The Modified Muskat Plot Method for Interference Interpretation: Cased study for Lower Oligocene reservoir, offshore Viet Nam

Le Minh Vu

The heterogeneity is a major factor affecting oil recovery efficiency, especially in marginal fields. This heterogeneity is expressed through the sand connection and the compartment. The producers of this object often have a high-pressure decline. Assessing the degree of connection between blocks through interference is necessary. This result will help to optimize the development plan to achieve maximum oil recovery.

In this article, the author will synthesize the design process and interference analysis. This process has been developed and applied practically at X field, the lower Oligocene reservoir. The results of the evaluation are based on dynamic data.  An assessment of the fault seal capacity is beyond this study.

The Lower Oligocene reservoir belongs to X Field, offshore Vietnam. This is a saturated oil reservoir which is a thin oil rim and a gas cap on the top. The results of the interfering evaluation have indicated that the reservoir is divided by fractures. The level of connection between wells X-5P vs X-9P and between X-3P vs X-10P is very poor. There are signs of interference between well X-9P vs X-7P and between X-5P vs X-10P. Muskat graphing method helps interference evaluation during the well shut-in. The drawback of the method is affected strongly by the noise. A justification of muskat graphs means not only simpler, easier to identify interference phenomenon but also help to apply in the drawdown stage. A justification of muskat graphs applied during the drawdown stage helped to minimize the loss of oil production.

Keywords: Interference test, well test, Muskat plot

1. Introduction

X Lower Oligocene (hereby named by X-OLI) reservoir was discovered from 3 exploration wells: X-1X, X-2X, and X-3X. Currently, there are 5 additional development wells are producing through the reservoir including X-3P, X-5P, X-7P, X-9P, and X-10P. The location of these wells is shown in Figure 1:

 

Figure 1: Location of development wells in X Lower Oligocene reservoir.

The X Lower Oligocene reservoir was started production on the 6th June 2014. Five producers have been drilled in this reservoir, and the highest oil production rate reached 5120 stb/day in 2015. Cumulative oil production as of 30th June 2019 of the Lower Oligocene reservoir was 4.91 MMstb, cumulative gas volume production about 9.98 bscf and cumulative water about 0.18 MMstb.

The lower Oligocene reservoir is currently producing with oil rate of about 2195 stb/day and 4 MMscf/day from for producers consist of X-2P, X-7P, X-9P, and X-10P.  After five years of production, the average reservoir pressure is currently 2500 psi. The high depletion of reservoir pressure leads to expansion rapidly of gas cap and gas release from oil breakthrough to producers only in a short time of production X-OLI reservoir has a large gas cap and is divided by some faults. There were pressure communication evaluations between blocks/compartments. However, current methods only show the possible interference. Evaluating the degree of pressure communication between blocks through interference is needed to carry out. The evaluation results will assist the operator to make an optimal production plan.

 2. Interference Test design

Interference test design is a proper challenge for a reservoir engineer. A reservoir engineer has to design a test simulation on the model based on the previous well test results. The pairs of wells to be evaluated are pre-selected.  Each pair of wells will include a well as the observation well (shut-in) and other wells as the active well (change the production regime). Difficulty in the design and evaluation of interference is shut in the duration of the observation wells to achieve both technical objectives and also minimizing loss of production.

 
Figure 2: Interference test design between X-5P and X-9P

Figure 2 is an illustration of the interference test design between X-5P and X-9P. Based on the well test model, the duration has to be up to 7 days to confirm if there is interference. The long shut-in time will affect the production. The remaining pairs of wells are also designed and evaluated for similar interference duration. Each case is considered some advantages and disadvantages to minimize production loss and still achieve the objective of interference evaluation. Table 1 summarizes the advantages/disadvantages of each case.

Table 1: Advantages/disadvantages of each interference option

Case	Advantages	Disadvantages	Loss of production
1. •   Observation well: X-3P •   Active wells: X-9P, X-7P, X-10P, X-5P	•    Minimize loss of production	•    Can not observe interference X-5P/X-9P (If have).	0.6 Mstb
2. •   Observation wells: X-9P, X-7P, X-10P •   Active wells: X-3P, X-5P	•    Enough gas for operation (fuel, gas lift)	•    High loss of production. •   Can not have longer shut-in duration to observe interference at X-5P.	24.7 Mstb
3. •   Observation wells: X-5P (7days),  X-10P (1day) •   Active wells: X-9P, X-7P	•   Canobserve interference X-5P/X-9P (If have). •    Enough gas for operation (fuel, gas lift) •    Can observe interference X-10XP/X-3P (If have).	•   Can not have longer shut-in duration to observe interference at X-5P.	6.7 Mstb

After evaluating the advantages & disadvantages of each option, Option 3 was selected. This option will shut in X-5P and X-10P wells to observe in X-9P, X-7P, and X-3P.

3. Preliminary evaluation of the interference test

Figure 3:  X-7P Build up Test Interpretation

Figure 4:  X-9P Build up Test Interpretation

Quick check pressure transient test shows the influence of the boundaries. That proves that the X-OLI reservoir is divided into compartments. However, the degree of communications is needed to evaluate by interference test.

