Recognizing double porosity system from well tests

Directed by: Mohamed Jamal AlRateeb

Supervisor: Dr. Waleed Mahmoud

Content

AbstractIntroduction (def: double porosity, models, well tests interpretation)

Mathematical modelAnalysis of well testConclusion

Abstract

Well tests give me indicators about some properties of reservoir.

This properties used in well test interpretation models to known type of this media flow

Double porosity model is one of this models, and it used with well test pressure data to identify or recognize double porosity behavior

Introduction

• A double-porosity medium is one in which the majority of the permeability is provided by fractures while the majority of the storage is provided by the porous matrix.

Examples of double porosity:

1-fissured reservoir (natural fracture) a high permeability fissure system delivers fluids to the well; low permeability "matrix" blocks "bleed" fluid into the fissure system, where it is subsequently delivered to the wellbore

conti…Introduction

2-Multilayer system, only one layer delivers fluids to the wellbore. The other layers act as sources of fluids.

• Double-porosity behavior is obtained when two different media are involved in the flow process: a higher-permeability medium that produces fluid into the well and a lower-permeability medium that recharges the higher-permeability medium.

conti…Introduction

Most of the fracturing fluids injected into reservoir-bearing formations possess non- Newtonian nature and these fluids are often approximated by Newtonian fluid flow models.

Several numerical and analytical models have been proposed to study the transient behavior of non-Newtonian fluid in porous media. Since all of them were published before the eighties, when the pressure derivative concept was inexistent, interpretation techn also, the slope of the pressure derivative during radial flow regime is related to the flow behavior index.

The well test interpretation model describes the pressure or rate behavior of the actual well/reservoir system during the test.

A well test interpretation model indicates primarily how many media with significantly different permeabilities and porosities are involved in the flow process and how these media interact.

One possible well test interpretation model is the double-porosity model, which describes double porosity behavior.

Mathematical model

• Escobar et al. (2010) provided equations for reservoir permeability and skin factor for homogeneous systems which can be extended to double-porosity systems.

• The figure displays the dimensionless pressure and pressure derivative behavior for a non-Newtonian fluid in a double-porosity system with wellbore storage and skin effects.

• That wellbore storage affects the minimum of the pressure derivative (trough).

Mathematical model

• The figure contains an ideal pressure and pressure derivative log-log plot for a Newtonian double porosity system. In such plot, the infinite-acting radial flow regime is represented by a horizontal straight line on the pressure derivative curve.

• The first segment corresponds to pressure depletion in the fracture network while the second portion is due to the pressure response of an equivalent homogeneous reservoir, On the other hand, the transition period which displays a trough on the pressure derivative curve during the transition period only depends on the dimensionless storativity ratio ω.

Analysis of well test: Conventional Analysis

• involves plotting test pressure data vs. some function of time on a semilog plot.

• double-porosity behavior yields two parallel straight lines on a semilog plot, provided there are no near-wellbore or outer-boundary effects as fig (a).

• In practice, however, the two parallel straight lines mayor may not be present.

• Fig (b) illustrates a case of double-porosity behavior where only the last semilog straight line exists.

• Thus a semilog plot is not an efficient tool for identifying double-porosity behavior.

Analysis of well test: Log-Log Analysis

• involves a log-log plot of pressure change vs. elapsed time.

• Double-porosity behavior yields an S-shaped log-log pressure curve on a log-log plot, as illustrated in figure.

• indicates, transition may start at very early times in the case of unrestricted interporosity flow; in such a case, the first homogeneous behavior may not be seen in practice.

• It is not fully reliable, however. For instance, the S shape is usually difficult to see in highly damaged wells; the well behavior can then be erroneously diagnosed as homogeneous.

Analysis of well test: Pressure-Derivative Analysis

• involves a log-log plot of the derivative of the pressure with respect to some function of elapsed time vs. elapsed time.

• Double-porosity behavior is characterized by the existence of a minimum on the pressure derivative.

• this minimum can be either preceded and followed by a stabilization, as in Fig.(a), or only followed by a stabilization, as in Fig.(b).

• The shape of the minimum depends on the type of double-porosity behavior, as shown in (Figs.7a and 7b), restricted interporosity flow yields a V-shaped minimum. Whereas unrestricted interporosity yields an open U-shaped minimum.

• Pressure derivatives provide the most efficient means for identifying double-porosity systems from well test data.

• The main limitation comes from the quality of the pressure data available and more importantly from the algorithm used for calculating pressure derivatives.

ConclusionDouble-porosity systems can be identified from

well test data, and the best method is to use pressure derivatives.

it is usually difficult to decide whether the reservoir is naturally fissured or multilayered. This requires additional information from sources other than well testing.