Constructing derivative profiles from discrete pressure data of transient well tests

A non-transitory, computer-readable medium storing one or more instructions executable by a computer system to perform operations comprising:

• arranging, in chronological order, discrete data for production of a well and an associated reservoir over a time period;
• determining, at a first focal point in the time period, first- and second-order derivatives of pressure versus a time series in the well and the associated reservoir, wherein the first- and second-order derivatives are determined using a five-point function, and wherein the five-point function considers beginning and ending points in the time period;
• determining, following the first- and second-order derivatives determined for the first focal point, the first- and second-order derivatives at a next (second) focal point;
• determining, applying the terminal corrections wherever deemed necessary, the first- and second-order derivatives at all the successive focal points;
• presenting, in a user interface, numerical values and plots of first- and second-order derivative profiles based on the first- and second-order derivatives;
• generating, using the first- and second-order derivative profiles, diagnostic plots and data for determining geological features for the associated reservoir and well parameters for the well;
• executing reservoir simulation models using an input reservoir description, including well and reservoir parameters, to generate a forecast of future production rates under different constraints;
• and
• managing a production strategy and future development plans for the well and providing estimates of future sales revenue for the well using the forecast of future production rates.

A computer-implemented system, comprising:

• one or more processors;
• and
• a non-transitory computer-readable storage medium coupled to the one or more processors and storing programming instructions for execution by the one or more processors, the programming instructions instructing the one or more processors to perform operations comprising:
• arranging, in chronological order, discrete data for production of a well and an associated reservoir over a time period;
• determining, at a first focal point in the time period, first- and second-order derivatives of pressure versus a time series in the well and the associated reservoir, wherein the first- and second-order derivatives are determined using a five-point function, and wherein the five-point function considers beginning and ending points in the time period;
• determining, following the first- and second-order derivatives determined for the first focal point, the first- and second-order derivatives at a next (second) focal point;
• determining, applying the terminal corrections wherever deemed necessary, the first- and second-order derivatives at all the successive focal points;
• presenting, in a user interface, numerical values and plots of first- and second-order derivative profiles based on the first- and second-order derivatives;
• generating, using the first- and second-order derivative profiles, diagnostic plots and data for determining geological features for the associated reservoir and well parameters for the well;
• executing reservoir simulation models using an input reservoir description, including well and reservoir parameters, to generate a forecast of future production rates under different constraints;
• and
• managing a production strategy and future development plans for the well and providing estimates of future sales revenue for the well using the forecast of future production rates.