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Petroleum & Petrochemical Engineering Journal Research Article 22 min read

Advancing Reservoir Performance Optimization through User-Friendly Excel VBA Software Development

Ebere FO*, Ekwueme H, Onwuama CN, Adu-Mensah D, Nkok L and Josephs R
* Corresponding author
ISSN: 2578-4846  10.23880/ppej-16000374  Received: November 30, 2023  Published: Janaury 23, 2024
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 47 references
 19 figures
 13 tables
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Keywords
Reservoir performance Excel VBA Oil and gas production Material balance Simulation
Abstract

This study addresses the pressing demand for streamlined field performance analysis within oil and natural gas development, which currently necessitates substantial expertise and time investment. The principal aim involves developing a user-friendly software tool dedicated to optimizing reservoir rendition. Leveraging the Havlena and Odeh material balance straight line equation form, this tool integrates a zero-dimensional reservoir model with Decline Curve Analysis. The implementation of this user-friendly software enables achievable material balance optimization by aligning cumulative produced fluid with historical production data, akin to the widely acknowledged concept of history matching in material balance analysis. This accomplishment not only facilitates further endeavors like pressure simulation and forecasting but also augments the comprehension of reservoir dynamics. The analysis incorporated three datasets: one modeled from L.P. Dake's textbook and two drawn from real-life reservoirs in the Niger Delta. Assessment of estimated water influx and cumulative oil production indicated minimal discrepancies between Np Real and Np model for these reservoirs. Consequently, material balance history matching for these reservoirs seems feasible. Achieving reservoir rendition optimization involved a Microsoft Excel VBA code consisting of two hundred and thirty-five (235) lines, meticulously designed to replicate MBAL functionality. The software demonstrated congruent outcomes with MBAL, affirming its reliability for history matching and enhancing reservoir performance. We strongly advocate the utilization of this software for optimizing reservoir performance across diverse global regions. Its capacity to streamline field analysis could significantly benefit the oil and natural gas industry.

Introduction

Forecasting the rendition of reservoirs support engineers in reserve estimation and develop a plan which requires a comprehensive knowledge of the features of the reservoir and optimization of production, to also create a model that will show the physical processes taking place in reservoirs [1, 2, 3]. In oil and gas reservoir development, projected field performance is the information required by oilfield workers that are into the design, risk, and decision-making process. Field performance analysis can require a substantial number of skills. Implementing the appropriate modeling approach is therefore the key to analyzing a field’s performance efficiently [4, 5]. Sophisticated and detailed models rely on the set of fluid and reservoir data that are available. Prediction of a field’s performance has to do with calculations of pressures, flow rates, cumulative productions, and expected production times using the available reservoir, production network, and production constraint data [6, 7, 8]. Every reservoir is made up of a unique arrangement of geometric form, rock properties, fluid properties and primary drive mechanisms. Though no two reservoirs are similar, they are categorized according to the primary recovery mechanism which they produce with. The performance characteristics of every producing mechanism are studied based on Decline rate of Pressure, Gas-oil ratio, Water production and Ultimate recovery [9, 10, 11]. The physical process behind material balance was reviewed and validated first by Schilthuis [9]. Odeh, et al. [12] put the equation into linear form making it simpler to understand and use. Plots were created considering the drive mechanism supporting the reservoir. Once a horizontal straight line is obtained in the plots, it means a purely depletion drive influence. If it deviates, then it’s not performing as anticipated which automatically suggests that other drive mechanisms effects are present. Coats, et al. [13] worked on the prediction of gas well performance. They investigated the gas well performance by developing a numerical model. Three field applications were conducted considering the effects of various parameters. The gas well performance was forecasted [14, 15, 16]. Miranda, et al. [17] in their work used cumulative reservoir withdrawals in place of the original fluid in place. DeSorcy [18] estimated the accuracy of each of the parameters. Galas [19] investigated an automated history matching system for the method by evaluating non- linear regression function and established that the boundary of matching parameters should not be overlooked. Esor, et al. [5] and Amudo, et al. [15] considered the application and methodology of the MBAL tool in developing connected oil and gas volumes in place. Bui, et al. [4] carried out their work to investigate the mature Samarang field’s reservoir compartmentalization using material balance analysis. They investigated the relationship between relative permeability curves and their effectiveness on history matching using the workflow of material balance analysis. Baker, et al. [20] provided a workflow process in Eclipse simulator. Mazloom, et al. [21] assessed the MB prognosis results from the models of single- and multi-tank. They discovered that the multi-tank model results were better than that of the single-tank model. Garcia, et al. [22] evaluated a meaningful parameter that disturbs material balance computation. His work showed the reservoir pressure and PVT data affects the OOIP calculation. Tarek [23, 24] stated in his work that MBE is used by reservoir engineers for future rendition forecast by continuously showing ways to optimally produce hydrocarbons in situ. Adeboye, et al. [14] used an enhanced model to forecast reservoir rendition. They stated that the parameters that govern decline must be understood. Mike, et al. [25] studied how reservoir rendition of reservoir changed with time. They stated in their work that the MBE is a handy tool for quickly defining reservoir drives, possible fluid contact, fluid-in-place for reservoirs and prediction of reservoir performance with time. Okotie, et al. [10] developed software called REPAT forecast reservoir rendition. MBE, expansion of Tarners method were utilized to produce the software which put into consideration aquifer influx and time. They discovered that water drive and fluid expansion drive supported the reservoir’s performance. Yong [26] made a method that showed reservoir variety and field development method change on the rendition of a reservoir. The time consumed by the new method is shorter than that of the tine reservoir simulation. Written computer programs known as software, are employed in performing this analysis that involves complex mathematical models [10, 27, 28, 29]. Most of the commercial software is very expensive and as such extremely difficult for students and researchers to purchase. With sound understanding of the physics behind reservoir analysis coupled with good mathematical and programming skill, one can design a software that can perform like or even better than most commercial software, in agreement with this vision, I thought it wise to develop a software using Microsoft Excel VBA that can perform Material balance optimization analysis.

