Finding the Best of the Best: Hydraulic Fracturing Design Optimization Study in Oman

Development of the tight gas Khazzan Field in Sultanate of Oman has progressed through an extensive learning curve over many years. Thereby, the hydraulic fracturing design was fine-tuned and optimized to properly fit the requirements of the challenging Barik reservoir in this area. In 2018, BP Oman started developing the Barik reservoir in the Ghazeer Field, which naturally extends the reservoir boundary south of Khazzan Field. However, the Barik reservoir in the Ghazeer area is thicker and more permeable than in the Khazzan Field; therefore, the hydraulic fracturing design required adjustment to be optimized to directly reflect the reservoir needs of the Ghazeer Field. A comprehensive hydraulic fracturing design software was used for this optimization study and sensitivity analysis. This software is a plug-in to a benchmark exploration and production software platform and provides a complete fracturing optimization loop from hydraulic fracturing design sensitivity modelled with a calibrated mechanical earth model to detailed production prediction using the incorporated reservoir simulator. One of the stimulated wells from Ghazeer Field was used as the reference for this study. The reservoir sector model was created and adjusted to match actual data from this well. The data include fracturing treatment execution response, surveillance data such as radioactive tracers, bottomhole pressure gauge, and pressure transient analysis. Reservoir properties were also adjusted to match long-term production data obtained for this reference well. After the reservoir model was fully validated against actual data, multiple completion and fracturing scenarios were simulated to estimate potential production gain and thus find an optimal hydraulic fracturing design for Ghazeer Field. Many valuable outcomes can be concluded from this study. The optimal treatment design was identified. The value of fracture half-length versus conductivity was clarified for this area. The comparison between single-stage fracturing versus multistage treatment across the thick laminated Barik reservoir in a conventional vertical well was derived. The drainage of different layers with variable reservoir properties was compared for a range of different scenarios.

Asymmetric Design Sensitivity and Isogeometric Shape Optimization Subject to Deformation-Dependent Loads

We present a design sensitivity analysis and isogeometric shape optimization with path-dependent loads belonging to non-conservative loads under the assumption of elastic bodies. Path-dependent loads are sometimes expressed as the follower forces, and these loads have characteristics that depend not only on the design area of the structure but also on the deformation. When such a deformation-dependent load is considered, an asymmetric load stiffness matrix (tangential operator) in the response region appears. In this paper, the load stiffness matrix is derived by linearizing the non-linear non-conservative load, and the geometrical non-linear structure is optimally designed in the total Lagrangian formulation using the isogeometric framework. In particular, since the deformation-dependent load changes according to the change and displacement of the design area, the isogeometric analysis has a significant influence on the accuracy of the sensitivity analysis and optimization results. Through several numerical examples, the applicability and superiority of the isogeometric analysis method were verified in optimizing the shape of the problem subject to deformation-dependent loads.

On the Identification of Individual Gravitational-wave Image Types of a Lensed System Using Higher-order Modes

Similarly to light, gravitational waves can be gravitationally lensed as they propagate near massive astrophysical objects such as galaxies, stars, or black holes. In recent years, forecasts have suggested a reasonable chance of strong gravitational-wave lensing detections with the LIGO–Virgo–KAGRA detector network at design sensitivity. As a consequence, methods to analyze lensed detections have seen rapid development. However, the impact of higher-order modes on the lensing analyses is still under investigation. In this work, we show that the presence of higher-order modes enables the identification of individual image types for the observed gravitational-wave events when two lensed images are detected, which would lead to unambiguous confirmation of lensing. In addition, we show that higher-order mode content can be analyzed more accurately with strongly lensed gravitational-wave events.

Continuum sensitivity and design optimization of superconducting systems under critical current densities with magnetic field dependence

This paper presents an approach for deriving the continuum sensitivity of superconducting systems operating at critical current densities and an optimization method based on the continuum sensitivity. In the sensitivity problem, the superconducting systems is represented by a variational state equation, wherein the magnetic permeability depends on the magnetic field, which is transformed from a state equation with a field-dependent source. The design sensitivity is derived using the material derivative concept of continuum mechanics and the adjoint variable method. The adjoint system has a material property represented as a symmetric tensor that contains the sensitivity of the current density with respect to the magnetic field. The design sensitivity is represented in the analytical form of a surface integral on the interface between the superconducting material and its surroundings, which depends on the sensitivity of the current density. The optimization scheme is constructed based on the continuum design sensitivity. In the design optimization, the level set method is used to express the shape variation of the superconducting materials. The numerical example of infinite solenoids demonstrates that the design sensitivity provides an accurate design solution considering the critical current condition. In addition, the design example of a magnetic resonance imaging solenoid shows that the derived design sensitivity has the inherent ability for attaining the compact design by treating the input current of a superconducting system as a critical condition.