KURVA TIPIKAL UNTUK SISTEM SUMUR TUNGGAL ALIRAN RADIAL MULTIFASA PADA RESERVOAR RFKAH ALAM DENGAN PENDEKATAN GEOMETRI FRAKTAL
ABSTRAK DISERTASI
Karya tulis sebagai salah satu syarat untuk memperoleh gelar Doktor dalam bidang Ilmu Teknik di Institut Teknologi Bandung Dipertahankan pada Sidang Terbuka Komis Program Doktor Program Pascasarjana Institut Teknologi Bandung Tanggal 11 November 2000
Oleh Dyah Rini Ratnaningsih
Promotor Ko-Promotor
: Prof.IR.J.C. Kana : Dr. Ir. Daddy Abdasaah Dr. Ir. Leksono Mucharam
INSTITUT TEKNOLOGI BANDUNG 2000
ABSTRAK Penelitian ini bertujuan untuk menghasilkan suatu kurva tipikal baru untuk reservoar yang bersifat fraktal atau reservoar rekah alam dengan matriks tidak berpartisipasi, dan aliran yang terjadi berasal dari fluida multifasa (minyak, gas dan air). Hasil penelitian ini berupa kurva tipikal yaitu grafik log-log dari perbedaan fungsi tekanan-semu-tak-berdimensi terhadap waktutak-berdimensi dan kurva turunan ("derivative") perbedaan fungsi tekanan-semu-tak berdimensi terhadap waktu-tak-berdimensi. Penelitian ini juga menghasilkan prosedur penggunaan kurva tipikal untuk karakterisasi reservoar rekah slam. Didalam mengembangkan persamaanpersamaan aliran, yang terjadi di reservoar fluida mengalir dari rekahan menuju lubang sumur sehingga berlaku antara linier dan radial. Oleh karenanya model hanya dihitung dengan harga parameter fraktal (dimensi fraktal) antara 1 < D < 2. Suatu persamaan kelakuan aliran yang melibatkan parameter fraktal telah dirumuskan secara numerik untuk aliran radial multifasa dengan menggunakan sistem koordinat silindris. Aliran radial multifasa di dalam reservoar rekah alam dalam pendekatan matematika baru ini, menggunakan model dengan menganggap semua kapasitas penyimpanan fluida hanya berasal dari jaringan rekahan (matrik tidak berpartisipasi). Anggapan lain yang digunakan dalam menggambarkan fenomena alran adalah tekanan kapiler dan pengaruh gravitasi diabaikan, tidak ada pengaruh wellbore storage serta tidak ada skin di sekitar sumur. Pendekatan model ini selanjutnya diselesaikan secara numerik dengan mengaplikasikan teknik solusi IIvIPES (IMplicit in Pressure, Explicit in Saturation). Model numerk ini menghasilkan suatu perangkat lunak yang juga disebut simulator. Simulator ini dikembangkan dengan memodifikasi model multifasa reservoar konvensional yang dikembangkan didalam disertasi Sukarno(1986). Modifikasi yang dilakukan adalah pada data masukan dengan melibatkan parameter fraktal, disamping juga memodifkasi pada subroutine perhitungan transmisibilitas dan perhitungan volume pori. Simulator tersebut selanjutnya diuji menggunakan metode Kesetimbangan Materi dan divalidasi dengan metode analitik serta perbandingan dengan simulator komersial yang umum digunakan di bidang teknik perminyakan yaitu TETRAD versi 9.46. Validasi ini dilakukan baik untuk aliran satu fasa maupun aliran multifasa untuk harga dimensi fraktal (D) sama dengan dua (homogen). Untuk menguji simulator lebih lanjut dilakukan perhitungan-perhitungan menggunakan data lapangan Vulkanik Jatibarang. Pengamatan dilakukan terhadap pengaruh heterogenitas reservoar pada respon tekanan. hal ini ditunjukkan dalam hubungan waktu-tak-berdimensi (tD) terhadap perbedaan fungsi tekanan-semu-tak-berdimensi (mwD) pads berbagai harga parameter
fraktal. Pada kasus lapangan Vulkanik Jatibarang digunakan berbagai harga dimensi fraktal (D ) untuk 0= 0; 0, I; 0,2; 0,3; 0,4; dan 0,5 serta berbagai harga 0 dengan D = l, l; 1,3; 1,5; 1,'7 dan 1,9. Pada kasus dengan menggunakan data lapangan tersebut, dari grafik log-log memperlihatkan bahwa semakin besar harga dimensi fraktal maka semakin kecil harga kemiringan kurva (mendatar). Kenampakan ini sesuai dengan studi sebelumnya yang dilakukan oleh Chang dan Yortsos (1990). Kurva log log dengan variasi harga indek konduktivitas (θ) diimana harga dimensi fraktal tetap, terlihat bahwa penurunan tekanan minimumnya pada harga indek konduktivitas yang semakin kecil (θ = 0). Fenomena disebabkan oleh harga konektivitas reservoar yang sangat tinggi. Besarnya penurunan tekanan ini merupakan fungsi dari dimensi fraktal dan konektivitas jaringan rekahan dari reservoar. Secara jelas kombinasi kedua parameter (D dan θ) tersebut, merupakan kontribusi dari respon fraktal. Aplikasi kurva tipikal baru telah dilakukan untuk 3 buah sumur yaitu; JTB162; JTB-110; dan JTB-48 dari reservoar rekah alam Vulkanik Jatibarang. Harga dimensi fraktal dari ketiga sumur yang mewakili lapangan Vulkanik Jatibarang, terlihat bervariasi yaitu D berkisar dari 1,6 hingga 1,8. Hal ini, menunjukkan bahwa lapangan Vulkanik Jatibarang memilild derajad keheterogenan yang cukup tinggi. Pada akhirnya, model yang dikembangkan dalam penelitian ini memberikan pengertian yang lebih baik dari reservoar rekah alam. Penelitian ini juga dapat menjawab rahasia alam yaitu kerumitan dari jaringan rekahan yang divisualisasikan dalam goemetri fraktal.