Predicting Reservoir Performance

Four methods are used in reservoir performance rendition. They include volumetric, Decline Curve Analysis, Reservoir simulation and Material balance methods [2, 3, 23, 24, 30, 31].

Volumetric

Volumetric technique deals with the calculation of reservoir rock volume, the hydrocarbon in place contained in that rock volume and that which can be recovered. Important considerations are Rock Volume, Elevation of fluid contacts, Petrophysical parameters such as porosity, permeability, and Recovery factor [32, 33].

Decline Curve Analysis

Historically, Arps’ observed that fluid production rate declines exponentially with time stimulated emergence and further development of decline curve analysis [34]. Many researchers Agarwal, et al. [35] and Fetkovich’s, et al. [36] contributed to the improvement and extension of this method applicability.

Reservoir Simulation

Reservoir simulation is based on the methodology put into a certain approach, where specific mathematical relationships describe ongoing physical processes in the reservoir Odeh [12]. These descriptions, i.e., models, define the engineering tasks that will be solved, and parameters used. By its nature, any methodology is developed considering specific assumptions, stipulations, simplifications, and solving methods, which further establishes opportunities, requirements, and constraints for the implementation of the specific method [37].

Material Balance

The Material Balance equation is the relationship that exists between the average reservoir pressure and reservoir performance [30, 38, 39] (Figure 1).

Figure 1: Material balance tank model assumption [2].
Click to enlarge
Figure 1: Material balance tank model assumption [2].

Generalized Material Balance Equation

Generalized material balance equation is:

$$ \text{Total underground withdrawal} = \text{oil produced} + \text{gas} $$

produced+ water produced.

$$ G a s p r o d u c e d, G _ {p} = \left(N _ {p} R _ {p} - N _ {p} R _ {s}\right) B _ {g} $$ $$ = N _ {p} \left(R _ {p} - R _ {s}\right) B _ {g} $$  Withdrawal = ( ) 0 p p p s g p w N B N R R B W B + − + The generalized material balance equation becomes:

        + − = − + − + − +             +   + + −   −  

B N B R R B N B B R R B mNB B

( ) ( )( ) g p p s g o oi si s g oi gi

0 1 (1) c s c NB m P W W B s Ä

( ) ( ) w wi f oi e p w wi

1 1

Predicting Reservoir Future Performance as a Function of Time

Prediction of future performance as a function of time is achieved by combining MBE with a fluid-flow equation and Darcy’s equation. Predicting the reservoir’s future performance is conducted in two phases [25]. Phase one predicts production of hydrocarbon cumulative as it links to the decline in reservoir performance. Phase two is relating reservoir performance with time.

Two kinds of reservoir with their prediction techniques considered are Under-saturated oil reservoir and Saturated oil reservoir.

