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Figure 3: Reservoir Grid and Well Positioning for Case Il 2.3.3 Case Ill: Horizontal Wells Here two horizontal wells Gi (production) and G2 (Injection) placed parallel to each other were considered (Figure 4). All other rock and fluid modeling parameters assume their previous values. Well G; is specified with a bottom hole pressure to estimate the oil and water production rates, while G2 is specified with a water injection rate to estimate the variation in the bottom hole pressure. From Figure 4, the production and injection wells were placed and perforated at the first two layers.

Figure 3 Reservoir Grid and Well Positioning for Case Il 2.3.3 Case Ill: Horizontal Wells Here two horizontal wells Gi (production) and G2 (Injection) placed parallel to each other were considered (Figure 4). All other rock and fluid modeling parameters assume their previous values. Well G; is specified with a bottom hole pressure to estimate the oil and water production rates, while G2 is specified with a water injection rate to estimate the variation in the bottom hole pressure. From Figure 4, the production and injection wells were placed and perforated at the first two layers.

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The rock compressibility at 4500 psia is given as 4x10-6 psi-|.The grid was divided into 3 sub grid data each having 25 cells defined in the reservoir geometry. The grid was extracted separately for the purpose of generating permeability on each defined sub grid data. For a heterogeneous distribution of permeability, cell data structure was created for the three cases in order to verify the range of distribution on each predefined cells in all three layers. Figure | shows the permeability distribution in each grid structure for all three cases.
The rock compressibility at 4500 psia is given as 4x10-6 psi-|.The grid was divided into 3 sub grid data each having 25 cells defined in the reservoir geometry. The grid was extracted separately for the purpose of generating permeability on each defined sub grid data. For a heterogeneous distribution of permeability, cell data structure was created for the three cases in order to verify the range of distribution on each predefined cells in all three layers. Figure | shows the permeability distribution in each grid structure for all three cases.
Arid Zone Journal of Engineering, Technology and Environment, September, 2020; Vol. 16(3) 561-568. ISSN 1596-2490; e-ISSN 254 5818; www.azojete.com.ng ME ee , - The ability of one phase to move strictly depends on the environment at a particular location; the relative permeability of one phase works in conjunction with the saturation of the other phase present at the same location (Adeniyi et al, 2008). Relative permeability was used to denote the movement of a phase in the present of multiple phases from one point to another taking into account of the saturation as a function (Ahmed, 2006). In the MATLAB interface, defining relative permeability and capillary pressure as a function of water saturation was done in a tabular form. The table is a four column array in which the first column is interpreted to be water saturation, the second column denotes water relative permeability, and the third is oil relative permeability while the fourth column denotes oil-water capillary pressure function. See Lie et al. (2012) for detailed explanation.
Arid Zone Journal of Engineering, Technology and Environment, September, 2020; Vol. 16(3) 561-568. ISSN 1596-2490; e-ISSN 254 5818; www.azojete.com.ng ME ee , - The ability of one phase to move strictly depends on the environment at a particular location; the relative permeability of one phase works in conjunction with the saturation of the other phase present at the same location (Adeniyi et al, 2008). Relative permeability was used to denote the movement of a phase in the present of multiple phases from one point to another taking into account of the saturation as a function (Ahmed, 2006). In the MATLAB interface, defining relative permeability and capillary pressure as a function of water saturation was done in a tabular form. The table is a four column array in which the first column is interpreted to be water saturation, the second column denotes water relative permeability, and the third is oil relative permeability while the fourth column denotes oil-water capillary pressure function. See Lie et al. (2012) for detailed explanation.
2.2 Net present Value (NPV) The possible worth of investment for all the three studied cases was estimated. Net present value is the value of all future cash flows (positive and negative) over the entire life of an investment discounted to the present (Grema and Cao, 2016). A positive NPV indicates that the projected earnings generated by a project or investment (in present dollars) exceed the anticipated costs (also in present dollars). Generally, an investment with a positive NPV will be profitable, and an investment with a negative NPV will result in a net loss. This concept is the basis for the Net Present Value Rule, which dictates that the only investments that should be made are those with positive NPV values. The Net Present Value is calculated using Equation 2 (Grema and Cao, 2016): ~
2.2 Net present Value (NPV) The possible worth of investment for all the three studied cases was estimated. Net present value is the value of all future cash flows (positive and negative) over the entire life of an investment discounted to the present (Grema and Cao, 2016). A positive NPV indicates that the projected earnings generated by a project or investment (in present dollars) exceed the anticipated costs (also in present dollars). Generally, an investment with a positive NPV will be profitable, and an investment with a negative NPV will result in a net loss. This concept is the basis for the Net Present Value Rule, which dictates that the only investments that should be made are those with positive NPV values. The Net Present Value is calculated using Equation 2 (Grema and Cao, 2016): ~
2.3.2 Case Il: Five-Spot Pattern ri is the Water injection cost, Ty, is the Water production cost, rp is the Oil price per barrel, Uyii is the Water injection rate, yy is the Water production rate, yo; is the Oil production rate, Nyroq is the Number of production wells, N;,; is the Number of injection wells, b is the Discount factor, At* is the Time step size, t* is the Actual time period for which NPV is computed, T is the time unit. Here, yearly discount factor was taken to be given as 0.05, oil price to be 70 dollars per barrel, water production handling cost to be 6 dollars per barrel and the water injection cost to be 6 dollars per barrel. The NPV parameter applies to all cases of the reservoir model.
