Search NASA⌕ Search

SEARCH · Search NASA

Results for “reservoir performance”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Carbonated Brine Injection for a Pilot Site as a Low-Risk Geologic Carbon Storage Strategy: A Simulation Study

This technical report presents a preliminary study for CBI implementation in the Pena Creek pilot site in Dimmit County, Texas, targeting the Edwards Limestone Formation for SWD, in collaboration with NGL Energy Partners. The objective of this study is to find the conservative CO 2 molality for safe storage and potential risks for CBI at this pilot site. Geomodel was performed to get site-specific reservoir geology information. Reservoir modeling was performed to investigate dissolved CO 2 molality and pressure changes at relevant injection conditions. Wellbore corrosion and compatibility was discussed with corrosion modeling. Dissolved CO 2 long-term fate in the reservoir was examined with reactive transport modeling. This plan would set the scientific foundation as the initial step for future implementation in the field.

58 GEOSCIENCES↗
DOE OSTI2023

Utah FORGE 3-2418: Wellbore Fracture Imaging Using Inflow Detection Measurements - Workshop Presentation

This is a presentation on the Wellbore Fracture Imaging Using Inflow Detection Measurements project by Stanford University, presented by Dr. Roland N. Horne. The project's objective was to make measurements in the Utah FORGE wells, both before and after fracturing experiments, to map the fractures and estimate their flow magnitude. The approach utilizes a ion-specific electrode that will measure chloride in the well. The idea is that water flowing into the well from the fractures will have a different concentration of chloride than the surrounding water. This presentation was featured in the Utah FORGE R&D Annual Workshop on September 8, 2023. The workshop provided a valuable opportunity to explore the progress made in each of the 17 Research and Development projects funded under Solicitation 2020-1 which aim to enhance our understanding of the crucial factors influencing the development of Enhanced Geothermal Systems (EGS) reservoirs and resources.

15 GEOTHERMAL ENERGY↗
DOE OSTI2020

A Non-Invasive Approach for Elucidating the Spatial Distribution of In Situ Stress in Deep Subsurface Geologic Formations Considered for CO 2 Storage (Task 2 Report Extracting Stress Data from Seismic Data)

This report describes research accomplishments achieved with funding provided through Department of Energy (DOE) Contract DE-FE0031686. The purpose of this DOE funding is to develop methods that can provide key information about stress fields that act on deep rocks without invading the earth to acquire that information. The research objective was to demonstrate methods that extract the azimuth directions of SHmax and SHmin stress in deep rocks from traditional seismic reflection data like the data that are used to explore for deep oil and gas reservoirs. Battelle performed two seismic investigations and achieved estimates of SHmax and SHmin azimuths in both efforts that agreed with local, non-seismic, ground-truth measurements of SHmax orientation. The first procedure utilized vertical seismic profiling (VSP) data; the second effort utilized three-dimensional (3D) seismic data.

58 GEOSCIENCES↗
DOE OSTI2026

One Earth Energy Static and Dynamic Reservoir Modeling

This report presents the static and dynamic reservoir modeling conducted for the CarbonSAFE Phase III Illinois Storage Corridor project to assess the feasibility of commercial-scale CO 2 storage in the Mt. Simon Sandstone at the One Earth Energy (OEE) site in McLean County, Illinois. Three-dimensional geocellular models of the Mt. Simon storage complex were developed in Petrel ® by integrating petrophysical log data, core analyses, and seismic surveys from the OEE #1 stratigraphic test well and two nearby wells, with multiple model versions created as new data became available. Dynamic reservoir simulations, performed using Landmark's Nexus software, progressed through three phases (preliminary, sensitivity, and UIC Class VI permit studies) evaluating injection scenarios across varying rates, well orientations, permeability models, and multi-well configurations. Results demonstrate that commercial-scale storage is feasible: three injection wells spaced approximately one mile apart can store a total of 90 million tonnes of CO 2 over 20 years, producing a combined plume with an equivalent radius of 3.2 miles and a maximum pressure-front-defined Area of Review of 178 mi 2 at the end of injection that diminishes to 34 mi 2 after 50 years of post-injection monitoring. Sensitivity analyses indicate that a 20% change in porosity or permeability yields approximately a 7% change in AoR radius, and that perforating the high-permeability arkosic zone minimizes the pressure front compared to injection in the upper Mt. Simon Sandstone.

