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Abstract Sometimes, a simple and quick material balance method is preferred to using a numerical simulation model. This preference can be justified when preparing the development plan and production optimization for a collection of hydrocarbon reservoirs (lean and rich gas condensate, oil rim and gas cap), some connected to an aquifer, and the reservoirs cannot be modelled separately. This situation can occur when multiple gas reservoirs are needed to be developed in order to provide enough gas for a particular project. A significant drawback of this modelling approach is the simplification introduced when a single tank model (Material balance method) is being used instead of a fine grid simulation model. The material balance method assumes every well contacts all hydrocarbons and that geological heterogeneity is not a factor in recovery. It is necessary to know how reliable are final gas and condensate recovery factors and gas, condensate and water production profiles predicted by a material balance model. In this study, we address all these uncertainties. A sensitivity analysis has been carried out on different aquifer strengths, gas condensate richness, and reservoir heterogeneity which are related to the real and field data set. Introduction of a generic method for selecting the important input data to the material balance model (relative permeabilities and well productivities) in order to have reliable results is the target of this study. The material balance results are compared to a fine grid simulation. It is observed that using the introduced method, the effect of reservoir heterogeneity and aquifer influx on final gas recovery factor can be captured in a material balance model. Introduction Predictions of oil and gas reservoirs behavior and hydrocarbon production profiles from them are crucial steps for planning fields development. Although it is believed numerical simulation (3 dimensional models) gives more reliable results than a material balance (zero dimensions) evaluation, a

material balance method can be utilized in an acceptable range of uncertainties. Material balance has been used as a reliable tool for calculating hydrocarbon volume initial in place and reservoir drive mechanism and prediction production profile1, 2. Sometimes material balance can be used for narrowing down uncertainties around in place volume and compartmentalization and presence of faults before simulation3. Recent years have witnessed efforts for improving the material balance method4, 5. Also, some studies have shown that material balance can be utilized for performance prediction of gas condensate reservoirs6. However, it is still important to understand whether field performance, as predicted by a tank model, is reliable enough for making a financial investment decision. In this paper, reservoir performance and production profiles predicted by material balance and 3D simulation model are compared with each other. It is explained how the tank model can capture the effect of aquifer and condensate drop-out on reservoir performance if the model is tuned properly. Model construction and sensitivity analysis

1. Simulation model construction A heterogeneous 3D geological model that had been constructed in GOCAD was selected as the reservoir model. General characteristics of the model can be found in table 1.

Table 1: Grid model characteristic

As the main cause of difference between outcomes from the material balance and 3D simulation methods is the high level of heterogeneity in geological properties (e.g. Porosity, NTG, Permeability), the authors believe the selected geological model is an appropriate example for purpose of this research. Figure 1 shows the porosity distribution in the reservoir.

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Capturing Complex Dynamic Behaviour in a Material Balance Model Jalal Mazloom and Mike Tosdevin, SPE, Sasol Petroleum International, and Dominique Frizzell, Bill Foley, and Mike Sibley, SPE, Chevron

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Figure 1: Porosity distribution in the selected reservoir

The reservoir permeability maps were calculated using the correlation between porosity and permeability. This equation has been generated based on the available log and core data. It is our belief that the question about the capability of the material balance method to capture the effect of water encroachment and condensate drop-out around the well-bore on reservoir performance and the final recovery has not been answered yet. In order to investigate this issue, sensitivity analyses have been carried out on the aquifer strength and gas condensate richness. The aquifer permeability has been selected as the only representative of strength, other parameters such as areal extent of the aquifer were not considered in this study. Aquifer permeabilities of 1, 50, 500 md indicate very weak, moderate and strong aquifer respectively. In order to simulate fluid phase behavior in the reservoir, black oil tables were generated for lean and rich gas samples. Table 2 shows the condensate gas ratio and the dew point for two fluid samples that were used as the lean and rich gases in this study.

Table 2: Fluid properties of Rich and Lean samples CGR(Stb/MMscf) Dew Point(Psi)

Lean Sample 15 3300Rich Sample 99 3818

The gas water contact of 7757ft and the initial pressure of 4200 psi were considered in model. The calculated initial gas and the vaporized condensate-in-place using two different fluid samples can be observed in table 3.

