• Surveys versus time with the tool in a fixed position in the wellbore yield the reservoir's transient response pattern to rate perturbations.
• LRTs [layered reservoir tests] are multi-rate tests in which stationary measurements are taken above each zone, and PL surveys are made across all zones just before changes in the surface rate.
• Dual porosity or layered system response patterns can be masked by lengthy wellbore storage. … If it is not possible to conduct a test using downhole shut-in, one alternative is to measure downhole flow-rates simultaneously with the pressure. Methods such as convolution, deconvolution, or rate-normalization can achieve an analogous reduction in the storage effect. These techniques work well when the flowmeter sensor can be positioned in a predominantly single phase environment in the wellbore, and the dynamic range of the measured flow rate is above the threshold level for the particular tool.
• Once the spinner rotation falls below the sensor threshold value, acquired data are no longer accurate, and extrapolation is usually necessary in practice. The extrapolated flow rates are usually computed by assuming that the wellbore fluid compressibility is constant and of small magnitude.
• There is therefore a certain benefit to testing while flowing the well [e.g. complications of closure]. This can be fully realizable if downhole flow rates are measured in addition to the pressure. Furthermore, spinner flowmeters actually perform much better when the well is flowing.
• The LRT is a commingled production test that alternates PL profiling immediately before a surface flow rate change with a stationary measurement of the transient induced by the rate change. The sonde is strategically located above each of the selected perforated intervals before the new flow rate change is induced and after a profile at the last prevailing rate has been completed. Permeability, skin and average pressure can then be determined for each zone tested in this fashion.
• It is quite common for the buildup response of a layered system to appear, and be interpreted, as a homogeneous single-layer system. LRT interpretation shows that this approach to the analysis may yield oversimplified results.

Two good reference, from which these rules of thumb were extracted are:

1. Joseph, J., Ehlig-Economides, C.A., and Kucuk, F.: "The Role of Downhole Flow and Pressure Measurements in Reservoir Testing," SPE 18379, SPE European Petroleum Conference, London, UK (October 16-19, 1988).
2. Ehlig-Economides, C.A.: "Testing and Interpretation in Layered Reservoirs," JPT (Sept. 1987) 1087-90.

Kucuk, F., Karakas, M., Ayestaran, L.: "Well Testing and Analysis Techniques for Layered Reservoirs," SPEFE (August 1986) 342-354.

• This is a "multilayer test" to estimate individual layer permeabilities and skin factors uniquely. A number of sequential tests are performed with a PLT measuring pressure and rate at the top of each different layer. In principle, the number of tests should at least equal the number of layers. During each flow test, the wellbore pressure and the downhole rate must be measured simultaneously at different locations along the wellbore.

• A PLT with rate and pressure capabilities is needed since it is necessary to measure the wellbore pressure and rate simultaneously as functions of depth and time.
• The threshold rate for the flowmeter must be acceptable! Kinetic and mechanical losses of a moving tool must be considered. The service company will (should) be able to confirm calibrations, adjustments for line speed and minimum spinner capabilities, etc.

• You measure the wellbore pressure and rate simultaneously as functions of depth and time.
• Remember that all of the layers open to the wellbore are in pressure equilibrium in the wellbore. The pressure will differ only because of friction and head, but the rate is a function of the specific layer properties, particularly during transient periods. This means that changes in rates in different zones will tell you about their transport properties.
• During early transient time (soon after you have made a change in rate) the rate into each zone is adjusting to the imposed change in surface rate. The rate is basically affected by layer permeabilities, thicknesses, and skin factors below the measurement point (i.e., all of the zones below the tool). As transients dissipate, the rate at any depth depends more on vertical permeability, porosity, compressibility and thickness as well as the drainage radius and the external radius pressure for each layer. You can see that, at least conceptually, if you can separate out the contributions from the different zones by running an appropriate survey in conjunction with changing the surface rates, you can analyze pressure and rate response at early and later times to learn about fundamental properties for the various zones.

