Derivative Profiles From Discrete Pressure Data
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Solution Overview
Problem
Conventional algorithms are not practical for computing second-order derivatives with discrete data points, especially at the end points of a time period, leading to inaccuracies in characterizing well and reservoir parameters under dynamic conditions.
Innovation Solution
A computer-implemented method using a five-point function to determine first- and second-order derivatives from discrete pressure data, applying terminal corrections where necessary, and generating derivative profiles to accurately represent well and reservoir parameters for reservoir simulation models.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional algorithms are used to compute second-order derivatives with discrete data points, then the computation can be performed, but the accuracy deteriorates especially at the end points of a time period
Solution Approach 1:
The patent segments the computation of second-order derivatives into two distinct parts: (1) interior points computation using a five-point function that considers beginning and ending points, and (2) terminal corrections specifically applied to end points. This segmentation allows each part to be optimized independently, resolving the accuracy-reliability contradiction at boundary points.
Solution Approach 2:
The patent applies different computational approaches to different locations in the data set. The five-point function is used for interior points where sufficient data is available, while special terminal corrections are applied specifically at end points. This local differentiation ensures optimal accuracy for each region, addressing the reliability issue at boundaries without compromising overall precision.
2Measurement precision
If dual derivatives are used to diagnose low-grade reservoir heterogeneity, then the diagnostic sensitivity improves, but the computational complexity increases
Solution Approach 1:
The patent performs preliminary computations of both first-order and second-order derivatives using the five-point function before combining them into dual derivatives. By pre-computing these components and storing them, the system reduces the computational burden during the actual dual derivative calculation, thus improving diagnostic sensitivity while managing computational complexity.
Solution Approach 2:
The patent introduces intermediate computational structures (the five-point function results for first and second derivatives) that serve as mediators between the raw pressure data and the final dual derivatives. These intermediaries organize the computation in a structured way that improves accuracy for detecting low-grade heterogeneity while keeping the overall process manageable through modular computation.
Data Source
AI summary
Systems and methods include a computer-implemented method for using first- and second-order derivatives from discrete pressure data of a well to characterize the well and intersected reservoir under dynamic conditions. Discrete data for the well and associated reservoir is arranged chronologically. First- and second-order derivatives of pressure versus a time series are determined at a first focal point using a five-point function considering beginning and ending points in a time period. First- and second-order derivatives are determined at successive focal points, applying terminal corrections. Numerical values and plots of first- and second-order derivative profiles are presented. Diagnostic plots and data for determining geological features for the associated reservoir and well parameters are generated. Reservoir simulation models are executed to generate a forecast of future production rates under different constraints. A production strategy and future development plans for the well are managed, and future sales revenue estimates are provided.