calculo de areas
DESCRIPTION
Trabajo de simulacion matematica de ReservoriosTRANSCRIPT
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Universidad Mayor Real y Pontificia De
San Francisco Xavier De Chuquisaca
FACULTAD DE TECNOLOGIA
Carrera: Ing. De Petrleo y Gas Natural
Materia: Simulacin de Reservorio (PGP-310)
Practica: 1
Ttulo: Calculo del rea de la Estructura por medio del Sistema de
Grillado o Mallado
Universitario: Julio Cesar Peralta Maturano
Fecha de entrega: 22/04/2014
Nombre de docente: Ing. Luis Alejandro Delgado Avila
Grupo: 1
Sucre Bolivia
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1
1. OBJETIVOS
1.1 Objetivos General
Determinar por simulacin el rea de C.G.P(Contacto Gas-Petrleo) y C.A.P (Contacto
Agua-Petrleo) del Reservorio, por los diferentes tipos de sistemas de grillado
(Constantes y Variables)
1.2 Objetivos Especficos
Construir una Grilla Ortogonal de dimensin 0,8cm.
Construir una Grilla Ortogonal de dimensin 1,2 cm
Construir una Grilla Circular de dimetro 1,2 cm.
Construir una Grilla Circular de dimetro 1,8 cm.
Construir una Grilla Hexagonal de lado 0,8cm.
Construir una Grilla Hexagonal de lado 1,3 cm.
Construir tabla de clculos y resultados.
2. INFORMACIN
Para la realizacin de la presente prctica dispondremos de la siguiente Informacin
El plano estructural del reservorio con el que se cuenta el siguiente:
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2
Tipos de Grilla
Area Tipo de Grilla
Ortogonal L (cm) Circular D (cm) Hexagonal L (cm)
CAP 0,8 1,2 0,8
CGP 1,2 1,8 1,3
La escala a utilizar ser de3,1: 100000 (cm)
3. HERRAMIENTAS Y/O ECUACIONES A UTILIZAR
Las ecuaciones a utilizar estn relacionadas al clculo del rea de dichas superficies.
3.1 Sistema de Grillado Ortogonal
El clculo del rea de un cuadrado est dado por la siguiente ecuacin:
3.2 Sistema de Grillado Circular
El clculo del rea de una circunferencia puede estar en funcin de dimetro o radio,
por lo est dado por las siguientes ecuaciones:
3.3 Sistema de Grillado Hexagonal
El clculo del rea de un hexgono est dado por la siguiente ecuacin:
L
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3
4. CONSTRUCCIN DE LA TABLA DE CLCULOS( AREA CONSTANTE)
4.1 Sistema Ortogonal de 0,8 cm de lado.
4.1.1 Contacto Agua- Petrleo (C.A.P).
Calculo del rea del Contacto Agua-Petrleo
tem i j Fc A_Total (cm^2) A_Total*Fc (cm^2) Area_Real (m^2) Area_Real(Acres)
1 1 6 0,140 0,64 0,090 9323,621 2,304
2 1 7 0,570 0,64 0,365 37960,458 9,380
3 1 8 0,930 0,64 0,595 61935,484 15,305
4 1 9 0,940 0,64 0,602 62601,457 15,469
5 1 10 0,520 0,64 0,333 34630,593 8,557
6 2 6 0,800 0,64 0,512 53277,836 13,165
7 2 7 1,000 0,64 0,640 66597,294 16,457
8 2 8 1,000 0,64 0,640 66597,294 16,457
9 2 9 1,000 0,64 0,640 66597,294 16,457
10 2 10 1,000 0,64 0,640 66597,294 16,457
11 2 11 0,550 0,64 0,352 36628,512 9,051
12 3 5 0,150 0,64 0,096 9989,594 2,468
13 3 6 1,000 0,64 0,640 66597,294 16,457
14 3 7 1,000 0,64 0,640 66597,294 16,457
15 3 8 1,000 0,64 0,640 66597,294 16,457
16 3 9 1,000 0,64 0,640 66597,294 16,457
17 3 10 1,000 0,64 0,640 66597,294 16,457
18 3 11 1,000 0,64 0,640 66597,294 16,457
19 3 12 0,320 0,64 0,205 21311,134 5,266
20 4 5 0,570 0,64 0,365 37960,458 9,380
21 4 6 1,000 0,64 0,640 66597,294 16,457
22 4 7 1,000 0,64 0,640 66597,294 16,457
23 4 8 1,000 0,64 0,640 66597,294 16,457
24 4 9 1,000 0,64 0,640 66597,294 16,457
25 4 10 1,000 0,64 0,640 66597,294 16,457
26 4 11 1,000 0,64 0,640 66597,294 16,457
27 4 12 0,950 0,64 0,608 63267,430 15,634
28 5 5 0,890 0,64 0,570 59271,592 14,646
29 5 6 1,000 0,64 0,640 66597,294 16,457
30 5 7 1,000 0,64 0,640 66597,294 16,457
31 5 8 1,000 0,64 0,640 66597,294 16,457
32 5 9 1,000 0,64 0,640 66597,294 16,457
33 5 10 1,000 0,64 0,640 66597,294 16,457
34 5 11 1,000 0,64 0,640 66597,294 16,457
35 5 12 1,000 0,64 0,640 66597,294 16,457
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4
36 5 13 0,320 0,64 0,205 21311,134 5,266
37 6 5 0,900 0,64 0,576 59937,565 14,811
38 6 6 1,000 0,64 0,640 66597,294 16,457
39 6 7 1,000 0,64 0,640 66597,294 16,457
40 6 8 1,000 0,64 0,640 66597,294 16,457
41 6 9 1,000 0,64 0,640 66597,294 16,457
42 6 10 1,000 0,64 0,640 66597,294 16,457
43 6 11 1,000 0,64 0,640 66597,294 16,457
44 6 12 1,000 0,64 0,640 66597,294 16,457
45 6 13 0,830 0,64 0,531 55275,754 13,659
46 7 5 0,960 0,64 0,614 63933,403 15,798
47 7 6 1,000 0,64 0,640 66597,294 16,457
48 7 7 1,000 0,64 0,640 66597,294 16,457
49 7 8 1,000 0,64 0,640 66597,294 16,457
50 7 9 1,000 0,64 0,640 66597,294 16,457
51 7 10 1,000 0,64 0,640 66597,294 16,457
52 7 11 1,000 0,64 0,640 66597,294 16,457
53 7 12 1,000 0,64 0,640 66597,294 16,457
54 7 13 0,970 0,64 0,621 64599,376 15,963
55 8 5 0,990 0,64 0,634 65931,322 16,292
56 8 6 1,000 0,64 0,640 66597,294 16,457
57 8 7 1,000 0,64 0,640 66597,294 16,457
58 8 8 1,000 0,64 0,640 66597,294 16,457
59 8 9 1,000 0,64 0,640 66597,294 16,457
60 8 10 1,000 0,64 0,640 66597,294 16,457