• Even the simplest pressure transient evaluations can be difficult to interpret. It is important to consult with your pressure transient specialist in terms of the precise design and operational methodologies.
• The basic protocols are as follows

1. A complete production flow profile should be obtained if the well is already injecting at a stabilized or constant rate. If the well is shut-in, it should be put on injection at a maximum (safe and tolerable) flow rate while the tool is recording pressure and rate at the top of the perforations or the injection zone(s).
2. During this first flow test, when the rate is stabilized or reaches a constant value, a complete profile should be obtained.
3. After this first test, specifically design the remaining measurements according to the contribution from each layer so that flow into any layer will not be below the threshold sensitivity of the rate-measuring device (the number of zones has also been identified).
4. Vary the surface rate between a maximum that can be tolerated by the well, the tubulars and the formations, and a minimum (be sure to stay above the bubble point if you are producing as well as the rate threshold for the tool). Examples are shown in Figure 1. Some possibilities include:
• Method 1 - Vary the rate from the maximum to the minimum for each flow test.
• Method 2 - The first rate is reduced to a minimum during the second flow test and is increased a step for each subsequent flow test. Wellbore crossflow can be minimized or eliminated completely, depending on the layer parameters and the size of the rate pulse during the second flow test - use this method if wellbore crossflow is suspected. However, it may also create a crossflow during the second flow test because the rate change is a maximum.
• Method 3 - If the surface rate is changed without moving to a new location, perform the second method for each layer.
• Method 4 - Start from the minimum rate when the tool is at the top of the formation. Increase the rate in steps and move to the top of the lower layers. The production profile can be taken between steps.



Figure 1.

Two example methodologies for performing multilayer testing (showing Methods 1 and 2).

5. After each flow test, and before changing the rate, get a new production/injection profile for the entire formation. After each profile, position the tool at the top of the next layer or set of perforations and change the rate according to the planned testing scheme.
6. When the tool is at the top of the bottom layer, the rate should also always be increased.
7. During each test, the surface rate should be held constant if possible.
8. Avoid rapid flow rate increases.
9. Run each flow test until an approximately stabilized bottomhole rate, or at least an infinite-acting (without storage) period, is reached.
10. Rate is designated as q_ij, and "i" indicates the flow test number and j indicates the layer number (see Figure 1).

• It is likely analyzed by a pressure transient specialist.
• Permeabilities and skins can be estimated for layers from early-time response whether there is reservoir crossflow or not.
• Intermediate and late time information can be used to infer layer pressures and vertical permeabilities.
• Step 1 applies the logarithmic convolution method to approximate permeabilities and skin factors.
• Step 2 refines these estimates with a least squares algorithm.
• Logarithmic convolution is also known as sandface rate convolution (SFRC) or convolution. You will get a straight line by plotting:



• and the slope will be m and the intercept will be mb (click on More Details for more discussion and for nomenclature).

  The effects of preceding transients are ignored in determining the average transmissibility and skins. Pressure can be inferred from extrapolation. After the permeability and skin are estimated for the bottom layer, the flow rate for Layer NL - 1 (second layer from bottom) is computed from the flow test data recorded at the top of the (NL - 1)th layer and the bottom-layer parameters. Then, using the above equation and the measured pressure, the permeability and skin can be determined for the NL - 1 layer, and so on.

  The SFRC method works fairly well when the system can be approximated as an equivalent single layer. It will not work if the wellbore geometry is not radial (i.e., fractured!!!!!!). Your specialist can find ways around this if this method is adopted.

• Kucuk and his colleagues recommended refining the predictions further using nonlinear least squares estimation using basic analytical formulations for a layered medium with no crossflow. They felt that this is necessary because it can provide a means for assessing the correctness of a given model or discriminating between several possible models.

Ehlig-Economides, C.A., and Joseph, J.: "A New Test for Determination of Individual Layer Properties in a Multilayered Reservoir," SPEFE (September 1987) 261-283.

• In the multilayered, commingled flow system, the wellbore pressure is sensitive only to the total system behavior. The layer flow rates are sensitive to the layer properties.
• The analysis of layer flow-rate transients provides a means for determining the layer permeabilities and skins and the effective vertical interlayer communication.

Figure 2.

Schematic wellbore in a layered scenario, showing the nomenclature used in Ehlig-Economides and Joseph.