2.3.2 Case Il: Five-Spot Pattern ri is the Water injection cost, Ty, is the Water production cost, rp is the Oil price per barrel, Uyii is the Water injection rate, yy is the Water production rate, yo; is the Oil production rate, Nyroq is the Number of production wells, N;,; is the Number of injection wells, b is the Discount factor, At* is the Time step size, t* is the Actual time period for which NPV is computed, T is the time unit. Here, yearly discount factor was taken to be given as 0.05, oil price to be 70 dollars per barrel, water production handling cost to be 6 dollars per barrel and the water injection cost to be 6 dollars per barrel. The NPV parameter applies to all cases of the reservoir model.
Figure 4: Reservoir Grid and Well Positioning for Case Ill Arid Zone Journal of Engineering, Technology and Environment, September, 2020; Vol. 16(3) 561-568. ISSN 1596-2490; e-ISSN 254. 5818; www.azojete.com.ng
Figure 4: Reservoir Grid and Well Positioning for Case Ill Arid Zone Journal of Engineering, Technology and Environment, September, 2020; Vol. 16(3) 561-568. ISSN 1596-2490; e-ISSN 254. 5818; www.azojete.com.ng
The production rates and well water cuts for Case | are shown in Figure 5. Figure 5 illustrates a maximal recovery of oil with a production rate of 955,346.89 stb/day during water injection period of 400 days. After that period, there was a reduction in production rates as the bottom hole pressure reduces (Figure 6), and then a steady rate of 11,582.45 stb/day was realized going down at a negligible rate for the complete period of 2000 days. The well water cut shows a negligible effect on the production rates during the span of PAF RLIAMS
The production rates and well water cuts for Case | are shown in Figure 5. Figure 5 illustrates a maximal recovery of oil with a production rate of 955,346.89 stb/day during water injection period of 400 days. After that period, there was a reduction in production rates as the bottom hole pressure reduces (Figure 6), and then a steady rate of 11,582.45 stb/day was realized going down at a negligible rate for the complete period of 2000 days. The well water cut shows a negligible effect on the production rates during the span of PAF RLIAMS
Case Il has a constant oil production rate of 37,343.089 stb/day for the next 400 days with < rapid decrease in water production (Figure 7). The oil production estimate verified ar incremental well water cut as a result of the number of water injection wells. Although it car be considered maximal due to the long term oil production estimate, it is obviously limited by the excessive amount of water breakthrough. Case Il shows an estimate of |7 billion dollars (€ trillion naira) of NPV calculated for a complete span of 2000 days (Figure 8). The production rates and well water cut for Case II are shown in Figure 7.
Case Il has a constant oil production rate of 37,343.089 stb/day for the next 400 days with < rapid decrease in water production (Figure 7). The oil production estimate verified ar incremental well water cut as a result of the number of water injection wells. Although it car be considered maximal due to the long term oil production estimate, it is obviously limited by the excessive amount of water breakthrough. Case Il shows an estimate of |7 billion dollars (€ trillion naira) of NPV calculated for a complete span of 2000 days (Figure 8). The production rates and well water cut for Case II are shown in Figure 7.
Case Ill indicates a maximal oil recovery of |,110,188.60 stb/day decreasing down to 11,019.06 stb/day as the reservoir pressure decreases within a span of 1200 days (Figure 9). There is no much flow discrepancy between case | and 2 since the same constant flow is recorded at the same time span, but it is seemingly a better choice since it has a maximal flow for a longer time span as compared to case | and case 2. This gives it a better choice of consideration. Case Ill shows an estimate of 19.5 billion dollars (6.8 trillion naira) NPV calculated for a complete span of 2000 days (Figure 10).
Case Ill indicates a maximal oil recovery of |,110,188.60 stb/day decreasing down to 11,019.06 stb/day as the reservoir pressure decreases within a span of 1200 days (Figure 9). There is no much flow discrepancy between case | and 2 since the same constant flow is recorded at the same time span, but it is seemingly a better choice since it has a maximal flow for a longer time span as compared to case | and case 2. This gives it a better choice of consideration. Case Ill shows an estimate of 19.5 billion dollars (6.8 trillion naira) NPV calculated for a complete span of 2000 days (Figure 10).
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Reservior SimulationPetroleum Engineering
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