ANALYTICAL MODEL OF CONVECTIVE TEMPERATURE RECOVERY IN SHUT-IN WELL

2021 ◽  
Vol 7 (3) ◽  
pp. 25-40
Author(s):  
Ayrat Sh. Ramazanov ◽  
Denis F. Islamov
Keyword(s):  
Inverse Problems ◽  
Analytical Model ◽  
Numerical Solutions ◽  
Flow Equation ◽  
Fiber Optic Sensor ◽  
Reservoir Properties ◽  
Geophysical Research ◽  
Unsteady Temperature ◽  
Distributed Fiber Optic Sensor ◽  
Pressure Independent

Thermometry is the most informative method in the complex of field geophysical research. The method is applied at all stages of the well’s life. Modern technologies for recording the temperature in the well, for example, using a distributed fiber-optic sensor, allow continuous research, and in particular, to carry out temperature probing of the developed formations. Temperature sensing data can be used as an additional (alternative to pressure) independent source of information on reservoir properties. To assess the parametric sensitivity of the temperature field in the well and to solve inverse problems of thermometry, mathematical models are needed to describe the thermohydrodynamic processes both in the reservoir and in the well. This article is devoted to the development of an analytical model describing the change in temperature and pressure in the reservoir after a well shut-in, taking into account some approximations: zero compressibility of the reservoir, fluid and thermal conductivity. The pressure distribution in the reservoir is found from the solution of the piezoconductivity equation. And the temperature distribution from the heat flow equation. The method of characteristics was used for the solution. The results of comparison of analytical and numerical solutions for temperature changes in a shut-in well are presented. It follows from the results obtained that the temperature after well shut-in is sensitive to the size of the near-wellbore zone with altered permeability and to the distribution of permeability in the formation. The proposed analytical solution can be used in thermosimulators to solve inverse problems in order to estimate the parameters of the near-wellbore formation zone based on actual measurements of unsteady temperature in the wellbore of production wells, as well as for planning production geophysical studies using the thermometry method.

The Partial Transformational Decomposition Method for a Hybrid Analytical/Numerical Solution of the 3D Gas-Flow Problem in a Hydraulically Fractured Ultralow-Permeability Reservoir

SPE Journal ◽  
2021 ◽  
pp. 1-28
Author(s):  
George Moridis ◽  
Niwit Anantraksakul ◽  
Thomas A. Blasingame
Keyword(s):  
Differential Equation ◽  
Decomposition Method ◽  
Gas Flow ◽  
Numerical Solutions ◽  
Flow Equation ◽  
Time Variable ◽  
Strong Nonlinearity ◽  
Fully Implicit ◽  
Ultralow Permeability ◽  
Klinkenberg Effects