09 BIOMASS FUELS↗
DOE OSTI2024

Workflow for Developing and Operating Subsurface Hydrogen Storage Facilities in Porous Reservoirs

Long-duration (seasonal) storage of natural gas (NG), which primarily consists of methane (CH 4 ), has been practiced for more than a hundred years at underground gas storage (UGS) facilities that use depleted hydrocarbon reservoirs, saline aquifers, and salt caverns. To enable hydrogen (H 2 ) to be used as a long-duration, energy-storage medium, similar facilities are envisioned for underground H 2 storage (UHS) of either H 2 or H 2 /NG mixtures. Experience with UGS can be used to guide recommended practices for developing and operating UHS facilities in porous reservoirs. The most important factors (formation/fluid properties and engineering choices) that influence the performance of UHS reservoirs have been identified and quantified in previous studies. These factors and choices influence phenomena that determine the sweep efficiency of the stored working gas. These phenomena include viscous fingering, hysteretic capillary trapping, and gravity override of the working gas, as well as the upconing of nonproductive fluid that determine the sweep efficiency of the stored working gas. This report describes initial recommended-practices and a project-development workflow for UHS facilities that utilize porous reservoirs, based on the current state-of-knowledge about H 2 behavior in the subsurface. The workflow sequentially addresses all aspects of UHS project development, including the identification of H 2 sources and users, site ranking and down-selection, geologic and reservoir-engineering characterization, reservoir design, testing, risk management, commissioning, operations, and monitoring for a UHS facility. The goal is to enable UHS facilities to be developed in an efficient and timely manner, while carefully managing project risks. This workflow is similar to that which has been developed for UGS facilities (see Figure 1 of API, 2022), with the addition of tasks and subtasks specific to H 2 and UHS. The project-development workflow is broken down into three major stages: (1) define the H 2 use case; (2) rank, down-select, and characterize potential, candidate UHS sites; and (3) reservoir design, integrity testing, risk assessment, commissioning, operations, and monitoring for selected UHS sites. Each major stage is further broken down into tasks and subtasks, which are described at a high level. This report also provides more detailed descriptions of all tasks and subtasks that involve reservoir analysis and testing.

08 HYDROGEN↗
DOE OSTI2021

NRAP-Open-IAM: FutureGen2 Component Models

This report describes the development and testing of three component models for NRAP-Open-IAM, the National Risk Assessment Partnership’s open-source integrated assessment model. The FutureGen2 Lookup Table Reservoir component model is based on interpolation of data from a set of lookup tables. The lookup tables contain pressures and saturations predicted by multiphase flow simulations performed with a reservoir simulator. The FutureGen2 Above Zone Monitoring Interval (AZMI) component is a surrogate model that can be used to estimate the impact that carbon dioxide (CO 2 ) and brine leaks from the CO 2 storage reservoir at the FutureGen 2.0 site might have had on overlying aquifers or monitoring units were a leak to occur. The model estimates the size of “impact plumes” according to five metrics: pH, Total Dissolved Solids (TDS), pressure, dissolved CO 2 and temperature. The FutureGen2 Aquifer component is similar, but is limited to four metrics: pH, Total Dissolved Solids (TDS), pressure, and dissolved CO 2 . The input parameters for each model are the same, but the Aquifer component is applicable to depths between 100 m and 700 m and the AZMI component is applicable from depths between 700 m and 1050 m.

42 ENGINEERING↗
DOE OSTI2023

Resource Characterization to Estimate Potential for Electricity Co-Production at Blackburn Oil Field, Nevada

