Simulation of single well chemical tracer tests

Simple analytical interpretation of single well chemical tracer (SWCT) is possible if one assumes uniform oil saturation, negligible hydrolysis during injection and production and assuming similar dispersion for all reservoir layers. In complex reservoir settings, including multilayer test zones, drift, cross-flow etc., reservoir simulation tools, capable of handling the hydrolysis reaction are commonly applied (Jerauld et al., 2010; Skrettingland et al., 2011). In practice, coupled flow and chemical reaction simulators (see e.g. CMG, 2010; and UTCHEM, 2000) are used. Such coupled simulations are CPU-demanding enough that execution time may be an issue, especially when small grid-size are applied to avoid numerical smearing. A significantly simpler and faster approach is possible by exploiting the fact that tracers do not influence on the fluid flow in the reservoir. In fact, simulation of tracer transport may be decoupled from the reservoir simulation itself (Sagen et al., 1996). By decoupling the tracer and fluid flow it is possible to state and solve the tracer problem based on previously solved and stored reservoir simulator runs (Huseby et al., 2012). This approach allows for fast tracer simulations with execution times of 1-5% of the corresponding reservoir simulation, and the possibility to re-state and solve the tracer problem without re-solving the flow.

Theory of simulation

Assumptions for ideal SWCT test modeling

Mathematical modeling of the ideal SWCT test assumes that:

• The carrier fluid flow is incompressible, pseudosteady state, single-phase, and radial only
• That the formation is a homogeneous layer of thickness (h) and porosity (ϕ) extending from the wellbore radius (r_w) to an external boundary radius (r_e), where reservoir pressure is constant

With these assumptions, the interstitial fluid velocity (v_fi) is given by

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

where r = radial position; q = fluid flow rate in the single well (q > 0 is injection and q < 0 is production); h = height of test zone; ϕ = porosity; and S_f = flowing fluid saturation, constant.

The additional assumptions regarding the tracers are:

• That K_A for tracer A is constant and that A is in local equilibrium between flowing fluid (saturation S_f) and residual fluid (saturation S_r). For Case 1, S_r = S_or and S_f = 1.0 – S_or.
• That tracer A (primary) reacts in situ to form tracer B (product) at a rate given by

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

where R_H = hydrolysis reaction rate, in moles of A per vol-day; C_A = concentration of A, in mol/volume; and k_H = hydrolysis rate constant (days^–1) in the aqueous phase. Tracers are dispersed in the radial flow with an effective dispersion coefficient (D_a), given by

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

where α = dispersivity (ft).

The material balance for tracer A is the partial differential equation:

....................(4)

Similar equations apply for product tracer B and the material-balance tracers.

SWCT test simulation requires the numerical solution of these equations for A, B, and the material-balance tracer. The equations first are converted to finite-differenced form, based on the perfectly mixed cell model. The simulation program then solves the finite-differenced equations for the concentrations of the tracers in a radial series of cells over the test time interval.

Simulation program inputs

Input to the simulation program consists of:

• Known parameters, which are: q as a function of time (injection, shut-in, production), injected concentration of tracer A (C_A) and concentration of tracer B (C_B) as a function of time; r_w, h, ϕ; K_A and K_B.
• Unknown (estimated) parameters, which are: k_H, S_or, and the radial dimension of the cells (ΔR). Note: according to the theory of the perfectly mixed cell model for small time intervals, ΔR = 2α.

How to simulate nonideal SWCT tests

The three major nonideal conditions observed in SWCT tests, in order of their potential encounter, include fluid movement in the formation at the test site; in carbonates, a lengthy time required for local equilibrium to be achieved by diffusion in liquids, as compared to test duration; and in sandstones, nonreversing flow behavior in formation layers.

Fluid movement

In active parts of a reservoir (i.e., when other producers or water injectors are close to the test well), there might be fluid movement in the formation at the test site. This is known as fluid drift. The tracers injected with the SWCT test fluids are subjected to a flow field that is not radial and reversible, as is assumed by the simulation theory above. Such was the situation during the first SWCT test. A specialized simulator was developed to interpret that test.

The simulation theory assumes that a linear flow field with a fixed drift velocity, v_D, is superimposed on the radial flow at the test well. This requires the numerical solution of partial differential equations involving two space dimensions and time. Obtaining a best fit to field data involves varying drift velocity, v_D, in addition to the unknowns ΔR, k_H, and S_or. The drift velocity is caused by a regional pressure gradient in the formation, where as the radial component of velocity is caused by injection or production at the test well. The original simulator is furnished to licensed users of the SWCT method.

