Weak Compactness Criterion in Wk,1 W^{k, 1} with an Existence Theorem of Minimizers

Nelson Dunford and Billy James Pettis [{\em Trans. Amer. Math. Soc.}, 47 (1940), pp. 323--392] proved that relatively weakly compact subsets of $L^1$ coincide with equi-integrable families. We expand it to the case of $W^{k,1}$ - the non-reflexive Sobolev space - by a tailor-made isometric operator. Herein we extend an existence theorem of minimizers from reflexive Sobolev spaces to non-reflexive ones

Explicit original gas in place determination of naturally fractured reservoirs in gas well rate decline analysis

Naturally fractured gas reservoirs have contributed significantly to global gas reserves and production. The classical gas-well decline analysis relies largely on Arps’ empirical decline models, or modern production decline analysis associating with pseudo-variables. The explicit original gas in place determination methodology is extended from homogeneous reservoir to naturally fractured reservoir under constant or variable bottom-hole pressure conditions in gas-well rate decline analysis. Then, the relationship between gas flow rate and average reservoir pseudo-pressure in the boundary-dominated flow period is re-derived. This formula is in the same format with the equation for homogeneous reservoir by due to the introduction of a new productivity index parameter that captures the inter-porosity flow between fracture and matrix in the natural fractured reservoir. The proposed step-by-step procedures are applied here, which enable the estimation of decline exponent and the explicit and straightforward determination of the original gas in place without any iterative calculations. Four simulated cases prove that our methodology can be successfully used in heterogeneous naturally fractured reservoirs with irregular boundary under constant or variable bottom-hole pressure conditions.Document Type: Original articleCited as: Wang, Y., Wang, J., Zhao, W., Ji, P., Cheng, S., Yu, H. Explicit original gas in place determination of naturally fractured reservoirs in gas well rate decline analysis. Advances in Geo-Energy Research, 2023, 9(2): 117-124. https://doi.org/10.46690/ager.2023.08.0

A numerical model to evaluate formation properties through pressure-transient analysis with alternate polymer flooding

A numerical pressure transient analysis method of composite model with alternate polymer flooding is presented, which is demonstrated by field test data provided by China National Petroleum Corporation. Polymer concentration distribution and viscosity distribution are obtained on the basis of polymer rheological model, considering shear effect, convection, diffusion, inaccessible pore volume and permeability reduction of polymer. Pressure analysis mathematical model is established by considering wellbore storage effect and skin effect. Type curves are then developed from mathematical model which have seven sections and parameter sensitivity is analyzed, among which the transient sections of low-concentration and high-concentration hydrolyzed polyacrylamides (HPAM) solution, high-concentration HPAM solution and crude oil show obvious concave shape on pressure derivative curve due to different viscosities of three zones. Formation parameters and viscosity distribution of polymer solution can be calculated by type-curve matching. The polymer flooding field tests prove that the three-zone composite model can reasonably calculate formation parameters in onshore oilfield with alternate polymer flooding, which demonstrate the application potential of the analysis method.Cited as: Zhang, J., Cheng, S., Zhu, C., Luo, L. A numerical model to evaluate formation properties through pressure-transient analysis with alternate polymer flooding. Advances in Geo-Energy Research, 2019, 3(1): 94-103, doi: 10.26804/ager.2019.01.0

Detecting Backdoors in Pre-trained Encoders

Self-supervised learning in computer vision trains on unlabeled data, such as images or (image, text) pairs, to obtain an image encoder that learns high-quality embeddings for input data. Emerging backdoor attacks towards encoders expose crucial vulnerabilities of self-supervised learning, since downstream classifiers (even further trained on clean data) may inherit backdoor behaviors from encoders. Existing backdoor detection methods mainly focus on supervised learning settings and cannot handle pre-trained encoders especially when input labels are not available. In this paper, we propose DECREE, the first backdoor detection approach for pre-trained encoders, requiring neither classifier headers nor input labels. We evaluate DECREE on over 400 encoders trojaned under 3 paradigms. We show the effectiveness of our method on image encoders pre-trained on ImageNet and OpenAI's CLIP 400 million image-text pairs. Our method consistently has a high detection accuracy even if we have only limited or no access to the pre-training dataset.Comment: Accepted at CVPR 2023. Code is available at https://github.com/GiantSeaweed/DECRE

LOTUS: Evasive and Resilient Backdoor Attacks through Sub-Partitioning

Backdoor attack poses a significant security threat to Deep Learning applications. Existing attacks are often not evasive to established backdoor detection techniques. This susceptibility primarily stems from the fact that these attacks typically leverage a universal trigger pattern or transformation function, such that the trigger can cause misclassification for any input. In response to this, recent papers have introduced attacks using sample-specific invisible triggers crafted through special transformation functions. While these approaches manage to evade detection to some extent, they reveal vulnerability to existing backdoor mitigation techniques. To address and enhance both evasiveness and resilience, we introduce a novel backdoor attack LOTUS. Specifically, it leverages a secret function to separate samples in the victim class into a set of partitions and applies unique triggers to different partitions. Furthermore, LOTUS incorporates an effective trigger focusing mechanism, ensuring only the trigger corresponding to the partition can induce the backdoor behavior. Extensive experimental results show that LOTUS can achieve high attack success rate across 4 datasets and 7 model structures, and effectively evading 13 backdoor detection and mitigation techniques. The code is available at https://github.com/Megum1/LOTUS.Comment: IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR 2024

Variable-Permeability Well-Testing Models and Pressure Response in Low-Permeability Reservoirs with non-Darcy Flow