Under-Saturated Oil Reservoir

Cumulative production prediction involves a straightforward determination. The MBE is:

$$ N = \frac {N _ {p} B _ {o}}{B _ {o i} C _ {e} \ddot {A} P} (2) $$

p o oi e Where; 1

$$ C _ {e} = \frac {1}{S _ {o}} \left[ S _ {o i} C _ {o} + S _ {w i} C _ {w} + C _ {f} \right] $$ $$ C _ {e} = \frac {B _ {o} - B _ {o i}}{B _ {o i} \ddot {\mathrm {A}} P} $$ o oi e oi From Equation (2), cumulative production will be derived for any given pressure decline as:

$$ N _ {p} = \frac {N C _ {e} B _ {o}}{B _ {o i}} \ddot {A} P \tag {3} $$

e o p oi

Saturated Oil Reservoir

The three techniques for predicting primary recovery performance are The Tarner’s technique, The technique of Muskata and The Tracy’s technique [40, 41, 42]. Material Balance Equation as a Linear Equation [12] Equate:

( ) p o p s g p w F N B R R B W B   = + − +     Production $$ E _ {o} = \left(B _ {o} - B _ {o i}\right) + \left(R _ {s i} - R _ {s}\right) B _ {g} $$

Oil + originally dissolved gas $$ = \left(\frac {B _ {g}}{B _ {g i}} - 1\right) B _ {o i} \Rightarrow 1 $$ B E B B

1 g g oi gi Free gas expansion $$ E _ {f, w} = B _ {o i} \left(C _ {w} S _ {w i} + C _ {f}\right) \ddot {A} P / \left(1 - S _ {w i}\right) $$

Connate water + rock $$ \therefore F = N \left[ E _ {o} + m E _ {g} + (1 + m) E _ {f, w} \right] + W _ {e} B _ {w} \tag {4} $$ Depletion Drive: A reservoir having no initial gas cap where m=0 and negligible influx of water, rock compressibility and connate water (We=0, Ef,w=0), the equation degrades to:

o F NE =  (Straight line) (5)

$$ F = N E _ {o} + W _ {e} \Rightarrow \frac {F}{E _ {o}} = N + \frac {W _ {e}}{E _ {o}} \tag {6} $$ e o e o o Water Drive: No initial gas-cap (m=0).

$$ F = N \left(E _ {o} + E _ {f, w}\right) + W _ {g} \tag {7} $$

But below bubble point, is negligible.

$$ \therefore F = N E _ {o} + W _ {e} \Rightarrow \frac {F}{E _ {0}} = N + \frac {w _ {e}}{E _ {o}} \tag {8} $$ e o e o

0 Gas-Cap Drive: No water drive, is negligible.

$$ \therefore F = N \left(E _ {o} + m E _ {g}\right) \Rightarrow \frac {F}{E _ {0}} = N + \frac {m N E _ {g}}{E _ {o}} \tag {9} $$ ( ) g o g o

0

Reservoir Drive Mechanisms

The drive mechanism is the energy responsible for transporting the hydrocarbon in the pore space of the reservoir to the wellbore. The common natural drive mechanism includes Depletion drive, Gas-cap drive, Water drive and Combination drive. Other drive mechanisms include Compaction drive, Imbibition and Gravity drainage drive [43, 44, 45] (Figure 2).

Figure 2: Reservoir drive mechanisms [45].
Click to enlarge
Figure 2: Reservoir drive mechanisms [45].

Reservoir Drive Indices

Each respective drive mechanism contributes to production. Therefore, reservoir Drive Index = individual production contribution total underground HC production [(B B ) (R R ) B ] s g oi si , [B (R R ) B ] o p s g N o Depletiondriven DDI N p − + − ∴ = + − (10) [(B B ) (R R ) B ] s g oi si , [B (R R ) B ] o p s g N o Depletiondriven DDI N p $$ \therefore D e p l e t i o n d r i v e n, D D I = \frac {N \left[ \left(\mathrm {B} _ {o} - \mathrm {B} _ {\mathrm {o i}}\right) + \left(\mathrm {R} _ {\mathrm {s i}} - 1\right) \right.}{N _ {p} \left[ \mathrm {B} _ {0} + \left(\mathrm {R} _ {\mathrm {p}} - \mathrm {R} _ {\mathrm {s}}\right) \right]} $$ (11) [(B B ) (R R ) B ] s g oi si , [B (R R ) B ] p s g o N o Depletiondriven DDI N p $$ \therefore D e p l e t i o n d r i v e n, D D I = \frac {N \left[ \left(\mathrm {B} _ {o} - \mathrm {B} _ {\mathrm {o i}}\right) + \left(\mathrm {R} _ {\mathrm {s i}} - \mathrm {R} _ {\mathrm {s}}\right) \mathrm {B} _ {\mathrm {g}} \right]}{N _ {p} \left[ \mathrm {B} _ {o} + \left(\mathrm {R} _ {\mathrm {p}} - \mathrm {R} _ {\mathrm {s}}\right) \mathrm {B} _ {\mathrm {g}} \right]} \tag {12} $$ [(B B ) (R R ) B ] s g oi si , [B (R R ) B ] o p s g N o Depletiondriven DDI N p $$ \therefore D e p l e t i o n d r i v e n, D D I = \frac {N \left[ \left(\mathrm {B} _ {o} - \mathrm {B} _ {\mathrm {o i}}\right) + \left(\mathrm {R} _ {\mathrm {s i}} - \mathrm {R} _ {\mathrm {s}}\right) \mathrm {B} _ {\mathrm {g}} \right]}{N _ {p} \left[ \mathrm {B} _ {\mathrm {o}} + \left(\mathrm {R} _ {\mathrm {p}} - \mathrm {R} _ {\mathrm {s}}\right) \mathrm {B} _ {\mathrm {g}} \right]} \tag {13} $$ DDI+SDI+EDI+WDI = 1.0 (14) The determination of each index shows the different contribution of each drive mechanism towards production and hence, shows the dominant drive mechanism.

