Course:- 28117Class:- 289023a HERIOT-WATT UNIVERSITY DEPARTMENT OF PETROLEUM ENGINEERING Examination for the Degree of MEng in Petroleum Engineering Reservoir Engineering 2 Wednesday 22nd April 1998 09.30 - 12.30 NOTES FOR CANDIDATES 1. This is a Closed Book Examination. 2. 15 minutes reading time is provided from 09.15 - 09.30. 3. Examination Papers will be marked anonymously. See separate instructions for completion of Script Book front covers and attachment of loose pages. Do not write your name on any loose pages which are submitted as part of your answer. 4. There are SIX questions. A maximum of FOUR numbered questions should be attempted. 5. All numbered questions have equal value. 6. This Examination represents 100% of the Class assessment. 8 State clearly any assumptions used and intermediate calculations made in numerical questions. No marks can be given for an incorrect answer if the method of calculation is not presented. 9. Answers must be written in separate, coloured books as follows:- Section A Blue Book Section B Green Book SECTION A A1 (a) Water injection is a common feature of many oilfield developments, particularly in the North Sea. List the reasons for selecting water drive as the main recovery mechanism in such an area. [5] (b) A core sample has oil / water relative permeabilities as indicated in Table 1a below. A series of core-flood experiments was performed using water and three different samples of crude oil. Viscosities for these fluids are listed in Table 1b below. Calculate the mobility ratio in each case and comment briefly on the one dimensional waterflooding of such a rock with respect to the three fractional flow relationships. Table 1a:- Core Data: Core porosity (ø) = 0.2 S w k rw k ro 0.2 0 1 0.25 0.008 0.650 0.30 0.020 0.470 0.35 0.031 0.345 0.40 0.046 0.250 0.45 0.062 0.175 0.50 0.082 0.114 0.55 0.110 0.070 0.60 0.138 0.037 0.65 0.170 0.014 0.70 0.200 0 Table 1b:- Fluid Viscosities mw = 0.4cp Case 1: m0 = 0.5cp Case 2: m0 = 5.0cp Case 3: m0 = 50cp [8] (c) Water is being injected at a constant rate of 1000 barrels per well per day in a direct line drive, into a reservoir which has the rock and fluid properties of Case 2 in (b) above. The reservoir characteristics are: Dip angle = 0° Reservoir thickness = 40ft Distance between injection wells = 600ft Distance between injectors and producers = 2000ft Further data are provided in Table 1c below. Assuming one dimensional flow conditions (ie not segregated/or layered) and that injection starts at the same time as oil production, Determine:- (i) The water saturation and fractional flow at breakthrough [2] (ii) The time when breakthrough occurs [3] (iii) The cumulative oil production up to breakthrough, in pore volumes [3] (iv) The cumulative oil production after breakthrough as a function of time. Comment briefly on the shape of this curve. [4] Table 1c:- Flow Equations The fractional flow of water for horizontal flow is: f k k w w o ro rw = + ⋅ 1 1 µ µ The Buckley-Leverett water drive equation is: V q A df ds sw t w w sw = φ SECTION B B2 Derive the equation which yields the skin factor for the buildup period of a well test. Suppose the skin is changing due to well clean-up in the drawdown period of a transient test and that the permeability, k, is known from a build-up analysis. Show how the skin factor can be obtained at each point of the drawdown and a graph of skin versus flowing time, t, prepared. [25] B3 Discuss the factors which influence the design of an exploration well test (DST) and show how the attainment of the objectives of a DST can be aided by good test design. [25] B4 Figure 4 illustrates the dynamics of a buildup. The pressure distribution in the reservoir is calculated by superposition of the exponential integral solution, plotted as a function of radius (distance from the well) at increasing shut-in times, ∆t. At a given shut-in time, ∆t, the pressure at the sandface in buildup corresponds to the pressure in the reservoir at the moment of shut-in, t p and a distance r p from the wellbore. Show that the distance, r p is given approximately by:- r k t c p e t = 4 ∆ γφµ where ∆ ∆ ∆ t t t t t e p p = + k = permeability γ = Eulers constant φ = porosity t = producing time µ = viscosity ∆t = shut-in time c t = compressibility q 0 ∆t ∆t 5 ∆t 4 ∆t 3 ∆t 2 ∆t 1 r t p p r r w p r (t p , r p2 ) p r (t p , r p1 ) p r (t p , r p3 ) p r (t p , r p4 ) p w =p r r = r w p r (t p , r p5 ) Peaceman probe radius concept Reservoir pressure distribution at moment of shut-in, p r (t p ) Pressure build-up in a reservoir B5 In the analysis of buildups, following a long period of production in which semi-steady-state has been attained, the Kazemi method suggests replacing the actual producing time, tp by tsss in the Horner time function for buildup analysis. Show by means of diagrams why the Kazemi method is applicable and discuss other methods for analysing buildups following long periods of production. t sss = time for drainage area to reach semi-steady-state [25] B6 The constant rate solution for the bottom-hole pressure of a well in drawdown is the familiar logarithmic expression: p p p kh q s D i wf tD = − = + ( ) ln 2 1 2 4 π µ γ where t kt c r D t w = φµ 2 For production at constant bottom-hole pressure, Fetkovich has shown that the above expression can be used to predict the rate with less than 5% error if total flowing time is used for t. Calculate the transient oil production as a function of time for the vertical well with the properties given below. Carry the calculations up to a period of 6 months. k = 0.1 md c t = 3.0*10 -5 psi -1 h = 300 ft p i = 6000 psia µ = 0.5cp p wf = 3000 psia φ = 0.2 [25] End of Paper