THE TYPE CURVES FOR SINGLE WELL MULTIPHASE FLOW SYSTEM IN A NATURALLY FRACTURED RESERVOIR WITH FRACTAL GEOMETRY APPROACH
ABSTRACT OF DISSERTATION
A dissertation submitted to the Institut Teknologi Bandung for the Degree of Doctor in the Discipline of Petroleum Engineering Defended in Open Assembly of Postgraduate Commission On Doctorate Programme of Institut Teknologi Bandung Date: November 11, 2000
By Dyah Rini Ratnaningsih
Promoter
Co-Promoter
: Prof.Ir. J.C. Kana
: Dr. Ir. Doddy Abdassah Dr. Ir. Leksono Mucharam
INSTITUT TEKNOLOGI BANDUNG 2000
ABSTRACT The objective of this research is to generate new type curves using numerical model for multiphase flow (oil, gas and water) in fractured reservoir without matrix participation (fractal reservoir). The type curves are log-log plot of dimensionless pseudo function pressure drop (mWD) versus dimensionless time (tD) and log-log plot of derivative dimensionless pseudo function pressure drop versus dimensionless time. This research also develops the type curves matching procedure to determine characteristics of the naturally fractured reservoir. In this model, it is assumed that the fluid flow from fracture to wellbore, so that is between linier and radial. That is why the model is only calculated using fractal parameter 1< D < 2. The flow equations in which fractai parameter is coupled, have been numerically formulated for multiphase radial flow using cylindrical coordinate system. In the formulation, it is assumed that all storage capacity of fluid is only from fracture network (no matrix participation). Other assumptions used in describing the flow phenomena are ignoring capillary pressure and gravitational effects. Effects of wellbore storage and skin around the well are also ignored. The system of equations are then solved numerically by incorporating the IIVIPES (Implicit in Pressure, Explicit in Saturation) solution technique. Basically, the simulator is developed by modification of the previous Sukarno's multiphase conventional reservoir model. It was performed by modifying the model to accommodate fractal parameters, subroutine for transmissibilities and pore volume calculations. Furthermore, the model. has been validated by involving the material balance check, comparing to the analytical method and comparing to a commercial simulator that is commonly used in Petroleum Industry, which is TETRAD version 9.46. This validation was done whether for both single phase and multi phase flow models, with fractal dimension (D) and conductivity index (θ) values of 2 and 0 respectively. To examine the simulator further, the run were performed using real field data of Jatibarang Volcanic field data. Observation on the field case runs was especially conducted on the pressure respons on heterogeneity reservoirs as shown by the plot of dimensionless time(tD) versus dimensionless pseudo function pressure drop(mWD) in various fractal parameter value. In the case of Jatibarang Volcanic field, the were performed at various fractal dimension (D) values of 1.1, 1.3. 1.5, 1.7, and 1.9 and the values conductivity index (θ ) of 0, 0. l, 0.2, 0.3, 0.4 and 0.5 respectively.
On the field case, the resulting plots (log mWD versus log tD)show that slopes of these lines are vary depending on their fractal dimension. This phenomena is confirmed with the earlier study held by Chang and Yortsos. In the curve with different values of θ for the same fractal dimension value will show a minimum pressure drop at minimum value of conductivity index (θ = 0). This phenomena is caused by high connectivity reservoir value. This pressure drop is a function from fractal dimension and reservoir fracture connectivity network. Therefore, that a combination of both parameters (D and θ), is actually representation of fractal geometry. Application of using new type curves were performed on 3 well tests in Jatibarang Volcanic naturally fractured reservoir, they are JTB-162, ITB110 and JTB-48. The values of fractal dimension predicted from these three wells ranges between 1.6 to 1.8. These may indicate high heterogeneity of Jatibarang Volcanic Reservoir. From the above validation and field runs, it has been convinced that the proposed model developed in this research able to predict and give a better understanding on a complex naturally fractured reservoir system. Moreover, this is a part of answering the secret of fractured reservoir's nature which is considered very complex.
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