自然裂縫地層中含有裂縫（Fracture）與岩基（Matrix）兩種孔隙介質，而這兩種孔隙介質分佈是極度不均勻，若要完整描述是非常困難的，因此，必須要進行一定程度的簡化以方便描述流體於自然裂縫地層中的流動特性，前人將裂縫與岩基的特性及接觸關係整理成三個參數：形狀因子σ（Shape Factor）、儲存容積比ω（Storage Ratio）以及竄流係數λ（Interporosity flow parameter）。
本研究的目的是以數值模擬法研究不同自然裂縫特性之自然裂縫地層在定產率生產過程之壓力行為以及壓力影響半徑於自然裂縫地層中隨時間的變化，並以自行推導之壓力影響半徑方程式計算壓力影響半徑隨時間變化，與解析解及數值解進行比較。
本研究使用驗證完成之單相流體均質均向地層數值模式加入不同的自然裂縫地層之特性，進行定產率生產，獲得井底流壓隨時間變化結果與文獻中之解析解進行比對，完成自然裂縫地層數值模式建立並研究自然裂縫地層特性對於定產率生產下的壓力行為影響。
然後，根據所建立之自然裂縫地層數值模式，計算自然裂縫地層中的生產井之壓力影響半徑，除了與文獻解析解進行比較，並研究自然裂縫地層特性對壓力影響半徑的影響。另外，在本研究中嘗試以自然裂縫地層暫態壓力解析解與近似解推求壓力影響半徑方程式，同時與數值模式計算結果進行比較，得到良好的結果。在自然裂縫地層壓力行為研究結果為：自然裂縫地層特性控制生產時的壓力行為，儲存容積比(ω)控制生產初期的壓力差以及位於過渡帶的時間長短，竄流係數(λ)控制壓力行為由前期進入過渡帶的時間。在自然裂縫地層壓力影響半徑的研究結果顯示：(1)在前期及後期的暫態行為，壓力傳遞為固定速度，過渡帶時則因為流體補充而有所減緩。(2)當生產時間橫跨前期、過渡帶及後期三個時期，壓力傳遞的總距離都會相等。(3)自行推導之壓力影響半徑方程式可估算前期及後期之壓力影響半徑。

In naturally fractured reservoirs, including fracture and matrix, the distribution of nature fractures in reservoirs is extremely uneven. It is very difficult to characterize the complication of naturally fractured reservoirs. Thus, when studying the fluid flow in the reservoir, the distribution of fracture in naturally fractured reservoirs must be simplified. The properties of naturally fractured reservoirs behaviors can be characterized by using three parameters, which are shape factor (σ), storage ratio (ω) and interporosity flow parameter (λ). The purpose of this study is to use the numerical simulation to study naturally fractured reservoirs pressure behavior when the well is producing with constant production rate, and to study the radius of investigation in naturally fractured reservoirs. Finally, the radius of investgation derived from the numerical simulation is to be compared with those from analytical solutions.
In this study, the numerical model of naturally fractured reservoirs is been set up, and well bottom hole pressure with given constant production rate is calculated. Both the calculated bottom hole pressure from homogeneous model (single porosity) and from naturally fractured model (dual porosity), are validated with available analytical solutions.
The numerical model of naturally fractured reservoir is been used to calculate the radius of the investigation, which are compared with analytical solution. In addition, an equation of radius of investigation of a naturally fractured reservoir is derived from this study. The results calculated from the derived equation are compared favorable with those from the numerical model.
The results of pressure behavior in naturally fractured reservoir from this study show that storage ratio controls the pressure drop in the early time and the duration of the transition period, and interporosity flow parameter controls the starting time of transition period. From the studies of the radius of investigation, the results show that speeds of pressure propagation are at different constant values in the early and later time. In the transition period, the speed of pressure propagation is decreasing, which is due to fluid flowing from matrix to fracture. The equation of radius of investigation derived from this study can be used to calculate radius of investigation at early and later time.
Key words: Naturally fractured reservoirs, Storage ratio, Interporosity flow parameter, Radius of investigation.

1.Aguilera, R.: “Well test Analysis of Naturally Fractured Reservoirs” SPE Formation Evaluation, pp. 239-252, September 1987.
2.Aguilera, R., Ng, M.C.: “Pressure Analysis of Infinite, Semi-infinite and Closed Rectangular Naturally Fractured Reservoirs”, Journal of Canadian Petroleum Technology, Vol. 36, No. 10, pp. 56-62, November 1997.
3.Aguilera, R.: “Radius and Linear Distance of Investigation and Interconnected Pore Volume in Naturally Fractured Reservoirs”, Journal of Canadian Petroleum Technology, Vol. 45, No. 12, pp. 72-77, December 2006.
4.Chaudhry, A. U. (2004). Oil Well Testing Handbook. Amsterdam: Elsevier Inc.
5.Cinco-Ley H., Fernando Samaniege V.: “Pressure Transient Analysis for Naturally Fractured Reservoirs”, Soc. Pet. Eng. J., Vol. 246. , pp. 1-24, September 1982.
6.Correia, M.G., Maschio, C., Schiozer, D.J., dos Santos, M.: “Sensitivity Analysis for Dual Porosity and Dual Permeability Systems to Small and Large Scale Heterogeneities in a Naturally Fractured Carbonate Reservoirs”, Soc. Pet. Eng. J., pp. 1-7, June 2011.