This paper proposes the concept of variable-permeability effect and sets up the one-dimensional and two-dimensional non-Darcy well testing models. The finite difference algorithm is employed to solve the differential equations of the variable-permeability model, and the non-convergence of the numerical solutions is solved by using the geometric mean of permeability. The type curves of pressure and pressure derivative with variable-permeability effect are obtained, and sensitivity analysis is conducted. The results show that the type curves upturn in the middle and late sections, and the curves turn more upward with the severer of the variable-permeability effect. The severer the non-Darcy effect is, the less obviously the curve upturns caused by boundary effect. Furthermore, the boundary effect is increased by increasing the number of impermeable boundaries or decreasing the distance between the well and boundary

Reservoir Permeability Prediction Based on Analogy and Machine Learning Methods: Field Cases in DLG Block of Jing’an Oilfield, China

AbstractReservoir permeability, generally determined by experimental or well testing methods, is an essential parameter in the oil and gas field development. In this paper, we present a novel analogy and machine learning method to predict reservoir permeability. Firstly, the core test and production data of other 24 blocks (analog blocks) are counted according to the DLG block (target block) of Jing’an Oilfield, and the permeability analogy parameters including porosity, shale content, reservoir thickness, oil saturation, liquid production, and production pressure difference are optimized by Pearson and principal component analysis. Then, the fuzzy matter element method is used to calculate the similarity between the target block and analog blocks. According to the similarity calculation results, reservoir permeability of DLG block is predicted by reservoir engineering method (the relationship between core permeability and porosity of QK-D7 in similar blocks) and machine learning method (random forest, gradient boosting decision tree, light gradient boosting machine, and categorical boosting). By comparing the prediction accuracy of the two methods through the evaluation index determination coefficient (R2) and root mean square error (RMSE), the CatBoost model has higher accuracy in predicting reservoir permeability, with R2 of 0.951 and RMSE of 0.139. Finally, the CatBoost model is selected to predict reservoir permeability of 121 oil wells in the DLG block. This work uses simple logging and production data to quickly and accurately predict reservoir permeability without coring and testing. At the same time, the prediction results are well applied to the formulation of DLG block development technology strategy, which provides a new idea for the application of machine learning to predict oilfield parameters

Elijah: Eliminating Backdoors Injected in Diffusion Models via Distribution Shift

Diffusion models (DM) have become state-of-the-art generative models because of their capability to generate high-quality images from noises without adversarial training. However, they are vulnerable to backdoor attacks as reported by recent studies. When a data input (e.g., some Gaussian noise) is stamped with a trigger (e.g., a white patch), the backdoored model always generates the target image (e.g., an improper photo). However, effective defense strategies to mitigate backdoors from DMs are underexplored. To bridge this gap, we propose the first backdoor detection and removal framework for DMs. We evaluate our framework Elijah on hundreds of DMs of 3 types including DDPM, NCSN and LDM, with 13 samplers against 3 existing backdoor attacks. Extensive experiments show that our approach can have close to 100% detection accuracy and reduce the backdoor effects to close to zero without significantly sacrificing the model utility.Comment: AAAI 202

Optimization of volume fracturing technology for shallow bow horizontal well in a tight sandstone oil reservoir

The physical property of Chang 6 reservoir in Yanchang oilfield is poor, and the heterogeneity is strong. Multistage fracturing of horizontal wells is easy to form only one large horizontal fracture, but it is difficult to control the fracture height and length. The new mining method of “bow horizontal well + multistage horizontal joint” can effectively increase the multistage horizontal joint’s spatial position, which improves the drainage area and stimulation efficiency of oil wells. Due to the reservoir’s low permeability and strong heterogeneity, the single well mode of “bow horizontal well + multistage horizontal fracture” cannot effectively produce Chang 6 reservoir. To improve the production degree of the g 6 reservoir, the fracture model is established using equivalent conductivity and the multigrid method. The pressure response functions of horizontal wells and volume fracturing horizontal wells are established by using the source function, and the relationship between reservoir permeability and starting pressure gradient in the block is calculated. On this basis, the reservoir productivity equation of the block is established, which provides a basis for optimizing the fracturing design parameters of horizontal wells. It is proposed that the flow unit should be considered in the design of fracturing parameters of horizontal fractures, the number of fractures should comprehensively consider whether the fractures can make each flow unit be used, and have large controlled reserves, and the scale of fracturing should comprehensively consider the output and cost. The fracture network model is established by using equivalent conductivity and multi-gridthod, and the volume fracturing design parameters of horizontal wells are optimized, considering the seepage characteristics of the flow unit. The fracturing design parameters of the horizontal section are further defined, which provides a theoretical basis for the efficient development of shallow tight reservoirs

Numerical Well Testing Interpretation Model and Applications in Crossflow Double-Layer Reservoirs by Polymer Flooding

This work presents numerical well testing interpretation model and analysis techniques to evaluate formation by using pressure transient data acquired with logging tools in crossflow double-layer reservoirs by polymer flooding. A well testing model is established based on rheology experiments and by considering shear, diffusion, convection, inaccessible pore volume (IPV), permeability reduction, wellbore storage effect, and skin factors. The type curves were then developed based on this model, and parameter sensitivity is analyzed. Our research shows that the type curves have five segments with different flow status: (I) wellbore storage section, (II) intermediate flow section (transient section), (III) mid-radial flow section, (IV) crossflow section (from low permeability layer to high permeability layer), and (V) systematic radial flow section. The polymer flooding field tests prove that our model can accurately determine formation parameters in crossflow double-layer reservoirs by polymer flooding. Moreover, formation damage caused by polymer flooding can also be evaluated by comparison of the interpreted permeability with initial layered permeability before polymer flooding. Comparison of the analysis of numerical solution based on flow mechanism with observed polymer flooding field test data highlights the potential for the application of this interpretation method in formation evaluation and enhanced oil recovery (EOR)