Table 3: Gas and vaporized condensate in places Gas in place(Bscf) Vaporized condensate in place(MMstb)

Lean samle 419.2 6.2Rich Sample 419.5 41.3

The relative permeability curves in figure 2 were used in model.

Gas, Condensate & Water Relative Permeability

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1Phase Saturation

Rel

ativ

e Pe

rmea

bilit

y

KrwKroKrg

Figure 2: Phases relative permeability curves

The reservoir produces gas through 9 wells. To prevent water coning, wells have been perforated in the top 21 layers. The well-head pressure of 700 psi is the only constraint in the model. A vertical well trajectory was used to generate the vertical lift curves and it has been assumed that the tubing extends from top of the reservoir to the surface. The software PROSPERTM (Petroleum Experts product) was utilized for generating VLP curves. According to the different fluid models and aquifer strength, 6 simulation models were generated at the end (Table 4).

Table 4: Simulation model cases Simulation model no. Description

Case1 Lean sample, strong aquifer Case2 Lean sample, moderate aquifer Case3 Lean sample, very weak aquifer Case4 Rich sample, strong aquifer Case5 Rich sample, moderate aquifer Case6 Rich sample, very weak aquifer

2. Material balance model construction

MBALTM (Petroleum Experts product) was utilized to generate and run zero dimensional models. The gas-in-place, initial volume average pressure, fluid properties in tank and simulation models are identical. Same as for the 3D models, Carter-Tracy aquifers are connected to the tanks and aquifer permeability is considered as strength criteria. Number of wells and VLP tables that have been used in 3D models were duplicated in the material balance model. Two sets of well productivities and Darcy factors have been calculated for wells in the material balance model. In the first method, similar productivity was calculated for all wells using average permeability and thickness of whole reservoir. In the second method, well productivity for each well was estimated based on the average reservoir permeability and thickness around each well. Therefore 12 tank models were generated in MBAL (Table-5). The results of the material balance models are compared with results of the corresponding simulation models in the result section.

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Table 5:Tank model cases

Results and recommendations 1. Results and discussion

In order to calculate the final gas and condensate recovery factors, two cut-offs were implemented on the gas and condensate production profiles.

1- Date cutoff: production profiles up to 6.5 years were used to calculate recovery factors

2- Rate cutoff: 20 MMSCF/d was considered as the minimum acceptable gas production rate from field.

Because the reservoir heterogeneities have been captured at a fine scale and because the reservoir fluid properties and relative permeabilities in the model initialization are coming from field data, results from the simulation model are considered to be representative of real field performance. Here we compare results from the material balance model with results from simulation to find out under what circumstances a single tank model can predict the field performance. Answers are given for predicting gas and condensate recovery and the impact of aquifer influx in separate sections.

1- Is a single tank model able to capture the effect of reservoir heterogeneity and condensate drop-out on field performance?

Figures 3&4 demonstrate the predicted final gas and condensate recoveries using the material balance method in the different cases that have been defined in table 5. As can be observed, two different methods of well productivity estimation (well productivities calculated based on the global average K&H and local average K&H around each well) generate very similar results. For example, recovery factors of cases 1a&b or cases 2a&b are close to each other. Therefore, for comparing the results of tank and simulation model outcomes, only one of a or b cases will be selected.

Predicted Gas Recovery Factors Using Single Tank Method

74.8 73.8 74.8 73.8 74.6 73.8 70.5 70 70.5 70 70.0 70

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Figure 3: Gas recovery factors predicted by tank model

Predicted Condensate Recovery Factors Using Single Tank Method

37.8 36.8 36.8 37.4 37.0 36.4

31.3 31.5 31.4 31.4 30.8 30.9

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Figure 4: Condensate recovery factors predicted by tank

model Figures 5 and 6 indicate the final gas and condensate recovery factors estimated using a 3D simulation model.