Methodology

In this study, Microsoft Excel Visual Basic for Application combined with a tank model of zero dimensions was developed to predict reservoir performance. It is a powerful programming language embedded by Microsoft. The program is fixed in MS-Office applications i.e., MS-Word, MS-Excel, MS-Access. Many engineers use VBA to establish calculation subroutine suchlike menus, toolbars, worksheets, charts, etc Walkenbach [46]. This makes MS-Excel, which has VBA, a very advantageous platform for developing models and simulations. The main reason is that most engineers are acquainted with MS-Excel applications. Microsoft Excel is a user-friendly workbook that contains several worksheets. It is easily used for data analysis. It also provides some ability for engineering calculations and analysis [47]. Microsoft Excel is easily available to every Microsoft user and ridiculously cheap when compared to other domain based commercial software. Behind Excel spreadsheet is another environment used by its users to execute complex calculations on the worksheet. This environment is called Visual Basic Application, thus the name Excel VBA. Excel has inbuilt functions that users can leverage on while manipulating through their data but in a circumstance where the user wants a new functionality that did not come with Excel as inbuilt function, the user can navigate to the VBA environment and write some lines of code as shown in figure 3, that works as functions in Excel. Figure 3 shows the coding page of the software. Reservoir analysis is a key task in oil and gas exploration. During such analysis, hydrocarbon reservoirs are studied using some mathematical models. These models have large runtime and require a computer to perform such tasks faster, and accurately. With this technology, Engineers can design Excel to execute the needed task.

Figure 3: Microsoft Excel Visual Basic for Application Coding Software Page.
Click to enlarge
Figure 3: Microsoft Excel Visual Basic for Application Coding Software Page.

Figure 4 shows the interface of the Application. With this software, material balance optimization can be done on the cumulative produced fluid to obtain the history production data to match the model data. The common concept in material balance analysis is called history matching. When this is achieved, other activities like pressure simulation and forecasting can be executed to have more understanding and knowledge about the reservoir.

Figure 4: Microsoft Excel Visual Basic for Application Homepage.
Click to enlarge
Figure 4: Microsoft Excel Visual Basic for Application Homepage.

Functionality of the Excel Based Software

There are five major functions used during the setting up of the PVT and Production data used for the material balance optimization. DeltaP, TD, DimensionlessWaterInflux, WaterInfluxA and CumulativeOilProdEstimate. There are other functions in this Microsoft Excel software but these listed are the major ones. The appendix page has some of the functions. The reservoir, production and PVT data are displayed in the software as shown in Figure 5.

Figure 5: Software displaying Reservoir, Production and PVT data.
Click to enlarge
Figure 5: Software displaying Reservoir, Production and PVT data.

To perform the optimization after setting up the algorithm for sum of the square difference between Np Measured (oil reservoir) and Np Model; followed using the Microsoft Excel Solver to conduct the final optimization. This is what helps the software to history match these two parameters and try to get them match closely by changing some of the reservoir properties.

Reservoir engineering judgment comes in when selecting the right parameters to regress on. The reservoir engineer should be able to identify if the values he/she estimated is much or low that might not be the true value, but now that we have cumulative production from the reservoir, trying to align the models is like changing the parameters to suit what is observe from the reservoir.

Data Gathering and Acquisition

Three groups of data were used in carrying out this study; the first is a modeled data from the textbook by Dake [2] on water influx estimation while the second and third are real life data of reservoirs in Niger Delta. Reservoir A is a wedged shape reservoir. Initially the reservoir existed at Pb but no initial gas cap (m=0). Reservoir B is a linear- aquifer drive reservoir with strong water drive. It is still under depletion drive condition meaning it has no gas cap size (m=0). Reservoir Properties, Production, pressure and PVT data for reservoir A, B and C over a period are presented in Tables 1-9 respectively.

Value
Pay Thickness100
Permeability200
Water Viscosity0.55
Water Compressibility0.000003
Rock Compressibility0.000004
STOIIIP312000000
Swc0.05
Porosity0.25
Ct0.000007
Reservoir Radius9200
Temperature200
Initial Pressure2740
Bw1
F (Encroachment angle)0.388888889
Rd5.033837773
Dimensionless Time5.668622493
Csch9.08E-05
Aquifer Constant6445.688667
STOIIIP (MMStb)312
Angle140

Table 1: Reservoir A Properties [2].

