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# Interpreting data from well to well tracer tests

To obtain high-quality tracer-response curves that are the basis for the further interpretation, a well-designed sampling program is needed. In general, more samples will give the potential for extraction of more information from field tests. Too often, interpretation is difficult because of limited tracer data.

The final objective of a well-to-well study is the interpretation of the response curves. A good analysis of the information given by the tracers, in combination with other available data, gives a better understanding of the flow in the reservoir, not just verification of communication between injector and producer.

## Different levels of interpretation

The response curve can be analyzed from three different points of view or complexity levels. The simplest interpretation is the qualitative one. By observing the curves, the following pattern characteristics can be derived: injection-water arriving time (breakthrough); existence of high-permeability channels, barriers, and fractures between wells; communication between different layers; stratification in the same layer; and preferential flow directions in the reservoir. Furthermore, the cumulative response can be obtained by integrating the concentration vs. time curve if the production flow rate is known. From this new curve, the fraction of injection water reaching each producer is easily calculated. A common spreadsheet is the best way to make these calculations. This type of interpretation can be carried out without any advanced simulation. It is important to integrate the data obtained from the geological model, primary production data, 4D seismic data (if available), and tracer data in a systematic way.

The second level of analysis uses basic mathematical models to fit simple response curves by means of theoretical expressions and to decompose complex responses in several simpler functions. In this way, partial residence times, as well as other parameters, can be determined for each function. Mathematical models also allow for the evaluation of important parameters, such as permeability, and make it possible to predict the behavior of unknown patterns.

Finally, complex mathematical models like numerical finite-element simulators or streamtube modeling can be used to achieve a deeper analysis. Most of the commercially available simulators have tracer options with varying degrees of complexity. Not all simulators include important physical effects like partitioning, dispersion, and adsorption. A tracer simulator that can be coupled to full-field reservoir simulators has been developed recently. Simulation is a tool to improve the existing reservoir model; therefore, it is crucial to have access to the best available model to enable an efficient optimization based on the tracer-production data.

## Evaluation based on hand calculation and adequate data presentation

Qualitative interpretation of field data is illustrated by examples from the Snorre field in the North Sea. **Fig. 1** shows the segment of the field that was tested and the location of injectors (triangles) and producers (circles). ^{[1]} A water-alternating-gas (WAG) injection program is being used in the field.

**Fig. 2** shows a way to present field data for a gas-tracer program. The data are plotted as a time response. Alternatively, the data can be plotted as a volumetric response. To obtain a better understanding, it is important to plot gas-tracer-production data with GOR. The tracer data are plotted relative to the amount of tracer injected, which means that the concentrations presented for each individual tracer can be compared directly.

From **Fig. 2**, it is possible not only to find communication but also to extract information about the prevailing flow regime. The gas tracer injected into Well P25 breaks through without any significant increase in GOR, which means that the gas has not followed a free gas layer but has been dissolved in the oil. Three different gas tracers were injected in Well P28 at three different times. These tracers were produced only after a significant GOR was recorded. All the tracers were produced at almost the same time. This shows that gas has been trapped and that the gas in the individual gas slugs has subsequently filled this trap. At a certain time, the gas trap has been filled and the gas moves on to the producers. When reaching the producer, the gas contains all three different tracers injected over a 3-year period.

From the data in **Fig. 2**, it is possible to carry out a spreadsheet calculation to estimate the recovery of the injected tracer in each individual production well. This shows that a large percentage of the injected gas has moved in different directions. Breakthrough time also may be estimated, either as the first sample that contains tracer above the detection limit or as an extrapolation backward of the initial phase of the production curve. However, the accuracy of this calculation is limited by the sampling frequency.

To fully understand the flow behavior, it is important to add all information available. The picture may be modified by the knowledge of injection rates and production rates in the neighboring wells.