Predicted Gas Recovery Factors by Simulation Model

50.556.1

68.1

37.842.2

54.7

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Figure 5: Final recovery factors predicted by simulation

model

Predicted Condensate Recovery Factors by Simulation Model

44.4

39.736.9 36.1 35.6

33.3

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Figure 6: Condensate recovery factors predicted by tank

model By comparing the results in figure 5 and figure 3, it can be concluded that the material balance model, significantly overestimates the gas recovery factor. This is due to the lack of capability for capturing the reservoir heterogeneity in the single tank model. In the single tank model, it is assumed that the entire area in the reservoir is accessible by all the wells and this is the main reason for predicting a high gas recovery factor by this method. Also, as can be observed in figure 5, the final gas recovery factors for the lean gas fluid are bigger than same parameter in the rich fluid sample by a maximum of 120%. The well

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productivity impairment due to the liquid drop-out in area very close to the well-bore is the main reason for this fact. But in the single tank model (Figure 3), the maximum difference between the final gas recovery factors of lean and rich fluid sample is only 4% and therefore material balance method doesnt capture this effect. Contrary to the predicted gas recovery factors, the cumulative condensate production has been underestimated slightly in the material balance model. This is again due to using only one grid block (Zero dimensional method) in the tank model for the whole volume of reservoir. In reality, as it has been captured in 3D simulation, the condensate drop-out happens only in a small volume around well-bore as long as the average reservoir pressure is above dew point. But in the tank model, liquid-dropout and condensate loss happens in the entire reservoir as soon as the average reservoir pressure drops below the dew point. Therefore, the answer to the question at the beginning of this section question is:

- Material Balance overestimates the gas recovery factor and predicts slightly less condensate production than 3D simulation model.

2- Does a single tank model have the capability of predicting the effect of aquifer influx on the gas condensate reservoir performance?

Water encroachment reduces the gas recovery factor by leaving gas behind a water front propagated at a higher pressure than abandonment pressure under volumetric behaviour7,8,9. The residual gas saturation controls the volume of gas trapped in that section of the reservoir that water encroachment has happened. The volume and location of the residual gas are controlled by the distribution of the petrophysical properties. More heterogeneity causes more residual gas in reservoir because of bypassing of lower permeability rock. The results of simulation models in figure 5 are consistent with this observation. As observed in figure 5, the gas recovery factors for the rich and lean gas condensate fluid are reduced by an increase in aquifer strength. But this fact is not seen in the material balance results. Figure5 shows that all the constructed tank models do not reflect the effect of the aquifer strength and the water encroachment on the reservoir performance. Not including reservoir heterogeneity/geometry in the tank model is the main source of this deficiency. It was mentioned that the volume of the residual gas is controlled by the petrophysical distribution and because in the single tank model there is no distribution of the reservoir properties, this control is missing. Another interesting observation that we came across during this research was the effect of pressure support by the aquifer on condensate recovery. As was discussed, the aquifer has a negative effect on gas recovery. But as it can be seen in figure 6, the condensate recovery increased slightly due to the provided pressure support by water encroachment. This situation causes less liquid drop-out and condensate loss in the reservoir and more condensate production at the surface. So, two main conclusions for this section are:

- Material balance method does not reflect the effect of an aquifer on the gas recovery factors.

- In the simulation model, due to the pressure support from the aquifer and less condensate drop-out inside reservoir, the condensate production increases with a stronger aquifer.

2. Multiple Tanks Material Balance

As was mentioned earlier, the lack of capability in the single tank model for capturing the reservoir heterogeneity/geometry is the main reason for the difference between the material balance and simulation models results. In the material balance model, it is assumed that the entire gas in-place in the model is accessible by all wells according to their well productivities. Also for the same reason (no heterogeneity in single tank model), it is not possible to predict an increase in the residual gas saturation and the reduction in the gas recovery factor due to the water influx in the single tank model. In order to have a better prediction by material balance method a multiple tanks model is suggested. The procedures of constructing of this model are as below:

