DAFTAR PUSTAKA
Arps’, J, J.1945. Analysis of Decline Curves. Trans. AIME.160-247. Marhaendrajana, Taufan. 2000. Modelling and Analysis of Flow Behavior in Single and Multiwell Bounded Reseroirs. Disertasi.Texas: Texas A&M University. Marhaendrajana, T, Schlumberger, Blasingame, T.A. 2001. Decline Curve Analysis Using Type Curves – Evaluation of Well Performance Behavior in a Multiwell Reservoir System. SPE 71517. 1-10. Saefulloh, Gan Gan. 2006. Estimasi Decline Menggunakan Sequential Kriging. Tugas Akhir. Bandung: Institut Teknologi Bandung. Wahyuningsih, Sri, dkk. 2007. Table Method for Hyperbolic Decline Curve.
37
LAMPIRAN A
Program perhitungan tekanan pada Multiwell Reservoir System dengan menggunakan Matlab. function [P] = TARahmad(tDa,QD,Xw,Yw,A,Mode) Z = sqrt(A);
%% cek variable input if nargin<5 error('Input arent sufficient') end if nargin == 5 Mode = 'Multip' end %% Kasus Khusus: Titik Pengamatan sama dengan Titik sumur if size(Xw) ~= size(Yw) error('Size of matrix Xw and Yw must be same') end matrixSize = size(Xw); sizeTda = size(tDa); if sizeTda(2) ~= 1 error('Please Enter Colum Matrix only for t') end
%P is 3 Dimentional, and will be extended later P = zeros(matrixSize(1),matrixSize(2)); PTemp = zeros(matrixSize(1),matrixSize(2)); %TermExpression = zeros(1,4); X = Xw;
38
Y = Yw; NPointX = matrixSize(1); NPointY = matrixSize(2); NWellX = matrixSize(1); NWellY = matrixSize(2); NTDa = sizeTda(1);
Xwd = X/Z; Ywd = Y/Z; Xd = X/Z; Yd = Y/Z; Xed = 3000/Z; %Panjang Reservoir Yed = 2500/Z; %Lebar Reservoir Nup = 10; Mup = 10; Term0 = 0; Term1 = 0; Term2 = 0; Term3 = 0; PTempTotalForEachWell = 0; indexTemp = 0; for nt = 1:NTDa Term0 = 2*pi*tDa(nt); for i = 1:NPointX %urutan Baris for j=1:NPointY %Urutan Kolom for Wx = 1:NWellX %bilangan Well Baris for Wy = 1:NWellY %bilangan Well Kolom PTempTotalForEachWell = 0; for n = 1:Nup %Bilangan n Temp0 = (1 - exp(-n^2*pi^2*tDa(nt)/(Xed^2))); Temp1 = n^2*pi^2/(Xed^2); Temp2 = cos(n*pi*Xd(i,j)/Xed)*cos(n*pi*Xwd(Wx,Wy)/Xed); Term1 = Temp0*Temp2/Temp1;
39
Temp3 = (1 - exp(-n^2*pi*2*tDa(nt)/(Yed^2))); Temp4 = n^2*pi^2/(Yed^2); Temp5 = cos(n*pi*Yd(i,j)/Yed)*cos(n*pi*Ywd(Wx,Wy)/Yed); Term2 = Temp3*Temp5/Temp4; TempTerm3 = 0; for m = 1:Mup %Bilangan m Temp6 = (1 - exp(-(m^2*pi^2*tDa(nt)/(Yed^2)) (n^2*pi^2*tDa(nt)/(Xed^2)))); Temp7 = (n^2*pi^2/(Xed^2))+(m^2*pi^2/(Yed^2)); Temp8 = cos(n*pi*Xd(i,j)/Xed)*cos(n*pi*Xd(i,j)/Xwd(Wx,Wy)); Temp9 = cos(m*pi*Yd(i,j)/Yed)*cos(m*pi*Yd(i,j)/Ywd(Wx,Wy)); TempTerm3 = TempTerm3 + (Temp6*Temp8*Temp9/Temp7); end %m Term3 = TempTerm3; end %n PTempTotalForEachWell = Term0+(4*pi*Term1)+(4*pi*Term2)+(8*pi*Term3); %PTempTotalForEachWell = (4*pi*Term1)+(4*pi*Term2)+(8*pi*Term3); indexTemp = indexTemp +1; TermExpression(indexTemp,:) = [Term0 Term1 Term2 Term3]; if Mode == 'single' if (i==Wx) & (j == Wy) PTemp(i,j) = PTempTotalForEachWell; end else %MULTIPLE WELL PTemp(i,j) = PTemp(i,j) + PTempTotalForEachWell; end
end %Wy end %Wx end %j
40
end %i if nt == 1 P = QD(nt,:).*PTemp; %P = PTemp; else P(nt,:,:) = QD(nt,:).*PTemp; %P(nt,:,:) = PTemp; end PTemp = zeros(matrixSize(1),matrixSize(2)); end %nt Catatan: A
= 7500000
qref
= 50
φ
= 0.2
μ
= 0.8
ct
= 0.000003
k
= 5
tDA
=0.00633kt / φ μ ct A
qD
= q(t) / qref
41
LAMPIRAN B
Penurunan solusi multiwell: Model matematika untuk sistem ini adalah:
φμ ct ∂p ∂ 2 p ∂ 2 p nwell qi ( t ) B δ ( x − xw , i , y − y w , i ) = + 2 −∑ 2 k ∂t ∂x ∂y i =1 Ah ( k / μ )
(B.1)
Bentuk (B.2) dalam dimensionless ditulis sebagai:
(B.2) Dimana:
pD =
2π kh ( pi − p ( x, y, t ) ) qref B μ
t DA =
kt φμ ct A
qD ( t DA ) =
q (t ) qref
x A y yD = A
xD =
42
Kemudian dengan menggunakan prinsip Duhamel kita dapat menentukan solusi persamaan (B.2) menjadi :
(
)
pD xD , yD , ⎡⎣ xwD ,1...xwD ,nwell ⎤⎦ , ⎡⎣ ywD ,1... ywD ,nwell ⎤⎦ , xeD , yeD , t DA = nwell tDA
d ∑ ∫ q (τ ) dτ ⎡⎣ p ( x , y i =1 0
D,i
Dcr
D
D
, xwD,i , ywD,i , xeD , yeD , [tDA −τ ]) ⎤⎦ dτ
(B.3)
Lalu solusi tekanan dimensionless sumur ditentukan dengan mengevaluasi persamaan (B.3) pada lokasi sumur “k” sehingga :
(
)
nwell tDA
d pD ⎣⎡xwD,k + ε ⎦⎤ , ⎣⎡ ywD,k + ε ⎦⎤ , tDA = ∑ ∫ qD,i (τ ) ⎡⎣ pDcr ( tDA −τ ) ⎤⎦k,i dτ (B.4) dτ i=1 0
Dengan memasukan “skin factor” sekitar sumur dalam persamaan (B.4) kita dapatkan :
(
)
nwell tDA
d pD ⎡⎣ xwD,k + ε ⎤⎦ , ⎡⎣ ywD,k + ε ⎤⎦ , tDA = ∑ ∫ qD,i (τ ) ⎡⎣ pDcr ( tDA − τ ) ⎤⎦ k ,i dτ dτ i =1 0
+ qDk ( t DA ) sk
(B.5)
Aspek komputasi: Perhatikan kembali persamaan (B.6), kita punyai :
(
)
nwell tDA
d pD ⎡⎣ xwD,k + ε ⎤⎦ , ⎡⎣ ywD,k + ε ⎤⎦ , tDA = ∑ ∫ qD,i (τ ) ⎡⎣ pDcr ( tDA − τ ) ⎤⎦ k ,i dτ dτ i =1 0
+ qDk ( t DA ) sk
(B.6)
Kita akan mengaproksimasi laju kontinu, qD ( t DA ) sebagai fungsi waktu dengan mendiskritisasi integral pada persamaan (B.6) menjadi :
43
(B.7)
Dimana:
Grafik dari aproksimasi diskrit laju produksi pada persamaan (B.7) sebagai berikut :