61 8 11 1,000 0,64 0,640 66597,294 16,457
62 8 12 1,000 0,64 0,640 66597,294 16,457
63 8 13 1,000 0,64 0,640 66597,294 16,457
64 8 14 0,330 0,64 0,211 21977,107 5,431
65 9 5 0,990 0,64 0,634 65931,322 16,292
66 9 6 1,000 0,64 0,640 66597,294 16,457
67 9 7 1,000 0,64 0,640 66597,294 16,457
68 9 8 1,000 0,64 0,640 66597,294 16,457
69 9 9 1,000 0,64 0,640 66597,294 16,457
70 9 10 1,000 0,64 0,640 66597,294 16,457
71 9 11 1,000 0,64 0,640 66597,294 16,457
72 9 12 1,000 0,64 0,640 66597,294 16,457
73 9 13 1,000 0,64 0,640 66597,294 16,457
74 9 14 0,480 0,64 0,307 31966,701 7,899
75 10 5 0,940 0,64 0,602 62601,457 15,469
76 10 6 1,000 0,64 0,640 66597,294 16,457
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5
77 10 7 1,000 0,64 0,640 66597,294 16,457
78 10 8 1,000 0,64 0,640 66597,294 16,457
79 10 9 1,000 0,64 0,640 66597,294 16,457
80 10 10 1,000 0,64 0,640 66597,294 16,457
81 10 11 1,000 0,64 0,640 66597,294 16,457
82 10 12 1,000 0,64 0,640 66597,294 16,457
83 10 13 1,000 0,64 0,640 66597,294 16,457
84 10 14 0,920 0,64 0,589 61269,511 15,140
85 11 5 0,960 0,64 0,614 63933,403 15,798
86 11 6 1,000 0,64 0,640 66597,294 16,457
87 11 7 1,000 0,64 0,640 66597,294 16,457
88 11 8 1,000 0,64 0,640 66597,294 16,457
89 11 9 1,000 0,64 0,640 66597,294 16,457
90 11 10 1,000 0,64 0,640 66597,294 16,457
91 11 11 1,000 0,64 0,640 66597,294 16,457
92 11 12 1,000 0,64 0,640 66597,294 16,457
93 11 13 1,000 0,64 0,640 66597,294 16,457
94 11 14 1,000 0,64 0,640 66597,294 16,457
95 11 15 0,350 0,64 0,224 23309,053 5,760
96 12 5 0,960 0,64 0,614 63933,403 15,798
97 12 6 1,000 0,64 0,640 66597,294 16,457
98 12 7 1,000 0,64 0,640 66597,294 16,457
99 12 8 1,000 0,64 0,640 66597,294 16,457
100 12 9 1,000 0,64 0,640 66597,294 16,457
101 12 10 1,000 0,64 0,640 66597,294 16,457
102 12 11 1,000 0,64 0,640 66597,294 16,457
103 12 12 1,000 0,64 0,640 66597,294 16,457
104 12 13 1,000 0,64 0,640 66597,294 16,457
105 12 14 1,000 0,64 0,640 66597,294 16,457
106 12 15 0,560 0,64 0,358 37294,485 9,216
107 13 5 0,880 0,64 0,563 58605,619 14,482
108 13 6 1,000 0,64 0,640 66597,294 16,457
109 13 7 1,000 0,64 0,640 66597,294 16,457
110 13 8 1,000 0,64 0,640 66597,294 16,457
111 13 9 1,000 0,64 0,640 66597,294 16,457
112 13 10 1,000 0,64 0,640 66597,294 16,457
113 13 11 1,000 0,64 0,640 66597,294 16,457
114 13 12 1,000 0,64 0,640 66597,294 16,457
115 13 13 1,000 0,64 0,640 66597,294 16,457
116 13 14 1,000 0,64 0,640 66597,294 16,457
117 13 15 0,880 0,64 0,563 58605,619 14,482
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6
118 14 5 0,580 0,64 0,371 38626,431 9,545
119 14 6 1,000 0,64 0,640 66597,294 16,457
120 14 7 1,000 0,64 0,640 66597,294 16,457
121 14 8 1,000 0,64 0,640 66597,294 16,457
122 14 9 1,000 0,64 0,640 66597,294 16,457
123 14 10 1,000 0,64 0,640 66597,294 16,457
124 14 11 1,000 0,64 0,640 66597,294 16,457
125 14 12 1,000 0,64 0,640 66597,294 16,457
126 14 13 1,000 0,64 0,640 66597,294 16,457
127 14 14 1,000 0,64 0,640 66597,294 16,457
128 14 15 0,930 0,64 0,595 61935,484 15,305
129 15 5 0,530 0,64 0,339 35296,566 8,722
130 15 6 1,000 0,64 0,640 66597,294 16,457
131 15 7 1,000 0,64 0,640 66597,294 16,457
132 15 8 1,000 0,64 0,640 66597,294 16,457
133 15 9 1,000 0,64 0,640 66597,294 16,457
134 15 10 1,000 0,64 0,640 66597,294 16,457
135 15 11 1,000 0,64 0,640 66597,294 16,457
136 15 12 1,000 0,64 0,640 66597,294 16,457
137 15 13 1,000 0,64 0,640 66597,294 16,457
138 15 14 1,000 0,64 0,640 66597,294 16,457
139 15 15 0,990 0,64 0,634 65931,322 16,292
140 16 5 0,510 0,64 0,326 33964,620 8,393
141 16 6 1,000 0,64 0,640 66597,294 16,457
142 16 7 1,000 0,64 0,640 66597,294 16,457
143 16 8 1,000 0,64 0,640 66597,294 16,457
144 16 9 1,000 0,64 0,640 66597,294 16,457
145 16 10 1,000 0,64 0,640 66597,294 16,457
146 16 11 1,000 0,64 0,640 66597,294 16,457
147 16 12 1,000 0,64 0,640 66597,294 16,457
148 16 13 1,000 0,64 0,640 66597,294 16,457
149 16 14 1,000 0,64 0,640 66597,294 16,457
150 16 15 1,000 0,64 0,640 66597,294 16,457
151 17 5 0,510 0,64 0,326 33964,620 8,393
152 17 6 1,000 0,64 0,640 66597,294 16,457
153 17 7 1,000 0,64 0,640 66597,294 16,457
154 17 8 1,000 0,64 0,640 66597,294 16,457
155 17 9 1,000 0,64 0,640 66597,294 16,457
156 17 10 1,000 0,64 0,640 66597,294 16,457
157 17 11 1,000 0,64 0,640 66597,294 16,457
158 17 12 1,000 0,64 0,640 66597,294 16,457
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7
159 17 13 1,000 0,64 0,640 66597,294 16,457
160 17 14 1,000 0,64 0,640 66597,294 16,457
161 17 15 0,990 0,64 0,634 65931,322 16,292
162 18 5 0,540 0,64 0,346 35962,539 8,887
163 18 6 1,000 0,64 0,640 66597,294 16,457
164 18 7 1,000 0,64 0,640 66597,294 16,457
165 18 8 1,000 0,64 0,640 66597,294 16,457
166 18 9 1,000 0,64 0,640 66597,294 16,457
167 18 10 1,000 0,64 0,640 66597,294 16,457
168 18 11 1,000 0,64 0,640 66597,294 16,457
169 18 12 1,000 0,64 0,640 66597,294 16,457
170 18 13 1,000 0,64 0,640 66597,294 16,457
171 18 14 1,000 0,64 0,640 66597,294 16,457