1- The number of tanks in the multiple tanks model should be equal to the number of wells in 3D simulation model. The well productivity for each well has been calculated according to the average reservoir thickness and permeability around well. As was mentioned earlier, in the single tank model it is assumed that the entire gas in reservoir is accessible by all wells. But in reality, only gas in the drainage area of each well can be produced according to the well productivity. In order to capture this fact in the multiple tanks model, the gas-in-place for each tank should be calculated based on distribution of gas volume vs. well productivity or K*h. So, the gas-in-place in each tank is defined using:

a. In the geological model, all the grid blocks

should be divided to the different districts according to their permeability and formation thickness. The average permeability and thickness at each district is equal to the average K&H that were used for well productivity calculation in the tank model.

b. In the geological model, the amount of gas in place that is located at each range of K&H should be defined. In this step we identify the distribution of gas-in-place vs. K*H.

c. These numbers should be used as gas-in-

place numbers for each tank in the multiple tanks model.

2- The residual gas saturation at each tank should be

defined according to the average reservoir porosity and the equation below (introduced equation at reference 9).

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5473.0*969.0 += Sgrm (1) This equation has been developed to be used in 3D simulation models, but since by using the multiple tanks we are trying to approach a heterogeneous simulation model from a single tank model, this assumption is valid to some extent. The implementation of this recommended method is given in an example below. Table 6 shows the average reservoir permeability and thickness that have been used for calculation of well productivities in the tank model. Table6: The average reservoir permeability and thickness

around each well Well No. K*H(md.m)

1&2 343 304 285 256 217 178 139 8

The percentage of the total gas in place which is located at the different range of permeability and thickness can be observed in table 7.

Table7: Percentage of the total gas in place which are located at different ranges of kh

Range of KH(md.m) Percentage of gas in place>34 50.0%

34>Kh>30 12.8%30>Kh>28 4.3%28>Kh>25 5.3%25>Kh>21 7.4%21>Kh>17 4.3%17>Kh>13 3.2%13>Kh>8 4.5%

8>Kh 8.3% Figure 7 show the configuration for the single tank model and figure 8 demonstrates the same model after implementing the suggested procedures.

Figure 7: Single tank model

In figure 7, all wells are connected to only one tank with gas in place of 419 Bscf. The residual gas saturation in the single tank model is coming from the relative permeability curves data that were showed in section 2. But in figure 8, each well

is connected to a different tank and in-place in each tank has been calculated by multiplying percentage number in table 7 and total gas-in-place. The residual gas saturation in each tank has been estimated using equation 1.

Figure 8: Multiple tank model with different gas in place

in each tank Figure 9 indicates the final gas recovery factors for cases that were defined in table 6. These numbers have been estimated using proposed method in this paper.

Predicted Gas Recovery Factors Using Proposed Method

60.0 62.065.0

55.0 57.060.0

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Case1 Case2 Case3 Case4 Case5 Case6

Fina

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Figure 9: The final recovery factors calculated using

proposed method As can be observed, the final recovery factors in figure 9 are relatively close to the numbers in figure 3 that have been calculated using 3D simulation model. Particularly, in the very weak aquifer cases (Case 3&6), there is a good consistency between outcomes of the 3D simulation and the proposed method. Also note that in Case3 the material balance approach actually under predicts recovery factor by 3%. Therefore, it can be concluded that applying the proposed method, the reservoir heterogeneity effect has been captured better than single tank model approach. Also by increasing aquifer strength, the final recovery factor is reduced; this trend was not captured in the single tank method but an improvement achieved using the multiple tanks approach. Additional sources of error not accounted for by this multi tank model approach include well interference due to the actual level of communications in the reservoir and any inaccessible pore volume thats not drained by the planned wells.

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Conclusions The effect of reservoir heterogeneity, water encroachment and condensate drop-out around well-bore on the gas condensate reservoir performance was studied by using a fine scale heterogeneous reservoir model. Using the geological model, the recovery factors of gas and condensate for lean and rich gas condensate reservoir connected to a strong or very weak aquifer were calculated. Single tank models identical to the simulation models were constructed and results of the material balance model were compared with 3D simulation model outcomes. Main results of this investigation are:

o The single tank method overestimates considerably the gas recovery factor. This is due to the inability for capturing the reservoir heterogeneity in the single tank model.