Grafik B.1. Aproksimasi diskrit laju produksi Substitusi persamaan (B.7) ke (B.6) dan evaluasi pada t DA[n] , kita peroleh :
44
(B.8) Kemudian kita dapat menuliskan persamaan (B.8) ke dalam bentuk superposisi sebagai berikut :
(
)
pD ⎡⎣ xwD , k + ε ⎤⎦ , ⎡⎣ ywD , k + ε ⎤⎦ , t DA[n] =
∑∑ ⎡⎢⎣( q [ ]
nwell n
D j ,i
i =1 j =1
) (
)
− qD[ j −1],i pDcr xwD,k , ywD,k , xwD,i , ywD,i , xeD , yeD , ⎡⎣tDA[n] − tDA[ j −1] ⎤⎦ ⎤⎥ ⎦
+ qD[ n],k sk
(B.9)
Keterangan : A
= luas area
B
= formation volume factor
pi
= tekanan awal
qi
= laju produksi awal
qref
= laju produksi reference
nwell
= jumlah sumur
x
= koordinat x
y
= koordinat y
t
= waktu
xw
= koordinat sumur pada sumbu x
45
yw
= koordinat sumur pada sumbu y
φ
= porositas
μ
= viskositas cairan
ct
= total compressibility
k
= permeabilitas
h
= ketebalan reservoir
pD
= dimensionless tekanan
xwD
= dimensionless jarak sumur - x
ywD
= dimensionless jarak sumur – y
xeD
= dimensionless jarak reservoir-x
yeD
= dimensionless jarak reservoir-y
tDA
= dimensionless waktu
qD
= dimensionless laju produksi
s
= skin factor
46
LAMPIRAN C
Penurunan Rumus Decline Exponential Decline p t = p0 e − Dt Decline ln p t = ln p0 − Dt Dt = ln p0 − ln p t
= ln
(C.1)
(C.2)
p0 pt
Kumulatif t
Pt = ∫ p τ dτ 0
t
= ∫ p0 e − Dτ dτ 0
p0 e − Dτ d(− Dτ) − D 0 t
=∫
t
⎡ p0 e − Dτ ⎤ =⎢ ⎥ ⎣ −D ⎦ 0 p0 e − Dt p0 e0 − −D −D p0 − p t = D =
47
Pt = p0 t =
p0 − p t D p0 t p0 p − t Dp 0 t Dp0 t
pt p0 = Dt 1−
(C.3) −1
⎛p ⎞ 1− ⎜ 0 ⎟ p = ⎝ t⎠ p ln 0 pt p 0 Jika 0 → 1 , persamaan (C.3) berbentuk maka kita gunakan aturan pt 0 p L’Hopital untuk persamaan (C.3) misal r = 0 pt
1 − r −1 L r −2 1 1 = lim = = 1 lim lim = → → r →1 r 1 r 1 ln r 1/ r r 1 Hyperbolic Decline p t =
p0 , 0
(C.4)
Kumulatif t
Pt = ∫ p τ dτ 0
48
t
p0 dτ 1/ b (1 bD ) + τ 0
Pt = ∫
t
1 − p0 (1 + bDτ) b d(bDτ) = bD ∫0 t
1 − +1 ⎤ p 1 ⎡ b (1 bD ) = 0 + τ ⎢ ⎥ bD − 1 + 1 ⎣ ⎦0 b 1 − +1 ⎞ p0 ⎛ =− ⎜ (1 + bDτ) b − 1⎟ (1 − b)D ⎝ ⎠
p0 ⎛ ⎛ p t ⎞ ⎜⎜ ⎟ =− (1 − b)D ⎜ ⎝ p 0 ⎠ ⎝
1− b
⎞ − 1⎟ ⎟ ⎠
p0 ⎛ ⎛ p t ⎞ ⎜1 − ⎜ ⎟ = (1 − b)D ⎜ ⎝ p 0 ⎠ ⎝
1− b
⎞ ⎟ ⎟ ⎠
=
p0 ⎛ p10− b − p1t − b ⎞ ⎜ ⎟ (1 − b)D ⎝ p10− b ⎠
=
p0b (p10− b − p1t − b ) (1 − b)D
(C.5)
Decline
pt =
p0 (1 + bDt)1/ b
1 − pt = (1 + bDt) b p0
⎛ pt ⎞ ⎜ ⎟ ⎝ p0 ⎠
−b
= (1 + bDt) −b
⎛p ⎞ bDt = ⎜ t ⎟ − 1 ⎝ p0 ⎠ −b
b
⎛ pt ⎞ ⎛ p0 ⎞ ⎜ ⎟ −1 ⎜ ⎟ −1 p p =⎝ t⎠ Dt = ⎝ 0 ⎠ b b
(C.6)
49
Pt p0b (p10− b − p1t − b ) = p 0 t (1 − b)D p0 t =
p 0b b
⎛ po ⎞ ⎜ ⎟ −1 p (1 − b) ⎝ t ⎠ b
= p0b (p10− b − p1t − b )
=
(p10− b − p1t − b ) p0
