Gas-Drive Reserve Calculation Using Logarithmic Permeability Transformation

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Solution Overview

Problem

Conventional methods for determining single-well dynamic and recoverable reserves in gas-drive reservoirs are inefficient and inaccurate due to the non-linear relationship between oil-gas relative permeability ratios and gas saturation, especially at non-intermediate stages.

Innovation Solution

A method and system that calculates gas saturation based on material balance, establishes a binomial relationship between oil-gas relative permeability ratios and gas saturation, and derives a gas-drive characteristic curve using Darcy's law and oil-gas seepage laws to determine dynamic and recoverable reserves.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Device complexity

If a linear relationship between oil-gas relative permeability ratio and gas saturation is assumed in a semi-log plot, then the calculation process is simplified, but the accuracy deteriorates because the relationship is actually non-linear except at intermediate gas saturation stages

Engineering Contradiction:

Improvecalculation process complexityVSAvoidreserve determination accuracy

Core Design Contradiction:

Device complexityVSMeasurement precision

Solution Approach 1:

The patent transforms the non-linear relationship between oil-gas relative permeability ratio and gas saturation into a linear relationship by applying logarithmic transformation to the relative permeability ratio. This parameter change allows the use of linear regression while maintaining accuracy across the full range of gas saturation values, not just intermediate stages.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent introduces a new dimensional transformation by plotting the logarithm of the oil-gas relative permeability ratio against gas saturation, creating a transformed space where the non-linear relationship becomes linear. This dimensional change enables accurate reserve determination without sacrificing computational simplicity.

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

2Productivity

If conventional linear relationship methods are used, then the calculation is faster and simpler, but the determination of single-well dynamic and recoverable reserves becomes less accurate

Engineering Contradiction:

Improvecalculation efficiencyVSAvoidreserve determination accuracy

Core Design Contradiction:

ProductivityVSMeasurement precision

Solution Approach 1:

The patent applies logarithmic transformation to the oil-gas relative permeability ratio, converting the non-linear relationship into a linear form that can be processed efficiently using linear regression techniques, thus maintaining high calculation efficiency while improving accuracy.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent replaces complex non-linear calculation mechanisms with a simplified linear regression approach in the transformed parameter space, achieving both computational efficiency and accuracy simultaneously.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

3Measurement precision

If the non-linear relationship is fully accounted for across all gas saturation stages, then the accuracy improves, but the calculation complexity increases

Engineering Contradiction:

Improvereserve determination accuracyVSAvoidcalculation process complexity

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The patent uses logarithmic transformation of the oil-gas relative permeability ratio to linearize the non-linear relationship, allowing accurate representation of the full range of gas saturation stages while maintaining calculation simplicity through linear regression methods.

Inventive Principle:

Principle #35Parameter changes

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

Improves calculation efficiency and accuracy of single-well dynamic and recoverable reserves by characterizing oil-gas relative permeability ratios and gas saturation with a semi-log binomial relationship, enabling quick determination under economic-limit gas-oil ratios.

Implementation Method 1

establishing a relationship between an oil-gas relative permeability ratio and oil-gas flow rates based on Darcy's law

Methodology Applied

Scientific EffectDarcy's law:

Implementation Method 2

calculating a gas saturation of a gas-drive reservoir based on a principle of material balance

Methodology Applied

Scientific EffectMaterial balance principle:

Data Source

PatentUS11320564B1Method and system for determining single-well dynamic reserve and recoverable reserve of gas-drive reservoir

Publication Date: 2022.05.03 SOUTHWEST PETROLEUM UNIV

AI summary

A method and system determines a single-well dynamic reserve and recoverable reserve of a gas-drive reservoir. An example method includes: calculating a gas saturation of a gas-drive reservoir based on a principle of material balance; establishing a relationship between an oil-gas relative permeability ratio and oil-gas flow rates based on Darcy's law; fitting a binomial relationship between the oil-gas relative permeability ratio and the gas saturation based on an oil-gas seepage law; and establishing a gas-drive characteristic curve relationship between a produced gas-oil ratio and a cumulative oil production under a steady seepage flow of the gas-drive reservoir based on the above relationships and the gas saturation, and calculating a single-well dynamic reserve and recoverable reserve of the gas-drive reservoir based on binomial regression coefficients of the binomial relationship and the gas-drive characteristic curve relationship.