Yatay kuyularda basınç düşümü ve verimliliğe etkisi

Abstract

Petrol kaynaklarının hızla azalmakta olduğu düşünülürse bu kaynakların en iyi kullanılması için üretim programı hazırlanması gerektiği sonucuna varılır. Bunun için üretimi optimum seviyede tutma çalışmaları önem kazanmaktadır. İyi bir üretim programı hazırlanması için basınç davranışlarının doğru olarak analiz edilmesi gerekmektedir. Bu çalışmada yatay kuyulardaki basınç düşümleri ve verimliliğe etkisini inceleyen literatür araştırması yapılmış, basınç düşümlerinin daha kolay hesaplanabilmesi için korelasyon geliştirilmiş, korelasyonun doğruluğu Özkan modeli ile karşılaştırılmıştır. Dikken' m sonlu ve sonsuz uzunluklu kuyular için geliştirdiği model, Novy'nin verimlilikteki %10'dan fazla azalmanın kuyu içi rezervuar sisteminden mi, sürtünmeden mi kaynaklandığım gösteren çalışması, Özkan' m yatay kuyu verimliliği üzerinde kuyu içi basınç düşümlerinin etkisini içeren modeli incelenmiştir. Kuyu içi basınç düşümlerini hesaplayan korelasyon, yatay kuyuyu sadece iki ucundan açık bir boru gibi düşünüp, bütün akışkanın kuyunun (x=L) ucundan girip, (x=0) ucundan üretildiğini kabul eden boru içi akış denklemi ve Özkan modelinden yararlanılarak geliştirilmiştir.

