Abstract

The analysis of oil production data using decline curves is a modeling and forecasting technique. Actual production rate and time data are history matched to a theoretical model using specialized graphs known as type curves.

This study begins with a review of the previously developed decline curve construction and analysis methods. It consists of reproducing Arps-Fetkovich type curves and the derivative type curves for advanced decline curve analysis. A Program was developed to generate the dimensionless rate-pressure and time data necessary to construct Fetkovich type curves.

Combining the analytical solution derivative for transient flow based on numerical analysis, and the empirical solution derivative for boundary dominated flow develops the derivative type curves.

The type curves is used to identify the transient versus depletion stages and to estimate reservoir parameters and future decline paths.

Field production data are generally difficult to match with the type curve for this reason a Universal Fitting Equation is proposed as an alternative to manual type curve matching. This equation combines both Arp's empirical equation and Fetkovich analytical solutions. It equation offer the following advantages:

  1. Fitting with the equation is more precise than type curve matching to obtain reservoir dimensionless radius reD, Arp's exponent b, matching points q/qDd, and tDd/t.

  2. The real production data can be fitted directly by the equation without using smoothing techniques.

  3. The radial and pseudosteady state regions are determined automatically and easily from fitting.

  4. Some production data that were insufficient to be analyzed with manual type-curve matching can be interpreted with the Fitting Equation.

This procedure has been applied to some Real field data from Hassi Messaoud field cases and it has given significant results.

Introduction

Decline curves are the most common means of forecasting production and estimating the value of oil and gas wells. The earliest literature refers to a mathematical decline analysis approach presented by Arnold and Anderson in 1908.

Arps developed the standard exponential, hyperbolic and harmonic decline equations in 1944.

In 1973, Fetkovich2 proposed a dimensionless rate-time type curve for decline curve analysis of wells producing at constant bottom-hole pressure. These type curves combined analytical solutions to the flow equations in the transient region and empirical decline curve equations in the pseudo-steady state region. This approach to decline curve analysis, known commonly referred to as "advanced decline curve analysis", has become widely used as a tool for formation evaluation and reserves estimation.

In 1980, Fetkovich2 demonstrated that decline curve analysis not only has a solid fundamental base but also provides a tool with more diagnostic power than had been previously suspected. Fetkovich2 constructed log-log type curves, which combine all these equations developed by Arps1 with the analytical constant pressure infinite and finite reservoir solutions. He showed that log-log type curves could be analyzed by the type curve matching technique.

The uses of pressure derivatives in well test interpretation was introduced by Tiab3 in 1975 and Bourdet et al. developed the use of derivative type curves for transient well test analysis in 1983. By multiplying the pressure derivative by the time, (or equivalently, by taking the derivative of pressure with respect to the natural log time), they were able to display both the pressure and the pressure derivative type curve on a single set of axes.

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