DAFTAR PUSTAKA. Arps, J, J Analysis of Decline Curves. Trans. AIME

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.

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);

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);

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 %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

q

ref

= 50

φ

= 0.2

μ

= 0.8

t

c

= 0.000003

k

= 5

t

DA

=0.00633kt /

φ

μ

c A

t

q

D

= q(t) / q

ref

LAMPIRAN B

Penurunan solusi multiwell:

Model matematika untuk sistem ini adalah:

( )

(

)

(

)

2 2 , , 2 2 1

,

/

well n i t w i w i i

q t B

c

p

p

p

x

x

y

y

x

y

Ah k

k

t

φμ

δ

μ

=

∂

₊

∂

₋

₋

₋

₌

∂

∂

∂

∑

∂

(B.1)

Bentuk (B.2) dalam dimensionless ditulis sebagai:

(B.2)

Dimana:

(

)

(

)

2

, ,

D i ref

kh

p

p

p x y t

q B

π

μ

=

−

DA t

kt

t

c A

φμ

=

( )

( )

D DA ref

q t

q

t

q

=

D D

x

x

A

y

y

A

=

=

Kemudian dengan menggunakan prinsip Duhamel kita dapat menentukan

solusi persamaan (B.2) menjadi :

(

,

,

,1

...

, _well

,

,1

...

, _well

,

,

,

)

D D D wD wD n wD wD n eD eD DA

p

x

y

_⎣

⎡

x

x

⎤ ⎡

_{⎦ ⎣}

y

y

_⎦

⎤

x

y

t

=

( )

(

[

]

)

, , , 1 0

,

,

,

,

,

,

DA wellt n D i Dcr D D wD i wD i eD eD DA i

d

q

p

x y x

y

x

y

t

d

d

τ

τ

τ

τ

=

⎡

−

⎤

⎣

⎦

∑ ∫

(B.3)

Lalu solusi tekanan dimensionless sumur ditentukan dengan mengevaluasi

persamaan (B.3) pada lokasi sumur “k” sehingga :

(

, ,

)

,

( )

(

)

_, 1 0

,

,

DA wellt n D wD k wD k DA D i Dcr DA _{k i} i

d

p

x

y

t

q

p

t

d

d

ε

ε

τ

τ

τ

τ

=

⎡

+

⎤ ⎡

+

⎤

=

⎡

_⎣

−

⎤

_⎦

⎣

⎦ ⎣

⎦

∑∫

(B.4)

Dengan memasukan “skin factor” sekitar sumur dalam persamaan (B.4)

kita dapatkan :

(

, ,

)

,

( )

(

)

_, 1 0

,

,

DA wellt n D wD k wD k DA D i Dcr DA _{k i} i

d

p

x

y

t

q

p

t

d

d

ε

ε

τ

τ

τ

τ

=

⎡

+

⎤ ⎡

+

⎤

=

⎡

_⎣

−

⎤

_⎦

⎣

⎦ ⎣

⎦

∑ ∫

( )

Dk DA k

q

t

s

+

(B.5)

Aspek komputasi:

Perhatikan kembali persamaan (B.6), kita punyai :

(

, ,

)

,

( )

(

)

_, 1 0

,

,

DA wellt n D wD k wD k DA D i Dcr DA _{k i} i

d

p

x

y

t

q

p

t

d

d

ε

ε

τ

τ

τ

τ

=

⎡

+

⎤ ⎡

+

⎤

=

⎡

_⎣

−

⎤

_⎦

⎣

⎦ ⎣

⎦

∑ ∫

( )

Dk DA k

q

t

s

+

(B.6)

Kita akan mengaproksimasi laju kontinu,

q

_D

( )

t

_DA

sebagai fungsi waktu

dengan mendiskritisasi integral pada persamaan (B.6) menjadi :

(B.7)

Dimana:

Grafik dari aproksimasi diskrit laju produksi pada persamaan (B.7) sebagai

berikut :

Grafik B.1. Aproksimasi diskrit laju produksi

(B.8)

Kemudian kita dapat menuliskan persamaan (B.8) ke dalam bentuk

superposisi sebagai berikut :

[ ]

(

,

,

,

,

)

D wD k wD k DA n

p

⎡

_⎣

x

+

ε

⎤ ⎡

_{⎦ ⎣}

y

+

ε

⎤

_⎦

t

=

[ ] [ ]

(

, 1 ,

)

(

, , , , [ ] [ ]1

)