b ⎛ ⎛ p ⎞b ⎞ p0 (1 − b) ⎜ ⎜ 0 ⎟ − 1⎟ ⎜ ⎝ pt ⎠ ⎟ ⎝ ⎠
⎛ ⎛ p ⎞1− b ⎞ ⎜1 − ⎜ 0 ⎟ ⎟ b ⎜ ⎝ pt ⎠ ⎟ ⎝ ⎠ ⎛ ⎛ p ⎞b ⎞ (1 − b) ⎜ ⎜ 0 ⎟ − 1⎟ ⎜ ⎝ pt ⎠ ⎟ ⎝ ⎠ b −1
(C.7)
⎛p ⎞ 1− ⎜ t ⎟ p ⎛ b ⎞ = ⎝ 0b ⎠ ⎜ ⎟ ⎝ 1− b ⎠ ⎛ p0 ⎞ ⎜ ⎟ −1 ⎝ pt ⎠ p 0 maka kita gunakan aturan Jika 0 → 1 , persamaan (C.7) berbentuk 0 pt p L’Hopital untuk persamaan (C.7) misal r = 0 pt lim r →1
1 − r b −1 ⎛ b ⎞ L (1 − b)r b − 2 ⎛ b ⎞ 1 lim ⎜ ⎟ ⎜ ⎟ = =1 r b − 1 ⎝ 1 − b ⎠ = r →1 br b −1 ⎝ 1 − b ⎠ 1
Harmonic Decline p t = Decline : pt = (1 + bDt) −1 p0 p0 = (1 + bDt) pt p Dt = 0 − 1 pt
p0 (1 + Dt)
(C.8)
(C.9)
50
Kumulatif : t
p0 dτ (1 + Dτ) 0
Pt = ∫
t
=
p0 (1 + bDτ) −1 d(bDτ) ∫ bD 0
p0 t [ ln(1 + Dτ)]0 bD p0 Pt = [ln(1 + Dt) − ln1] bD p (1 + Dt) = 0 ln bD 1 p0 = ln(1 + Dt) bD p0 ⎛ p0 ⎞ ln ⎜ ⎟ D ⎝ pt ⎠ Pt = p0 t p0 t =
⎛p ⎞ ln ⎜ 0 ⎟ p0 −1 ⎝ pt ⎠ pt = t p0 t p0
(C.10)
⎛p ⎞ ln ⎜ 0 ⎟ p = ⎝ t⎠ p0 −1 pt p 0 Jika 0 → 1 , persamaan (C.10) berbentuk maka kita gunakan aturan 0 pt p L’Hopital untuk persamaan (C.10) misal r = 0 pt
lim r →1
ln r L 1/ r 1 1 lim = lim = = 1 = r →1 1 r →1 r r −1 1
51
LAMPIRAN D
Penentuan nilai decline tekanan dengan eksponential decline Tabel L.D.1 ln Tekanan Multiwell Reservoir System No
Tekanan KMJ-11
ln(Tekanan KMJ-11)
Tekanan KMJ-14
ln(Tekanan KMJ-14)
1
114.91
4.74
114.91
4.74
2
114.83
4.74
114.87
4.74
3
114.75
4.74
114.82
4.74
4
114.67
4.74
114.78
4.74
5
114.60
4.74
114.74
4.74
6
114.53
4.74
114.69
4.74
7
114.46
4.74
114.64
4.74
8
114.37
4.74
114.61
4.74
9
114.30
4.74
114.54
4.74
10
114.26
4.74
114.52
4.74
11
114.19
4.74
114.48
4.74
12
114.10
4.74
114.45
4.74
13
114.03
4.74
114.41
4.74
14
113.94
4.74
114.37
4.74
15
113.88
4.74
114.33
4.74
16
113.82
4.73
114.30
4.74
17
113.66
4.73
114.18
4.74
18
113.59
4.73
114.17
4.74
19
113.51
4.73
114.13
4.74
20
113.42
4.73
114.08
4.74
21
113.42
4.73
114.05
4.74
22
113.34
4.73
114.04
4.74
23
113.25
4.73
113.97
4.74
24
113.22
4.73
113.96
4.74
25
113.13
4.73
113.96
4.74
26
113.15
4.73
113.92
4.74
27
112.96
4.73
113.89
4.74
52
28
112.89
4.73
113.84
4.73
29
112.71
4.72
113.70
4.73
30
112.59
4.72
113.68
4.73
31
112.52
4.72
113.63
4.73
32
112.45
4.72
113.60
4.73
33
112.35
4.72
113.55
4.73
34
112.22
4.72
113.51
4.73
35
112.20
4.72
113.48
4.73
36
112.13
4.72
113.43
4.73
37
112.04
4.72
113.40
4.73
38
112.00
4.72
113.08
4.73
39
111.92
4.72
113.30
4.73
40
111.78
4.72
113.27
4.73
41
111.96
4.72
113.22
4.73
42
111.64
4.72
113.01
4.73
43
111.53
4.71
113.07
4.73
44
111.53
4.71
113.08
