TAILIEUCHUNG - Reservoir Formation Damage Episode 3 Part 4

Tham khảo tài liệu 'reservoir formation damage episode 3 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Model Assisted Analysis and Interpretation of Laboratory Field Tests 557 dependent on various factors including 1 the adequacy of the model 2 the accuracy of the input data and 3 the accuracy of the solution technique. Various sources of uncertainties affect the reliability of the predictions of models as described in Figure 17-1 by Bu and Damsleth 1996 . Experimental measurements taken under controlled test conditions to determine the input-output or cause-and-affect or the parity relationship response of systems such as core plugs undergoing a flow test also involve uncertainties. In general solutions of models called model predictions and the response of the test systems under prescribed conditions can be represented numerically or analytically by functional relationships mathematically expressed as y x1 x2 . x 17-6 INPUT DATA MATHEMATICAL RESULT NUMERICAL PARAMETERS MODEL Uncertainty interval I---1 Model parameters J Equations Model Figure 17-1. Sources of errors and uncertainty associated with mathematical modeling after Bu and Damsleth 1996 SPE reprinted by permission of the Society of Petroleum Engineers . 558 Reservoir Formation Damage in which f is a system response and Xj x2 x3 . denote the various input variables and parameters. Uncertainties involved in actual calculations predictions or measurements experimental testing lead to estimated or approximate results the accuracy of which depend on the errors involved. Therefore the actual values are the sum of the estimates and the errors. Thus if f Xị x2 . x indicate the estimated values of the function and its variables and A Aip Ax2 . xn represent the errors or uncertainties associated with these quantities the following equations expressing the actual quantities as a sum of the estimated values and the errors associated with them can be written Xj Xj AXị x2 x2 Ax2 17-7 17-8 Xn Xn X 17-9 f f 6f 17-10 The estimation of the propagation and impact of errors is usually based on a Taylor series expansion .