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SPE 131787 Analysis of Production Data from Fractured Shale Gas Wells
D.M. Anderson, M. Nobakht, S. Moghadam, and L. Mattar, Fekete Associates Inc.
Copyright 2010, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Unconventional Gas Conference held in Pittsburgh, Pennsylvania, USA, 23–25 February 2010. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.
Abstract
Long-term shale gas well performance characteristics are generally not well understood. The ultra-low permeability of shale ensures the continuing presence of pressure transient effects during well production. This makes production forecasting a difficult and non-unique exercise. Conventional methods have proven to be too pessimistic, in many cases, because they assume a depletion-dominated system. Recently, more suitable forecasting methods have been developed that account for long-term transient effects. These methods incorporate a transient model (usually linear flow) which transitions into a conventional boundary-dominated flow model after a prescribed time or upon achieving a certain region of investigation. The underlying concept assumes that once a transition to boundary-dominated flow is observed, depletion will dominate the production going forward. Although this methodology has been successfully applied for a variety of tight gas reservoirs, it may not be the right model for fractured shale gas (and some conventional tight gas) reservoirs. Fractured shale gas reservoirs get their productivity from the stimulated reservoir volume (SRV), which may be quite limited in areal extent but is surrounded by a low-permeability reservoir (matrix). Thus, the mechanism for long-term production includes a late-time transition from depletion of the SRV, back to infinite acting (linear or pseudo-radial) flow. This “return” to infinite acting flow may or may not provide contribution to recoverable reserves within a practical time-frame, but it should be considered nonetheless. In this paper we present a straight forward methodology for determining the major well performance characteristics of fractured horizontal shale gas wells, considering the impact of uncertainty and non-uniqueness. The focus will be on determining the dominant flow regimes and bulk properties from the data, and then defining a suitable, simple reservoir model for production forecasting, using practical experience and all available information. Field examples from the Barnett, Marcellus, and Haynesville shales are included.
Background
Shale gas reservoirs differ from conventional gas reservoirs in that the completion “makes” the reservoir. Since the matrix permeability is thought to be very low (1e-6 to 1e-4 md), an enormous conductive surface area is required between the well completion and the reservoir to attain commercial production rates. To achieve this surface area, massive multi-stage hydraulic fracture treatments are used to create (or enhance) complex networks of fractures connected to the well. The geometry, areal extent, conductivity, storativity, and spacing of these induced fracture networks are generally not well understood. However, producing companies are clearly motivated to improve their understanding of these characteristics for two reasons: 1) to obtain more reliable production forecasts and reserves estimates; and 2) to use the information to improve their field development strategies and drill better wells. Production analysis has proved to be a valuable reservoir characterization tool because it is practical, reliable and inexpensive. Some of the more popular techniques, such as those proposed by Arps (1945), Fetkovich et al. (1987; 1996), Palacio and Blasingame (1993), Doublet et al. (1994) and Agarwal et al. (1999) are well documented in the literature. However, since these techniques are designed for conventional reservoirs and primarily vertical wells, there are two major problems encountered when using them for tight and shale gas reservoirs: 1.
Pre-disposition towards boundary-dominated flow: Observations have shown that this is not always the right assumption for tight and shale gas reservoirs. Often, linear flow is dominant, and boundary-dominated flow is never observed in the data. In other cases, early boundary-dominated flow is observed, followed by a transition back to infinite acting flow. As a result, there is a tendency for these techniques to underpredict long-term performance of fractured shale gas (and tight gas) reservoirs.
2 SPE 131787
2.
Characterization of bulk reservoir properties: The dominant flow regime observed in fractured shale gas and tight gas reservoirs is usually linear flow. Conventional type curve analysis methods interpret this as a single fracture and associated reservoir permeability. Horizontal fractured shale gas wells, however, have stimulated reservoir volumes containing multiple fractures. Furthermore, the solution for fracture area and permeability (independently of each other) is non-unique, with only the bulk reservoir property
Ak
being uniquely defined. Wattenbarger et al. (1998) have created type curves, based on a simple bounded linear flow model, that elegantly utilize this
Ak
product. However, the bounded linear flow model contains only a single fracture, so it does not properly capture the complexity of a multi-fractured horizontal well. To overcome these limitations, we propose an analysis method and model that follows the work of Wattenbarger et al. (1998), but accounts for multiple transverse fractures in a horizontal well, and allows the stimulated reservoir volume (SRV) to reside within an infinite acting reservoir. The inclusion of the “fracture network” concept, as opposed to a single fracture, allows for a more comprehensive long-term performance forecast. Wattenbarger’s bounded linear flow model follows a progression of linear to boundary-dominated flow. The shale gas model proposed here follows a progression of linear to boundary-dominated flow back to infinite acting (linear or radial) flow. It is important to note that the matrix permeability does not appear explicitly in Wattenbarger’s bounded linear flow model, because it depends only on
Ak
. This is not true for the shale gas model we propose here. The magnitude of long-term contribution from the infinite acting matrix is highly dependent on the assumed matrix permeability. The components of the shale gas model that we will consider are as follows: 1.