4.73
45
111.60
4.71
112.85
4.73
46
111.51
4.71
112.39
4.72
47
111.46
4.71
112.64
4.72
48
111.38
4.71
112.45
4.72
49
111.18
4.71
112.47
4.72
50
111.30
4.71
112.59
4.72
51
111.19
4.71
112.57
4.72
52
111.11
4.71
112.62
4.72
53
111.07
4.71
112.22
4.72
54
110.96
4.71
112.45
4.72
55
110.89
4.71
112.46
4.72
56
110.83
4.71
112.40
4.72
57
110.78
4.71
112.22
4.72
58
110.73
4.71
112.11
4.72
59
110.67
4.71
112.16
4.72
60
110.63
4.71
112.16
4.72
61
110.70
4.71
112.15
4.72
62
110.56
4.71
112.03
4.72
63
110.58
4.71
112.05
4.72
64
110.42
4.70
112.04
4.72
65
110.37
4.70
112.04
4.72
66
110.31
4.70
112.05
4.72
53
67
110.30
4.70
111.98
4.72
68
110.23
4.70
111.94
4.72
69
110.16
4.70
111.92
4.72
70
110.03
4.70
111.39
4.71
71
109.98
4.70
111.72
4.72
72
109.91
4.70
111.78
4.72
73
109.48
4.70
111.36
4.71
74
109.43
4.70
111.73
4.72
75
109.38
4.69
111.76
4.72
76
109.39
4.69
111.80
4.72
77
109.22
4.69
110.91
4.71
78
109.12
4.69
111.13
4.71
79
109.07
4.69
111.04
4.71
80
109.00
4.69
110.89
4.71
81
109.00
4.69
111.35
4.71
82
109.05
4.69
111.51
4.71
83
108.93
4.69
111.51
4.71
84
108.55
4.69
111.49
4.71
85
108.53
4.69
111.44
4.71
86
108.84
4.69
111.42
4.71
87
108.95
4.69
110.40
4.70
88
109.04
4.69
110.98
4.71
89
108.38
4.69
110.87
4.71
90
108.54
4.69
111.19
4.71
91
108.65
4.69
111.39
4.71
92
108.25
4.68
110.45
4.70
93
108.38
4.69
110.92
4.71
94
108.43
4.69
111.00
4.71
95
108.49
4.69
110.07
4.70
96
108.51
4.69
110.77
4.71
97
108.41
4.69
110.84
4.71
98
108.64
4.69
110.70
4.71
99
108.70
4.69
110.81
4.71
100
108.69
4.69
110.77
4.71
101
107.52
4.68
110.77
4.71
102
107.37
4.68
110.88
4.71
103
107.39
4.68
110.88
4.71
104
107.44
4.68
110.85
4.71
105
107.44
4.68
110.11
4.70
54
106
107.46
4.68
110.44
4.70
107
107.40
4.68
110.50
4.71
108
107.37
4.68
110.56
4.71
109
107.25
4.68
110.53
4.71
110
106.96
4.67
110.49
4.70
111
106.99
4.67
109.94
4.70
112
106.95
4.67
109.96
4.70
113
106.91
4.67
110.20
4.70
114
106.83
4.67
110.25
4.70
115
107.10
4.67
110.25
4.70
116
106.96
4.67
110.18
4.70
117
106.95
4.67
110.19
4.70
118
106.92
4.67
110.17
4.70
119
106.97
4.67
110.29
4.70
120
107.01
4.67
110.28
4.70
121
106.96
4.67
110.23
4.70
122
106.98
4.67
110.20
4.70
123
106.98
4.67
110.16
4.70
124
106.54
4.67
110.09
4.70
125
106.58
4.67
109.63
4.70
126
106.65
4.67
109.58
4.70
127
106.69
4.67
110.05
4.70
128
106.35
4.67
110.09
4.70
129
106.70
4.67
110.00
4.70
130
106.79
4.67
109.74
4.70
131
106.84
4.67
109.88
4.70
132
106.78
4.67