Summary The analysis of gas production from fractured ultralow-permeability (ULP) reservoirs is most often accomplished using numerical simulation, which requires large 3D grids, many inputs, and typically long execution times. We propose a new hybrid analytical/numerical method that reduces the 3D equation of gas flow into either a simple ordinary-differential equation (ODE) in time or a 1D partial-differential equation (PDE) in space and time without compromising the strong nonlinearity of the gas-flow relation, thus vastly decreasing the size of the simulation problem and the execution time. We first expand the concept of pseudopressure of Al-Hussainy et al. (1966) to account for the pressure dependence of permeability and Klinkenberg effects, and we also expand the corresponding gas-flow equation to account for Langmuir sorption. In the proposed hybrid partial transformational decomposition method (TDM) (PTDM), successive finite cosine transforms (FCTs) are applied to the expanded, pseudopressure-based 3D diffusivity equation of gas flow, leading to the elimination of the corresponding physical dimensions. For production under a constant- or time-variable rate (q) regime, three levels of FCTs yield a first-order ODE in time. For production under a constant- or time-variable pressure (pwf) regime, two levels of FCTs lead to a 1D second-order PDE in space and time. The fully implicit numerical solutions for the FCT-based equations in the multitransformed spaces are inverted, providing solutions that are analytical in 2D or 3D and account for the nonlinearity of gas flow. The PTDM solution was coded in a FORTRAN95 program that used the Laplace-transform (LT) analytical solution for the q-problem and a finite-difference method for the pwf problem in their respective multitransformed spaces. Using a 3D stencil (the minimum repeatable element in the horizontal well and hydraulically fractured system), solutions over an extended production time and a substantial pressure drop were obtained for a range of isotropic and anisotropic matrix and fracture properties, constant and time-variableQ and pwf production schemes, combinations of stimulated-reservoir-volume (SRV) and non-SRV subdomains, sorbing and nonsorbing gases of different compositions and at different temperatures, Klinkenberg effects, and the dependence of matrix permeability on porosity. The limits of applicability of PTDM were also explored. The results were compared with the numerical solutions from a widely used, fully implicit 3D simulator that involved a finely discretized (high-definition) 3D domain involving 220,000 elements and show that the PTDM solutions can provide accurate results for long times for large well drawdowns even under challenging conditions. Of the two versions of PTDM, the PTD-1D was by far the better option and its solutions were shown to be in very good agreement with the full numerical solutions, while requiring a fraction of the memory and orders-of-magnitude lower execution times because these solutions require discretization of only the time domain and a single axis (instead of three). The PTD-0D method was slower than PTD-1D (but still much faster than the numerical solution), and although its solutions were accurate for t < 6 months, these solutions deteriorated beyond that point. The PTDM is an entirely new approach to the analysis of gas flow in hydraulically fractured ULP reservoirs. The PTDM solutions preserve the strong nonlinearity of the gas-flow equation and are analytical in 2D or 3D. This being a semianalytical approach, it needs very limited input data and requires computer storage and computational times that are orders-of-magnitude smaller than those in conventional (numerical) simulators because its discretization is limited to time and (possibly) a single spatial dimension.

Disturbance Detection in Distributed Fiber-Optic Sensor Based on Time-Delay Estimation

2010 ◽  
Vol 30 (6) ◽  
pp. 1603-1607 ◽  
Author(s):  
许海燕 Xu Haiyan ◽  
徐锲 Xu Qie ◽  
肖倩 Xiao Qian ◽  
张毅 Zhang Yi ◽  
贾波 Jia Bo
Keyword(s):  
Time Delay ◽  
Fiber Optic ◽  
Time Delay Estimation ◽  
Fiber Optic Sensor ◽  
Delay Estimation ◽  
Optic Sensor ◽  
Distributed Fiber Optic Sensor ◽  
Disturbance Detection

High Spatial Resolution Crack Monitoring in Concrete Structures Using a Distributed Fiber Optic Sensor

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Kevin (Wenhai) Li ◽  
Michel Gaudet
Keyword(s):  
Spatial Resolution ◽  
Fiber Optic ◽  
High Spatial Resolution ◽  
Early Stage ◽  
Large Strain ◽  
Fiber Optic Sensor ◽  
Crack Location ◽  
Four Point Bending ◽  
Optic Sensor ◽  
Distributed Fiber Optic Sensor

Abstract A method to monitor the mechanical behavior and identify crack location and growth in a concrete structure element using a distributed fiber optic sensor (FOS) system is demonstrated experimentally by testing concrete specimens in four-point bending. The sensor system consisted of an optical frequency domain reflectometry (OFDR) interrogator unit paired with an all-grating sensing fiber that was bonded to the surface of the concrete test specimen. Strain measurements with high spatial resolution of <10 mm were obtained at various points along a single fiber cable. Large strain values at the crack locations indicated strain concentrations that could be used to assess the crack growth. The distributed sensing system demonstrated the capability to detect localized, early stage cracks, with crack width smaller than 0.1 mm, well before they become observable by visual inspection.

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