T(days)Pressure @ OWCPlateau PressureNp_Measured (MMstb)
00274027400
1365250026207.88
27302290239518.42
310952109219929.15
414601949202940.69
518251818188350.14
621901702176058.42
725551608165565.39
829201535157170.74
932851480150774.54
1036501440146077.43

Table 2: Production and Pressure Data of Reservoir A.

TimeT(days)Pressure @ OWCPlateau PressureNp_ Measured (MMstb)
00274027400
1365250026207.88
27302290239518.42
310952109219929.15
414601949202940.69
518251818188350.14
621901702176058.42
725551608165565.39
829201535157170.74
932851480150774.54
1036501440146077.43

Table 3: PVT Data of Reservoir A.

PropertyValue
Pay Thickness230
Permeability8
Water Viscosity0.279463
Water Compressibility0.000003
Rock Compressibility0.000004
STOIIP220000000
Swc0.15
Porosity0.23
Ct0.000007
Reservoir Radius2000
Temperature250
Initial Pressure4000
Bw1
F (Encroachment angle)0.361111111
Rd6.108042106
Dimensionless Time5.668622493
Csch9.08E-05
Aquifer Constant598.5282333
STOIIP (MMStb)220
Angle130

Table 4: Reservoir B Properties.

TimeT(days)Pressure @ OWCNp Measured (MMStb)Gas Produced (MMScf)Water Produced
(MMStb)
13654000000
27303885.640.356222178.1110
310953836.750.586151293.0750
414603762.570.927019463.5090
518253705.211.24942624.7080
621903655.341.57649788.2450
725553707.561.57649788.2450
829203647.761.89402947.0120
932853602.542.205271102.630
1036503565.382.501731250.870
1140153531.512.803951401.980
1243803502.163.092821546.410
1347453471.133.398311699.160
1451103442.893.700511850.250
1554753418.263.980421990.210
1658403393.394.276952138.470
1762053370.54.561382280.690
1865703348.374.850762425.380
1969353327.595.128572564.290
2073003306.685.413452706.730
2176653286.275.696142848.070
2280303266.935.967652983.830
2383953247.36.246163123.080
2487603228.616.513713256.860
2591253212.066.778933389.460
2694903195.217.04233521.150
2798553179.947.278543639.270
281022031637.538363769.180
29105853146.667.78838940
30109503129.828.044154022.070
31113153109.138.284154142.070.028936
32116803088.148.532154266.070.059586
33120453067.38.780154390.070.091
34124103047.29.020154510.070.122132
35127753026.489.268154634.070.15504
36131403006.469.508154754.070.18761
37135052985.819.756154878.070.221995
38138702965.1910.00415002.070.257123
39142352946.5910.22815114.070.289503
40146002926.0110.47615238.070.326034
41149652906.1210.71615358.070.362088
42153302885.5810.96425482.070.400052
43156952865.7311.20425602.070.437484
44160602845.2411.45215726.070.476864
45164252824.7711.70015850.070.516957
46167902804.9811.94015970.070.556438
47171552784.5512.18826094.070.597924
48175202764.8112.42816214.070.638744
49178852744.4212.67616338.070.681605
50182502724.0712.92416462.070.725159
51186152705.713.14816574.070.765106
52189802685.3913.39616698.070.809969
53193452665.7613.63616818.070.854039
54197102645.513.88416942.070.900239
55200752625.9314.12427062.070.945597
56204402605.7314.37217186.070.993121
57208052585.5614.62017310.071.04131
58211702566.0814.86017430.071.08858
59215352545.9815.10827554.071.13808
60219002526.5715.34817674.071.1866
61222652506.5415.59617798.071.23738
62226302486.5515.84417922.071.28881
63229952467.8916.07618038.071.33751
64233602447.9816.32418162.071.39019
65237252428.7516.56418282.071.44177
66240902408.9216.81218406.071.4957

Table 5: Production Data of Reservoir B.