o The cumulative condensate production is

underestimated slightly in the material balance model. This is due to using only one grid block (Zero dimensional method) in the tank model for the whole volume of reservoir. In reality, as it has been captured in 3D simulation, the condensate drop-out happens only in a small volume around well-bore as long as the average reservoir pressure is above dew point. But in the tank model, liquid-dropout and condensate loss happens in the entire reservoir as soon as average reservoir pressure drops below the dew point.

o Material balance method does not reflect the

effect of the aquifer on the gas recovery factors.

o In the simulation model, due to the pressure support from the aquifer and less condensate drop-out inside the reservoir, condensate production is increased by a stronger aquifer.

o Using the proposed multiple tanks method, the

effect of heterogeneity/geometry is captured in a reasonable range

o In the multiple tanks method, by increasing

aquifer strength final recovery factor decreases. This trend was not captured in the single tank method. But it seems this method still doesn't reflect the aquifer effect on gas recovery factor perfectly.

o 3D simulation models are useful to help verify the

accuracy of material balance models and can be used to help fine tune then in order to account for the effects of reservoir heterogeneity.

Nomenclatures

:X Average grid block size in X direction :Y Average grid block size in Y direction :Z Average grid block size in Z direction

nX: Number of grid blocks in X direction

nY: Number of grid blocks in Y direction nZ: Number of layers in the grid model CGR: Condensate gas ratio

Ave : Average porosity :Sgrm Residual gas saturation

AveK : Average permeability :h Formation thickness

VFP: Vertical flow performance Acknowledgments The authors wish to thank the management of Sasol Chevron, Chevron, and Sasol Petroleum International for permission to write this paper. Some of the ideas explained in this research came from helpful discussion with Duke Snyder. The authors wish to thank their colleagues particularly Anand Rao, at Sasol Petroleum International; Rachel Preece, Shah Kabir and Andrew Harding at Chevron for their technical support to conduct this research. References 1. Farough, Ali, S.M., Nielsen, R.F., 1970. The Material

Balance Approach vs reservoir Simulation as an aid to Understanding Reservoir Mechanics. Paper SPE 3080, presented at the 45th annual fall meeting of SPE, Houston, Tex, October 47.

2. Merchant, A.R., Arnold, M.D., 1973. A Technique for Improving Material balance Accuracy in Reservoir simulation Model. Paper SPE 4548, presented at the 48th annual fall meeting of SPE, Las Vegas, Nev., October.

3. Eugene, E., Dresda, S., Monico, C., 2004. Use of Material Balance to enhance 3D Reservoir Simulation: A Case Study. Paper SPE 90362, presented at the SPE Annual Technical Conference, Houston, Tex., 26-29 September.

4. Pletcher, J.L., 2000. Improvements to Reservoir Material-Balance Methods. Paper SPE 75354, presented at the SPE Annual Technical Conference, Dallas, Tex., 1-4 October.

5. Yildiz, T., Khosravi, A., 2006. An Analytical Bottom Water Drive Aquifer Model for Material Balance analysis. Paper SPE 103283, presented at the SPE Annual Technical Conference, Sanantonio, Tex., 24-27 September.

6. Zeidouni, M., Movazi, M., Pourghasam, B.,2006. Performance Prediction of a Rich Gas Condensate Reservoir through Material balance and PVT Behavior Case Study. Paper SPE 99830, presented at the SPE Gas Technology Symposium, Calgary, Alberta, 15-17 May.

7. Hower, T.L., Jones, R.E., 1991. Prediction Recovery of Gas Reservoirs under Water Drive Conditions. Paper SPE 22937, presented at the SPE 66th annual technical conference, Dallas, Tex., October.

8. Cronquiest, C.,1973. Effect of Permeability Variation and Production Rate on Recovery from Partial Water Drive Gas Reservoirs. Paper SPE 4635, presented at the SPE 48th annual fall meeting, Las Vegas, Nev., October.

9. Holtz, M.H., 2002. Residual Gas Saturation to Aquifer Influx: A Calculation Method for 3-D Reservoir Model construction. Paper SPE 75502, presented at the SPE Gas Technology Symposium, Calgary, Alberta, 15-17 May.