Abstract

By the transient pressure for horizontal well with constant flow rate and Duhamel's principle, this paper presents the method to calculate the transient pressure for DST flow period or slug flow of horizontal well, pressure analysis method of DST flow period or Slug period for horizontal well in homogeneous reservoir is given the field example is treated by this method.

Introduction

DST (Drill-Stem Testing) is a kind of testing method used to determine properties of reservoirs and formation fluids by switching well or opening well at the bottomhole. It also can be used to estimate the productivity of horizontal wells by DST testing before completion. There is much research about buildup test and drawdown test of horizontal wells, but there is less research about DST of horizontal well. Since that there is difference to much extent between characteristics of DST and conventional drawdown test. DST pressure analysis using conventional interpretation methods will inevitably create analytical error. DST flow period at opening well is essentially a production process on which liquid face rises in the borehole and reservoir flow rate is ever-decreasing.

The flowing feature of this process is called slug flow. This paper presents method to calculate the transient pressure of DST flow periods of horizontal wells in the homogeneous reservoir based on the Duhamel's principle. Formation parameters can be estimated by automatic history matching method.

Dimensionless Variables Definition

  1. Dimensionless pressure of DST flow period or slug flow for horizontal well

    Equation (1) (Available in full paper)

  2. Dimensionless bottomhole pressure of DST flow period or slug flow for horizontal well

    Equation (2) (Available in full paper)

  3. Dimensionless pressure for horizontal well with sandface constant-rate

    Equation (3) (Available in full paper)

  4. Dimensionless bottomhole pressure for horizontal well with sandface constant rate

    Equation (4) (Available in full paper)

  5. Dimensionless time

    Equation (5) (Available in full paper)

  6. Dimensionfess wellbore storage coefficient

    Equation (6) (Available in full paper)

  7. Dimensionfess flow rate

    Equation (7) (Available in full paper)

THEORY

  1. Relationships between bottomhole flowing pressure and sandface flow rate for DST flow period or slug flow of horizontal well. In terms of the characteristic of horizontal DST flow period or slug flow, DST flow period or slug flow is a flow procession in which sandface flow rate is gradually decreasing and bottomhole flow pressure is gradually increasing. Soliman[1] has shown that in many cases transient pressure for DST flow period or slug flow is approximately given in following polynomial:

    Equation (8) (Available in full paper)

    Therefor, the sandface flow rate is:

    Equation (9) (Available in full paper)

    dimensionless form is:

    Equation (10) (Available in full paper)

    Where,

    Equation (10) (Available in full paper)

  2. Duhamel's principle

    Duhamel's principle shows the relationships between transient pressure of constant flow rate and variable flow rate. Dimensionless form of Duhamel's principle is flowing:

    Equation (11) (Available in full paper)

    Substituting Eq.10 into Eq.11 and taking the Laplace transformation, we have:

    Equation (12) (Available in full paper)

    Where,

    Equation (12) (Available in full paper)

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