Completion: The completion is a horizontal well that fully penetrates the formation. The horizontal well may be cased or open hole. 2.
Fracture network: The fracture network consists of multiple parallel planar fractures, that intersect the horizontal well at 90
angle, as shown in
Figure 1
. The fracture network is assumed to have finite conductivity and limited areal extent. 3.
Stimulated Reservoir Volume (SRV): The SRV describes connected hydrocarbon pore volume (HCPV) that is accessible by the fracture network. It consists of a network of fractures and matrix blocks. The perimeter of the SRV defines the interface between the fracture network and the unfractured, infinite acting shale matrix. 4.
Matrix Blocks: Matrix blocks are the parts of the matrix that lie within the fracture network, occupying the space between the fractures. The matrix is assumed to be homogeneous with very low permeability (1e-6 to 1e-4 md). The gas content within the matrix is assumed to be free (porosity) gas. Adsorbed gas can easily be included in the model, but is not considered in this paper. 5.
Infinite Acting (Unstimulated) Reservoir: The SRV is surrounded by an infinite acting, homogeneous shale gas reservoir with the same permeability and porosity as the matrix blocks.
Analyzing Production From Horizontal Shale Gas Wells
The mode of production decline in shale gas wells is similar to that of conventional tight gas wells. Initial production is dominated by the high permeability but low storativity fracture system, and therefore declines rapidly. The ultra-low permeability matrix provides stable long-term production. Rate transient analysis methods for analyzing production data are well documented in the literature. Three plots are particularly well suited for tight and shale gas production analysis. They are as follows: 1.
Log-log plot 2.
Specialized plot – Square Root-Time plot 3.
Flowing Material Balance plot Proper usage of these plots will provide a reliable identification of dominant flow regimes exhibited in the data, as well as estimates of bulk reservoir properties such as
Ak
, apparent skin and hydrocarbon pore volume (HCPV). Armed with this information, we can then construct a suitable reservoir model, which can be used to generate a type curve (or series of type curves) and a long-term production forecast for estimating reserves.
Log-Log Plot
The Log-Log plot is used to identify flow regimes. It is important to ensure that operational noise and problematic rates/pressures have been filtered from the data set. Be very wary of productivity fall-off due to liquid loading in the wellbore. Such data will detract from the proper interpretation of reservoir flow regimes (Anderson et al., 2006; Nobakht and Mattar, 2009). The normalized rate and the inverse semi-log derivative should be plotted together on log-log coordinates:
SPE 131787 3
pipwf
q pp
and
1 pipwf a
ppd dlntq
versus
a
t
(1a) or
pipwf
q pp
and
1 pipwf ca
pp
d dlntq
versus
ca
t
(1b) Where
q
is gas rate,
pi
p
and
pwf
p
are pseudo-pressures at initial pressure and flowing pressure, respectively,
t
a
is pseudo-time and
t
ca
is material balance pseudo-time.
Equation (1a)
offers an advantage in wells that produce at close to constant pressure conditions, in that the log-log plot is not susceptible to the superposition bias that is sometimes present when using
Equation (1b)
. However, if significant changes in operating conditions occur, then
Equation (1b)
should be used. The inverse semi-log derivative (same as PTA derivative, but inversed) is a valuable tool for interpreting fractured shale gas reservoirs because it is not influenced by skin. As we will show in the examples, shale gas production, more than any other kind of production, exhibits linear flow with a significant apparent skin. Bello and Wattenbarger (2009) have discussed this skin effect in detail, attributing its presence primarily to flow convergence in a horizontal well. It also accounts for the pressure drop within the fracture due to the finite conductivity of the fractures. When present, the skin effect masks the expected classic linear flow behavior (half slope on log-log plot) in the rate data function, but does not impact the derivative. Accordingly, because the derivative retains the slope of one-half, it is a much better indicator of linear flow than the rate function itself. The following is the equation for linear flow with skin, at constant rate, in dimensionless form:
DD
'
pCts
(2) Where
p
D
and
t
D
are dimensionless pressure and time, respectively,
C
is a constant and
s
is skin. Taking the semilog derivative of both sides of
Equation (2)
, the dimensionless pressure drop due to skin (s) disappears, because it is a constant:
DDD
1'ln2
dpCt dt
(3) The flow regimes most often observed on log-log plots of horizontal shale gas wells are linear flow followed by boundary-dominated flow. However, bi-linear flow and radial flow are sometimes also observed early in the production life. These are often caused by transient flow in the fractures, but they are relatively short-lived, and in this study, they are not analyzed in any detail, but they are accounted for in the apparent skin.