172 18 15 0,980 0,64 0,627 65265,349 16,127
173 19 5 0,620 0,64 0,397 41290,323 10,203
174 19 6 1,000 0,64 0,640 66597,294 16,457
175 19 7 1,000 0,64 0,640 66597,294 16,457
176 19 8 1,000 0,64 0,640 66597,294 16,457
177 19 9 1,000 0,64 0,640 66597,294 16,457
178 19 10 1,000 0,64 0,640 66597,294 16,457
179 19 11 1,000 0,64 0,640 66597,294 16,457
180 19 12 1,000 0,64 0,640 66597,294 16,457
181 19 13 1,000 0,64 0,640 66597,294 16,457
182 19 14 1,000 0,64 0,640 66597,294 16,457
183 19 15 0,950 0,64 0,608 63267,430 15,634
184 20 5 0,880 0,64 0,563 58605,619 14,482
185 20 6 1,000 0,64 0,640 66597,294 16,457
186 20 7 1,000 0,64 0,640 66597,294 16,457
187 20 8 1,000 0,64 0,640 66597,294 16,457
188 20 9 1,000 0,64 0,640 66597,294 16,457
189 20 10 1,000 0,64 0,640 66597,294 16,457
190 20 11 1,000 0,64 0,640 66597,294 16,457
191 20 12 1,000 0,64 0,640 66597,294 16,457
192 20 13 1,000 0,64 0,640 66597,294 16,457
193 20 14 1,000 0,64 0,640 66597,294 16,457
194 20 15 0,870 0,64 0,557 57939,646 14,317
195 21 5 0,970 0,64 0,621 64599,376 15,963
196 21 6 1,000 0,64 0,640 66597,294 16,457
197 21 7 1,000 0,64 0,640 66597,294 16,457
198 21 8 1,000 0,64 0,640 66597,294 16,457
199 21 9 1,000 0,64 0,640 66597,294 16,457
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8
200 21 10 1,000 0,64 0,640 66597,294 16,457
201 21 11 1,000 0,64 0,640 66597,294 16,457
202 21 12 1,000 0,64 0,640 66597,294 16,457
203 21 13 1,000 0,64 0,640 66597,294 16,457
204 21 14 1,000 0,64 0,640 66597,294 16,457
205 21 15 0,780 0,64 0,499 51945,890 12,836
206 22 4 0,350 0,64 0,224 23309,053 5,760
207 22 5 1,000 0,64 0,640 66597,294 16,457
208 22 6 1,000 0,64 0,640 66597,294 16,457
209 22 7 1,000 0,64 0,640 66597,294 16,457
210 22 8 1,000 0,64 0,640 66597,294 16,457
211 22 9 1,000 0,64 0,640 66597,294 16,457
212 22 10 1,000 0,64 0,640 66597,294 16,457
213 22 11 1,000 0,64 0,640 66597,294 16,457
214 22 12 1,000 0,64 0,640 66597,294 16,457
215 22 13 1,000 0,64 0,640 66597,294 16,457
216 22 14 1,000 0,64 0,640 66597,294 16,457
217 22 15 0,450 0,64 0,288 29968,783 7,405
218 23 4 0,400 0,64 0,256 26638,918 6,583
219 23 5 1,000 0,64 0,640 66597,294 16,457
220 23 6 1,000 0,64 0,640 66597,294 16,457
221 23 7 1,000 0,64 0,640 66597,294 16,457
222 23 8 1,000 0,64 0,640 66597,294 16,457
223 23 9 1,000 0,64 0,640 66597,294 16,457
224 23 10 1,000 0,64 0,640 66597,294 16,457
225 23 11 1,000 0,64 0,640 66597,294 16,457
226 23 12 1,000 0,64 0,640 66597,294 16,457
227 23 13 1,000 0,64 0,640 66597,294 16,457
228 23 14 1,000 0,64 0,640 66597,294 16,457
229 23 15 0,310 0,64 0,198 20645,161 5,102
230 24 4 0,460 0,64 0,294 30634,755 7,570
231 24 5 1,000 0,64 0,640 66597,294 16,457
232 24 6 1,000 0,64 0,640 66597,294 16,457
233 24 7 1,000 0,64 0,640 66597,294 16,457
234 24 8 1,000 0,64 0,640 66597,294 16,457
235 24 9 1,000 0,64 0,640 66597,294 16,457
236 24 10 1,000 0,64 0,640 66597,294 16,457
237 24 11 1,000 0,64 0,640 66597,294 16,457
238 24 12 1,000 0,64 0,640 66597,294 16,457
239 24 13 1,000 0,64 0,640 66597,294 16,457
240 24 14 0,970 0,64 0,621 64599,376 15,963
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9
241 25 4 0,280 0,64 0,179 18647,242 4,608
242 25 5 1,000 0,64 0,640 66597,294 16,457
243 25 6 1,000 0,64 0,640 66597,294 16,457
244 25 7 1,000 0,64 0,640 66597,294 16,457
245 25 8 1,000 0,64 0,640 66597,294 16,457
246 25 9 1,000 0,64 0,640 66597,294 16,457
247 25 10 1,000 0,64 0,640 66597,294 16,457
248 25 11 1,000 0,64 0,640 66597,294 16,457
249 25 12 1,000 0,64 0,640 66597,294 16,457
250 25 13 1,000 0,64 0,640 66597,294 16,457
251 25 14 0,780 0,64 0,499 51945,890 12,836
252 26 5 0,870 0,64 0,557 57939,646 14,317
253 26 6 1,000 0,64 0,640 66597,294 16,457
254 26 7 1,000 0,64 0,640 66597,294 16,457
255 26 8 1,000 0,64 0,640 66597,294 16,457
256 26 9 1,000 0,64 0,640 66597,294 16,457
257 26 10 1,000 0,64 0,640 66597,294 16,457
258 26 11 1,000 0,64 0,640 66597,294 16,457
259 26 12 1,000 0,64 0,640 66597,294 16,457
260 26 13 1,000 0,64 0,640 66597,294 16,457
261 26 14 0,280 0,64 0,179 18647,242 4,608
262 27 6 0,870 0,64 0,557 57939,646 14,317
263 27 7 1,000 0,64 0,640 66597,294 16,457
264 27 8 1,000 0,64 0,640 66597,294 16,457
265 27 9 1,000 0,64 0,640 66597,294 16,457
266 27 10 1,000 0,64 0,640 66597,294 16,457
267 27 11 1,000 0,64 0,640 66597,294 16,457
268 27 12 1,000 0,64 0,640 66597,294 16,457
269 27 13 0,670 0,64 0,429 44620,187 11,026
270 28 7 0,350 0,64 0,224 23309,053 5,760
271 28 8 0,720 0,64 0,461 47950,052 11,849
272 28 9 0,940 0,64 0,602 62601,457 15,469
273 28 10 0,980 0,64 0,627 65265,349 16,127
274 28 11 0,890 0,64 0,570 59271,592 14,646
275 28 12 0,580 0,64 0,371 38626,431 9,545
AREA TOTAL
164,051 17070884,495 4218,307
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4.2 Sistema Ortogonal de 1,2 cm de lado.
4.2.1 Contacto Petrleo-Gas (C.P.G).
Calculo del rea del Contacto Petrleo-Gas
tem i j Fc A_Total (cm^2) A_Total*Fc (cm^2) Area_Real (m^2) Area_Real(Acres)