1 1

,

,

,

,

,

,

well n n Dcr wD k wD k wD i wD i eD eD D j i D j i DA n DA j i j

q

q

₋

p

x

y

x

y

x

y

t

t

₋ = =

⎡

₋

⎡

₋

⎤

⎤

⎢

⎣

⎦

⎥

⎣

⎦

∑∑

[ ], k D n k

q

s

+

(B.9)

Keterangan :

A =

luas area

B

= formation volume factor

p

i

= tekanan awal

q

i

= laju produksi awal

q

ref

= laju produksi reference

n

well

= jumlah sumur

x

= koordinat x

y

= koordinat y

t

= waktu

y

w

= koordinat sumur pada sumbu y

φ

= porositas

μ

= viskositas cairan

t

c

= total compressibility

k

= permeabilitas

h

= ketebalan reservoir

p

D

= dimensionless tekanan

x

wD

=

dimensionless

jarak sumur - x

y

wD

= dimensionless jarak sumur – y

xe

D

= dimensionless jarak reservoir-x

y

eD

= dimensionless jarak reservoir-y

t

DA

=

dimensionless

waktu

q

D

=

dimensionless

laju produksi

LAMPIRAN C

Penurunan Rumus Decline

Exponential Decline

p

_t

=

p e

₀ −Dt

(C.1)

Decline

ln p

_t

=

ln p

₀

−

Dt

0 t 0 t

Dt

ln p

ln p

p

ln

p

=

−

=

(C.2)

Kumulatif

t t 0 t D 0 0 t D 0 0 t D 0 0 Dt 0 0 0 0 t

P

p d

p e

d

p e

d( D )

D

p e

D

p e

p e

D

D

p

p

D

τ − τ − τ − τ −

=

τ

=

τ

=

− τ

−

⎡

⎤

= ⎢

₋

⎥

⎣

⎦

=

−

−

−

−

=

∫

∫

∫

0 t t 0 0 0 t 0 0 t 0 1 0 t 0 t

p

p

P

_D

p t

p t

p

p

Dp t

Dp t

p

1

p

Dt

p

1

p

p

ln

p

−

−

=

=

−

−

=

⎛

⎞

− ⎜ ⎟

⎝

⎠

=

(C.3)

Jika

0 t

p

1

p

→ , persamaan (C.3) berbentuk

0

0

maka kita gunakan aturan

L’Hopital untuk persamaan (C.3) misal

0

t

p

r

p

=

1 L 2 r 1 r 1 r 1

1 r

r

1

1

lim

lim

lim

1

ln r

1/ r

r

1

− − → → →

−

=

= =

=

Hyperbolic Decline

0 t 1/ b

p

p

(1 bDt)

=

+

,

0<b<1

(C.4)

Kumulatif

t t 0

P

p d

τ

=

_∫

τ

t 0 t 1/ b 0 t 1 0 b 0 t 1 1 0 b 0 1 1 0 b 1 b 0 t 0 1 b 0 t 0 0

p

P

d

(1 bD )

p

(1 bD ) d(bD )

bD

p

1

(1 bD )

1

bD

1

b

p

(1 bD )

1

(1 b)D

p

p

1

(1 b)D

p

p

p

1

(1 b)D

p

p

(1

− − + − + − −

=

τ

+

τ

=

+

τ

τ

⎡

⎤

=

_⎢

+

τ

_⎥

⎣

⎦

− +

⎛

⎞

= −

_⎜

+

τ

−

_⎟

−

_⎝

_⎠

⎛

_⎛

_⎞

⎞

⎜

⎟

= −

_⎜

_⎟

−

⎜

⎟

−

_⎝

_⎝

_⎠

_⎠

⎛

_⎛

_⎞

⎞

⎜

⎟

=

_{− ⎜ ⎟}

⎜

⎟

−

_⎝

_⎝

_⎠

_⎠

=

−

∫

∫

1 b 1 b 0 t 1 b 0 b 1 b 1 b 0 0 t

p

p

b)D

p

p

(p

p

)

(1 b)D

− − − − −

⎛

−

⎞

⎜

⎟

⎝

⎠

=

−

−

(C.5)

Decline

0 t 1/ b

p

p

(1 bDt)

=

+

1 t b 0

p

(1 bDt)

p

−

= +

b t 0

p

(1 bDt)

p

−

⎛

⎞

= +

⎜

⎟

⎝

⎠

b t 0

p

bDt

1

p

−

⎛

⎞

=

_⎜

_⎟

−

⎝

⎠

b b t 0 0 t

p

p

1

1

p

p

Dt

b

b

−

⎛

⎞

⎛

⎞

−

−

⎜

⎟

⎜

⎟

⎝

⎠

⎝

⎠

=

=

(C.6)

b 1 b 1 b t 0 0 t 0 0 b 1 b 1 b 0 0 t b 0 o t b 1 b 1 b 0 0 t b 0 0 t 1 b 0 t b 0 t b t 0