Notice the following:

• You can see three overall zones in contact with the well. There can be non-perforated or impermeable sections between the zones.
• Zones can contain layers with their own discrete properties. There can be vertical crossflow between layers, but this is assumed to occur just at the layer contacts and flow is represented as horizontal. The parameters l characterize the vertical communication between the layers.
• Each layer is characterized by skin, porosity, permeability, and thickness. Initial pressure varies hydrostatically relative to a common datum. Larsen has published on how to get around this.
• Rate from each layer is determined and wellbore crossflow is possible.

Like any analytical pressure transient analysis, there are certain assumptions - most of them are similar to those made in all pressure transient analyses. To overcome these assumptions, numerical simulation may be necessary. The basic assumptions are:

1. Each layer is homogeneous and isotropic.
2. The flow is single-phase and the fluid has constant viscosity and a small, constant compressibility.
3. Permeability, porosity and thickness for each layer may be different.
4. Crossflow may occur in the reservoir between adjacent layers.
5. There is no crossflow between adjacent zones (Figure 2 shows the difference between layers and zones).
6. The well is symmetrically located and fully penetrating. You can probably fool the analysis to overcome the partial penetration restriction to some extent. If the inclination is significant and the well is not symmetrically placed you will have to rethink the interpretation procedures. For example, you can presumably include a skin for inclination. In a near or completely horizontal well, you will need to modify the basic flow relationships that the calculations are based on.
7. Each layer has an arbitrary skin. This is important for PWRI because you will be able to identify preferential plugging.
8. Wellbore storage is assumed to be constant. Because bottomhole measurements are made and most of the calculations involve normalizing by bottomhole rates, you likely don't have to worry about wellbore storage.
9. There can be crossflow in the wellbore.
10. All resistance to vertical flow is concentrated in the "walls (layer top, bottom).
11. The pressure difference between adjacent layers depends only on radial position and flow within the layer is only horizontal.

Flow in each layer is governed by:

This shows a darcy-like relationship between the permeability and thickness of a layer (layer( "j"), the pressure gradient with radial position, the compressibility, viscosity, porosity and the change in pressure with time - similar to what you would find in the equation for radial flow into a well. It is modified by two terms "X" which account for any vertical movement of fluid into the zone above or the zone below. where:

Simplified procedures are outlined below. More details are available. ALWAYS CONSULT WITH YOUR IN-HOUSE SPECIALIST.

1. Determine thicknesses and porosities from logs.
2. It is desired to determine k and s for each layer, k_v for the crossflow layers, the nature of the outer boundary, and if there is a no-flow outer boundary, what is r_ej.
3. A two-rate flow test was proposed.
   • Flow (inject into) the well at a constant rate for an extended period of time.
   • Run a combination of flow rate and pressure survey versus depth before the next step.
   • Change the surface rate to about one-half that of the initial rate and record pressure and flow rate versus depth and time after the rate change.
4. Let q be the first constant flow rate (STB/D), Dq is the change in the surface flow rate (STB/D), t₁ is the time at which the rate change is made, measured from the instant of producing/injecting into the well (hr):

   

5. The early transient flow period resembles that for a homogeneous reservoir. The semilog plot of DP = P_i - P_wf versus t should be a straight line with slope m and can be determined conventionally. It is also possible to calculate the derivative DP' and plot this versus Dt (log-log). Noise free data are required.

   

6. The net kh changes with time because of charging of the high permeability layers.
7. For a complete interpretation, it has been recommended that six different calculations be performed for each Dt (More details are available.).
8. Determining the boundary curves requires the type curves generated by Ehlig-Economides and Joseph (1987).
9. To determine permeability and skin for each layer, plot DP/Dq_j versusDt (semilog).

   

10. From the slope of the straight line, m_qj, determine:

    

Consider a case where m = 1 cP, B = 1.2 RB/STB, C_t = 2.1 x 10^-5 psi^-1) [refer to Figure 3]. The wellbore radius is 4 inches and there is a no-flow boundary at 500 feet. This is a case for a wellbore flowing at 500 bbl/D, followed by 200 B/D for another 200 hours (EXACTLY ANALAGOUS CALCULATIONS CAN BE DONE FOR INJECTION BUT YOU GIVE THE RATE A NEGATIVE SIGN).

Figure 3.

Schematic for an example with in-reservoir crossflow.

The properties of the layers and zones (Figure 3) are shown below.

The rate and pressure behaviors are shown in Figures 4 and 5.

Figure 4.