The U.S. Department of Energy estimates that an annual average of 25 billion barrels of hot water are produced from oil and gas wells within the United States. The thermal energy available in the co-produced water stream is usually discarded, as the produced waters are considered an inconvenience by the operators and are disposed of using injection wells. However, utilizing organic Rankine cycle (ORC) generators, a vast amount of thermal energy can be captured and converted into electricity (albeit at relatively low efficiency due to the low temperatures). The National Renewable Energy Laboratory (NREL), in collaboration with Transitional Energy and Grant Canyon Oil & Gas, evaluated the feasibility of geothermal co-production of electricity by utilizing existing oil wells in Blackburn oil field in Nevada. The once prolific Blackburn oil field is located in Pine Valley, approximately 45 miles east-southeast of Elko, Nevada. Currently, the wells targeting the highly fractured Devonian Nevada dolomite reservoir are operating at a water cut ratio of more than 99%, with individual fluid (oil and water) production rates reaching 7.4 L/s (4,021 BBL/day). Analysis of publicly available data showed that the combination of the suitable wells' maximum historical production rates reached 22.90 L/s. The production from these wells occurs naturally and the wells are choked (and even shut down) by the operator to mitigate excessive water production, indicating a strong reservoir recharge and future opportunity to increase the water production for geothermal electricity generation. The main goal of this study was to evaluate the productivity of the existing wells, the performance of the reservoir, the surface network, and the operational constraints in order to achieve 1 MWe of electricity production from the field's water production. Utilizing the GEOPHIRES tool, we have determined that a twofold to threefold increase in the total fluid production, compared to the historical production under artificial restraint (choke), is required to reach a 1-MWe net target output for a low-temperature ORC system with air-cooled condensers. Lower flow rates would be required when utilizing water-based condensers instead of air-cooled condensers. However, that would require a constant supply of cold water, which may be challenging given the arid environment of the project site.

Blackburn↗
DOE OSTI2022

Evaluating power grid model hydropower feasibility with a river operations model

Production cost models (PCMs) simulate dispatch of generators across a large power grid and are used widely by planners to study the reliability of electricity supply. As energy systems transition away from the thermoelectric technologies that have traditionally balanced electricity supply and demand, hydropower and its representation in PCMs is of increasing importance. A limitation of PCMs applied to continental power grids with diverse generation portfolios is that hydropower generation is simulated without full consideration of complex river dynamics, leading to possible misrepresentation of grid flexibility and performance. In addition, data used in PCMs may reflect outdated operating policies. In this paper we propose a hydropower generation feasibility test for PCMs. The approach uses a detailed hydropower model to determine whether the hourly hydropower schedule from a PCM with simplified monthly parameterization can be attained after accounting for realistic river dynamics and operating policies, such as spill requirements and general water movement and balance through a cascade reservoir system. We perform this hydropower generation test for the ‘Big 10’ hydropower system on the Columbia River (part of the Western Interconnect of the United States), revealing 9% overestimation of available hydropower generation in a PCM solution in an average hydrologic year. Our evaluation provides insight on the cost and opportunities for better representing hydropower in PCMs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Synaptic Functionality and Neuromorphic Information Processing in Membrane Ion Channel Junctions

The human brain performs complex memory and computational tasks with high energy efficiency by regulating ion transport through membrane channels. These signaling mechanisms have been inspiring the development of nanofluidic memristors that emulate synaptic behavior. Here, in this study, we describe a membrane ion channel synapse (MICS), constructed from aqueous droplets linked by gramicidin A channels, that achieves neuromorphic functionality. MICS exhibits memristive ion transport with hysteretic current–voltage behavior arising from voltage-dependent channel formation and ion transport dynamics. MICS emulates a range of synaptic behaviors including associative learning. We further demonstrate its application in reservoir computing by performing handwritten digit classification and tic-tac-toe game and explore the system parameters that improve the computational performance. This droplet-based biomimetic synapse offers a potentially scalable and energy-efficient platform for next-generation neuromorphic computing systems.

Droplet interface bilayer↗
DOE OSTI2022

Reconfigurable training and reservoir computing in an artificial spin-vortex ice via spin-wave fingerprinting

