The 4-D microgravity method for waterflood surveillance: A model study for the Prudhoe Bay reservoir, Alaska

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 78-87 ◽  
Author(s):  
Jennifer L. Hare ◽  
John F. Ferguson ◽  
Carlos L. V. Aiken ◽  
Jerry L. Brady
Keyword(s):  
Total Mass ◽  
Least Squares Method ◽  
Gravity Data ◽  
Water Injection ◽  
Gravity Modeling ◽  
Inversion Method ◽  
Model Parameters ◽  
Worst Case ◽  
Inverse Models ◽  
Prudhoe Bay

Forward and inverse gravity modeling is carried out on a suite of reservoir simulations of a proposed water injection in the Prudhoe Bay reservoir, Alaska. A novel surveillance technique is developed in which surface gravity observations are used to monitor the progress of a gas cap waterflood in the reservoir at 8200-ft (2500-m) depth. This cost‐effective method requires that high‐precision gravity surveys be repeated over periods of years. Differences in the gravity field with time reflect changes in the reservoir fluid densities. Preliminary field tests at Prudhoe Bay indicates survey accuracy of 5–10 μGal can be achieved for gravity data using a modified Lacoste & Romberg “G” type meter or Scintrex CG-3M combined with the NAVSTAR Global Positioning System (GPS). Forward gravity modeling predicts variations in surface measurements of 100 μGal after 5 years of water injection, and 180–250 μGal after 15 years. We use a constrained least‐squares method to invert synthetic gravity data for subsurface density distributions. The modeling procedure has been formulated and coded to allow testing of the models for sensitivity to gravity sampling patterns, noise types, and various constraints on model parameters such as density, total mass, and moment of inertia. Horizontal‐feature resolution of the waterflood is about 5000 ft (1520 m) for constrained inverse models from synthetic gravity with 5 μGal standard deviation (SD) noise. The inversion method can account for total mass of injected water to within a few percent. Worst‐case scenarios result from inversion of gravity data which are contaminated by high levels (greater than 10–15 μGal SD) of spatially correlated noise, in which case the total mass estimate from inverse models may over or underestimate the mass by 10–20%. The results of the modeling indicate that inversion of time‐lapse gravity data is a viable technique for the monitoring of reservoir gas cap waterfloods.

scholarly journals Evaluation of induced polarization measurements using a new inversion method

2021 ◽  
Author(s):  
Tamás Fancsik ◽  
Endre Turai ◽  
Norbert Péter Szabó ◽  
Judit Somogyiné Molnár ◽  
Tünde Edit Dobróka ◽  
...  
Keyword(s):  
Objective Function ◽  
Series Expansion ◽  
Least Squares Method ◽  
Delta Function ◽  
Induced Polarization ◽  
General Definition ◽  
Inversion Method ◽  
Model Parameters ◽  
Ore Minerals ◽  
Inversion Procedure

AbstractIn this paper, a new inversion method is proposed to process laboratory-measured induced polarization (IP) data. In the new procedure, the concept of the series expansion-based inversion is combined with a more general definition of the objective function. The time constant spectrum of the IP effect is assumed a line spectrum approximated by a series of Dirac’s delta function resulting in a square-integrable forward problem formula. This gives the applicability of the generalized objective function. The expansion coefficients as unknowns represent the model parameters of the inversion procedure. We use the new inversion procedure on an apparent polarizability dataset measured on a rock sample originated from the Recsk ore complex, northeast Hungary. The inversion results was compared to those of three additional laboratory datasets, which were measured on samples rich in ore minerals collected from the same area. The results are compared to those given by the traditional series expansion-based least squares method. It is shown that the newly proposed method gives more accurate and stable parameter estimation.

scholarly journals 3D Gravity Inversion on Unstructured Grids

2021 ◽  
Vol 11 (2) ◽  
pp. 722
Author(s):  
Siyuan Sun ◽  
Changchun Yin ◽  
Xiuhe Gao
Keyword(s):  
Objective Function ◽  
Unstructured Grids ◽  
Gravity Data ◽  
Depth Resolution ◽  
Continuous Model ◽  
Gravity Inversion ◽  
Inversion Method ◽  
Model Parameters ◽  
Fuzzy C Means ◽  
Fuzzy C Means Clustering

Compared with structured grids, unstructured grids are more flexible to model arbitrarily shaped structures. However, based on unstructured grids, gravity inversion results would be discontinuous and hollow because of cell volume and depth variations. To solve this problem, we first analyzed the gradient of objective function in gradient-based inversion methods, and a new gradient scheme of objective function is developed, which is a derivative with respect to weighted model parameters. The new gradient scheme can more effectively solve the problem with lacking depth resolution than the traditional inversions, and the improvement is not affected by the regularization parameters. Besides, an improved fuzzy c-means clustering combined with spatial constraints is developed to measure property distribution of inverted models in both spatial domain and parameter domain simultaneously. The new inversion method can yield a more internal continuous model, as it encourages cells and their adjacent cells to tend to the same property value. At last, the smooth constraint inversion, the focusing inversion, and the improved fuzzy c-means clustering inversion on unstructured grids are tested on synthetic and measured gravity data to compare and demonstrate the algorithms proposed in this paper.

