113 Consideraciones generales para su llenado:
DECIMA TERCERA
11. Criterios para la presentación de entregables y documentación al FINAFIM:
To compare the seismic and well activity in one domain, certain assumptions need to be stated:
Produced and injected volumes between surveys should be comparable and sufficient to be detectable by the seismic. 4D seismic signatures, as they are the result of well activity, only detect changes in the reservoir state which were initiated by wells. Definitely, threshold exists, below which the seismic cannot capture any reservoir changes. These changes are defined by volumes produced from and/or injected into the reservoir. This assumption allows us to link produced/injected volumes with the seismic signal and so use seismic in a quantitative way (see Chapter 7). A validation of this approach can be achieved using well data along with seismic. As we know, wells are sources of seismic amplitude changes and at the same time they are sources of saturation (pressure) changes. Here I will focus more on saturation (in other words, wells cause more changes in saturation, than in pressure), but in the more general case, pressure and saturation act simultaneously. The next question asks how it is possible to tie the well’s signal with seismic changes?
First of all, we need to understand the differences between typical data organisation and representation in the ‘wells’ domain and in the ‘4D seismic’ domain. Historical well data usually looks like the graph in Figure 3.10. Only a few parameters are presented, the oil (gas) flow rate, cumulative production and water production (or watercut) for the production well, and the injection flow rate for the injection well. Any other curves, such as BHP and GOR are optional. Discretisation in presenting the data depends on the engineer, it can be daily, weekly or monthly. Each of these curves reflects a crucial parameter for reservoir performance. Exactly these curves (and some others) are used for history matching.
Figure 3.10 Typical well production history, with oil and water production rate indicated by red and blue lines. Cumulative liquid production is shown by orange dots. The time of the time-lapse surveys is shown by the green dots.
All the plotted data are in surface conditions and need to be converted into reservoir conditions using corresponding formation factors for oil, gas and water, according to the following equation:
Qres=B*qsur (3.3)
Time- lapse seismic surveys are discrete in time, usually carried out not more than once a year. So between two surveys (T1, T2, T3 and T4 in the figure), the reservoir is influenced
by a number of wells active during that time segment. 4D difference is related to changes in saturation and pressure and S and P, in turn, are related to the cumulative produced/injected volumes, rather than just to flow rates. In simple form it can be shown as:
4 (3.4)
This equation is valid for any cell of the model (point of the reservoir) for the fixed time period dT (see Figure 3.11). For a given patch in a reservoir (xi, yi), some depositional
features such as a channel, high permeability conduit, fractures, etc. determine that fluid will preferentially flow through certain paths,. Reservoir parts can be affected by well activity (i.e. can be detected by seismic surveying) only if they have connectivity with these wells, so time-lapse can be interpreted for understanding connectivity between wells and different reservoir parts. In addition, when the well activity changes, it will subsequently cause changes at parts of the reservoir being considered (xi, yi). It is reasonable to assume that,
apart from the well’s activity, there are some other factors that affect the seismic, and the ones most related to this work are the petro-elastic properties of the reservoir which are in charge of the response to pressure and saturation changes in this particular point. So, the seismic change at a given location should be the function of the nearby wells.
Figure 3.11 Reservoir part affected by three wells. Influence is extended through the connectivity in the reservoir (depicted by lines with arrows). This reservoir part produces a 4D signature which will be determined by differently weighted sums of cumulative produced/injected volumes (-ΔV and +ΔV). If some reservoir parts are not connected to the wells, then seismic will not detect any changes in such reservoir parts.
This function will represents the influence that the neighbouring wells will impose on a given location in the reservoir. We need to ask: what should it look like? Let us assume changes in the affected reservoir part on the upper figure are described by ΔA, so, for the depicted example: ∆ , ∑ Δ …. (3.5) 1, ( , )i i [ p( , ) (i i p j, ij) s( , ) (i i s j, ij)] j N A x y x y f V G x y f V G
. (3.6)According to MacBeth and Huang, the coefficients p( , )x yi i and
s( , )x yi i determine the strength of the response to local pressure and saturation change, respectively, and are related to local geological conditions (the petroelastic model). These two coefficients are considered to be unchanged throughout the time of production. The functions fp(V Gj, ij) and( , )
s j ij
f V G convert the cumulative fluid volumes injected or produced into vertically- averaged changes in pressure and saturation at location (xi,yi). These two functions are
controlled by G which is related to connectivity between the well and location (ij xi,yi), the boundary conditions and initial state of the reservoir. Given the complexities for fluid flow in a heterogeneous reservoir, it is usually not possible to determine the explicit forms for
( , )
p j ij
f V G and (fs V Gj, ij). According to equation 3.6, it may not be straightforward to relate the 4D response Aat location (xi ,yi) and well activity V injected or produced at
a particular well over a survey period T. For instance, consider that the 4D signature is driven by pressure change: the amount of pressure change caused by a given well (e.g. water injection well) may be balanced by the pressure effect of the neighbouring wells (negative
V
for producer and positive V for injector), resulting in no significant pressure change in the region. This may explain why there could be no 4D changes observed around a well that has been actively producing or injecting. However, most 4D study is based on understanding the 4D signal, which is solely controlled by a production effect related to a single well. Under this condition, equation 3.6 can be simplified. For instance, consider an area influenced by a single well and the seismic change driven by pressure change: the equation can be written in the following format:
( , )
i i p( , ) (
i i p j,
ij)
A x y
x y f
V G
where, fp(V Gj, ij) represents the function linking the pressure changes to the fluid volume injected or produced at the well over the survey period. Thus, it should reflect two different pressure regimes - the transient and the stable state - established after a well is activated. The function fp(V Gj, ij)can be as simple as a linear relationship in a closed compartment, once the stable state is established, where equation 3.6 can be further simplified as:
( ) k p j t V f V c V . (3.8) This gives ( , ) ( , , ) p i i . k k k t x y A x y T V cV
, (3.9)where ct is the total compressibility of the reservoir rock and V is the total volume of the
compartment studied. This relationship is shown to be valid for pressure changes of up to ±8MPa (Floricich 2006). Interpretation of the 4D signals in this work is based on this linear relationship.