Due to the advances in drilling and completion technologies, the number of horizontal wells drilled around the world has increased rapidly. The major advantage of drilling a horizontal well is to increase the contact area between the well and the reservoir, to decrease the pressure lossen in the reservoir, and thereby improve well productivity. The other benefits of horizontal wells are to intersect multiple pay zones and vertical fractures, and to reduce water and/or gas coning. Horizontal wells may also be used as injection wells. As an injection well, a horizontal well improves well injectivity and can provide a better sweep efficiency. In many cases, a horizontal well can be considered as infinitely conductive; that is to say, pressure along the horizontal wellbore is uniform and pressure drop inside the wellbore is small and negligible. On the other hand, horizontal wells drilled in very high permeability formations can be produced at high flow rates of 30.000-50.000 stb/day. Long horizontal wells in high permeability formations require relatively small pressure drops in the reservoir. High flow rates increase the pressure drops inside the horizontal wells. Thus, in some cases, the magnitude of pressure losses in the wellbore can be comparable to the magnitude of the pressure drops in the formation. High pressure drops along the horizontal wellbore is also possible in case of high viscosity, oil production from tar sands and heavy oil fields. High wellbore pressure losses is detrimental to well productivity and drilling a longer well may not result any additional improvement in production. There have been many studies on how to estimate inflow performance of horizontal wells. Many predictive equations have been presented. However, in the most studies, it is assumed that horizontal well can be considered as an infinite- conductivity wellbore, ignoring the influence of pressure losses inside the wellbore. The effect of the wellbore pressure losses on horizontal well performance has been investigated in only a few studies. A finite-conductivity wellbore model is needed to implement the impact of wellbore pressure losses on horizontal well productivity. A finite-conductivity wellbore model can be constructed in three steps; 1) Modeling of the flow in the reservoir. 2) Modeling the fluid flow in the wellbore. 3) Coupling the wellbore and reservoir flow equations. The most difficult part of constructing a finite-conductivity wellbore is the complexity of the interaction between the wellbore and reservoir. Development of such a model requires advanced knowledge of applied mathematics with which the most engineers are not familiar. When the wellbore pressure losses are negligible compared to the pressure drops, simple steady state solutions presented by Borisov, Giger, Renard and Dupuy, and Joshi can be used to predict the horizontal well productivity. There have been several models presented to calculate the productivity of finite-conductivity horizontal wells under the influence of wellbore pressure losses. These studies are; 1) Dikken' s model 2) Novy's model 3) Özkan et al. model The models proposed by Dikken and Novy are simple but the accuracy of these models is questionable. On the other hand, Özkan et al model rigorously handles the interaction between the reservoir and the wellbore. However, Özkan et al model is complex. In this study, a simple empirical equation to calculate the effect of wellbore pressure losses on horizontal well productivity is developed. The rigorous Özkan et al model was used to develope the empirical method. The first study regarding the wellbore pressure drop and its effect on the well productivity was carried out by Dikken. Dikken whose work paved the way for the subsequent works used a simple model. In Dikken' s model, flow in the wellbore is single phase, turbulent, and steady. He used the conventional Moody friction factor correlation in his study. Dikken defined a specific productivity index which is independent of the location along the wellbore to describe the flow from reservoir to the wellbore. Then, he considered a vahime balance across the circumferential area of the well and obtained an ordinary differential equation. The differential equation was solved for the flow rate distribution along the wellbore using numerical methods. Although Dikken' s model is simple, it does not properly describe the coupling between the reservoir and the wellbore equations. The assumption regarding the constant productivity index along the wellbore is not justified. Later, Novy extended the model used by Dikken to the horizontal gas wells as well as the oil wells. Novy constructed his model equations on the foundations laid by Dikken. In Novy's model, the system of interest is made up of two distict components; a reservoir and a horizontal pipe. In herited in Novy's reservoir model is the assumption that the productivity index per unit length of the well is constant along the wellbore. The reservoir flow equations are oversimplified in Novy's model. Novy also used the traditional friction factor concept to represent the wellbore pressure losses in his model equations. Jain's empirical equation was used to calculate the friction factor. Novy presented an analytical solution for laminar flow in the wellbore. For turbulent flow, he used finite-difference scheme to solve the boundary-value problems. Using his finite-difference scheme, he developed creteria to recognize the flow conditions at which the effect of wellbore pressure losses is negligible. Özkan et al developed a comprehensive model that properly and accurately describe the fluid flow in the reservoir and in the wellbore. The principial features in Özkan et al model are; 1) No restrictions are imposed on the way in that fluid flows into the wellbore. 2) Productivity index and its distribution along the wellbore are calculated as a result of computations. XI 3) Laminar or turbulent flow regimes within the wellbore are also determined from the flux distribution along the horizontal well. 4) The interaction between the reservoir and wellbore is rigoriously handled. In this study, a simple empirical correlation is developed to account for the effect of wellbore pressure losses on the inflow performance of horizontal wells. The rigorous solution presented by Özkan et al was used to derive the empirical correlation. The following stepwise alghorithm was used to construct the correlation: 1) For a specifed flow rate, q, and other required set of data, the reservoir pressure drop for infinite-conductivity wellbore condition, APiC, was computed using Özkan et al model. The same model was also run for finite-conductivity wellbore condition considering wellbore pressure losses and total pressure drop in the reservoir and wellbore, AP&, was determined. 2) The difference between the finite-conductivity pressure drop, APfC, and infinite-conductivity pressure drop, APjC, was considered to be the pressure drop in the wellbore APwb = APfc - APic (S.l) 3) For single-phase flow of oil through a horizontal pipe, the relationship between the flow rate and frictional pressure drop is given as; d5APwb q = 1.14644 xKT5fmpL -5fmpT (S.2) where; q: volumetric flow rate d: pipe diameter APWb: frictional pressure drop fm: Moody friction factor p: density of the fluid L: pipe length The wellbore pressure drop calculated in the second step was substituted in Eq. (S.2) and an apparent flow rate, qap, was computed. Since a horizontal well cannot be considered as a pipe, the fictitous flow rate would be lower than actual producing flow rate. 4) Then, the ratio of apparent flow rate to actual flow rate was calculated; Hratio (S.3) Xll 5) The calculations in steps 1-4 were repeated for different sets of data and qratio was correlated with the other reservoir and wellbore parameters. It was found that the parameter qratio could be correlated with the correlation group defined below; cor = _P_B K ^,(50 + L0-2)(l + 4(rw -0.25)) (s.4) 7.395 x101Wl A Vw ;; \*-v The empirical relationship between qrati0 and Tcor is given below; 4 ratio - _TL - n ^c2^ = c,e (S.5) Where ci and c2 are constants. (ct=0.479729, c2=3.60543 x 10"5) The range of reservoir and well parameters used to develop the correlation is given in Table S.l The relationship between qratio and the correlation group, Tcor, is given in Fig. S.l. Xlll The correlation developed in this study was compared back with Özkan et al model in terms of wellbore pressure losses, APW. The maximum difference between the results from the correlation and Özkan et al model was found to be 7%. 0.48 0.46 0.44 0.42 0.40 -i 0.38 0.36 2000 4000 6000 8000 10000 Correlation Figure S.1 Relation between qratio TCorrelation xrv