Bo (rb/stb)Bg (rb/scf)Rp (scf/stb)Rs (scf/stb)
1.291220.00461180500
1.292240.0047099500500
1.29270.0047546499.999147500
1.293410.0048249499.9994606500
1.293990.0048818499.9983993500
1.29450.0049332500500
1.293980.0048805500500
1.294590.0049414500.001056500
1.295070.0049894499.9977327500
1.295470.0050302500.0019986500
1.295850.0050684500.0017832500
1.296180.0051024500500
1.296540.0051388500.0014713500
1.296870.0051727499.9986488500
1.297190.0052053500500
1.297480.0052357499.9988309500
1.297760.0052645500500
1.298030.0052928500500
1.298290.0053199500.0009749500
1.298560.0053476500.0009236500
1.298820.0053752500500
1.299070.0054017500.0008379500
1.299330.005429500500
1.299580.0054554500.0007676500
1.29980.0054792499.9992624500
1.300030.0055036500500
1.300250.0055261500500
1.300480.0055513500500
1.300710.005576500500
1.300950.0056017499.9993784500
1.301250.0056337499.9993964500
1.301560.0056668499.999414500
1.301870.0057002499.9994305500
1.302170.0057329499.9994457500
1.302480.0057672499.9994605500
1.302790.0058009499.9994741500
1.303120.0058363499.9994875500
1.303440.0058722500.0019992500
1.303720.0059024500.0019554500
1.304060.0059401500.0019091500
1.304390.0059768500.0018664500
1.304740.0060153499.9972638500
1.305080.0060531499.9973224500
1.305430.0060927500.0017464500
1.305790.0061329500.0017094500
1.306140.0061725500.001675500
1.306510.006214499.9975386500
1.306880.0062548500.0016093500
1.307250.0062977500.0015778500
1.307640.0063413500.0015475500
1.307990.0063812500.0015211500
1.308380.0064262500.001493500
1.308770.0064704500.0014667500
1.309170.0065169500.0014405500
1.309570.0065626499.997876500
1.309990.0066106500.0013916500
1.310410.0066594500.001368500
1.310820.0067074500.0013459500
1.311250.0067579499.9980143500
1.311680.0068075500.0013031500
1.312120.0068597500.0012824500
1.312580.0069127500.0012623500
1.313030.0069665500.0012441500
1.313490.0070206500.0012252500
1.313940.0070741500.0012074500
1.314420.0071304500.0011896500

Table 6: PVT Data of Reservoir B.

PropertyValue
Pay Thickness230
Permeability8
Water Viscosity0.302872
Water Compressibility0.000003
Rock Compressibility0.000004
STOIIP130000000
Swc0
Porosity0.25
Ct0.000007
Reservoir Radius2000
Temperature210
Initial Pressure3266.32
Bw1
F (Encroachment angle)0.361111111
Rd3
Dimensionless Time5.668622493
Csch9.08E-05
Aquifer Constant650.5741667
STOIIP (MMStb)130
Angle130
Gas Cap Size0.2

Table 7: Reservoir C Properties.

TimeT(days)Pressure @ OWCNp Measured (MMStb)Gas Produced (MMScf)Water Produced (MMStb)
13653266.32000
27303216.223.441232214.550.00852448
310953186.26.732554303.10.0442557
414603158.789.898396290.550.109722
518253132.7712.9428182.310.203372
621903107.8615.87079985.280.323232
725553100.6718.626311666.70.463631
829203072.7921.208613230.60.619443
932853010.5123.645714696.70.787383
1036502987.8625.957916079.40.964876
1140152950.0928.143617379.61.14834

Table 8: Production Data of Reservoir C.

Bo (rb/stb)Bg (rb/scf)Rp (scf/stb)Rs (scf/stb)
1.319810.00537810650
1.313960.0054502643.5344339637.663
1.310820.0054904639.1486138631.027
1.307720.005531635.5124419624.47
1.304760.0055708632.2291763618.186
1.30190.0056101629.1644351612.129
1.299670.0056415626.3562812607.397
1.297710.0056694623.8318418603.238
1.295950.005695621.537954599.502
1.29440.0057179619.4414802596.191
1.293040.0057382617.5329382593.297

Table 9: PVT Data of Reservoir C.

Results and Conclusion

The Microsoft excel software was developed first for each of the three different reservoirs. For unmatched Reservoir A, when the Np measured is 7.88 MMstb, the Np model is 7.93 MMstb. After history matching, the Np model gives a value of 7.91 MMstb with a square difference of 0.000767118 as clearly shown in Table 10 and Table 11 respectively.

Np Measured (MMstb)Np Model
(MMstb)
00
7.887.92996777
18.4218.7664914
29.1530.4817589
40.6943.8164223
50.1455.7345093
58.4267.0134398
65.3977.4142619
70.7486.4666023
74.5492.763234
77.43101.264173

Table 10: Np Model and Np Real (Unmatched Reservoir A).

Np Measured (MMstb)Np Model (MMstb)Square Difference
000
7.887.907696890.000767118
18.4218.451237180.000975761
29.1529.230595830.006495687
40.6940.857210890.027959481
50.1450.367167790.051605204
58.4258.6794710.0673252
65.3965.68187460.08519078
70.7471.070913530.109503766
74.5473.307506721.519039686
77.4377.816076880.149055356

Table 11: Np Model and Np Real of Matched Reservoir A with their Square Differences.