Figure 2
presents a log-log plot of simulated shale gas performance data, based on the model shown in
Figure 1
, along with log-log plots from real shale production data from various fields. Flow regimes are clearly identified. The combination of linear flow with apparent skin is by far the most common flow regime in wells with less than 1 year of data. This has been observed in all producing shale gas fields. The appearance of boundary-dominated flow is also common, but there is a major variation in timing. For example, we have looked at several Haynesville shales and seen the early onset of apparent boundary-dominated flow (1-3 months after on-stream date). In many of these wells, linear flow develops later on, as shown in
Figure 2
. By contrast, there are Barnett shale examples where boundary-dominated flow is not observed during the first three years of production. This underlines the critical importance of proper flow regime identification using the log-log plot (and focusing on the derivative).
Square Root-Time Plot – Linear Flow
The square root-time plot,
pipwf
ppq
versus
t
, is probably the single most important plot for characterizing long-term shale gas well performance. This is because fractured shale gas reservoirs will typically be dominated by linear flow. Linear flow appears as a straight line on the square root-time plot. To be certain about the presence of linear flow, a clear half-slope trend should be observed on the log-log derivative, in addition to observing a straight line on the square root-time plot. Note that the half-slope trend may or may not appear on the log-log normalized rate, as the presence of skin damage may mask it.
Linear Flow Parameter
The dominant flow regime observed in most fractured shale gas wells is linear flow. In some cases, the observed linear flow may prevail for several years. For the purpose of this work, we will make the assumption that the observed linear flow is
4 SPE 131787
a result of transient matrix drainage into the fractures. This is a reasonable assumption, but it may not be the case if the fracture spacing is very dense and/or conductivity is low. The slope of the square root-time plot yields the linear flow parameter (
LFPAk
), which is half of the product of total matrix surface area draining into fracture system,
2
A
, and square root of permeability:
gti
63081
.T LFPAk mc
(4) Where
m
is the slope of the square root-time plot,
T
is reservoir temperature,
is reservoir porosity,
g
is gas viscosity and
t
c
is total compressibility. There is no way to decouple the flow area from the permeability from linear flow analysis. One must be independently estimated before the other can be determined. It should be noted that
Equation (4)
is derived based on the assumption of a constant flowing pressure at the well. The constant pressure solution is presented in this study as many shale gas wells produce under high drawdown due to the extremely low reservoir permeability. Consider a single vertical fracture of length “
x
” (see
Figure 3a
). The
A
in
Ak
would now be defined as the product of the fracture length,
x
, and the net pay thickness,
h
. We could now use
Equation (4)
to calculate the permeability as follows:
2
LFPk xh
(5) If we consider a cased horizontal well with multiple parallel fractures (see
Figure 3b
) that are equally spaced, then the area becomes the sum of all the individual fracture areas.
SRV
A x Ayhyhh LL
(6) Where
y
is stimulated reservoir width, A
SRV
is the area of the SRV and
L
is fracture spacing. Combining
Equation
(4)
and
Equation (6)
, we get:
22SRV
LFPLLFPLk xyhAh
(7) There are three unknowns in
Equation (7)
,
k
(permeability),
L
(fracture spacing) and
y
(stimulated reservoir width). Thus, we must independently specify two of these. As we will see, stimulated reservoir width can be estimated from the interpreted SRV on the Flowing Material Balance (FMB) plot, provided that boundary-dominated flow is achieved. In the absence of boundary-dominated flow, a suitable stimulated reservoir width is chosen based on microseismic (if available), well spacing or analogs. As stated previously, the range of expected permeability for shales is from 1e-6 to 1e-4 md. Thus, upon choosing suitable matrix permeability, we could rearrange
Equation (7)
to solve for fracture spacing.
xyhk L LFP
(8)
Apparent Skin
In fractured shale gas wells exhibiting matrix to fracture linear flow, a significant skin effect can be observed from the pressure loss due to finite conductivity in the fracture system, even if there is no mechanical skin damage at the wellbore. This skin effect may have a significant impact on well productivity and therefore, is an important parameter for production forecasting. The y-intercept on the square root-time plot,
b
, represents a constant pressure loss, from which the apparent skin,
s
’, can be calculated using the following equation: '1417
khsbT
(9)

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