The 4D microgravity method for waterflood surveillance: Part IV — Modeling and interpretation of early epoch 4D gravity surveys at Prudhoe Bay, Alaska

Geophysics ◽  
2008 ◽  
Vol 73 (6) ◽  
pp. WA173-WA180 ◽  
Author(s):  
Jennifer L. Hare ◽  
John F. Ferguson ◽  
Jerry L. Brady
Keyword(s):  
Mass Distribution ◽  
Structural Control ◽  
Water Movement ◽  
Gravity Data ◽  
Water Injection ◽  
Distribution Models ◽  
Linear Inversion ◽  
Reservoir Simulations ◽  
Large Water ◽  
Prudhoe Bay

Between March 2003 and March 2007, four high-precision 4D absolute microgravity surveys were performed at Prudhoe Bay, Alaska. These surveys are part of an ongoing effort to monitor the progress of a very large water-injection project in the gas cap of the Prudhoe Bay reservoir at a depth of [Formula: see text]. These carefully acquired gravity data must be modeled and interpreted in terms of water movement within the reservoir. A constrained linear inversion scheme was tested on reservoir simulations during the planning and development phase of this project (preinjection). The inver-sion methodology has been applied to data for three epochs (2005–2003, 2006–2003, and 2007–2003), and mass-distribution models have been produced for the reservoir. The time evolution of the water-mass distribution in the reservoir is visualized from these three snapshot models. The waterflood is expanding into the gas cap at the expected rate but is exhibiting nonsymmetric behavior that is consistent with a greater degree of structural control than expected. The waterflood seems to be restrained episodically and guided by fault barriers. These barriers are overcome and fault-bounded blocks filled with water in stages.

Gravity modeling for crustal-scale models of rifted continental margins using a constrained 3D inversion method

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. G25-G39 ◽  
Author(s):  
Meixia Geng ◽  
J. Kim Welford ◽  
Colin G. Farquharson ◽  
Xiangyun Hu
Keyword(s):  
Weighting Function ◽  
Gravity Data ◽  
A Priori ◽  
Probabilistic Approach ◽  
Gravity Modeling ◽  
Inversion Method ◽  
Continental Margins ◽  
Linear Equality Constraints ◽  
Boundary Information ◽  
Regional Gravity

We have developed a new constrained inversion method that is based on a probabilistic approach for resolving crustal structure from regional gravity data. The smoothness of estimated structures is included in the inversion by using a model covariance matrix, and the sparse boundary information obtained from seismic data is incorporated in the inversion by using linear equality constraints. Moreover, constraints on the average anomalous densities expected for different crustal layers are applied instead of using a depth-weighting function. Bathymetric data and sediment thicknesses are included in the inversion by using an a priori model. Using the proposed method, model structures with sharp boundaries can be obtained while the existing boundary information and sparse seismic constraints are honored. We determine through a synthetic example and a real-world example that the proposed constrained inversion method is a valid tool for studying crustal-scale structures.

2-D inversion of gravity data using sources laterally bounded by continuous surfaces and depth‐dependent density

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1128-1141 ◽  
Author(s):  
Juan García‐Abdeslem
Keyword(s):  
Sensitivity Analysis ◽  
Gravity Data ◽  
Synthetic Data ◽  
Gravity Modeling ◽  
Inversion Method ◽  
Data Sets ◽  
Nonlinear Inversion ◽  
Correlation Matrices ◽  
Significant Difference ◽  
Dependent Density