The analysis of Reservoir A was done using the developed software depicted in Figure 6 which gives the correct values of DeltaP, Np model and Np measured with the respective time.

Figure 6: The Analysis page of matched Reservoir A.
Click to enlarge
Figure 6: The Analysis page of matched Reservoir A.

The uncertainty analysis of matched Reservoir A with STOIIP of 312MMstb gives a dimensionless radius of 5.03 alongside the objection function, pay thickness, permeability, angle, upper bound and lower bound values as shown in Figure 7.

Figure 7: The Uncertainty Analysis of Matched Reservoir A.
Click to enlarge
Figure 7: The Uncertainty Analysis of Matched Reservoir A.

The history matching of the Np model and Np measured were carried out with their respective pressures. The plot of the matched reservoir A Np model value blended so perfectly with the Np measured as clearly depicted in Figure 8 and Figure 9.

Figure 8: Plot of Np Measured Versus Np Real for Unmatched Reservoir A.
Click to enlarge
Figure 8: Plot of Np Measured Versus Np Real for Unmatched Reservoir A.
Figure 9: Plot of Np Measured Versus Np Real for Matched Reservoir A.
Click to enlarge
Figure 9: Plot of Np Measured Versus Np Real for Matched Reservoir A.

To test the accuracy of the developed software results, it was validated with MBAL. The blue in Figure 10 is with aquifer influx and the red line is without aquifer influx. It shows a high match points status.

Figure 10: MBAL validation of Reservoir A.
Click to enlarge
Figure 10: MBAL validation of Reservoir A.

Same process was repeated for reservoir B and C. The Np measured value of 9.78MMstb gives 10.04MMstb Np model with a square difference of 0.08 as shown in Table 12. Figure

11 shows the analysis page of Reservoir B indicating the reservoir properties, Production and PVT data.

Np Measured (MMStb)Np ModelSquare Difference
000
0.3562220.47650310.014467535
0.5861511.05303750.217982955
0.9270191.63491440.501115831
1.249422.2372530.97581412
1.576492.78082291.450417746
1.576492.85881251.644350891
1.894023.08737041.42408523
2.205273.51633711.718896884
2.501733.9059981.971968721
2.803954.2705922.151038763
3.092824.60479662.286073077
3.398314.93094042.348955917
3.700515.24411952.38273017
3.980425.5347562.415960258
4.276955.80541072.336192163
4.561386.06391032.257597233
4.850766.30884862.126022497
5.128576.54198211.99773373
5.413456.76945341.838745229
5.696146.99101351.676697441
5.967657.20442211.529605184
6.246167.41507131.366353556
6.513717.62034241.224635173
6.778937.8110361.065242869
7.04237.99562270.908824239
7.278548.17238120.798952042
7.538368.34845690.656256927
7.7888.52577660.544314258
8.044158.70408710.435516994
8.284158.88098050.356206678
8.532159.07134490.290731161
8.780159.26527810.235349315
9.020159.45788390.191610943
9.268159.65139630.146877705
9.508159.84546150.113779074
9.7561510.0414080.081372128
10.004110.2367010.054103401
10.228110.4227590.037892257
10.476110.6141880.019068193
10.716110.8070770.008276873
10.964211.0021090.001437091
11.204211.1957197.19E-05
11.452111.3890810.003971397
11.700111.5852860.013182348
11.940111.7788030.026016722
12.188211.9738330.045953194
12.428112.1685390.067371741
12.676112.3615960.098912781
12.924112.5586930.133522594
13.148112.7470990.160801655
13.396112.9369010.210863618
13.636113.1298570.256281579
13.884113.3228430.315009085
14.124213.5166120.369163631
14.372113.7111970.436793254
14.620113.9069690.508556114
14.860114.1002170.577422278
15.108214.2946510.66186171
15.348114.4888750.738267487
15.596114.6827350.834235793
15.844114.8804790.928564882
16.076115.0752831.001633857
16.324115.267651.116085701
16.564115.4602111.218571443
16.812115.6553581.338052854

Table 12: Table of Np Model and Np Real of Matched Reservoir B with their Square Differences.

Figure 11: The Analysis page of matched Reservoir B.
Click to enlarge
Figure 11: The Analysis page of matched Reservoir B.

The uncertainty analysis yields a dimensionless radius of 6.10 with a STOIIP value of 220MMstb, reservoir radius of 2000 ft, pay thickness and the upper bound and lower bound values as shown in Figure 12.

Figure 12: The Uncertainty Analysis page of Matched Reservoir B.
Click to enlarge
Figure 12: The Uncertainty Analysis page of Matched Reservoir B.
Figure 13: Plot of Np Measured Versus Np Real for Unmatched Reservoir B.
Click to enlarge
Figure 13: Plot of Np Measured Versus Np Real for Unmatched Reservoir B.