1 3 6 0,300 1,440 0,432 44953,174 11,108
2 3 7 0,850 1,440 1,224 127367,326 31,473
3 3 8 0,670 1,440 0,965 100395,421 24,808
4 4 6 0,790 1,440 1,138 118376,691 29,252
5 4 7 1,000 1,440 1,440 149843,913 37,027
6 4 8 0,920 1,440 1,325 137856,400 34,065
7 4 9 0,270 1,440 0,389 40457,856 9,997
8 5 6 0,750 1,440 1,080 112382,934 27,770
9 5 7 1,000 1,440 1,440 149843,913 37,027
10 5 8 1,000 1,440 1,440 149843,913 37,027
11 5 9 0,620 1,440 0,893 92903,226 22,957
12 6 6 0,520 1,440 0,749 77918,835 19,254
13 6 7 1,000 1,440 1,440 149843,913 37,027
14 6 8 1,000 1,440 1,440 149843,913 37,027
15 6 9 0,960 1,440 1,382 143850,156 35,546
16 6 10 0,080 1,440 0,115 11987,513 2,962
17 7 6 0,320 1,440 0,461 47950,052 11,849
18 7 7 1,000 1,440 1,440 149843,913 37,027
19 7 8 1,000 1,440 1,440 149843,913 37,027
20 7 9 1,000 1,440 1,440 149843,913 37,027
21 7 10 0,300 1,440 0,432 44953,174 11,108
22 8 6 0,180 1,440 0,259 26971,904 6,665
23 8 7 1,000 1,440 1,440 149843,913 37,027
24 8 8 1,000 1,440 1,440 149843,913 37,027
25 8 9 1,000 1,440 1,440 149843,913 37,027
26 8 10 0,460 1,440 0,662 68928,200 17,033
27 9 7 0,970 1,440 1,397 145348,595 35,916
28 9 8 1,000 1,440 1,440 149843,913 37,027
29 9 9 1,000 1,440 1,440 149843,913 37,027
30 9 10 0,560 1,440 0,806 83912,591 20,735
31 10 7 0,870 1,440 1,253 130364,204 32,214
32 10 8 1,000 1,440 1,440 149843,913 37,027
33 10 9 1,000 1,440 1,440 149843,913 37,027
34 10 10 0,570 1,440 0,821 85411,030 21,106
35 11 7 0,820 1,440 1,181 122872,008 30,362
36 11 8 1,000 1,440 1,440 149843,913 37,027
37 11 9 1,000 1,440 1,440 149843,913 37,027
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11
38 11 10 0,480 1,440 0,691 71925,078 17,773
39 12 7 0,870 1,440 1,253 130364,204 32,214
40 12 8 1,000 1,440 1,440 149843,913 37,027
41 12 9 1,000 1,440 1,440 149843,913 37,027
42 12 10 0,380 1,440 0,547 56940,687 14,070
43 13 7 0,960 1,440 1,382 143850,156 35,546
44 13 8 1,000 1,440 1,440 149843,913 37,027
45 13 9 1,000 1,440 1,440 149843,913 37,027
46 13 10 0,08 1,440 0,115 11987,513 2,962
47 14 6 0,120 1,440 0,173 17981,270 4,443
48 14 7 1,000 1,440 1,440 149843,913 37,027
49 14 8 1,000 1,440 1,440 149843,913 37,027
50 14 9 0,820 1,440 1,181 122872,008 30,362
51 15 6 0,250 1,440 0,360 37460,978 9,257
52 15 7 1,000 1,440 1,440 149843,913 37,027
53 15 8 0,980 1,440 1,411 146847,034 36,287
54 15 9 0,360 1,440 0,518 53943,809 13,330
55 16 7 0,820 1,440 1,181 122872,008 30,362
56 16 8 0,830 1,440 1,195 124370,447 30,733
AREA TOTAL 61,531 6402830,385 1582,174
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12
4.3 Sistema Circular de 1,2 cm de dimetro.
4.3.1 Contacto Agua-Petrleo (C.A.P).
Calculo del rea del Contacto Agua-Petrleo
tem i j Fc A_Total (cm^2) A_Total*Fc (cm^2) Area_Real (m^2) Area_Real(Acres)
1 1 5 0,150 1,131 0,170 17653,070 4,362
2 1 6 0,750 1,131 0,848 88265,350 21,811
3 1 7 0,920 1,131 1,040 108272,163 26,755
4 1 8 0,480 1,131 0,543 56489,824 13,959
5 2 5 0,830 1,131 0,939 97680,321 24,137
6 2 6 1,000 1,131 1,131 117687,134 29,081
7 2 7 1,000 1,131 1,131 117687,134 29,081
8 2 8 1,000 1,131 1,131 117687,134 29,081
9 2 9 0,430 1,131 0,486 50605,468 12,505
10 3 5 1,000 1,131 1,131 117687,134 29,081
11 3 6 1,000 1,131 1,131 117687,134 29,081
12 3 7 1,000 1,131 1,131 117687,134 29,081
13 3 8 1,000 1,131 1,131 117687,134 29,081
14 3 9 0,990 1,131 1,120 116510,262 28,790
15 4 5 1,000 1,131 1,131 117687,134 29,081
16 4 6 1,000 1,131 1,131 117687,134 29,081
17 4 7 1,000 1,131 1,131 117687,134 29,081
18 4 8 1,000 1,131 1,131 117687,134 29,081
19 4 9 1,000 1,131 1,131 117687,134 29,081
20 4 10 0,430 1,131 0,486 50605,468 12,505
21 4 4 0,230 1,131 0,260 27068,041 6,689
22 5 4 0,280 1,131 0,317 32952,397 8,143
23 5 5 1,000 1,131 1,131 117687,134 29,081
24 5 6 1,000 1,131 1,131 117687,134 29,081
25 5 7 1,000 1,131 1,131 117687,134 29,081
26 5 8 1,000 1,131 1,131 117687,134 29,081
27 5 9 1,000 1,131 1,131 117687,134 29,081
28 5 10 0,820 1,131 0,927 96503,450 23,847
29 6 4 0,350 1,131 0,396 41190,497 10,178
30 6 5 1,000 1,131 1,131 117687,134 29,081
31 6 6 1,000 1,131 1,131 117687,134 29,081
32 6 7 1,000 1,131 1,131 117687,134 29,081
33 6 8 1,000 1,131 1,131 117687,134 29,081
34 6 9 1,000 1,131 1,131 117687,134 29,081
35 6 10 0,980 1,131 1,108 115333,391 28,500
36 7 4 0,230 1,131 0,260 27068,041 6,689
-
13
37 7 5 1,000 1,131 1,131 117687,134 29,081
38 7 6 1,000 1,131 1,131 117687,134 29,081
39 7 7 1,000 1,131 1,131 117687,134 29,081