Because of maintenance and operational problems, production wells may be shut in for some periods. Because of fluid drift in the reservoir during shut-in, samples collected immediately after such periods may give unexpected results. This additional information can be exploited to better understand the pressure distribution in the field. Somaruga *et al.*^{[2]} used well shut-in in a systematic way to obtain additional information. If the changes that may occur during shut-in are not considered, it may cause misinterpretation of the tracer-response curves.

The water-tracer-response curves should be presented together with the water cut. **Fig. 3** shows water-tracer-response curves in the same well as discussed previously. Initially, a small water-cut increase is recorded. The tracer injected in Well P34 follows this increase. When the water cut starts to increase more rapidly, one of the other tracers starts production while the concentration of the first tracer vanishes. This method of presentation increases the understanding of the flow behavior and the water contribution from the different injectors.

### Response curves

The time response is the graphic representation of the concentration of activity (after background subtraction and decay correction) as a function of time. Preprocessing the experimental data can smooth the response. From this curve, the cumulative response (recovered activity vs. time) is derived by a simple numeric integration.

Concerning the cumulative response, the **Eq. 1** gives the cumulative tracer recovered up to an instant, *t*_{i}.

where = the total tracer recuperation up to *t*_{i}, = the production water flow rate as a function of time, *C*_{t} = tracer concentration as a function of time, and *t*_{i} = the elapsed time (days after the injection). often will be available as a discrete value representing each day. *C*_{t} will be available only as an individual measurement according to the sampling program. The accuracy of the total recovery will depend on the sampling frequency.

### Sweep volume

Instead of the time-response curves, the data are often presented as volumetric-response curves. The presentation is especially convenient for estimating the swept volume between the particular injector and producer pair. Swept volume, *V*_{S}, can be estimated from the product of the mean produced volume, , and the ratio of the mean volumetric water rate between the injector and the producer, *Q*_{m}, to the mean volumetric water production rate, *Q*_{p}.^{[3]}

is calculated from the first moment of the produced-tracer concentration, *C*.

*Q*_{m}, the flow rate between injector and producer, is estimated from the fraction of injected tracer produced at the well at the mean injection rate, *Q*_{i}.

where *m* = the amount of tracer produced at a given well and *M* = the amount of tracer originally injected. The swept volume can be expressed in terms of the injected and produced flow rates and the fraction, *m*/*M*, of water going from the injector to the producer.

Because of limited data, the tracer-production curve is composed of a discontinuous set of points and, in practice, the integral in **Eq. 3** is approximated by

The calculation of swept volume often is complicated by a lack of data. The mean produced volume may need to be estimated on the basis of extrapolated tracer-production curves. In many cases, the sampling program is either not finished or it has been stopped without following the tail of the production curve. To fit the missing data in the tail of the production curve, an exponential decline approximation can be applied.

where *C*_{e} = the measured tracer concentration at the value of V e from which the exponential fit starts. The slope of the line is represented by 1/*a*. If **Eq. 7** is substituted for *C* in **Eq. 3** and the integral replaced by a finite sum, the following expression is valid:

To find the swept volume in an incomplete data set, this equation is used for in **Eq. 5**.

## Evaluation based on analytical solutions

**Eq. 9** gives the fundamental equation for tracer breakthrough in a streamtube. A correlation into a single breakthrough curve for various repeated homogeneous-flooding patterns has been found. ^{[4]} In a layered system, the overall tracer-response curve is a combination of responses from individual layers. The individual-layer responses are predictable from the correlated pattern-breakthrough curve; however, the tracer arrival time at the production well and the concentration contribution from each layer are functions of the porosity, permeability, and thickness of that layer. Conversely, the decomposition of an actual tracer-production curve from a multilayered system into the individual-layer responses can yield individual-layer parameters. Computer algorithms exist that deconvolve the overall tracer profile into the individual-layer responses and compute *ϕ* h and *kh*/Σ*kh* of the individual layers.

