Flow models time 4D seismic surveys

March 15, 1999
Integrated flow models can be used to optimize the timing of 4D seismic surveys for gathering reservoir engineering information, as well as for tracking flood fronts Consensus building between disciplines is an essential task in the reservoir-modeling process. The emergence of time-lapse (4D) seismic monitoring has expanded the role of seismic analysis to include estimation of fluid types, flow patterns, and rock properties over the extent of the reservoir. 1 2
John R. Fanchi
Colorado School of Mines
Golden, Colo.
Integrated flow models can be used to optimize the timing of 4D seismic surveys for gathering reservoir engineering information, as well as for tracking flood fronts

Consensus building between disciplines is an essential task in the reservoir-modeling process. The emergence of time-lapse (4D) seismic monitoring has expanded the role of seismic analysis to include estimation of fluid types, flow patterns, and rock properties over the extent of the reservoir.1 2

These parameters can be predicted by extending existing flow simulators to include a petrophysical model that calculates reservoir geophysical attributes as a function of time.3 4 The resulting flow model is referred to here as an integrated flow model.

Integrated flow models enhance consensus building by blurring the distinction between reservoir geophysics and reservoir engineering.

This article uses a realistic source of petrophysical data in several reservoir engineering examples to illustrate the application of integrated flow models to time-lapse seismic monitoring.

Integrated flow model

The integrated flow model consists of a petrophysical model and a traditional flow model. The flow simulator used in this study is called IFLO. It includes a petrophysical model and is a Fortran 90 program that contains the best features of the extended black oil simulator Master 5 and the black oil simulator with a petrophysical model Boast4D. 3

The petrophysical model must be able to calculate reservoir geophysical attributes that can be compared with seismic measurements. Gassmann's equation6 is the basis of the petrophysical model used in the integrated flow model.

Gassmann's equation is strictly valid only for isotropic, homogeneous, monomineralic media. Other petrophysical models could be used in an integrated flow model; however, Gassmann's equation is widely used in petrophysics because of its relative simplicity and limited data requirements.

The four petrophysical parameters that must be included in an integrated flow model (IFM) to allow the use of Gassmann's equation are:

  • Bulk modulus of the porous matrix, KB
  • Bulk modulus of the grains, KG
  • Effective shear modulus, µ*
  • Matrix density, þma.
The parameters K B, K G, µ *, and rma are entered during simulator initialization. 4

Bulk and fluid densities and porosities are usually derived from a combination of the neutron porosity and density logs. Moduli can be obtained from seismic velocities.7-9

The primary reservoir geophysical attributes that are calculated by the petrophysical model are bulk density, acoustic impedance, reflection coefficient, compressional velocity, and shear velocity. The calculated reservoir geophysical attributes are available as user-requested output variables.

These attributes can be used to estimate the sensitivity of seismic monitoring to a particular reservoir management strategy. They can be provided at times when seismic surveys are performed, or used to predict times when a seismic survey would yield useful information relative to a previously completed survey.

They can also be used in the history matching process to better define fluid movement between wells.

Examples

Four examples illustrate the application of the integrated flow model to commonly encountered reservoir management scenarios.

Correlations published by Murphy, et al.,10 for sandstone were used to compute shear and compressional velocities for these integrated flow model examples.

The linear correlation between modulus and porosity (Fig. 1 [66,596 bytes]) is approximately correct for porosity values less than 35%. The correlation shows that sandstone moduli decrease as porosity increases.

Table 1 [31,921 bytes] summarizes the steady-state values of the velocity ratio Vp/Vs before and after the flood front passed the observation cell for Examples 1-3. These examples were first discussed in an earlier article, Reference 4, using an arbitrary set of moduli.

The results shown in Table 1 are based on the more realistic moduli presented in Fig. 1.

The velocity ratio changed most in all examples when free gas saturation either developed in a cell that contained only liquid or completely disappeared from a cell that had nonzero gas saturation.

In addition to tracking flood fronts, Example 4 shows that an integrated flow model can also be used to optimize the timing of 4D seismic surveys.

Waterflood

The first example determines the acoustic response of a system in which undersaturated oil is subjected to displacement by injected water.

Fluid properties in this example are from the case study given in Chapter 13 of Reference 3. For simplicity, a horizontal, single layer, linear 10-cell model is used. Water is injected into one end of a linear, horizontal model and produced from the other end.

Acoustic impedance is monitored as a function of time at a central location, which serves as an observation point.

Gas injection

The second example is based on the first SPE comparison project. 11 A saturated, light (59° API) oil is produced from a corner block in the lowermost layer of a three-layer square grid. Lean gas is injected into the upper layer at the opposite corner.

An observation point was selected in the upper layer midway between the injector and producer. This point allows one to observe the gas front pass, as the injected gas flows toward the pressure sink at the production well.

Aquifer influx

A gas reservoir with aquifer influx was studied (Chapter 12, Reference 3). The reservoir is represented as a dipping, two-layer cross section.

A downdip aquifer provides pressure support and water invasion as the reservoir is produced.

The lowermost cell adjacent to the aquifer was selected as the observation cell. This cell responds most quickly to water invasion and exhibits the acoustical response associated with water front advance.

The velocity ratio Vp/Vs in this application is sensitive to a change in irreducible gas saturation (Sgr).

An Sgr of 0% results in complete displacement of gas from the water invaded zones.

The resulting elimination of gas from the calculation of reservoir geophysical attributes in the water invaded part of the reservoir causes a significant change in the ratio Vp/Vs.