40 7 8 1,000 1,131 1,131 117687,134 29,081
41 7 9 1,000 1,131 1,131 117687,134 29,081
42 7 10 1,000 1,131 1,131 117687,134 29,081
43 7 11 0,380 1,131 0,430 44721,111 11,051
44 8 4 0,260 1,131 0,294 30598,655 7,561
45 8 5 1,000 1,131 1,131 117687,134 29,081
46 8 6 1,000 1,131 1,131 117687,134 29,081
47 8 7 1,000 1,131 1,131 117687,134 29,081
48 8 8 1,000 1,131 1,131 117687,134 29,081
49 8 9 1,000 1,131 1,131 117687,134 29,081
50 8 10 1,000 1,131 1,131 117687,134 29,081
51 8 11 0,840 1,131 0,950 98857,192 24,428
52 9 4 0,190 1,131 0,215 22360,555 5,525
53 9 5 1,000 1,131 1,131 117687,134 29,081
54 9 6 1,000 1,131 1,131 117687,134 29,081
55 9 7 1,000 1,131 1,131 117687,134 29,081
56 9 8 1,000 1,131 1,131 117687,134 29,081
57 9 9 1,000 1,131 1,131 117687,134 29,081
58 9 10 1,000 1,131 1,131 117687,134 29,081
59 9 11 0,920 1,131 1,040 108272,163 26,755
60 10 5 1,000 1,131 1,131 117687,134 29,081
61 10 6 1,000 1,131 1,131 117687,134 29,081
62 10 7 1,000 1,131 1,131 117687,134 29,081
63 10 8 1,000 1,131 1,131 117687,134 29,081
64 10 9 1,000 1,131 1,131 117687,134 29,081
65 10 10 1,000 1,131 1,131 117687,134 29,081
66 10 11 1,000 1,131 1,131 117687,134 29,081
67 11 5 1,000 1,131 1,131 117687,134 29,081
68 11 6 1,000 1,131 1,131 117687,134 29,081
69 11 7 1,000 1,131 1,131 117687,134 29,081
70 11 8 1,000 1,131 1,131 117687,134 29,081
71 11 9 1,000 1,131 1,131 117687,134 29,081
72 11 10 1,000 1,131 1,131 117687,134 29,081
73 11 11 1,000 1,131 1,131 117687,134 29,081
74 12 5 1,000 1,131 1,131 117687,134 29,081
75 12 6 1,000 1,131 1,131 117687,134 29,081
76 12 7 1,000 1,131 1,131 117687,134 29,081
77 12 8 1,000 1,131 1,131 117687,134 29,081
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14
78 12 9 1,000 1,131 1,131 117687,134 29,081
79 12 10 1,000 1,131 1,131 117687,134 29,081
80 12 11 1,000 1,131 1,131 117687,134 29,081
81 13 5 1,000 1,131 1,131 117687,134 29,081
82 13 6 1,000 1,131 1,131 117687,134 29,081
83 13 7 1,000 1,131 1,131 117687,134 29,081
84 13 8 1,000 1,131 1,131 117687,134 29,081
85 13 9 1,000 1,131 1,131 117687,134 29,081
86 13 10 1,000 1,131 1,131 117687,134 29,081
87 13 11 0,980 1,131 1,108 115333,391 28,500
88 14 4 0,300 1,131 0,339 35306,140 8,724
89 14 5 1,000 1,131 1,131 117687,134 29,081
90 14 6 1,000 1,131 1,131 117687,134 29,081
91 14 7 1,000 1,131 1,131 117687,134 29,081
92 14 8 1,000 1,131 1,131 117687,134 29,081
93 14 9 1,000 1,131 1,131 117687,134 29,081
94 14 10 1,000 1,131 1,131 117687,134 29,081
95 14 11 0,860 1,131 0,973 101210,935 25,010
96 15 4 0,520 1,131 0,588 61197,310 15,122
97 15 5 1,000 1,131 1,131 117687,134 29,081
98 15 6 1,000 1,131 1,131 117687,134 29,081
99 15 7 1,000 1,131 1,131 117687,134 29,081
100 15 8 1,000 1,131 1,131 117687,134 29,081
101 15 9 1,000 1,131 1,131 117687,134 29,081
102 15 10 1,000 1,131 1,131 117687,134 29,081
103 15 11 0,680 1,131 0,769 80027,251 19,775
104 16 4 0,750 1,131 0,848 88265,350 21,811
105 16 5 1,000 1,131 1,131 117687,134 29,081
106 16 6 1,000 1,131 1,131 117687,134 29,081
107 16 7 1,000 1,131 1,131 117687,134 29,081
108 16 8 1,000 1,131 1,131 117687,134 29,081
109 16 9 1,000 1,131 1,131 117687,134 29,081
110 16 10 1,000 1,131 1,131 117687,134 29,081
111 16 11 0,450 1,131 0,509 52959,210 13,087
112 17 4 0,460 1,131 0,520 54136,082 13,377
113 17 5 1,000 1,131 1,131 117687,134 29,081
114 17 6 1,000 1,131 1,131 117687,134 29,081
115 17 7 1,000 1,131 1,131 117687,134 29,081
116 17 8 1,000 1,131 1,131 117687,134 29,081
117 17 9 1,000 1,131 1,131 117687,134 29,081
118 17 10 1,000 1,131 1,131 117687,134 29,081
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15
119 17 11 0,120 1,131 0,136 14122,456 3,490
120 18 5 0,900 1,131 1,018 105918,420 26,173
121 18 6 1,000 1,131 1,131 117687,134 29,081
122 18 7 1,000 1,131 1,131 117687,134 29,081
123 18 8 1,000 1,131 1,131 117687,134 29,081
124 18 9 1,000 1,131 1,131 117687,134 29,081
125 18 10 0,670 1,131 0,758 78850,380 19,484
126 19 6 0,460 1,131 0,520 54136,082 13,377
127 19 7 0,860 1,131 0,973 101210,935 25,010
128 19 8 0,890 1,131 1,007 104741,549 25,882
129 19 9 0,570 1,131 0,645 67081,666 16,576
AREA TOTAL 129,983 13525782,281 3342,294
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16
4.4 Sistema Circular de 1,8 cm de dimetro.
4.4.1 Contacto Petrleo-Gas (C.P.G).
Calculo del rea del Contacto Petrleo-Gas
tem i j Fc A_Total (cm^2) A_Total*Fc (cm^2) Area_Real (m^2) Area_Real(Acres)