Strongly interacting artificial spin systems are moving beyond mimicking naturally occurring materials to emerge as versatile functional platforms, from reconfigurable magnonics to neuromorphic computing. Typically, artificial spin systems comprise nanomagnets with a single magnetization texture: collinear macrospins or chiral vortices. Here, by tuning nanoarray dimensions we have achieved macrospin–vortex bistability and demonstrated a four-state metamaterial spin system, the ‘artificial spin-vortex ice’ (ASVI). ASVI can host Ising-like macrospins with strong ice-like vertex interactions and weakly coupled vortices with low stray dipolar field. Vortices and macrospins exhibit starkly differing spin-wave spectra with analogue mode amplitude control and mode frequency shifts of Δf = 3.8 GHz. The enhanced bitextural microstate space gives rise to emergent physical memory phenomena, with ratchet-like vortex injection and history-dependent non-linear fading memory when driven through global magnetic field cycles. We employed spin-wave microstate fingerprinting for rapid, scalable readout of vortex and macrospin populations, and leveraged this for spin-wave reservoir computation. ASVI performs non-linear mapping transformations of diverse input and target signals in addition to chaotic time-series forecasting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

HydroDCM: Hydrological Domain-Conditioned Modulation for Cross-Reservoir Inflow Prediction

Deep learning models have shown promise in reservoir inflow prediction, yet their performance often deteriorates when applied to different reservoirs due to distributional differences, referred to as the domain shift problem. Domain generalization (DG) solutions aim to address this issue by extracting domain-invariant representations that mitigate errors in unseen domains. However, in hydrological settings, each reservoir exhibits unique inflow patterns, while some metadata beyond observations like spatial information exerts indirect but significant influence. This mismatch limits the applicability of conventional DG techniques to many-domain hydrological systems. To overcome these challenges, we propose HydroDCM, a scalable DG framework for cross-reservoir inflow forecasting. Spatial metadata of reservoirs is used to construct pseudo-domain labels that guide adversarial learning of invariant temporal features. During inference, HydroDCM adapts these features through light-weight conditioning layers informed by the target reservoir’s metadata, reconciling DG’s invariance with location-specific adaptation. Experiment results on 30 real-world reservoirs in the Upper Colorado River Basin demonstrate that our method substantially outperforms state-of-the-art DG baselines under many-domain conditions and remains computationally efficient.

Hu, Pengfei [ORNL] (ORCID:0009000367130950)↗
DOE OSTI2020

Milestone Report for MS8: Extend Quantitative Brine and CO 2 Leakage Calculations

This report summarizes results of the risk analysis and characterization of CO 2 and brine leakage potential of Farnsworth Unit (FWU) wells. U.S. DOE’s National Risk Assessment Partnership (NRAP) program works on quantitatively assess long-term environmental risks amidst significant geologic uncertainty and variability. NRAP risk assessment and computational tools are developed to quantify uncertainties and calculate risk associated with geologic sequestration of carbon dioxide (CO 2 ). For this study, we have developed a workflow from University of Utah’s physics-based reservoir simulators to performing leakage calculations using NRAP Tools. NRAP tools (NRAP-IAM-CS, RROM-Gen) are used to conduct leakage risk analysis based on Eclipse simulation results, and characterize wellbore leakage at the Farnworth Site. This report summarizes results of the risk analysis and characterization of CO 2 and brine leakage potential of Farnsworth Unit (FWU) wells.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Subtask 1.5 – CO2 Injection Monitoring with an Optimized Scalable, Automated, Semipermanent Seismic Array