If the example is run with an Sgr of 3%, the relatively large change in Vp/Vs is no longer observed because the presence of a small amount of gas significantly changed the compressibility of the system.

Scheduling surveys

The fluid properties in the gas injection case were used with the reservoir characterization described in the second SPE comparative solution project. 12 This example shows how to use the integrated flow model to optimize the timing of a 4D seismic survey.

Fig. 2 [92,404 bytes] presents the flow capacity and oil productive capacity of each layer in the model cross section.

Flow capacity is the product of permeability and thickness, while oil productive capacity is the product of flow capacity, porosity, and oil saturation.

For a heterogeneous geology, oil productive capacity is a useful identifier of the most desirable oil-bearing layers.

In this undersaturated oil reservoir cross section, Layer 9 is the best oil target. The lowermost layer is a thick, water-bearing aquifer layer. Although it appears as

the layer with the largest flow capacity, it disappears from the oil productive capacity figure because it does not contain any oil.

Gas was injected into the upper layers (Layers 1-3) of the undersaturated oil reservoir cross section while oil was being produced from the lower layers (Layers 9-12). All layers are in vertical communication.

The advance of the injected gas into the cross section is shown in Fig. 3 [134,353 bytes] at two times: 180 days and 270 days. Displaying the change in gas saturation from the beginning of the flood to the current time highlights the gas front.

Fig. 4 [130,824 bytes] shows the corresponding change in the ratio of compressional to shear velocities. The presence of injected gas shows up clearly at both 180 days and 270 days at the left-hand side of the figure.

Fig. 4 also shows the presence of a gas cone in the layers above the perforated interval of the oil production well at 270 days. The appearance of the cone is explained by looking at the pressure distribution in the reservoir relative to the bubblepoint pressure.

Fig. 5 [1360,107 bytes] shows the change in the ratio of compressional to shear velocities at 270 days and the difference in reservoir pressure relative to bubblepoint pressure. The right-hand side of the pressure difference display shows the region of the model with pressure below the bubblepoint. It shows the cone of free gas that is coming out of solution as reservoir pressure in the vicinity of the production well drops below the bubblepoint pressure of the oil.

A seismic survey at 180 days would see the gas front advance but not the gas cone, while a seismic survey at 270 days would see both the gas front advance and the gas cone. The later survey would provide more information for use in a history match.

Results

Table 1 summarizes the steady-state values of the velocity ratio V p/V s before and after the flood front passed the observation cell for Examples 1-3.

The velocity ratio changed most in all examples when free gas saturation either developed in a cell that contained only liquid or completely disappeared from a cell that had nonzero gas saturation.

In addition to tracking flood fronts, Example 4 shows that an integrated flow model can be used to optimize the timing of 4D seismic surveys for gathering reservoir engineering information.

Acknowledgment

I would like to thank Mike Batzle at the Colorado School of Mines for valuable discussions and petrophysical references.

References

  1. He, W., Anderson, R.N., Xu, L., Boulanger, A. Meadow, B., and Neal, R., "4D seismic monitoring grows as production tool," OGJ, May 20, 1996, pp. 41-46.
  2. Wang, Z-J., "Feasibility of Time-Lapse Seismic Reservoir Monitoring: the Physical Basis," The Leading Edge, Vol. 16, September 1997, pp. 1327-29.
  3. Fanchi, J.R., Principles of Applied Reservoir Simulation, Gulf Publishing, Houston, 1997.
  4. Fanchi, J.R., "Flow models predict 4D suitability," OGJ, July 6, 1998, pp. 59-63.
  5. Ammer, J.R., Brummert, A.C., and Sams, W.N., Miscible Applied Simulation Techniques for Energy Recovery-Version 2.0, Report DOE/BC-91/2/SP, U.S. Department of Energy, Morgantown Energy Technology Center, 1991.
  6. Gassmann, F., "Elastic Waves Through a Packing of Spheres," Geophysics, Vol. 16, 1951, pp. 673-85.
  7. Castagna, J.P., Batzle, M.L., and Eastwood, "Relationships Between Compressional Wave and Shear Wave Velocities in Clastic Silicate Rocks," Geophysics, Vol. 50, 1985, pp. 571-81.
  8. Han, D.L., Nur, A., and Morgan, D., "Effects of Porosity and Clay Content on Wave Velocities in Sandstones," Geophysics, Vol. 51, 1986, pp. 2093-2107.
  9. Vernik, L., "Acoustic Velocity and Porosity Systematics in Siliciclastics," Log Analyst, Vol. 39, July-August 1998, pp. 27-35.
  10. Murphy, W., Reischer, A., and Hsu, K., "Modulus decomposition of compressional and shear velocities in sand bodies," Geophysics, Vol. 58, 1993, pp. 227-39.
  11. Odeh, A.S.. "Comparison of Solutions to a Three-Dimensional Black-Oil Reservoir Simulation Problem," JPT, 1981, pp. 13-25.
  12. Weinstein, H.G., Chappelear, J.E., and Nolen, J.S., "Second Comparative Solution Project: A Three-Phase Coning Study," JPT, 1986, pp. 345-53.

The Author

John R. Fanchi is a professor in the petroleum engineering department at the Colorado School of Mines. He has worked in the technology centers of three major oil companies and his oil and gas industry responsibilities have revolved around reservoir modeling, both in the areas of simulator development and practical reservoir management applications. Fanchi has a PhD in physics, and his publications include simulation software, three books, and numerous articles.

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