1 3 3 0,780 2,545 1,985 206540,920 51,037
2 3 4 0,830 2,545 2,112 219780,722 54,309
3 4 3 0,920 2,545 2,341 243612,367 60,198
4 4 4 1,000 2,545 2,545 264796,051 65,433
5 4 5 0,370 2,545 0,942 97974,539 24,210
6 5 3 0,780 2,545 1,985 206540,920 51,037
7 5 4 1,000 2,545 2,545 264796,051 65,433
8 5 5 0,760 2,545 1,934 201244,999 49,729
9 6 3 0,480 2,545 1,221 127102,104 31,408
10 6 4 1,000 2,545 2,545 264796,051 65,433
11 6 5 0,930 2,545 2,367 246260,327 60,852
12 7 3 0,310 2,545 0,789 82086,776 20,284
13 7 4 1,000 2,545 2,545 264796,051 65,433
14 7 5 1,000 2,545 2,545 264796,051 65,433
15 8 3 0,280 2,545 0,713 74142,894 18,321
16 8 4 1,000 2,545 2,545 264796,051 65,433
17 8 5 0,940 2,545 2,392 248908,288 61,507
18 9 3 0,350 2,545 0,891 92678,618 22,901
19 9 4 1,000 2,545 2,545 264796,051 65,433
20 9 5 0,820 2,545 2,087 217132,762 53,655
21 10 3 0,480 2,545 1,221 127102,104 31,408
22 10 4 1,000 2,545 2,545 264796,051 65,433
23 10 5 0,450 2,545 1,145 119158,223 29,445
24 11 3 0,460 2,545 1,171 121806,183 30,099
25 11 4 0,920 2,545 2,341 243612,367 60,198
26 12 4 0,180 2,545 0,458 47663,289 11,778
AREA TOTAL 48,451 5041716,810 1245,835
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17
4.5 Sistema hexagonal de 0,8 cm de lado.
4.5.1 Contacto Agua-Petrleo (C.A.P).
Calculo del Area del Contacto Agua-Petrleo
tem i j Fc A_Total (cm^2) A_Total*Fc (cm^2) Area_Real (m^2) Area_Real(Acres)
