Formation Pressure Inversion Method Based on Multisource Information

Summary The exploration and development of offshore oil and gas have greatly alleviated the tension of global oil and gas resources. However, the abnormal pressure of offshore reservoirs is more common compared with terrestrial oil and gas reservoirs, and the marine geological structure is complex, with the development of faults, fractures, and high and steep structures, which leads to the strong anisotropy of formation pore pressure distribution and uncertainty of pressure system change. In this paper, considering the corresponding characteristics of the randomness of the formation pressure prediction results in the Eaton equation for their respective variables, a formation pressure inversion method based on multisource information, such as predrilling data, bottomhole while drilling data, seabed measured data, and surface measured data, is established. On this basis, combined with the data of a well in the South China Sea, the variation law of the uncertainty of formation pressure prediction results under the conditions of predrilling data, measurement while drilling (MWD) data, and their mutual coupling is analyzed. The simulation results show that the uncertainty distribution of formation pressure prediction based solely on predrilling data shows linear accumulation trend with well depth, and the formation pressure inversion method based on multisource information can significantly curb the increasing trend of uncertainty when MWD data are introduced. Therefore, through the analysis of typical change patterns of monitoring parameters under normal/abnormal conditions during drilling, combined with the method of multisource information, the abnormal pressure information can be accurately predicted and inversed, which provides important support for wellbore pressure regulation under complex formation conditions.

Some Theorems for Inverse Uncertainty Distribution of Uncertain Processes

In real life, indeterminacy and determinacy are symmetric, while indeterminacy is absolute. We are devoted to studying indeterminacy through uncertainty theory. Within the framework of uncertainty theory, uncertain processes are used to model the evolution of uncertain phenomena. The uncertainty distribution and inverse uncertainty distribution of uncertain processes are important tools to describe uncertain processes. An independent increment process is a special uncertain process with independent increments. An important conjecture about inverse uncertainty distribution of an independent increment process has not been solved yet. In this paper, the conjecture is proven, and therefore, a theorem is obtained. Based on this theorem, some other theorems for inverse uncertainty distribution of the monotone function of independent increment processes are investigated. Meanwhile, some examples are given to illustrate the results.

A New Formula for Calculating Uncertainty Distribution of Function of Uncertain Variables

As a mathematical tool to rationally handle degrees of belief in human beings, uncertainty theory has been widely applied in the research and development of various domains, including science and engineering. As a fundamental part of uncertainty theory, uncertainty distribution is the key approach in the characterization of an uncertain variable. This paper shows a new formula to calculate the uncertainty distribution of strictly monotone function of uncertain variables, which breaks the habitual thinking that only the former formula can be used. In particular, the new formula is symmetrical to the former formula, which shows that when it is too intricate to deal with a problem using the former formula, the problem can be observed from another perspective by using the new formula. New ideas may be obtained from the combination of uncertainty theory and symmetry.

Modeling RL Electrical Circuit by Multifactor Uncertain Differential Equation

The symmetry principle of circuit system shows that we can equate a complex structure in the circuit network to a simple circuit. Hence, this paper only considers a simple series RL circuit and first presents an uncertain RL circuit model based on multifactor uncertain differential equation by considering the external noise and internal noise in an actual electrical circuit system. Then, the solution of uncertain RL circuit equation and the inverse uncertainty distribution of solution are derived. Some applications of solution for uncertain RL circuit equation are also investigated. Finally, the method of moments is used to estimate the unknown parameters in uncertain RL circuit equation.

Robust minimum cost consensus models with aggregation operators under individual opinion uncertainty

Individual opinion is one of the vital factors influencing the consensus in group decision-making, and is often uncertain. The previous studies mostly used probability distribution, interval distribution or uncertainty distribution function to describe the uncertainty of individual opinions. However, this requires an accurate understanding of the individual opinions distribution, which is often difficult to satisfy in real life. In order to overcome this shortcoming, this paper uses a robust optimization method to construct three uncertain sets to better characterize the uncertainty of individual initial opinions. In addition, we used three different aggregation operators to obtain collective opinions instead of using fixed values. Furthermore, we applied the numerical simulations on flood disaster assessment in south China so as to evaluate the robustness of the solutions obtained by the robust consensus models that we proposed. The results showed that the proposed models are more robust than the previous models. Finally, the sensitivity analysis of uncertain parameters was discussed and compared, and the characteristics of the proposed models were revealed.

Quantifying the unknown impact of segmentation uncertainty on image-based simulations

Image-based simulation, the use of 3D images to calculate physical quantities, relies on image segmentation for geometry creation. However, this process introduces image segmentation uncertainty because different segmentation tools (both manual and machine-learning-based) will each produce a unique and valid segmentation. First, we demonstrate that these variations propagate into the physics simulations, compromising the resulting physics quantities. Second, we propose a general framework for rapidly quantifying segmentation uncertainty. Through the creation and sampling of segmentation uncertainty probability maps, we systematically and objectively create uncertainty distributions of the physics quantities. We show that physics quantity uncertainty distributions can follow a Normal distribution, but, in more complicated physics simulations, the resulting uncertainty distribution can be surprisingly nontrivial. We establish that bounding segmentation uncertainty can fail in these nontrivial situations. While our work does not eliminate segmentation uncertainty, it improves simulation credibility by making visible the previously unrecognized segmentation uncertainty plaguing image-based simulation.

Uncertain Circuit Equation

Differential equation is a powerful tool for investigating the transient and steady-state solutions of electrical circuit in the time domain. By considering the noise in actual circuit system, this paper first presents an uncertain circuit equation, which is a type of differential equation driven by Liu process. Then the solution of uncertain circuit equation and the inverse uncertainty distribution of solution are derived. Following that, two applications of solution are provided as well. Based on the observations, the method of moments is used to estimate the unknown parameters in uncertain circuit equation. In addition, a paradox for stochastic circuit equation is also given.

Three-dimensional uncertain heat equation

Heat equation is a partial differential equation describing the temperature change of an object with time. In the traditional heat equation, the strength of heat source is assumed to be certain. However, in practical application, the heat source is usually influenced by noise. To describe the noise, some researchers tried to employ a tool called Winner process. Unfortunately, it is unreasonable to apply Winner process in probability theory to modeling noise in heat equation because the change rate of temperature will tend to infinity. Thus, we employ Liu process in uncertainty theory to characterize the noise. By modeling the noise via Liu process, the one-dimensional uncertain heat equation was constructed. Since the real world is a three-dimensional space, the paper extends the one-dimensional uncertain heat equation to a three-dimensional uncertain heat equation. Later, the solution of the three-dimensional uncertain heat equation and the inverse uncertainty distribution of the solution are given. At last, a paradox of stochastic heat equation is introduced.

Complex uncertain differential equations with application to time integral

In this paper, we propose complex uncertain differential equations (CUDEs) based on uncertainty theory. In order to describe the evolution of complex uncertain phenomenon related to belief degrees, we apply the complex Liu process to CUDEs. Firstly, we pose a concept of a linear CUDE and prove that homogeneous linear CUDE and general linear CUDE have solutions. Then, we prove existence and uniqueness theorem of a special CUDE. Further, we design a numerical algorithm to obtain inverse uncertainty distribution of the solution. Finally, as an application, we analyse the inverse uncertainty distributions of time integral of CUDEs and design numerical algorithms to obtain inverse uncertainty distributions of time integral.