Abstract

For a heterogeneous reservoir, the shape of a buildup curve is strongly dependent on the length of the preceding flow period. Therefore, in exploration well testing, where the flow period is usually short, modification of the pressure buildup pattern caused by insufficient flow time can lead to erroneous interpretation of well behavior. Buildup pattern, as a function of flow time, is discussed here for various types of pattern, as a function of flow time, is discussed here for various types of ideal heterogeneities such as linear reservoir discontinuities, natural fractures, vertical stratification, pressure support, and lateral permeability loss. A relationship is provided for the dimensionless flow permeability loss. A relationship is provided for the dimensionless flow time required to produce a certain buildup pattern. The effect of flow time on quantitative assessment of reservoir parameters is determined aswell.

Introduction

Well test analysis traditionally has been based on techniques developed for either drawdown calculations or buildup calculations after long flow periods. In exploration well testing, however, flow times prior to buildup periods. In exploration well testing, however, flow times prior to buildup tests are usually short. For a well in a reservoir with homogeneous properties and of infinite extent, the shape of neither the drawdown curve properties and of infinite extent, the shape of neither the drawdown curve nor the ensuing buildup curve is affected by flow time duration. Both are straight lines of a certain slope on a semilog plot of pressure vs. time. However, this is not the case for a reservoir with heterogeneous properties. For a heterogeneous reservoir in which a well shows a drawdown properties. For a heterogeneous reservoir in which a well shows a drawdown curve with multiple slopes on a semilog plot as production progresses, the drawdown as well as the buildup patterns become essentially dependent or the producing time. Moreover, for a given flow time, the drawdown curve and the following buildup curve may have different shapes. In well test analyses where the shape of pressure curves is used to evaluate reservoir properties, recognition of the pressure pattern alterations caused by properties, recognition of the pressure pattern alterations caused by insufficient flow time becomes important. In the case of a linear discontinuity such as a sealing fault, for example, it has been found that the buildup data on a Homer plot would show the second, double-slope straight-line characteristic of the fault only if the radius of investigation, before the well is shut in exceeds at least four times the distance, to the fault, = . Even this criterion is optimistic from a practical point of view. All buildup data exhibiting this characteristic double slope will be at relatively long shut-in times for which the Homer time ratio ( + ) is less than1.5. Since actual data seldom extend into this range, longer flow time swill be necessary. In what follows, the modification of buildup pattern caused by insufficient flow time is considered along with the specification of both the flow time and buildup time necessary to recognize a heterogeneity from its characteristic buildup pattern . The heterogeneities considered are

  1. single no-flow and constant pressure boundaries,

  2. single boundary with permeability and storage contrasts,

  3. multiple boundaries,

  4. radial loss in permeability,

  5. vertical stratification, and

  6. natural fractures.

Reservoir Limited by One or More Boundaries
Linear No-Flow Boundary.

Drawdown at a well producing a reservoir limited by an impermeable barrier, such as a sealing fault, according to the method of images that duplicates such a boundary mathematically, is

and

............................(1)

where ( ) is the exponential integral function, is the distance from the well to the fault, and = is the dimensionless flow lime. The characteristic drawdown pattern for a well near a sealing boundary, described by Eq. 1 and illustrated by the insert in Fig. 1, depicts on a semilog plot a curve consisting of two straight lines joined by a smooth transition. The first straight line represents the well response before the fault exerts any influence. The slope of this straightline, is inversely proportional to the reservoir transmissibility. This line is referred to as the middle-time region (MTR) line. The second straight line, formed after a smooth transitional period, represents the well behavior as affected by the fault. Its slope is twice that of the first straight line. The intersection of the two straight lines occurs at a nondimensional time

............................(2)

The transition region between these two straight lines lasts, however, for more than one log cycle. The slope of the drawdown curve,

............................(3)

SPEJ

p. 294

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