1 1 3 0,160 1,663 0,266 27683,163 6,841
2 1 4 0,330 1,663 0,549 57096,524 14,109
3 1 5 0,280 1,663 0,466 48445,536 11,971
4 2 3 0,010 1,663 0,017 1730,198 0,428
5 2 4 0,410 1,663 0,682 70938,106 17,529
6 2 5 0,930 1,663 1,546 160908,387 39,761
7 2 6 1,000 1,663 1,663 173019,771 42,754
8 3 2 1,000 1,663 1,663 173019,771 42,754
9 3 3 1,000 1,663 1,663 173019,771 42,754
10 3 4 0,490 1,663 0,815 84779,688 20,950
11 3 5 0,670 1,663 1,114 115923,247 28,645
12 3 6 1,000 1,663 1,663 173019,771 42,754
13 4 2 1,000 1,663 1,663 173019,771 42,754
14 4 3 1,000 1,663 1,663 173019,771 42,754
15 4 4 1,000 1,663 1,663 173019,771 42,754
16 4 5 1,000 1,663 1,663 173019,771 42,754
17 4 6 0,910 1,663 1,513 157447,992 38,906
18 4 7 0,120 1,663 0,200 20762,373 5,130
19 5 2 0,590 1,663 0,981 102081,665 25,225
20 5 3 1,000 1,663 1,663 173019,771 42,754
21 5 4 1,000 1,663 1,663 173019,771 42,754
22 5 5 1,000 1,663 1,663 173019,771 42,754
23 5 6 1,000 1,663 1,663 173019,771 42,754
24 5 7 1,000 1,663 1,663 173019,771 42,754
25 6 2 1,000 1,663 1,663 173019,771 42,754
26 6 3 1,000 1,663 1,663 173019,771 42,754
27 6 4 0,340 1,663 0,565 58826,722 14,536
28 6 5 0,400 1,663 0,665 69207,908 17,102
29 6 6 1,000 1,663 1,663 173019,771 42,754
30 6 7 1,000 1,663 1,663 173019,771 42,754
31 6 8 1,000 1,663 1,663 173019,771 42,754
32 7 2 1,000 1,663 1,663 173019,771 42,754
33 7 3 1,000 1,663 1,663 173019,771 42,754
34 7 4 1,000 1,663 1,663 173019,771 42,754
35 7 5 1,000 1,663 1,663 173019,771 42,754
36 7 6 1,000 1,663 1,663 173019,771 42,754
37 7 7 0,450 1,663 0,748 77858,897 19,239
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18
38 8 2 0,040 1,663 0,067 6920,791 1,710
39 8 3 1,000 1,663 1,663 173019,771 42,754
40 8 4 1,000 1,663 1,663 173019,771 42,754
41 8 5 1,000 1,663 1,663 173019,771 42,754
42 8 6 1,000 1,663 1,663 173019,771 42,754
43 8 7 1,000 1,663 1,663 173019,771 42,754
44 8 8 1,000 1,663 1,663 173019,771 42,754
45 9 2 1,000 1,663 1,663 173019,771 42,754
46 9 3 1,000 1,663 1,663 173019,771 42,754
47 9 4 1,000 1,663 1,663 173019,771 42,754
48 9 5 0,460 1,663 0,765 79589,095 19,667
49 9 6 0,610 1,663 1,014 105542,060 26,080
50 9 7 1,000 1,663 1,663 173019,771 42,754
51 9 8 1,000 1,663 1,663 173019,771 42,754
52 10 3 1,000 1,663 1,663 173019,771 42,754
53 10 4 1,000 1,663 1,663 173019,771 42,754
54 10 5 1,000 1,663 1,663 173019,771 42,754
55 10 6 1,000 1,663 1,663 173019,771 42,754
56 10 7 1,000 1,663 1,663 173019,771 42,754
57 10 8 1,000 1,663 1,663 173019,771 42,754
58 10 9 1,000 1,663 1,663 173019,771 42,754
59 11 2 0,320 1,663 0,532 55366,327 13,681
60 11 3 0,040 1,663 0,067 6920,791 1,710
61 11 4 1,000 1,663 1,663 173019,771 42,754
62 11 5 1,000 1,663 1,663 173019,771 42,754
63 11 6 1,000 1,663 1,663 173019,771 42,754
64 11 7 1,000 1,663 1,663 173019,771 42,754
65 11 8 1,000 1,663 1,663 173019,771 42,754
66 12 3 1,000 1,663 1,663 173019,771 42,754
67 12 4 1,000 1,663 1,663 173019,771 42,754
68 12 5 1,000 1,663 1,663 173019,771 42,754
69 12 6 1,000 1,663 1,663 173019,771 42,754
70 12 7 1,000 1,663 1,663 173019,771 42,754
71 12 8 0,210 1,663 0,349 36334,152 8,978
72 12 9 0,510 1,663 0,848 88240,083 21,805
73 13 2 1,000 1,663 1,663 173019,771 42,754
74 13 3 1,000 1,663 1,663 173019,771 42,754
75 13 4 1,000 1,663 1,663 173019,771 42,754
76 13 5 1,000 1,663 1,663 173019,771 42,754
77 13 6 1,000 1,663 1,663 173019,771 42,754
78 13 7 1,000 1,663 1,663 173019,771 42,754
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19
79 13 8 1,000 1,663 1,663 173019,771 42,754
80 14 2 1,000 1,663 1,663 173019,771 42,754
81 14 3 1,000 1,663 1,663 173019,771 42,754
82 14 4 1,000 1,663 1,663 173019,771 42,754
83 14 5 0,100 1,663 0,166 17301,977 4,275
84 14 6 0,890 1,663 1,480 153987,596 38,051
85 14 7 1,000 1,663 1,663 173019,771 42,754
86 14 8 1,000 1,663 1,663 173019,771 42,754
87 15 2 1,000 1,663 1,663 173019,771 42,754
88 15 3 1,000 1,663 1,663 173019,771 42,754
89 15 4 1,000 1,663 1,663 173019,771 42,754
90 15 5 1,000 1,663 1,663 173019,771 42,754
91 15 6 1,000 1,663 1,663 173019,771 42,754
92 15 7 1,000 1,663 1,663 173019,771 42,754
93 15 8 1,000 1,663 1,663 173019,771 42,754
94 16 2 0,990 1,663 1,646 171289,573 42,327
95 16 3 0,010 1,663 0,017 1730,198 0,428
96 16 4 0,130 1,663 0,216 22492,570 5,558
97 16 5 1,000 1,663 1,663 173019,771 42,754
98 16 6 1,000 1,663 1,663 173019,771 42,754
99 16 7 1,000 1,663 1,663 173019,771 42,754
100 16 8 1,000 1,663 1,663 173019,771 42,754
101 17 2 1,000 1,663 1,663 173019,771 42,754
102 17 3 1,000 1,663 1,663 173019,771 42,754
103 17 4 1,000 1,663 1,663 173019,771 42,754
104 17 5 1,000 1,663 1,663 173019,771 42,754
105 17 6 1,000 1,663 1,663 173019,771 42,754
106 17 7 1,000 1,663 1,663 173019,771 42,754
107 18 3 0,810 1,663 1,347 140146,015 34,631
108 18 4 0,510 1,663 0,848 88240,083 21,805
109 18 5 1,000 1,663 1,663 173019,771 42,754
110 18 6 1,000 1,663 1,663 173019,771 42,754
111 18 7 1,000 1,663 1,663 173019,771 42,754