7.Craft, B.C., Hawkins, M.F. (1959). Applied Petroleum Reservoirs Engineering. Englewood Cliffs, N.J.: Prentice-Hall.
8.Hurst, W., Haynie, C.K., Walker, R.N.: “Some Problems in Pressure Buildup”, Soc. Pet. Eng. J., pp. 1-6, October 1961.
9.Hsieh, B.Z., Chilingar, G.V., and Lin, Z.S.: “Propagation of Radius of Investigation from Producing Well”, Energy Sources, Vol. 29, No. 5, pp. 403-417, April 2007.
10.Hsieh, B.Z., Chilingar, G.V., and Lin, Z.S., “Determination of the Constant Coefficient in Pressure Propagation Equation”, Energy Source, Vol. 30, No. 23, pp. 1223-1232, August 2008.
11.Lee, J. (1982) Well Testing. Dallas, TX: Society of Petroleum Engineers of the AIME.
12.Jones, P.: “Reservoir Limit Test on Gas Wells”, Journal of Petroleum Technology, pp. 217-223, June 1962.
13.Kazemi, H.: “Pressure Transient Analysis of Naturally Fractured Reservoirs with Uniform Fractures Distribution” Soc. Pet. Eng. J., Vol. 246. , pp. 451-462, June 1969a.
14.Kazemi, H., Seth, M.S., Thomas, G.W., “The Interpretation of Interference Tests in Naturally Fractured Reservoirs with Uniform Distribution”, Soc. Pet. Eng. J., Vol. 246, pp. 463-472, December 1969b.
15.Kazemi, H.: “Pressure Buildup in Reservoir Limit Testing of Stratified Systems”, Journal of Petroleum Technology, pp. 503-511, April 1970.
16.Mavor, M.J. and Cinco-Ley, H.: “Transient Pressure Behavior of Naturally Fractured Reservoirs,” Soc. Pet. Eng. J. pp. 1-9, April 1979.
17.Matthews, C.S., Russell, D.G. (1967). Pressure Buildup and Flow Tests in Wells. Dallas, TX: Society of Petroleum Engineers of the AIME.
18.Mora, C.A., Wattenbarger R.A.: “Analysis and Verification of Dual Porosity and CBM Shape Factors”, Journal of Canadian Petroleum Technology, Vol. 48, No. 2, pp.17-21, February 2009.
19.Muskat, M.: “The Flow of Compressible Fluids through Porous Media and Some Problems in Heat Conduction”, Physics, Vol. 5, pp. 71-94, March 1934.
20.Najurieta, H.L.: “A Theory for Pressure Transient Analysis in Naturally Fractured Reservoirs”, Journal of Canadian Petroleum Technology, pp. 1241-1250, July 1980.
21.Odeh, A.S.: “Unsteady-State Behavior of Naturally Fractured Reservoir,” Soc. Pet. Eng. J., Vol. 234, pp. 60-66., March 1965.
22.Odeh, A.S., Nabor, G.W.: “The Effect of Production Histroy on Determination of Formation Characteristics from Flow Tests”, Journal of Petroleum Technology, pp. 1343-1350, October 1966.
23.Olarewaju, J.S., Lee, W.J.: “New Pressure-Transient Analysis Model for Dual-Porosity Reservoirs” SPE Formation Evaluation, pp. 384-388, September 1989.
24.Petak, K.R., Soilman, M.Y., Anderson, M.F.: “Type Curves for Analyzing Naturally Fractured Reservoirs”, Soc. Pet. Eng. J., pp. 1-15, October 1986.
25.Pruss, K., Narasimhan, T.N.: “A Practical Method for Modeling Fluid and Heat Flow in Fractured Porous Media”, Soc. Pet. Eng. J., pp.14-26, February 1985.
26.Silder, H.C. (1983). Worldwide Practical Petroleum Reservoir Engineering Methods. Tulsa, Oklahoma. PennWell Publishing Co.
27.Sobbi, F.A., Badakhshan, A.: “Radius of Investigation for Well Tests in Dual Porosity Reservoirs”, Journal of Canadian Petroleum Technology, Vol. 35, No. 6, pp.49-54, June 1996.
28.Stewart, G., Sobbi, F.A.: “Well Test Interpretation for Naturally Fractured Reservoirs”, pp. 1-16, October 1988.
29.Tek, M.R., Grove, M.L., Poettmann F.H.: “Method for Predicting the Back-Pressure Behavior of Low-Permeability Natural-Gas Wells”, Trans. AIME, Vol. 210, pp. 302-309, November 1957.
30.van Everdingen, A.F., Hurst, W.: “The application of Laplace transformation to fluid problem in reservoir”, Petroleum Transactions, AIME, Vol. 186, pp. 305-324, December 1949.
31.Van Poolen, H.K.: “Radius of Drainage and Stabilization Time Equations”, The Oil and Gas Journal, pp. 138-146 September 1964.
32.Warren, J. E. and Root, P. J.: “The Behavior of Naturally Fractured Reservoir,” Soc. Pet. Eng. J., Vol. 228, pp. 245-255, September 1963.
33.Zhu, Yadong,: “Well Testing Analysis in Double Porosity Reservoir”, Soc. Pet. Eng. J., pp. 651-661, March 1986.