Spe-192002-ms case Study Applied Machine Learning to Optimise pcp completion Design in a cbm field
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- GPR for PCP Runlife
| Stationary Representation There are two notable transformations used in this paper with both utilizing cumulative production rates of both gas and water. The first describes the water rate decline as a function of cumulative water production in equation 7 . This method solves for rate directly and it is empirically derived and although it is not derived from first principles its utility lies in the fact that is readily consumable. This method uses the declining water production to define a tank model and then uses the cumulative GLR of the well to predict the gas rate. It is best used during periods of pseudo steady flow. The daily water production data was automatically filtered to remove transients when used with equation 7 , which can be simply seen as an empirical fit to linearise the observed behavior of the data. (7) The second describes the relationship of the cumulative gas produced versus the cumulative water produced. Again it can be simply seen as an empirical fit to linearise the observed behavior of the data. (8) These relationships were derived experimentally with the purpose of making the relationships of water rate, cumulative produced water and cumulative produced gas linear. Unlike estimation of reservoir production through the use of engineering models such as King or Shi-Durucan which require a lot a core analysis to use the use of the simple empirical relationships proposed here can be more readily used because in practice engineers are faced with very limited data. Downloaded from http://onepetro.org/SPEAPOG/proceedings-pdf/18APOG/2-18APOG/D021S016R002/1220497/spe-192002-ms.pdf/1 by Vedanta Limited - Cairn Oil & Gas user on 28 June 2023 SPE-192002-MS 5 GPR for PCP Runlife The runlife of a PCP is the time between start of operation and failure of the PCP. Regression models of failure time in maintainable systems, such as pumps, compressors, and heavy mobile equipment, have been extensively studied over second half of last century by statisticians and reliability engineers (Meeker and Escobar, Until the start of this century, the failure time regression models were predominantly parametric, requiring an assumption or understanding of the function between the variables of the system and failure time. The work of the statistician and engineer was finding the parameters that fit the function to the data. Parametric models are useful for relatively simple systems with a few variables (e.g. fatigue life of a plastic under different levels of stress amplitude and temperature, the parameters of the function are independent of the variables, and failure time data is collected in a controlled laboratory environment. Parametric models have limitations for most maintainable systems in industrial environments. The failure times of most systems are affected by numerous variables, and numerous failure modes can exist within the system. Inmost cases, engineers do not know with certainty which variables, and which interactions of variables, affect the failure time. Parametric models also rely on smooth and continuous relationship between variables and failure time, which is often not satisfied with numerous variables and interactions. Additionally, the data collected from maintainable systems in industry are not controlled experiments where a sufficient quantity of data fora set of variables is acquired to obtain statistical significance in the prediction. Regression models based on Gaussian process are non-parametric. A Gaussian process (GP) is a generalisation of the Gaussian (or normal) probability distribution (Rasmussen and Williams, p, and represents a collection of random variables. Typically, a probability distribution describes a scalar variable or vector for multivariate distributions. For the application of Gaussian processes to regression, the random variables are functions. The functions are not defined algebraically, but as vectors "one can loosely think of a function as a very long vector, each entry in the vector specifying the function value f(x) at a particular input x". The collection of random variables (i.e. the functions of the GP) are completely specified by mean function and covariance function of the GP. Algebraically, f(x) GP(m(x),k(x,x')), where f(x) is distributed according to the gaussian process, with m(x) as the mean function and k(x,x') as the covariance function. Download 1.89 Mb. Share with your friends:
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