112 18 8 1,000 1,663 1,663 173019,771 42,754
113 19 3 1,000 1,663 1,663 173019,771 42,754
114 19 4 1,000 1,663 1,663 173019,771 42,754
115 19 5 1,000 1,663 1,663 173019,771 42,754
116 19 6 1,000 1,663 1,663 173019,771 42,754
AREA TOTAL 165,806 17253531,571 4263,441
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20
4.6 Sistema hexagonal de 1,3 cm de lado.
4.6.1 Contacto Petrleo-Gas (C.P.G).
Calculo del Area del Contacto Petrleo-Gas
tem i j Fc A_Total (cm^2) A_Total*Fc (cm^2) Area_Real (m^2) Area_Real(Acres)
1 2 3 0,780 4,391 3,425 356366,660 88,060
2 2 4 0,350 4,391 1,537 159908,117 39,514
3 3 2 0,550 4,391 2,415 251284,183 62,094
4 3 3 1,000 4,391 4,391 456880,333 112,898
5 3 4 0,280 4,391 1,229 127926,493 31,611
6 4 3 0,880 4,391 3,864 402054,693 99,350
7 4 4 0,980 4,391 4,303 447742,726 110,640
8 4 5 0,090 4,391 0,395 41119,230 10,161
9 5 2 0,280 4,391 1,229 127926,493 31,611
10 5 3 1,000 4,391 4,391 456880,333 112,898
11 5 4 0,860 4,391 3,776 392917,086 97,092
12 6 3 0,580 4,391 2,547 264990,593 65,481
13 6 4 1,000 4,391 4,391 456880,333 112,898
14 6 5 0,320 4,391 1,405 146201,707 36,127
15 7 3 0,980 4,391 4,303 447742,726 110,640
16 7 4 0,770 4,391 3,381 351797,856 86,931
17 8 3 0,620 4,391 2,722 283265,806 69,997
18 8 4 0,960 4,391 4,215 438605,120 108,382
19 9 2 0,340 4,391 1,493 155339,313 38,385
20 9 3 1,000 4,391 4,391 456880,333 112,898
21 9 4 0,340 4,391 1,493 155339,313 38,385
22 10 3 0,480 4,391 2,107 219302,560 54,191
23 10 4 0,280 4,391 1,229 127926,493 31,611
AREA TOTAL 64,630 6725278,502 1661,853
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21
5. CONSTRUCCIN DE LA TABLA DE CLCULOS( AREA VARIABLE)
5.1 Contacto Agua- Petrleo
tem Dimensiones A_Total (cm^2) Area_Real (m^2) Area_Real(Acres)
1 7,5 3,5 26,25 2731529,657 674,9756778
2 7,5 3,5 26,25 2731529,657 674,9756778
3 7,5 3,5 26,25 2731529,657 674,9756778
4 7,5 3,5 26,25 2731529,657 674,9756778
5(a,b) 3,5 1,7 5,95 619146,7222 152,994487
6(a,b) 3 7 21 2185223,725 539,9805422
7(a,b) 2,6 3 7,8 811654,5265 200,5642014
8(a,b) 7,5 1,5 11,25 1170655,567 289,2752905
AREA TOTAL 15712799,17 3882,717232
5.2 Contacto Petrleo Gas
Item Dimensiones A_Total (cm^2) Area_Real (m^2) Area_Real(Acres)
1 11,2 2,5 28 2913631,634 719,9740563
2(a,b) 11,2 2,5 28 2913631,634 719,9740563
3(a,b) 2,5 2,5 6,25 650364,204 160,7084947
4(a,b) 2,5 2,5 6,25 650364,204 160,7084947
AREA TOTAL 7127991,675 1761,365102
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22
6. RESULTADOS
6.1 Area Constante
6.2 Area Variable
Para hallar el rea real se utiliz la regla de tres simple:
Si Esc.: 3,1cm: 100 000cm por lo cual referido al trmino de rea seria:
9,61cm2: 1000 000 m2
9,6
( )
Para la conversin de m2 a acres el factor de conversin es:
TABLA DE RESULTADOS DEL AREA C.A.P(Acres)
Sist. Ortogonal Sist. Circular Sist. Hexagonal
L=0,8 cm D=1,2 cm
L=0,8 cm
4218,30743
3342,29359
4263,4405
TABLA DE RESULTADOS DEL AREA C.P.G(Acres)
Sist. Ortogonal Sist. Circular Sist. Hexagonal
L =1,2 cm
D=1,8 cm
L=1,3 cm
1582,17384
1245,83536
1661,85251
TABLA DE RESULTADOS AREA VARIABLE (Acres)
C.A.P. C.P.G.
3882,717232
1761,365102
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23
0
500
1000
1500
2000
2500
3000
3500
4000
4500
1
Resultados Contacto Agua-Petroleo
Sist. Ortogonal de L=0,8 cm
Sist. Cicular de D=1,2 cm
Sist. Hexagonal de L=0,8 cm
0
200
400
600
800
1000
1200
1400
1600
1800
1
Resultados Contacto Petroleo-Gas
Sist. Ortogonal de L=1,2 cm
Sist. Circular de D=1,8 cm
Sist. Hexagonal de L=1,3 cm
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24
7. CONCLUSIONES
Se determin el rea del contacto Agua-Petrleo y del contacto Petrleo-
Gas de la estructura mediante los diferentes tipos de sistemas de grillado o
mallado de manera exitosa pero con variaciones de acuerdo al sistema de
grillado.
El sistema de grillado o mallado ms exacto es el ortogonal puesto es ms
fcil leer el factor de correccin, y adems que entre ms pequeo sea el
rea del grillado o malla el rea total ser ms prximo al verdadero, es
como la integracin numrica puesto que mientras ms pequeo sea el
delta de integracin mejor ser la integracin.
El sistema de grillado o mallado circular es el que tiene ms error, puesto
que no se toma en cuenta el espacio que se deja entre circunferencias,
adems verificando en nuestra grafica la variacin de resultados por lo
cual no es recomendable utilizar este tipo de grillado o mallado en la
prctica.
El sistema de grillado hexagonal es otra alternativa para hacer el clculo de
rea ya que se comente menos error a comparacin del grillado circular,
debido a que los resultados existe una variacin menor con respecto al
sistema circular pero la dificultad se presenta a la hora de leer el factor de
correccin.
Por la facilidad tanto de graficar y como as su lectura del factor de
correccin se recomienda utilizar grilladas o malas ortogonales en las
prximas prcticas.
8. ANEXOS