109.84
4.70
133
106.80
4.67
109.81
4.70
134
106.79
4.67
109.81
4.70
135
106.78
4.67
109.91
4.70
136
106.77
4.67
110.02
4.70
137
106.77
4.67
108.83
4.69
138
106.69
4.67
109.42
4.70
139
104.93
4.65
109.47
4.70
140
104.89
4.65
109.49
4.70
141
105.07
4.65
108.85
4.69
142
105.13
4.66
109.32
4.69
143
105.28
4.66
109.36
4.69
144
105.28
4.66
109.40
4.69
55
145
105.35
4.66
108.50
4.69
146
105.39
4.66
109.28
4.69
147
105.33
4.66
107.38
4.68
148
105.36
4.66
108.26
4.68
149
105.34
4.66
108.35
4.69
150
105.48
4.66
108.39
4.69
151
105.33
4.66
108.36
4.69
152
105.34
4.66
108.33
4.69
153
105.28
4.66
108.39
4.69
154
105.10
4.65
108.38
4.69
155
104.78
4.65
108.39
4.69
156
104.92
4.65
108.32
4.69
157
105.02
4.65
108.29
4.68
158
105.06
4.65
108.27
4.68
159
104.98
4.65
108.24
4.68
160
104.91
4.65
108.23
4.68
161
104.87
4.65
108.23
4.68
162
104.89
4.65
108.29
4.68
163
104.97
4.65
108.26
4.68
164
104.95
4.65
108.30
4.68
165
104.91
4.65
108.39
4.69
166
104.74
4.65
108.36
4.69
167
104.91
4.65
107.90
4.68
168
104.80
4.65
107.75
4.68
169
104.91
4.65
108.22
4.68
170
104.84
4.65
108.23
4.68
171
104.76
4.65
107.47
4.68
172
104.57
4.65
108.15
4.68
173
104.31
4.65
108.17
4.68
174
104.06
4.64
106.78
4.67
56
Tekanan
Tekanan Multiwell 4.76 4.74 4.72 4.7 4.68 4.66 4.64 4.62
y = -0.0004x + 4.7425 2 R = 0.9687
KMJ-11 KMJ-14 Linear (KMJ-11) Linear (KMJ-14)
y = -0.0006x + 4.7399 2 R = 0.9856 0
50
100
150
200
Bulan
Grafik L.D.1 Tekanan Multiwell Reservoir System
Sebagaimana telah di bahas dalam Bab III bahwa:
y = α t + β , dimana y = ln (p(t))
;α =D
; β = ln (po)
Dari grafik dapat ditentukan: Decline KMJ-11 = 0.0006 dan Decline KMJ14 = 0.0004. Tabel L.D.2 ln Tekanan Single Well Reservoir System Waktu (Bulan)
Tekanan KMJ-11
Ln(Tekanan KMJ-11)
Tekanan KMJ-14
ln(Tekanan KMJ-14)
1
114.91
4.74
114.91
4.74
2
114.87
4.74
114.89
4.74
3
114.83
4.74
114.87
4.74
4
114.79
4.74
114.85
4.74
5
114.75
4.74
114.82
4.74
6
114.72
4.74
114.80
4.74
7
114.69
4.74
114.77
4.74
8
114.64
4.74
114.76
4.74
9
114.60
4.74
114.73
4.74
10
114.59
4.74
114.71
4.74
11
114.55
4.74
114.70
4.74
12
114.51
4.74
114.68
4.74
13
114.47
4.74
114.66
4.74
14
114.43
4.74
114.64
4.74
15
114.39
4.74
114.62
4.74
16
114.36
4.74
114.61
4.74
57
17
114.29
4.74
114.55
4.74
18
114.25
4.74
114.54
4.74
19
114.21
4.74
114.52
4.74
20
114.17
4.74
114.50
4.74
21
114.17
4.74
114.48
4.74
22
114.13
4.74
114.47
4.74
23
114.08
4.74
114.44
4.74
24
114.07
4.74
114.43
4.74
25
114.02
