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TPG4150 Reservoir Recovery Techniques 2017 2 9,Hand out note 4 Buckley Leverett Analysis. kk ro A Pcow, For the simplest case of horizontal flow with negligible capillary pressure the expression. reduces to, Typical plots of relative permeabilities and the corresponding fractional flow curve are. Typical oil water relative permeabilities Typical fractional flow curve. Relative permeability,0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1. 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1,Water saturation.

Water saturation,Derivation of the Buckley Leverett equation. For a displacement process where water displaces oil we start the derivation with the. application of a mass balance of water around a control volume of length x of in the. following system for a time period of t,The mass balance may be written. qw w x qw w x x t A x Sw w t t Sw w t, which when x 0 and t 0 reduces to the continuity equation. qw w A Sw w, Norwegian University of Science and Technology Professor Jon Kleppe. Department of Geoscience and Petroleum,TPG4150 Reservoir Recovery Techniques 2017 3 9.

Hand out note 4 Buckley Leverett Analysis, Let us assume that the fluid compressibility may be neglected ie. w constant,Also we have that,the equation may be rewritten as. df w Sw A Sw, This equation is known as the Buckley Leverett equation above after the famous paper by. Buckley and Leverett1 in 1942,Derivation of the frontal advance equation. we can write the following expression for saturation change. dSw dx w dt, In the Buckley Leverett solution we follow a fluid front of constant saturation during the.

displacement process thus,0 w dx w dt, Substituting into the Buckley Leverett equation we get. Integration in time, Buckley S E and Leverett M C Mechanism of fluid displacement in sands Trans. AIME 146 1942 107 116, Norwegian University of Science and Technology Professor Jon Kleppe. Department of Geoscience and Petroleum,TPG4150 Reservoir Recovery Techniques 2017 4 9. Hand out note 4 Buckley Leverett Analysis,dt A dS dt.

yields an expression for the position of the fluid front. which often is called the frontal advance equation. The Buckley Leverett solution, A typical plot of the fractional flow curve and it s derivative is shown below. Fractional flow curve and it s derivative,0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1. Water saturation, Using the expression for the front position and plotting water saturation vs distance we get. the following figure, Clearly the plot of saturations is showing an impossible physical situation since we have two. saturations at each x position However this is a result of the discontinuity in the saturation. function and the Buckley Leverett solution to this problem is to modify the plot by defining a. Computed water saturation profile,0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1.

Norwegian University of Science and Technology Professor Jon Kleppe. Department of Geoscience and Petroleum,TPG4150 Reservoir Recovery Techniques 2017 5 9. Hand out note 4 Buckley Leverett Analysis, saturation discontinuity at x f and balancing of the areas ahead of the front and below the. curve as shown,The final saturation profile thus becomes. Balancing of areas,0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1. Final water saturation profile,0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1.

Norwegian University of Science and Technology Professor Jon Kleppe. Department of Geoscience and Petroleum,TPG4150 Reservoir Recovery Techniques 2017 6 9. Hand out note 4 Buckley Leverett Analysis, The determination of the water saturation at the front is shown graphically in the figure below. Determination of saturation at the front,0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1. Water saturation, The average saturation behind the fluid front is determined by the intersection between the. tangent line and f w 1,Determination of the average saturation.

behind the front,0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1. Water saturation, At time of water break through the oil recovery factor may be computed as. The water cut at water break through is,WCR f wf in reservoir units. Since qS qR B and f wS we may derive f wS,q wS qoS 1. Norwegian University of Science and Technology Professor Jon Kleppe. Department of Geoscience and Petroleum,TPG4150 Reservoir Recovery Techniques 2017 7 9.

Hand out note 4 Buckley Leverett Analysis,WCS in surface units. For the determination of recovery and water cut after break through we again apply the frontal. advance equation, At any water saturation Sw we may draw a tangent to the f w curve in order to determine. saturations and corresponding water fraction flowing. Determining recovery after break through,0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1. Water saturation, Norwegian University of Science and Technology Professor Jon Kleppe. Department of Geoscience and Petroleum,TPG4150 Reservoir Recovery Techniques 2017 8 9.

Hand out note 4 Buckley Leverett Analysis, The effect of mobility ratio on the fractional flow curve. The efficiency of a water flood depends greatly on the mobility ratio of the displacing fluid to. the displaced fluid rw ro The lower this ratio the more efficient displacement and the. curve is shifted right Ulimate recovery efficiency is obtained if the ratio is so low that the. fractional flow curve has no inflection point ie no S shape Typical fractional flow curves for. high and low oil viscosities and thus high or low mobility ratios are shown in the figure below. In addition to the two curves an extreme curve for perfect displacement efficiency so called. piston like displacement is included,Effect of mobility ratio on fractional flow. Low oil viscosity,0 9 High oil viscosity,Piston displacement. 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1,Effect of gravity on fractional flow curve. In a non horizontal system with water injection at the bottom and production at the top gravity. forces will contribute to a higher recovery efficiency Typical curves for horizontal and vertical. flow are shown below,Effect of gravity on fractional flow.

0 9 Horizontal flow,Vertical flow,0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1. Effect of capillary pressure on fractional flow curve. Norwegian University of Science and Technology Professor Jon Kleppe. Department of Geoscience and Petroleum,TPG4150 Reservoir Recovery Techniques 2017 9 9. Hand out note 4 Buckley Leverett Analysis, As may be observed from the fractional flow expression. kk ro A Pcow, capillary pressure will contribute to a higher f w since 0 and thus to a less efficient. displacement However this argument alone is not really valid since the Buckley Leverett. solution assumes a discontinuous water oil displacement front If capillary pressure is included. in the analysis such a front will not exist since capillary dispersion ie imbibition will take. place at the front Thus in addition to a less favorable fractional flow curve the dispersion will. also lead to an earlier water break through at the production well. Norwegian University of Science and Technology Professor Jon Kleppe. TPG4150 Reservoir Recovery Techniques 2017 Hand out note 4 Buckley Leverett Analysis Norwegian University of Science and Technology Professor Jon Kleppe

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