The scalable, automated, semipermanent seismic array (SASSA) method is a flexible and relatively cost-effective surface geophysical method for regular time-lapse monitoring of the movement of injected carbon dioxide (CO2) in a reservoir for CO2 enhanced oil recovery (EOR) or geologic CO2 storage operations. It has the advantages of a low-environmental-footprint while monitoring regions of a reservoir from the surface without the need for a regular grid distribution of receivers. Automated data collection is possible. As only time-lapse amplitude changes at the reservoir level due to CO2 movement within the reservoir are monitored, the turnaround time to deliver results from the SASSA method can be short, without the need for long, time-consuming data-processing workflows. As data is collected and processed, incremental information can be provided to the field operator. The Energy & Environmental Research Center (EERC) conducted a SASSA field test from September 2018 to November 2020 in a portion of the Bell Creek Field in Montana, which implemented new CO2 EOR field activities during the study period. Lessons learned from a proof-of-concept study were incorporated to improve the data quality of the SASSA method and demonstrate the viability of the technology. The EERC implemented several enhancements to improve data quality, including 1) an iterative survey design, which allowed placing the receivers in strategic locations where the movement of the CO2 in the reservoir could be tracked with minimum interference by the cultural noise in the study area; 2) the use of powerful seismic sources in the form of surface orbital vibrators, and 3) data acquisition during optimal periods. History-matched reservoir simulation was performed to predict gas saturation and pressure response induced by CO2 injection in the study area. The results were compared with the SASSA-measured responses to CO2 injection as a partial validation technique. A match between the two methods was observed for most of the SASSA points predicted to have intersected a CO2 saturation change. The validated results provide confidence that the SASSA method can be used independently as a CO2 saturation monitoring technique. As data are collected and processed, incremental information can be provided to the field operator. The critical components of the SASSA workflow for a successful application of the method are the following: Iterative survey design with information about CO2 injection activities from the oilfield operator. A detailed CO2 injection plan is the key driver to select the strategic monitoring location of the SASSA sensors. After this information is incorporated in the initial distribution of sources and receivers in the study area, high-resolution satellite images are used to identify ground locations not affected by cultural noise sources, such as power lines, pipelines/flow lines, or roadways. In the next iteration of the survey design, a scouting trip to the study area is needed to understand more details of the noise sources identified in the previous step and the intensity of the field activities that can also generate noise during the monitoring. Integrating the information from the scouting trip into the survey design to select the optimum source and receiver locations is the final step. Noise attenuation. The variety of noise types during seismic monitoring of an oil field is enormous. Tailored noise characterization and processing at a node-by-node level can enhance the performance and sensitivity of the SASSA technique. Future advancements that could improve the efficiency and application of the SASSA technology include: Gaining a better understanding of the noise field produced by the seismic source to aid the choice of receiver location. Surface noise from the source can overwhelm the small signal changes due to CO2 that the SASSA method measures. Improved data-processing workflow to automatically analyze and adapt to dynamic noise conditions associated with industrial settings. This subtask was funded through the EERC–DOE Joint Program on Research and Development for Fossil Energy-Related Resources Cooperative Agreement No. DE- FE0024233.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

History Matching and Prediction of a Polymer Flood Pilot in Heavy Oil Reservoir on Alaska North Slope

The first-ever polymer flood pilot to enhance heavy oil recovery on Alaska North Slope is ongoing. After more than 3 years of polymer injection, significant benefit has been observed from the decrease in water cut from 65% to less than 15% in the project producers. The primary objective of this study is to develop a robust history-matched reservoir simulation model capable of predicting future polymer flood performance. In this work, the reservoir simulation model has been developed based on the geological model and available reservoir and fluid data. In particular, four high transmissibility strips were introduced to connect the injector-producer well pairs, simulating short-circuiting flow behavior that can be explained by viscous fingering and reproducing the water cut history. The strip transmissibilities were manually tuned to improve the history matching results during the waterflooding and polymer flooding periods, respectively. It has been found that higher strip transmissibilities match the sharp water cut increase very well in the waterflooding period. Then the strip transmissibilities need to be reduced with time to match the significant water cut reduction. The viscous fingering effect in the reservoir during waterflooding and the restoration of injection conformance during polymer flooding have been effectively represented. Based on the validated simulation model, numerical simulation tests have been conducted to investigate the oil recovery performance under different development strategies, with consideration for sensitivity to polymer parameter uncertainties. The oil recovery factor with polymer flooding can reach about 39% in 30 years, twice as much as forecasted with continued waterflooding. Besides, the updated reservoir model has been successfully employed to forecast polymer utilization, a valuable parameter to evaluate the pilot test’s economic efficiency. All the investigated development strategies indicate polymer utilization lower than 3.5 lbs/bbl in 30 years, which is less than that of the same polymer used in a polymer pilot in Argentina.

