.83, and 0.85, respectively, and R2 were 0.88, 0.84, and 0.86, respectively. The NSE of the modified SWAT model was 0.09 higher than that of the original SWAT model in simulating baseflow, which effectively improved the simulation accuracy of daily runoff. In addition, the modified SWAT model had a lower uncertainty within the same parameter ranges than the original one. Therefore, the modified SWAT model is more applicable to karst watersheds.

Maximizing Asset Value & Field Recovery with Advanced Completion Solutions – A Digital Twin Field Case Study with Multilateral, Intelligent Completion, and AICD Completion Technologies

The drilling and completion of multilateral wells continues to expand and advance within the oil industry after three decades of accelerating adoption. The performance of these wells can be increased when integrated with advanced well completion techniques. The addition of intelligent completions (IC) and inflow control devices (ICD/AICD) enhances well performance and improves field recovery. This paper discusses a reservoir simulation case study that evaluates the productive impact these technologies provide when combined with multilateral technology (MLT), and the mechanism by which they achieve it. A reservoir model is devised and simulates under dynamic reservoir conditions the field production of dual lateral and single bore horizontal wells. The simulation is conducted for three separate scenarios where AICD and IC are incrementally implemented. The results are compared across the scenarios and their value quantified. The mechanisms by which estimated ultimate recovery (EUR) is increased will be discussed, including the increase of reservoir contact, drawdown distribution optimization, and the control and delay of water production. The study will provide an overview on the theory behind the technologies. It will also review the workflow used to conduct the study, utilizing a combination of steady state nodal analysis software and dynamic reservoir simulation software. Additional information about the reservoir model, initial and boundary conditions are detailed, to provide insight into reservoir simulation methodology.

Probabilistic Economical Evaluation for Business Decisions Through Integrated Uncertainty Assessment and Reliable Ensemble-Based Production Forecasts

Economic evaluation of exploration and production projects ensures a positive return for asset operators and stakeholders and evaluates risk in field development decisions related to both reservoir model uncertainties and fluctuations in oil and gas prices. Traditionally, such evaluation is performed manually and deterministically using single or limited number of cases (limited number of reservoir models and few values of economic parameters). Such traditional approach does not integrate seismic-to-simulation reservoir model uncertainties, the reservoir model used is often unreliable due to inconsistent property modifications during the history matching process, full span of prediction uncertainty isn't properly propagated for economic evaluation and the whole process is not fully automated. This paper presents an integrated and automated forward modelling approach where static and dynamic models are connected to integrate the impact of uncertainties at the different modelling stages (seismic interpretation through geological modelling to dynamic simulation and further to economic evaluations). The approach is demonstrated using synthetic 3D model data mimicking a real North Sea field. It starts by building an integrated modelling workflow that can capture the various reservoir model uncertainties at different stages to automatically generate multiple probable model realisations. Proxy models are constructed and used to refine the history match in successive batches. For each prediction development scenario, prediction probabilities are estimated using posterior ensemble of geologically consistent runs that matches historical observed data. The ensemble of reservoir models is automatically evaluated against different possible economic scenarios. The approach presents a seamless and innovative workflow that benefits from new-generation hardware and software, enables faster simultaneous realisations, produces consistent and more reliable reservoir models. Probabilistic economic evaluation concept is implemented to calculate the statistical probabilities of economic indicators.