4.74
114.43
4.74
26
114.03
4.74
114.42
4.74
27
113.93
4.74
114.40
4.74
28
113.90
4.74
114.38
4.74
29
113.81
4.73
114.31
4.74
30
113.75
4.73
114.29
4.74
31
113.72
4.73
114.27
4.74
32
113.68
4.73
114.25
4.74
33
113.63
4.73
114.23
4.74
34
113.57
4.73
114.21
4.74
35
113.56
4.73
114.19
4.74
36
113.52
4.73
114.17
4.74
37
113.48
4.73
114.15
4.74
38
113.46
4.73
114.00
4.74
39
113.42
4.73
114.11
4.74
40
113.34
4.73
114.09
4.74
41
113.44
4.73
114.06
4.74
42
113.28
4.73
113.96
4.74
43
113.22
4.73
113.99
4.74
44
113.22
4.73
114.00
4.74
45
113.26
4.73
113.88
4.74
46
113.21
4.73
113.65
4.73
47
113.18
4.73
113.77
4.73
48
113.14
4.73
113.68
4.73
49
113.04
4.73
113.69
4.73
50
113.10
4.73
113.75
4.73
51
113.05
4.73
113.74
4.73
52
113.01
4.73
113.76
4.73
53
112.99
4.73
113.57
4.73
54
112.94
4.73
113.68
4.73
55
112.90
4.73
113.69
4.73
58
56
112.87
4.73
113.66
4.73
57
112.84
4.73
113.57
4.73
58
112.82
4.73
113.51
4.73
59
112.79
4.73
113.53
4.73
60
112.77
4.73
113.54
4.73
61
112.81
4.73
113.53
4.73
62
112.73
4.73
113.47
4.73
63
112.75
4.73
113.48
4.73
64
112.66
4.72
113.48
4.73
65
112.64
4.72
113.47
4.73
66
112.61
4.72
113.48
4.73
67
112.61
4.72
113.45
4.73
68
112.57
4.72
113.43
4.73
69
112.53
4.72
113.42
4.73
70
112.47
4.72
113.15
4.73
71
112.45
4.72
113.31
4.73
72
112.41
4.72
113.35
4.73
73
112.19
4.72
113.14
4.73
74
112.17
4.72
113.32
4.73
75
112.14
4.72
113.33
4.73
76
112.15
4.72
113.35
4.73
77
112.06
4.72
112.91
4.73
78
112.01
4.72
113.02
4.73
79
111.99
4.72
112.98
4.73
80
111.96
4.72
112.90
4.73
81
111.96
4.72
113.13
4.73
82
111.98
4.72
113.21
4.73
83
111.92
4.72
113.21
4.73
84
111.73
4.72
113.20
4.73
85
111.72
4.72
113.18
4.73
86
111.87
4.72
113.16
4.73
87
111.93
4.72
112.66
4.72
88
111.97
4.72
112.95
4.73
89
111.65
4.72
112.89
4.73
90
111.73
4.72
113.05
4.73
91
111.78
4.72
113.15
4.73
92
111.58
4.71
112.68
4.72
93
111.64
4.72
112.91
4.73
94
111.67
4.72
112.95
4.73
59
95
111.70
4.72
112.49
4.72
96
111.71
4.72
112.84
4.73
97
111.66
4.72
112.88
4.73
98
111.78
4.72
112.81
4.73
99
111.80
4.72
112.86
4.73
100
111.80
4.72
112.84
4.73
101
111.22
4.71
112.84
4.73
102
111.14
4.71
112.90
4.73
103
111.15
4.71
112.90
4.73
104
111.18
4.71
112.88
4.73
105
111.17
4.71
112.51
4.72
106
111.19
4.71
112.67
4.72
107
111.16
4.71
112.71
4.72
108
111.14
4.71
112.73
4.73
109
111.08
4.71
112.72
4.72
110
110.93
4.71
112.70
4.72
111
110.95
4.71
112.43
4.72
112
110.93
4.71
112.44
4.72
113
110.91
4.71
112.55
4.72