A description is given of numerical methods for 2-D gravity modeling and nonlinear inversion. The forward model solution is suitable for calculating the gravity anomaly caused by a 2-D source body with depth‐dependent density that is laterally bounded by continuous surfaces and can easily accommodate different kinds of geologic structures. The weighted and damped discrete nonlinear inverse method addressed here can invert both density and geometry of the source body. Both modeling and inversion methods are illustrated with several examples using synthetic and two field gravity data sets—one over a sulfide ore body and other across a sedimentary basin. A sensitivity analysis is carried out for the resulting solutions by means of the resolution, covariance, and correlation matrices, providing insight into the capabilities and limitations of the inversion method. The inversion of synthetic data provides meaningful results, showing that the method is robust in the presence of noise. Its sensitivity analysis indicates an almost perfect resolution and small covariance, but high correlation between some parameters. Differences in the asperity aspect of the inverted‐field data sets turned out to be important for the inversion capabilities of the algorithm, making a significant difference in the resolution achieved, its covariance, and the degree of correlation among parameters.

scholarly journals 3D Gravity Modeling of Complex Salt Features in the Southern Gulf of Mexico

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Mauricio Nava-Flores ◽  
Carlos Ortiz-Aleman ◽  
Mauricio G. Orozco-del-Castillo ◽  
Jaime Urrutia-Fucugauchi ◽  
Alejandro Rodriguez-Castellanos ◽  
...  
Keyword(s):  
Gravity Data ◽  
Three Dimensional ◽  
Complex Salt ◽  
Gravity Modeling ◽  
Gravity Inversion ◽  
Inversion Method ◽  
Oil Exploration ◽  
Potential Field Data ◽  
Estimation Algorithms ◽  
3D Gravity

We present a three-dimensional (3D) gravity modeling and inversion approach and its application to complex geological settings characterized by several allochthonous salt bodies embedded in terrigenous sediments. Synthetic gravity data were computed for 3D forward modeling of salt bodies interpreted from Prestack Depth Migration (PSDM) seismic images. Density contrasts for the salt bodies surrounded by sedimentary units are derived from density-compaction curves for the northern Gulf of Mexico’s oil exploration surveys. By integrating results from different shape- and depth-source estimation algorithms, we built an initial model for the gravity anomaly inversion. We then applied a numerically optimized 3D simulated annealing gravity inversion method. The inverted 3D density model successfully retrieves the synthetic salt body ensemble. Results highlight the significance of integrating high-resolution potential field data for salt and subsalt imaging in oil exploration.

Constructing and model-fitting receiver operator characteristics using continuous data.

2018 ◽  
Author(s):  
Josephine Ann Urquhart ◽  
Akira O'Connor
Keyword(s):  
Signal Detection ◽  
Least Squares Method ◽  
Model Fitting ◽  
Simulated Data ◽  
Continuous Variable ◽  
Continuous Data ◽  
Model Parameters ◽  
Operating Characteristics ◽  
Unequal Variance ◽  
Discrete Discrimination

Receiver operating characteristics (ROCs) are plots which provide a visual summary of a classifier’s decision response accuracy at varying discrimination thresholds. Typical practice, particularly within psychological studies, involves plotting an ROC from a limited number of discrete thresholds before fitting signal detection parameters to the plot. We propose that additional insight into decision-making could be gained through increasing ROC resolution, using trial-by-trial measurements derived from a continuous variable, in place of discrete discrimination thresholds. Such continuous ROCs are not yet routinely used in behavioural research, which we attribute to issues of practicality (i.e. the difficulty of applying standard ROC model-fitting methodologies to continuous data). Consequently, the purpose of the current article is to provide a documented method of fitting signal detection parameters to continuous ROCs. This method reliably produces model fits equivalent to the unequal variance least squares method of model-fitting (Yonelinas et al., 1998), irrespective of the number of data points used in ROC construction. We present the suggested method in three main stages: I) building continuous ROCs, II) model-fitting to continuous ROCs and III) extracting model parameters from continuous ROCs. Throughout the article, procedures are demonstrated in Microsoft Excel, using an example continuous variable: reaction time, taken from a single-item recognition memory. Supplementary MATLAB code used for automating our procedures is also presented in Appendix B, with a validation of the procedure using simulated data shown in Appendix C.

scholarly journals Water-retaining properties of NCZ composite dust suppressant and its wetting ability to hydrophobic coal dust

2021 ◽  
Author(s):  
Jianguo Liu ◽  
Shu Wang ◽  
Longzhe Jin ◽  
Tianyang Wang ◽  
Zihao Zhou ◽  
...  
Keyword(s):  
Least Squares Method ◽  
Coal Dust ◽  
Water Injection ◽  
Synthesis Method ◽  
Underground Mines ◽  
Initial Contact ◽  
Clean Water ◽  
Mining Operations ◽  
Thermal Synthesis ◽  
Wetting Ability