Local equilibrium time length

The pore geometry of most carbonates is such that the basic assumption of local equilibrium of partitioning tracers is not valid. A significant fraction of the pore space is not directly in the flow paths, but is only in diffusional contact with these paths. Because the time required for local equilibrium to be achieved by diffusion in liquids can be long compared to the duration of the SWCT test, dual-porosity models must be used to simulate SWCT tests in carbonates. In addition to ΔR, k_H, and S_or discussed earlier, several new unknown parameters must be added to the list:

• The fraction of the total PV that appears to be poorly connected for flow (dead-end fraction).
• The effective diffusion parameter for each tracer in the poorly connected fraction.
• S_or in the poorly connected pores.

The dual-porosity simulator has been used to interpret more than 30 tests to date. Case 3 below uses the dual-porosity simulation model.

For a summary of SWCT test experience in carbonate formations, see Deans and Carlisle.

Non-reversing flow

Interpretation of SWCT tests in sandstone formations has revealed a very common nonideality. The formations tested appear to consist of two or more layers, as might be expected, but reversing behavior is not observed. One likely explanation is the existence of local pressure differences between the layers, caused by activity at other wells in the reservoir. Qualitatively, the effects of such pressure differences on the SWCT test results are:

1. A layer at higher pressure accepts less fluid during injection and produces more fluid during production than a parallel layer at lower pressure. This results in a nonideal profile because the tracer bank from the higher-pressure layer will return earlier than it should and the tracer from the lower-pressure layer will be late.
2. During the shut-in period for ester hydrolysis, fluid will flow through the wellbore from the higher-pressure layer to the lower-pressure layer. One tracer bank moves back toward the well and the other moves away during the shut-in period. This special flow condition, called crossflow, adds to the separation caused by effect 1.
3. As mentioned earlier, apparent differences in S_or sometimes are observed in different layers in the same formation. Along with nonreversing flow, these differences require the use of a multilayer simulator program to interpret certain SWCT tests.

Once the specific nonideal conditions are recognized, the SWCT test simulation proceeds as before. The unknown parameter set now contains an estimate of the number of layers present, the fraction of total fluid injected/produced from each layer, the crossflow between layers, and the S_or for each layer. Because of the large number of adjustable parameters, semiautomated optimum-seeking subprograms have been developed help find the best fit. Seetharam and Deans demonstrate that an accurate flow-weighted S or is obtainable using such a multilayer simulator to match field data, even though the layering parameters are not unique. Case 2 (below) presents an example of a SWCT test in a layered sandstone formation.

In all SWCT test simulations, the objective is to find the simplest simulator model that adequately matches the observed tracer profiles. The same model must match all tracers used in a given test (ester, product alcohol, and material-balance tracers). In some tests, one or more additional tracers may be used in different injection patterns to identify wellbore and/or formation flow irregularities. The more tracers that are used, the more difficult it is for the simulator to find a reasonable model to fit all field-measured tracer profiles. Our experience suggests, however, that several models can adequately describe a given set of profiles, and that the least-sensitive parameter to changing models is the main target, S_or.

Applications and case studies of SWCT simulation

Case 1: finding best-fit parameters using the simulator

Simulation of a relatively ideal test now will be demonstrated using tracer profiles, shown in Fig. 1. The known parameters are input to the program, along with estimated values for ΔR, k_H, and S_or.

First, several runs are made with different ΔR values, keeping all other parameters constant. The simulation predicts values for tracer concentrations vs. volume produced. Fig. 2 shows the C_A results superimposed on the field data, for different values of ΔR. The best-fit value appears to be approximately 0.50 ft. (Further refinement, using least-squares criteria, yields a value of 0.52 ft.) Note that ΔR affects the shapes of the concentration peaks, not their average positions on the produced volume axis. The shapes of C_A and C_B peaks are similarly affected.

• 

  Fig. 2 – Variation of ΔR shown for three cases.

The next step is to find the best-fit value of k_H, which determines how much product tracer B will form. In Fig. 3, the simulated profiles for C_B are superimposed on the field data for C_B, for a range of values of k_H. Note that k_H affects the height of the C_B peak, but not its position. Because of the relatively small amount of hydrolysis in this case (less than 10% of the injected ester was hydrolyzed), the height of the simulated C_A peak changes very little when k_H is varied in this range of values.

• 

  Fig. 3 – Variation of k_H shown for three cases.

Finally, the input value for S_or is varied. Minor adjustments are made in k_H to keep the height of the C_B peak constant. As Fig. 4 shows, changing the S_or moves the position of the product tracer peak on the "produced volume" axis. Changing the S_or does not affect the predicted position of the unreacted ester peak because of the reversibility effect that was discussed earlier.

• 

  Fig. 4 – Varying S_or to match the ethyl alcohol profile.

The final best-fit simulation is shown with the field data in Fig. 4. The best-fit estimates of the unknown parameters for Case 1 are ΔR = 0.52 ft, k_H = 0.011 days^–1, and S_or = 0.13. To indicate the level of precision expected in the test, simulated C_B peaks also are shown for S_or = 0.11 and S_or = 0.15. S_or = 0.13 ± 0.02 is the best estimate for S_or for this reservoir, using the SWCT method.