Flow distribution in each layer when there is in-reservoir crossflow.

Figure 5.

Pressure variation for a situation where there is in-reservoir crossflow. The derivative of the pressure is also shown. Derivatives are commonly used in pressure transient analysis to accentuate trends.

What do you see?

• During the infinite-acting radial time period, the layer flow rate transients approach the fraction of the total flow rate equal to the layer permeability-thickness fraction.
• In early time, layer flow rate transients are sensitive to skin and layer permeability and in later time to formation crossflow effects.
• Although not shown here, unequal layer skins cause an apparent flattening of the derivative, which does not correspond to the same semilog slope as, was found for the cases with equal layer skins until very late time. Generally, boundary effects can occur before the correct semilog slope is evident. Thus conventional semilog analysis should be used with caution for determination of the total permeability-thickness product.
• In early time, layer flow rate transients are sensitive to skin and layer permeability and in later time to formation crossflow effects.

Consider a case where m = 1 cP, B = 1.2 RB/STB, C_t = 2.1 x 10^-5 psi^-1) [refer to Figure 6]. The wellbore radius is 4 inches and there is a no-flow boundary at 500 feet. This is a case for a wellbore flowing at 500 bbl/D, followed by 200 B/D for another 200 hours (EXACTLY ANALAGOUS CALCULATIONS CAN BE DONE FOR INJECTION BUT YOU GIVE THE RATE A NEGATIVE SIGN).

Figure 6.

Schematic for an example with no crossflow in the reservoir.

The properties of the layers and zones (Figure 6) are shown below. Notice that the vertical permeability (k_z is zero.

The rate and pressure behaviors are shown in Figures 7 and 8.

Figure 7.

Flow distribution in each layer when there is NO in-reservoir crossflow.

Figure 8.

Pressure variation for a situation where there is NO in-reservoir crossflow. The derivative of the pressure is also shown. Derivatives are commonly used in pressure transient analysis to accentuate trends.

What do you see?

• Early time behavior (in this example with no crossflow) is similar to the previous case (with in-reservoir crossflow) but late time behavior is completely different.
• Although the pressure behavior indicates that the system has not yet reached pseudo-steady state, the rate transients have nearly reached the porosity-thickness fraction. Wellbore crossflow usually results when the porosity-thickness for a given zone is significantly different from its permeability-thickness (e.g. Zone 2 in this example).
• Notice that wellbore crossflow is not evident after the rate change for the previous example but is dramatic in this case.

Consider a case where m = 1 cP, B = 1.2 RB/STB, C_t = 2.1 x 10^-5 psi^-1) [refer to Figure 6]. The wellbore radius is 4 inches and there is a no-flow boundary at 500 feet. This is a case for a wellbore flowing at 500 bbl/D, followed by 200 B/D for another 200 hours. Synthetic data were used.

This is a five layer case. The pressure-rate history for the five zones is shown below. NOTE THAT THE CALCULATIONS THAT FOLLOW ARE VERY SIMPLIFIED - FOR DEMONSTRATION PURPOSES ONLY - YOU SHOULD READ THE REFERENCE AND CONSULT WITH YOUR PTA SPECIALIST.

The variation in bottomhole pressure versus time (it is a flowing situation but the same concepts apply to injection) is shown in Figure 9 (Cartesian and semilog).

Figure 9.

The variation of measured bottomhole pressure with time during the test. The early time linear behavior allows for estimation of the total permeability-thickness product.

The semilog slope is 11.2 psi/log cycle and the early transient flow period is a straight line on a semilog plot. These are synthetic data and the basic reservoir properties are known in advance. The average kh is:

The actual value is 10,000 md-ft.

You can then evaluate characteristics of individual layers. An approximation is shown below for illustrative purposes only (refer to the original paper for more detailed treatment and consideration of boundary conditions, as well as type curve generation and rate time convolution). The solution shown here involved plotting the pressure difference normalized by the rate difference against the time. The normalized data are shown below and Figure 10 is a plot of rate normalized pressure versus time for Layer 1.

Figure 10.

Semilog plot of rate normalized pressure versus time data for Layer 1. Some early time data is interpretable using conventional methods.

The slope m_q1 is 0.1 psi/STB/D. The permeability and the skin are:

The actual values are k = 200 md and zero skin for this layer.