114
110.87
4.71
112.58
4.72
115
111.00
4.71
112.58
4.72
116
110.94
4.71
112.55
4.72
117
110.93
4.71
112.55
4.72
118
110.91
4.71
112.54
4.72
119
110.94
4.71
112.60
4.72
120
110.96
4.71
112.59
4.72
121
110.93
4.71
112.57
4.72
122
110.94
4.71
112.55
4.72
123
110.94
4.71
112.53
4.72
124
110.73
4.71
112.50
4.72
125
110.74
4.71
112.27
4.72
126
110.78
4.71
112.25
4.72
127
110.80
4.71
112.48
4.72
128
110.63
4.71
112.50
4.72
129
110.80
4.71
112.45
4.72
130
110.85
4.71
112.32
4.72
131
110.87
4.71
112.39
4.72
132
110.85
4.71
112.38
4.72
133
110.85
4.71
112.36
4.72
60
134
110.85
4.71
112.36
4.72
135
110.85
4.71
112.41
4.72
136
110.84
4.71
112.46
4.72
137
110.84
4.71
111.87
4.72
138
110.80
4.71
112.17
4.72
139
109.92
4.70
112.19
4.72
140
109.90
4.70
112.20
4.72
141
109.99
4.70
111.88
4.72
142
110.02
4.70
112.11
4.72
143
110.10
4.70
112.13
4.72
144
110.10
4.70
112.15
4.72
145
110.13
4.70
111.70
4.72
146
110.15
4.70
112.09
4.72
147
110.12
4.70
111.15
4.71
148
110.13
4.70
111.59
4.71
149
110.13
4.70
111.63
4.72
150
110.20
4.70
111.65
4.72
151
110.12
4.70
111.64
4.72
152
110.12
4.70
111.62
4.72
153
110.10
4.70
111.65
4.72
154
110.00
4.70
111.65
4.72
155
109.85
4.70
111.65
4.72
156
109.91
4.70
111.62
4.72
157
109.96
4.70
111.60
4.71
158
109.99
4.70
111.59
4.71
159
109.95
4.70
111.57
4.71
160
109.91
4.70
111.57
4.71
161
109.89
4.70
111.57
4.71
162
109.90
4.70
111.60
4.71
163
109.94
4.70
111.59
4.71
164
109.93
4.70
111.60
4.71
165
109.91
4.70
111.65
4.72
166
109.82
4.70
111.64
4.72
167
109.91
4.70
111.41
4.71
168
109.86
4.70
111.33
4.71
169
109.91
4.70
111.57
4.71
170
109.87
4.70
111.57
4.71
171
109.83
4.70
111.19
4.71
172
109.74
4.70
111.53
4.71
61
173
109.61
4.70
111.54
4.71
174
109.49
4.70
110.85
4.71
175
109.61
4.70
111.35
4.71
176
109.83
4.70
111.50
4.71
177
109.75
4.70
111.51
4.71
178
109.46
4.70
111.54
4.71
179
109.42
4.70
111.53
4.71
180
109.43
4.70
111.50
4.71
181
109.44
4.70
111.49
4.71
182
109.40
4.70
111.47
4.71
183
109.32
4.69
112.28
4.72
184
108.98
4.69
111.94
4.72
185
109.25
4.69
111.52
4.71
186
109.50
4.70
111.59
4.71
Tekanan Single Well 4.75 y = -0.0002x + 4.7433 R2 = 0.9687
Tekanan
4.74 4.73
KMJ-11
4.72
KMJ-14
4.71
Linear (KMJ-14) Linear (KMJ-11)
4.70 y = -0.0003x + 4.7418 R2 = 0.9847
4.69 4.68 0
50
100
150
200
Bulan
Grafik L.D.2 Tekanan Single Well Reservoir System
Dari grafik di atas dapat ditentukan nilai decline tekanan KMJ-11 = 0.0003 dan decline KMJ-14 = 0.0002
62