Case 2: simulation of SWCT tests in layered formations

The second field test example is from a candidate test zone with the following characteristics:

• Produced water cut of 0% (100% oil).
• Reservoir temperature of 234°F.
• Lithology is sandstone.
• Produced by gas lift.
• Production rate of 500 B/D.
• Perforated interval of 45 ft.
• Average porosity of 22%.
• Brine salinity of 43,000 ppm.

No well was available in this field that produced water only. In this case, the test well initially produced 100% oil. To generate residual oil saturation near the well, 6,500 bbl of filtered water first was injected into the test zone. The waterflood injection took eight days to complete, after which the well produced 100% water during a short test.

Samples of produced oil and water were collected for ester K value measurement. Ethyl acetate was selected as a suitable partitioning tracer. Its K value was 3.65, based on laboratory measurements at reservoir conditions. With an assumed S_or of 25%, the corresponding value of β is 0.94, which is close to the optimum value of 1.0.

For the test that followed the waterflood, 135 bbl of formation water was injected containing ethyl acetate (7,000 ppm), normal propyl alcohol (NPA) (3,900 ppm), and isopropyl alcohol (IPA) (12,700 ppm). This was followed by 550 bbl of formation water carrying only isopropyl alcohol (12,700 ppm). The injection rate was 650 B/D and wellhead pressure was 1,200 psia during injection. Wellhead pressure was monitored carefully during injection to avoid fracturing the test zone.

The SWCT test injection required 1.15 days. The well then was shut in for five days to allow hydrolysis of a fraction of the ethyl acetate tracer. After hydrolysis, the gas lift system was turned on and the well was produced through a separator at an average rate of 500 B/D, with a stable gas lift ratio of 620 scf/bbl.

The production period was 2.7 days, throughout which samples of the produced water were taken at 5- to 15-minute intervals and analyzed immediately at the wellsite for tracer content. Total produced volume was carefully recorded at the time of each sampling. Total produced volume was 1,350 bbl. No oil cut was observed in the produced fluids at the end of the 1,350-bbl production period.

The field data from this test are plotted in Figs. 5 and 6 as tracer concentration vs. total produced volume, along with simulation results. The best-fit simulation required four layers, with minor irreversible flow. The ethyl acetate contributions from the four layers are shown in Fig. 5, along with the composite concentration, which is the flow-weighted sum of the four layers. The two main layers accepted 73% of the injected tracer, and produced the same fraction. The early layer took 13% of the injection and gave back 19% of the production, and the late layer took 14% of the injected fluid, but only produced back 9%.

• 

  Fig. 5 – Ethyl acetate field data and simulation, Case 2.

• 

  Fig. 6 – Ethanol field data and simulation results, Case 2.

The predicted ethanol concentrations for the same four-layer model are shown in Fig. 6 . To obtain the ethanol best fit, only the S or was varied for the four layers. The two main layers have an S or ranging from 22 to 28%. A radial gradient of oil saturation caused by the waterflood performed before the SWCT test would produce a similar effect.

On the basis of this model, the tracer-injection average S or is calculated to be 26 ± 2%. This is a permeability-thickness-weighted average for the PV accessed by the ethyl acetate, which is roughly the volume of a cylinder 8 ft in radius and 45 ft high.

Case 3: simulation of SWCT tests in carbonate formations

The field test example for Case 3 demonstrates the extreme nonidealities that are possible in carbonate formations. The test well in this case was completed in a carbonate reef structure in Alberta, Canada. Test well characteristics were:

• Produced water cut of 99%.
• Reservoir temperature of 133°F.
• Lithology is vuggy carbonate.
• Production rate of 320 B/D.
• Perforated interval of 13 ft.
• Average porosity of 12.8%.
• Brine salinity of 113,000 ppm.
• S_or (anticipated) of 20%.

Because of the low reservoir temperature and high brine salinity, ethyl formate was chosen as the partitioning tracer for this test. This was designed to be a relatively small-volume test because previous large-volume tests in the same formation had not produced definitive results and had taken many days to complete production. Because ethyl formate is highly reactive, a decision was made to try to complete the test in less than 5 days. At an injection rate of approximately 300 B/D, 20 bbl of formation water was injected carrying ethyl formate (10,800 ppm), IPA (cover tracer) (4,700 ppm), and NPA (material-balance tracer) (2,300 ppm). This bank was followed with a net push injection of 50 bbl of water containing NPA (2,300 ppm).

The well was shut in for 1.3 days to allow part of the ethyl formate to hydrolyze, producing the secondary tracer, ethyl alcohol. The well then was produced at a rate of 300 B/D for 3.0 days. Samples were taken at regular intervals and analyzed at the wellsite for ethyl formate, ethyl alcohol, NPA, and IPA. These data are plotted as concentration vs. produced volume in Figs. 7 through 11.