AbstractCoal dust is a primary threat to underground coal miners. The most common approach to control coal dust is hydraulic methods, such as water spray and coal seam water injection. To improve the dust suppressant efficiency of hydraulic methods, a novel chemical composite dust suppressant, called NCZ, was prepared in this study using calcium chloride (CaCl2), magnesium chloride (MgCl2), and nonionic surfactants using a thermal synthesis method. The water-retaining properties of NCZ powder and its solutions were characterized using the water absorption rate (WAR) and evaporation rate (ER), respectively, and the wetting abilities of the NCZ solutions on coal dust were tested using the initial contact angle (ICA) and sink rate (SR). The results indicate that the NCZ solutions have anti-evaporation effects, and the ER of the solution with a 20.0 wt% NCZ is reduced by 11.7% compared with that of clean water. Furthermore, NCZ solutions have remarkable enhancement effects on the wettability of coal dust. The ICA and SR of clean water and the NCZ solution at 20.0 wt% are 141.9° and 0 mg/s, and 29.3° and 1.46 mg/s, respectively. Finally, quantitative relationships between the solution surface tension and the ICA and IR were established using the least squares method. This study provides a new product for dust suppression in underground mines, which is significant for the optimum applied concentration of dust suppressant in mining operations.

scholarly journals Determination of synchronous generator nonlinear model parameters based on power rejection tests using a gradient optimization algorithm

2017 ◽  
Vol 65 (4) ◽  
pp. 479-488 ◽  
Author(s):  
A. Boboń ◽  
A. Nocoń ◽  
S. Paszek ◽  
P. Pruski
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Least Squares Method ◽  
Synchronous Generator ◽  
Operating Conditions ◽  
Model Parameters ◽  
State Variables ◽  
Starting Point ◽  
Gradient Optimization

AbstractThe paper presents a method for determining electromagnetic parameters of different synchronous generator models based on dynamic waveforms measured at power rejection. Such a test can be performed safely under normal operating conditions of a generator working in a power plant. A generator model was investigated, expressed by reactances and time constants of steady, transient, and subtransient state in the d and q axes, as well as the circuit models (type (3,3) and (2,2)) expressed by resistances and inductances of stator, excitation, and equivalent rotor damping circuits windings. All these models approximately take into account the influence of magnetic core saturation. The least squares method was used for parameter estimation. There was minimized the objective function defined as the mean square error between the measured waveforms and the waveforms calculated based on the mathematical models. A method of determining the initial values of those state variables which also depend on the searched parameters is presented. To minimize the objective function, a gradient optimization algorithm finding local minima for a selected starting point was used. To get closer to the global minimum, calculations were repeated many times, taking into account the inequality constraints for the searched parameters. The paper presents the parameter estimation results and a comparison of the waveforms measured and calculated based on the final parameters for 200 MW and 50 MW turbogenerators.

scholarly journals Mass outflow of the X-ray emission line gas in NGC 4151

2020 ◽  
Vol 15 (S359) ◽  
pp. 131-135
Author(s):  
S. B. Kraemer ◽  
T. J. Turner ◽  
D. M. Crenshaw ◽  
H. R. Schmitt ◽  
M. Revalski ◽  
...  
Keyword(s):  
Emission Line ◽  
Total Mass ◽  
High Energy ◽  
Model Parameters ◽  
Zeroth Order ◽  
Space Telescope ◽  
X Ray ◽  
Ngc 4151 ◽  
Outflow Rate ◽  
Mass Outflow

AbstractWe have analyzed Chandra/High Energy Transmission Grating spectra of the X-ray emission line gas in the Seyfert galaxy NGC 4151. The zeroth-order spectral images show extended H- and He-like O and Ne, up to a distance r ˜ 200 pc from the nucleus. Using the 1st-order spectra, we measure an average line velocity ˜230 km s–1, suggesting significant outflow of X-ray gas. We generated Cloudy photoionization models to fit the 1st-order spectra; the fit required three distinct emission-line components. To estimate the total mass of ionized gas (M) and the mass outflow rates, we applied the model parameters to fit the zeroth-order emission-line profiles of Ne IX and Ne X. We determined an M ≍ 5.4 × 105Mʘ. Assuming the same kinematic profile as that for the [O III] gas, derived from our analysis of Hubble Space Telescope/Space Telescope Imaging Spectrograph spectra, the peak X-ray mass outflow rate is approximately 1.8 Mʘ yr–1, at r ˜ 150 pc. The total mass and mass outflow rates are similar to those determined using [O III], implying that the X-ray gas is a major outflow component. However, unlike the optical outflows, the X-ray emitting mass outflow rate does not drop off at r > 100pc, which suggests that it may have a greater impact on the host galaxy.

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