4. Interference test analysis

4.1 Muskat plot method

The Muskat plot method has been commonly used for oil and gas reservoirs in the world.

This method applies to pressure build-up. The overview of Muskat equations are described as follows:

With square reservoir model, wells at the center; a, b are calculated as follows:

The coefficient a&b corresponds to the square reservoir model. Different reservoir models will apply different coefficients. Take the derivative for equation (1), get:

Equation (1) can be re-written as follows:

Combine equations (4) and (5), get:

Solve equation (6) to calculate Pws, get:

Instead of b from equation (3) into (7), get:

Equation (7) is used to estimate average reservoir pressure by graph method. In which, plotting Pws and (dPws / d∆t) will have a linear relation (straight line) with a slope of 1 / b and intersect with vertical axis is determined as the average reservoir pressure. Figure 6 illustration of the Muskat plot for the C-I-18 well (A-096) in the Arun reservoir (Indonesia).

 

Figure 5: Muskat plot

In the pressure Build up of observation, wells include the transition period, the boundary effect, an interference area. In the boundary effect, the pressure Build up is on the straight side (also called "Muskat-line"). One of the applications from the Muskat plot is to interpret average reservoir pressure (extrapolate from the Muskat line).

4.3 Muskat plot into pressure build-up test

Applying Muskat plot into pressure Build up for X-7P, X-9P, X-10P and X-5P. The result shows that X-7P, X-9P, and X-10P can not see clearly the signal being interfered with. However, at the X-5P it is very clearly affected (well is influencing is impossible to determine).

4.4 Muskat plot into drawdown test

Limitations of the Muskat plot method when applied for pressure Build up due to very noisy data. Therefore, it is very difficult to determine whether interfere or not. One of the requirements is how to determine interference during the production/drawdown test (not shut-in wells). The results of applying the Muskat plot method for three wells in production are shown below.

Result of utilizing Muskat plot for production at X-7P, X-9P and X-10P (X-5P is still shut-in). There are indications of interference at all three wells. However, because the signal disperses at all stages, it is difficult to evaluate interference.

obviously, the plot also shows all three-stage like the pressure build-up (transition region, boundary effect, and interference area (if have)). The signal also reveals at 3 wells. However, it is very difficult to determine which pair of wells are interfering, which well is being affected or absorbing. Therefore, modifying the Muskat plot is necessary.

4.5 Modified Muskat plot method

Realizing both during the pressure build-up and drawdown, there are 3 stages: transitions, boundary effects, and interference area (if have).

 From equation (7), the re-write the following:

The author modified the plot as below:

-    
 It means  show that observation well is making influence (absorbing). Otherwise, the well is affected. The duration of each stage is easily determined on the time axis.

 
Figure 13: The modified Muskat Plot

 The effect of the Muskat plot method is very useful:

-           -Applicable for pressure drawdown and Build up test.

-           -Reducing maximum noise data through derivatives.

-           -Determine easily the interference area (if have).

     -Determine the transition zone time (Tt) to calculate permeability and radius of -investigation.

-          -Determine the affected interfering time (Ti) to define which pair of wells are interfering.

-            -Evaluate the observation well is being affected or absorbing.

 Apply the modified Muskat plot method for X-OLI reservoir

 

Based on starting of interference time (Ti), the X-5P and X-10P wells are interfering with each other. Inside, X-10P acts as the influencing well (the positive derivative) while the X-5P well is affected (the negative derivative). The same similar with identifying well pairs X-9P and X-7P with poor interference (small amplitude).

Based on the modified Muskat plot, the effect of the noisy signal has reduced significantly. Identify easily pairs of wells that are interfering through Ti interference time. Define easily wells playing a role in influencing or are affected by the deflection of the derivative line. And the degree of interference also reveals through the deviation of the derivative line.

5. Conclusion

-       Evaluate interference among production wells has an important significance for the next field development. Interference evaluation indicates the degree of pressure communication among wells as well as different compartments. In addition, interference also assists to confirm the block capacity analysis of split faults.

-       Designing and evaluating interference has been designed optimally for the margin field. This process has helped not only minimize the loss of production but also still ensure the maximum data is needed to evaluate. It has been applied successfully at X field.

-   Modified Muskat Method is a simple and effective method to evaluate interference. However, this method is restricted in determining the interference of the affected object due to noisy data.

-    The Modified Muskat Method method has solved limitations of the traditional Muskat method and is easily applied for both pressure build-up and products based on the interference interpretation, it is shown that there is very poor communication between the well X-5P and X-9P. The Muskat plot showed indication of interference between X-10P and X-5P (strong); X-9P and X-7P (weak).

References

1.    1.T.Marhaendrajana, Texas A&M U., and N.J.Kaczorowski, Mobil Oil (Indonesia),
and T.A.Blasingame, Texas A&M University. Analysis and Interpretation of Well
Test Performance at Arun Field, Indonesia. SPE 56487. SPE Annual Technical
Conference and Exhibition. 6 October 1999.

2.   2. Taufan Marhaendrajenda. Modeling and Analysis of Flow Behaviour in Single and Multiwell Bounded Reservoir. Thesis. 2000. Texas A&M University.