The history matching of the Np model and Np measured improved in the matched reservoir B plot compared to the unmatched reservoir B. The plots of pressure against the measured and model cumulative oil produced are shown in Figure 13 (Unmatched) and Figure 14 (Matched) respectively.

Figure 14: Plot of Np Measured Versus Np Real for Matched Reservoir B.
Click to enlarge
Figure 14: Plot of Np Measured Versus Np Real for Matched Reservoir B.

Figure 15 shows the software validation with MBAL. The Tank temperature is 250 deg F and tank pressure of 4000 psi. The calculated aquifer volume is 38296.9 MMft3 with aquifer permeability of 9.36911 md.

Figure 15: MBAL validation of Reservoir B.
Click to enlarge
Figure 15: MBAL validation of Reservoir B.
Np ModelNp Measured (MMStb)Square Difference
000
5.9713610263.441236.401563009
9.2210390616.732556.192577805
12.360850179.898396.063710103
15.324556112.9425.676573566
18.1387016315.87075.143831381
20.3212183718.62632.872748293
22.227281121.20861.037711176
23.9765291823.64570.109447944
25.5190740925.95790.192568183
26.8439456128.14361.689101526

Table 13: Table of Np Model and Np Real of Matched Reservoir C with their Square Differences.

Figure 16: The Analysis page of matched Reservoir C.
Click to enlarge
Figure 16: The Analysis page of matched Reservoir C.
Figure 17: The Uncertainty Analysis page of Matched Reservoir C.
Click to enlarge
Figure 17: The Uncertainty Analysis page of Matched Reservoir C.
Figure 18: Plot of Np Measured Versus Np Real for Unmatched Reservoir C.
Click to enlarge
Figure 18: Plot of Np Measured Versus Np Real for Unmatched Reservoir C.
Figure 19: Plot of Np Measured Versus Np Real for Matched Reservoir C.
Click to enlarge
Figure 19: Plot of Np Measured Versus Np Real for Matched Reservoir C.

Reservoir A has no gas cap initially (m=0) and the compressibility term is negligible meaning that Eg and Efw term of the MBE will cancel out. Aquifer to reservoir radius value has a great impact in history matching for material balance. From LP Dake example, the first Np model estimation was done with aquifer to reservoir radius value of 10. The difference in the Np Model was extremely large but when we reduced it to 5, the two values matched each other. With the Excel VBA software, this was accomplished with ease. Reservoir B water-drive energy is strong like a typical Niger Delta reservoir, and still under depletion drive condition meaning no initial gas cap (m=0). Thus, material balance history matching of these two reservoirs will no longer be a difficult task as such. If the differences are too large, it will call for another water influx estimation or perhaps tedious iterative guessing on the aquifer parameters because uncertainties in the given data are as result of unknown aquifer parameters.

The optimization of reservoir performance by means of the 235 lines of code of the Microsoft Excel VBA mimics that of MBAL. The software gave results the same as MBAL, thus its usage for history matching is encouraged. For reservoir A, an example 9.2 in L.P. Dake, the difference in Np real and Np model were not significantly large. The Np model of the software follows the trend of the real when it was history matched. With little or no square differences. For reservoir B and C in this study, difference in Np real and Np model were not significantly large for real NIGER DELTA reservoirs. The Np model of the software follows the trend of the real when it was history matched. With little or no square differences. With the results obtained with this Excel VBA software, we can confidently say that the performance of any reservoir in any region can be enhanced using the obtained reservoir properties, production, and PVT data.

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@article{ebere2024,
  title   = {Advancing Reservoir Performance Optimization through User-Friendly Excel VBA Software Development},
  author  = {Ebere FO, Ekwueme H, Onwuama CN, Adu-Mensah D, Nkok L and Josephs R},
  journal = {Petroleum & Petrochemical Engineering Journal},
  year    = {2024},
  volume  = {8},
  number  = {1},
  doi     = {10.23880/ppej-16000374}
}
Ebere FO, Ekwueme H, Onwuama CN, Adu-Mensah D, Nkok L and Josephs R (2024). Advancing Reservoir Performance Optimization through User-Friendly Excel VBA Software Development. Petroleum & Petrochemical Engineering Journal, 8(1). https://doi.org/10.23880/ppej-16000374
TY  - JOUR
TI  - Advancing Reservoir Performance Optimization through User-Friendly Excel VBA Software Development
AU  - Ebere FO, Ekwueme H, Onwuama CN, Adu-Mensah D, Nkok L and Josephs R
JO  - Petroleum & Petrochemical Engineering Journal
PY  - 2024
VL  - 8
IS  - 1
DO  - 10.23880/ppej-16000374
ER  -