P

p

(p

p

)

p t

(1 b)D

p t

p

(p

p

)

p

p

1

p

(1 b)

b

b

p (p

p

)

p

p (1 b)

1

p

p

1

b

p

p

(1 b)

1

p

p

1

p

− − − − − − −

−

=

−

−

=

⎛

⎞

−

⎜

⎟

⎝

⎠

−

=

−

⎛

_⎛

_⎞

⎞

⎜

⎟

−

_⎜

_⎟

−

⎜

_⎝

_⎠

⎟

⎝

⎠

⎛

_⎛

_⎞

⎞

⎜

_{− ⎜ ⎟}

⎟

⎜

_⎝

_⎠

⎟

⎝

⎠

=

⎛

_⎛

_⎞

⎞

⎜

⎟

−

_⎜

_⎟

−

⎜

_⎝

_⎠

⎟

⎝

⎠

⎛

⎞

− ⎜ ⎟

⎝

⎠

=

1 b 0 t

b

1 b

p

1

p

−

⎛

⎞

⎜

₋

⎟

⎝

⎠

⎛

⎞

−

⎜

⎟

⎝

⎠

(C.7)

Jika

0 t

p

1

p

→ , persamaan (C.7) berbentuk

0

0

maka kita gunakan aturan

L’Hopital untuk persamaan (C.7) misal

0

t

p

r

p

=

b 1 L b 2 b b 1 r 1 r 1

1 r

b

(1 b)r

b

1

lim

lim

1

r

1 1 b

br

1 b

1

− − − → →

−

⎛

⎞

−

⎛

_{⎞ = =}

⎜

⎟

⎜

⎟

−

⎝

−

⎠

=

⎝

−

⎠

Harmonic Decline

0 t

p

p

(1 Dt)

=

+

(C.8)

Decline

:

1 t 0

p

(1 bDt)

p

−

= +

0 t

p

(1 bDt)

p

= +

p

=

− (C.9)

Kumulatif :

[

]

t 0 t 0 t 1 0 0 t 0 0

p

P

d

(1 D )

p

(1 bD ) d(bD )

bD

p

ln(1 D )

bD

−

=

τ

+ τ

=

+

τ

τ

=

+ τ

∫

∫

[

]

0 t 0 0

p

P

ln(1 Dt) ln1

bD

p

(1 Dt)

ln

bD

1

p

ln(1 Dt)

bD

=

+

−

+

=

=

+

0 0 t t 0 0 0 0 0 t t 0 0 t 0 t

p

p

ln

D

p

P

p t

p t

p

p

ln

p

p

1

p

t

p t

p

ln

p

p

1

p

⎛

⎞

⎜

⎟

⎝

⎠

=

⎛

⎞

⎜

⎟

⎝

⎠

−

=

⎛

⎞

⎜

⎟

⎝

⎠

=

−

(C.10)

Jika

0 t

p

1

p

→ , persamaan (C.10) berbentuk

0

0

maka kita gunakan aturan

L’Hopital untuk persamaan (C.10) misal

0

t

p

r

p

=

L r 1 r 1 r 1

ln r

1/ r

1

1

lim

lim

lim 1

r 1

1

r

1

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

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

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

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

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

Tekanan Multiwell

y = -0.0004x + 4.7425 R2 = 0.9687 y = -0.0006x + 4.7399 R2 = 0.9856 4.62 4.64 4.66 4.68 4.7 4.72 4.74 4.76 0 50 100 150 200 Bulan T ekan an KMJ-11 KMJ-14 Linear (KMJ-11) Linear (KMJ-14)

Grafik L.D.1Tekanan Multiwell Reservoir System

Sebagaimana telah di bahas dalam Bab III bahwa:

y

=

α

t

+

β

, dimana y = ln (p(t)) ; α = D ;

β

= ln (p

o

)

Dari grafik dapat ditentukan: Decline 11 = 0.0006 dan Decline

KMJ-14 = 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

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

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

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

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

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

y = -0.0002x + 4.7433 R2 = 0.9687 y = -0.0003x + 4.7418 R2 = 0.9847 4.68 4.69 4.70 4.71 4.72 4.73 4.74 4.75 0 50 100 150 200 Bulan T eka n a n KMJ-11 KMJ-14 Linear (KMJ-14) Linear (KMJ-11)

Grafik L.D.2TekananSingle Well Reservoir System

Dari grafik di atas dapat ditentukan nilai decline tekanan KMJ-11 = 0.0003

dan decline KMJ-14 = 0.0002