## Evaluation of tracer-response curves with numerical simulation

The most thorough analyses of tracer data are carried out in combination with a reservoir simulator applied for that particular field. Many of the applied reservoir simulators, based on numerical solution of flow equations applying finite-difference methods, have options for handling tracers. ^{[5]} In addition, streamline models^{[6]}^{[7]} exist that handle tracer flow. However, normal simulators have limitations. One problem is the limited possibilities for including physical properties such as partitioning between phases and adsorption to grain surfaces. This problem is of special importance for gas tracers. There is also a problem connected to handling of dispersion because the tracer pulse is, in its initial phase, much smaller than a typical gridblock size.

To overcome some of these problems, Sagen *et al.*^{[8]} developed a simulation module to improve the accuracy of the calculations. To resolve the influence of reservoir heterogeneities on the measured tracer response, an accurate numerical treatment of the tracer equation is needed. This is especially important when narrow tracer slugs are injected in a reservoir. This tracer module calculates tracer flow with an explicit method for integration of the convection part of the tracer equation. To reduce numerical smearing of the tracer pulses, the timestep for the tracer calculation is selected as large as possible but may still be much smaller than the timesteps of the host reservoir simulator, which most often uses an implicit formulation. In the tracer module, the main tool for reducing numerical dispersion is the use of a second-order numerical scheme for integrating the tracer equation. A separate grid-refinement option for tracer calculation is available. In combination, these methods lead to a good resolution of narrow slugs propagating through the reservoir. The method of separate grid refinement is far less time consuming than performing the whole reservoir simulation on a refined grid. This tracer simulation module has been coupled to some of the standard reservoir simulation tools.

## Nomenclature

## References

- ↑
^{1.0}^{1.1}^{1.2}^{1.3}Dugstad, Ø., Aurdal, T., Galdiga, C. et al. 1999. Application of Tracers to Monitor Fluid Flow in the Snorre Field: A Field Study. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 3–6 October. SPE-56427-MS. http://dx.doi.org/10.2118/56427-MS - ↑ Somaruga, C., Gazzera, C., and Wouterland, C. 2001. Application of BIPI Tests Employing Natural and Artificial Tracers in Waterflooded Oil Fields of the Neuqina Basin (Argentina). Proc., Tracers and tracing methods, First International Congress, Vol. 15, No. 79, Nancy, France.
- ↑ Zemel, B. 1995. Tracers in the Oil Field, 43. Amsterdam, The Netherlands: Developments in Petroleum Science, Elsevier Science.
- ↑ Abbaszadeh-Dehghani, M. and Brigham, W.E. 1984. Analysis of Well-to-Well Tracer Flow To Determine Reservoir Layering. J Pet Technol 36 (10): 1753–1762. SPE-10760-PA. http://dx.doi.org/10.2118/10760-PA
- ↑ Agca, C., Pope, G.A., and Sepehrnoori, K. 1990. Modeling and analysis of tracer flow in oil reservoirs. J. Pet. Sci. Eng. 4 (1): 3–19. http://dx.doi.org/10.1016/0920-4105(90)90042-2
- ↑ Yoon, S., Barman, I., Datta-Gupta, A. et al. 1999. In-Situ Characterization of Residual NAPL Distribution Using Streamline-Based Inversion of Partitioning Tracer Tests. Presented at the SPE/EPA Exploration and Production Environmental Conference, Austin, Texas, USA, 1–3 March. SPE-52729-MS. http://dx.doi.org/10.2118/52729-MS
- ↑ King, M.J. and Datta-Gupta, A. 1998. Streamline Simulation: A Current Perspective. In Situ 22 (1): 91–140.
- ↑ Sagen, J., Cvetkovic, B., Brendesdal, E. et al. 1996. Reservoir Chemical-Thermal Simulation with Tracers. Presented at the European Petroleum Conference, Milan, Italy, 22–24 October. SPE-36921-PA.

## Noteworthy papers in OnePetro

Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read

## External links

https://www.corelab.com/protechnics/spectraflood

## See also

Tracer flow in porous reservoir rock

Planning and design of well to well tracer tests

Field experience with well to well tracer tests