Wang, Xindan↗
DOE OSTI2021

A New Modeling Framework for Multi-Scale Simulation of Hydraulic Fracturing and Production from Unconventional Reservoirs

This paper describes a new modeling framework for microscopic to reservoir-scale simulations of hydraulic fracturing and production. The approach builds upon a fusion of two existing high-performance simulators for reservoir-scale behavior: the GEOS code for hydromechanical evolution during stimulation and the TOUGH+ code for multi-phase flow during production. The reservoir-scale simulations are informed by experimental and modeling studies at the laboratory scale to incorporate important micro-scale mechanical processes and chemical reactions occurring within the fractures, the shale matrix, and at the fracture-fluid interfaces. These processes include, among others, changes in stimulated fracture permeability as a result of proppant behavior rearrangement or embedment, or mineral scale precipitation within pores and microfractures, at µm to cm scales. In our new modeling framework, such micro-scale testing and modeling provides upscaled hydromechanical parameters for the reservoir scale models. We are currently testing the new modeling framework using field data and core samples from the Hydraulic Fracturing Field Test (HFTS), a recent field-based joint research experiment with intense monitoring of hydraulic fracturing and shale production in the Wolfcamp Formation in the Permian Basin (USA). Below, we present our approach coupling the reservoir simulators GEOS and TOUGH+ informed by upscaled parameters from micro-scale experiments and modeling. We provide a brief overview of the HFTS and the available field data, and then discuss the ongoing application of our new workflow to the HFTS data set.

58 GEOSCIENCES↗
DOE OSTI2023

A multiscale recurrent neural network model for predicting energy production from geothermal reservoirs

Optimization of energy production from geothermal reservoirs requires reliable prediction of energy production performance under alternative operation and development scenarios. Traditionally, reservoir simulation models are used for the evaluation and screening of alternative production and development plans. However, simulation models require extensive data collection and modeling efforts and are time-consuming to build, run, and update. Data-driven predictive models, on the other hand, can serve as efficient prediction tools that can be used for decision support and management of daily operations and surveillance activities. Data-driven models become particularly attractive when a reservoir simulation model for a field does not exist and/or is difficult to build. Machine learning (ML)-based data-driven models that have recently become popular in several fields exploit statistical patterns and relations in training data to generate predictions. As such, they tend to perform better in interpolation problems (that is, prediction within the training data range) than when they are used to extrapolate beyond the training data. Production data from geothermal reservoirs tend to exhibit short-term variabilities as well as long-term trends, such as monotonically declining production temperatures. Capturing both short-term features and long-term trends with ML-based models is not trivial. We evaluate the use of recurrent neural networks (RNN) for the prediction of energy production from geothermal reservoirs. RNN is a class of ML architectures that are used to represent and predict sequential/dynamic data. Thus, it can be challenging to apply RNN to problems where long-term trends must be captured and extrapolation beyond the training data range is needed. We introduce the multiscale RNN architecture to extend the application of RNN to detect and predict both short-term variabilities and long-term trends in geothermal data. The developed architecture consists of a long-term component to only capture low-frequency data patterns, and a short-term component to detect features with higher frequency and more nonlinearity. The final prediction is obtained by combining the long-term and short-term predictions. Both synthetic and field data are used to evaluate the presented multiscale RNN model. The prediction performance of the multiscale RNN is compared against those obtained from the regular RNN and the autoregressive (AR) model. The results suggest that the multiscale architecture improves the long-term prediction performance of the regular RNN and enhances its robustness against noise.

15 GEOTHERMAL ENERGY↗
DOE OSTI2021

Microfluidic Investigation of Salinity-Induced Oil Recovery in Porous Media during Chemical Flooding

High and low salinity water flooding are common oil recovery processes performed in the oil fields for extracting crude oil from the reservoir. These processes are often performed sequentially, naturally establishing non-uniform salinity in the porous subsurface. In this article, we investigate oil transport in porous media induced by salinity change upon flooding with high and low salinity water. As we observe a large number of impervious dead-ends from three-dimensional imaging of the actual reservoir, we identify that these areas play an important role in oil recovery where the oil transport is governed by the salinity change rather than hydrodynamics. The salinity gradients induced upon high salinity water flooding provide pathways to enhance the transport of oil drops trapped in the dead-end regions via non-equilibrium effects. However, above a critical salinity, we observe a rapid aggregation of drops that lead to the complete blockage of the pore space, thereby inhibiting oil recovery. We also find that, at an intermediate salinity where the drop aggregation is modest, the aggregation rather promotes the oil recovery. Furthermore, our observations suggest that there exist optimal salinity conditions for maximizing oil recovery during chemical flooding.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