• 

  Fig. 7 – NPA field data and ideal simulation, Case 3.

• 

  Fig. 8 – NPA material-balance tracer simulation, dual-porosity model, Case 3.

• 

  Fig. 9 – IPA cover tracer simulation, dual-porosity model, Case 3.

• 

  Fig. 10 – Ethyl formate simulation, dual-porosity model, Case 3.

• 

  Fig. 11 – Ethanol simulation, dual-porosity model, Case 3.

Fig. 7 shows the simulation of the NPA material-balance tracer profiles with an ideal model that assumes local equilibrium. Several features are obvious:

• The ideal model is inadequate.
• Although all the injected water contained 2,300 ppm of NPA, the first returns from the formation contain significantly lower concentrations.
• The field data "tail" very badly—NPA is still being produced after 600 bbl, even though only 70 total bbl containing NPA were injected into the formation.

Figs. 8 through 11 show the dual-porosity test simulation results for each of the four tracers. The fraction of dead-end pores is 0.80 for all these simulated profiles. The S_or in both flowing and dead-end pores was 0.24. The dimensionless diffusion parameters ranged from 0.22 for ethyl formate to 0.28 for NPA and IPA.

Simulation of SWCT tests in dual-porosity media

Tracer test results from many carbonate formations seem far from ideal when compared to those from sandstone formations. One of the fundamental assumptions of the SWCT test—local equilibrium of tracer in all the available fluid—is invalid for carbonates. This also is the case with fractured sandstones.

Fig. 12 shows the assumed situation in these cases. Tracer material being transported through the well-connected pores can diffuse into the fluid in the dead-end pores. Depending on the geometry of the pore system and the flow rates, however, the tracer might not have enough time to approach equilibrium by diffusion during the test.

• 

  Fig. 12 – Schematic of dual-porosity system.

A dual-porosity simulator accounts for this effect. First, a "source" term is added to each tracer material-balance equation, which now describes the flow of tracer in the well-connected pores. New material-balance equations then are written to describe the diffusion of each tracer in the local dead-end pores. The diffusion equations are connected to the flowing pore equations through the source term in the original material balances.

The new model introduces three new parameters:

• The S_or in the dead-end pores, which is not necessarily the same as S_or for the well-connected pore space.
• The fraction of total porosity that is in the dead-end pores.
• A diffusion parameter that controls the rate at which tracers diffuse in the dead-end pores (this parameter is smaller for long, thin pores and larger for short, fat pores).

For details on the numerical solution of the dual-porosity model equations, consult Deans and Carlisle.

Nomenclature

CA	=	concentration of tracer A, mol/vol
DE	=	effective dispersion coefficient, ft2/D
h	=	thickness, ft
kH	=	hydrolysis rate constant (days–1) in the aqueous phase
q	=	fluid-flow rate in a single well, B/D
r	=	radial position, ft
re	=	external boundary radius, ft
rw	=	wellbore radius, ft
RH	=	hydrolysis reaction rate, mol/vol-day
Sf	=	flowing fluid saturation, fraction of PV
Sor	=	residual oil saturation, fraction of PV
vfi	=	interstitial fluid velocity, ft/D
α	=	dispersivity
βA	=	retardation factor for tracer A
ϕ	=	porosity

Noteworthy papers in OnePetro

Olaf Kristoffer Huseby O., Sagen J., Dugstad Ø.: Single Well Chemical Tracer Tests - Fast and Correct Simulations. SPE-155608-MS. SPE EOR Conference at Oil and Gas West Asia, 16-18 April 2012, Muscat. DOI http://dx.doi.org/10.2118/155608-MS

Skrettingland K, Holt T, Tweheyo MT and Skjevrak I, Snorre low salinity water injection - core flooding and single well field pilot. SPE 129877, SPE Reservoir Evaluation & Engineering, Vol 14, No. 2, pp. 182-192, 2011.

Jerauld GR, Mohammadi H and Webb KJ: Interpreting Single Well Chemical Tracer Tests. SPE paper 129724. SPE Improved Oil Recovery Symposium, 24-28 April, Tulsa, Oklahoma, USA, 2010

Noteworthy books

UTCHEM: User's Guide & Technical Documentation for UTCHEM-9.0 A Three-Dimensional Chemical Flood Simulator, The University of Texas at Austin, 2000.

CMG (Computer Modelling Group) Ltd: STARS Users Manual, Version 2010. Calgary, Canada, 2010.

External links

Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro

See also

Single well chemical tracer test

Well to well tracer tests

PEH:The_Single-Well_Chemical_Tracer_Test_-_A_Method_For_Measuring_Reservoir_Fluid_Saturations_In_Situ