流體在非均質地層的流動遠比在均質的流動複雜。為了研究方便，會將非均質地層視為均質地層再進行研究。在此過程中，經常利用平均的概念，將非均質分佈的滲透率和孔隙率用一個具有代表性的平均數值取代之。因此，本文的主要目的是將非均質地層視為均質地層後，研究兩者之間的地下流體流動行為（壓力及流率）變化。
本研究以達西定率為基礎，推導出平均滲透率估算方程式；以物質平衡法為基礎，推導出平均孔隙率估算方程式。再利用數值模擬法分別計算非均質地層與均質地層，在不同的流體流動狀態及不同操作條件下，比較及研究流體流動的壓力與流率之差異。在本研究中，非均質地層可分為線性流動串聯地層、線性流動並聯地層、徑向流動串聯地層和徑向流動並聯地層四種模式；流體流動狀態則分為穩態流動與暫態流動；操作條件有定壓力操作條件與定流率操作條件兩種。
本研究獲得以下結果，若為穩態流動，平均滲透率估算方程式可以適用於線性流動與徑向流動的地層中。若為暫態流動，對於線性流動並聯地層與徑向流動並聯地層而言，地層越複雜，平均滲透率與孔隙率估算方程式越不適用。對於愈複雜的非均質地層，其誤差越大，非均質分佈越複雜的地層，越難用簡單的平均數值去簡化為均質地層。

The fluid flow in a heterogeneous reservoir is more complex than that in a homogeneous reservoir. To simplify the complexity, the reservoir properties (for example, permeability and porosity) in a heterogeneous reservoir may be replaced by using average reservoir properties. The purpose of this study was to study the pressure and flow rate affected by using average reservoir parameters in a heterogeneous reservoir.
In this study, equations based on Darcy’s law are used to calculate an average permeability for a heterogeneous reservoir by considering flow in series and in parallel. The equations based on the material balance equation are used to calculate an average porosity for a heterogeneous reservoir by considering flow in series and in parallel. The pressures and flow rates from reservoirs of heterogeneous reservoirs and reservoirs with average properties were compared using the results of reservoir simulation studies. The heterogeneous reservoirs considered in this included linear flow bed in series, linear flow bed in parallel, radial flow bed in series, and radial flow bed in parallel. The flow regime was divided into steady-state flow and transient flow. The constant terminal rate and constant terminal pressure of operating conditions were considered in reservoir simulation.
The major results and conclusions obtained from this study are: (1) In steady-state flow, the equation for average permeability estimation can be used in linear flow and radial flow. (2) In transient flow, the equations for average permeability and for average property estimation were incorrect for linear flow and radial flow. (3) For the more complex heterogeneous reservoirs, the error is greater. Therefore, it is difficult to use simple average parameters to simplify a heterogeneous reservoir when it has a complex rather than an average formation.

1.Ahmed, Tarek, “Reservoir Engineering Handbook”, Gulf Publishing Company, Houston, Texas, 2000
2.Ahmed, T., and Mckinney, P.D., Advanced Reservoir Engineering. Elsevier Science and Technology, Oxford, UK, 2005.
3.Archer, J. S., and Wall, C.G., Petroleum Engineering— principles and practice, Graham & Trotman, MD, 1986
4.Begg, S.H., Carter, R.R., and Dranfield, P.: "Assigning Effective Values to Simulator Gridblock Parameters for Heterogeneous Reservoirs," SPE Reservoir Engineering, pages 455–463, November 1989.
5.Cardwell, W. T. and Parsons, R. L.: "Average Per¬meabilities of Heterogeneous Oil Sands", Trans., AlME (1945) Vol. 160, 34.
6.Desbarats, A.J.: "Numerical Estimation of Effective Permeability in Sand-Shale Formations," Water Resources Res. (Feb. 1987) 23, No. 2,273-86.
7.Deutsch, c.v.: "Calculating Effective Absolute Permeability in Sandstone/ Shale Sequences," SPEFE (September 1989) 343; Trans., AIME, 287.
8. Earlougher, R.C., Jr., “Advances in Well Test Analysis,” Society of Petroleum Engineers of AIME, Monograph volume.5, Dallas, 1977.
9.H. B. Bradley, Petroleum Engineering Handbook, Society of Petroleum Engineers, Richardson, Texas, 2nd printing, 1989, sect. 12-3
10.Jensen, Jerry L., Hinkley, David V. and Lake, Larry W.: “A Statistical Study of Reservoir Permeability: Distributions,. Correlations, and Averages,” SPE Formation Evaluation,(Dec 1987)461-468.
11.Jensen, J.L. and Lake, L.W. 1988. The Influence of Sample Size and Permeability Distribution on Heterogeneity Measures. SPE Reservoir Engineering, 3 (2): 629-637. SPE-15434-PA.
12. Journel, A.G., Deutsch, C.V., and Desbarats, A.J.: "Power Averag¬ing for Block Effective Permeability," paper SPE 15128 presented at the 1986 SPE California Regional Meeting. Oakland, April 2-4
13.Journel, C. Deutsch, and A. Desbarats. Power averaging for block effective permeability. In 56th California Regional Meeting, pages 329–334. Society of Petroleum Engineers, April 1986
14.Katz, D. L., Handbook of Natural Gas Engineering, McGraw: New York (1959).
15.Law, J.:"A Statistical Approach to the Interstitial Heterogeneity of Sand Reservoirs," Trans.,AIME (1944) Vol. 155, 202-22.
16.Lee, J., “Well Testing,” Society of Petroleum Engineers of AIME, New Work, 1982.
17.Miller, F. G. “Theory of Unsteady-State Influx of Water in Linear Reservoirs”, Journal. Institute. Of Petroleum. (Nov.1962): 48 ,365-379
18.Nutakki, R. And Mattar, L. (1982). Pressure transient analysisof wells in very long narrow reservoirs. 57th Annual Fall Technical Conference and Exhibition of the Society of Petroleum Engineers, Dallas, TX, Sept. 26-29. SPE 11221.
19.Rowland David A. and Miller. F.G. 1969. The Evaluation of Heterogeneous Skin Effect Reservoirs. SPE Reservoir Engineering,. SPE-2619.
20.Tiab, D. and Donaldso, EC, Petrophysics-Theory and Practice of Measuring Reservoir Rock and Fluid Transport Properties; Gulf Publishing Company, Houston, TX, 2004
21.Trudgen,P. and Hoffmann, F.:” Statistically Analyzing Core Data”,J. Pet. Tech.（April,1967）497-503.
22.Warren, J. E., and H. S. Price, Flow in heterogeneous porous media, Soc. Pet. Eng. J., 1, 153-169, 1961
23.孫習之和關明義編著，1979、石油地質學，中國石油學會。
24.蕭寶宗和紀文榮編著，1988、石油地質，中油公司及中國學會共同出版。