yo . FEDERAL UNIVERSITY OF TECHNOLOGY, OWERRI L SCHOOL OF ENGINEERING AND ENGINEERING TECHNOLOGY x) DEPARTMENT OF PETROLEUM ENGINEERING 2021/2022 HARMATTAN SEMESTER EXAMINATION yw Course Title: Reservoir Modelling And Simulation Date: April 19, 2023 ° Course Code: PET 50S Time: 3 Hours Instructions: Answer any 2 Questions from Section A and any 3 questions from SECTION B, Units: 3 SECTION A iestion 1 ‘a. (i) What do you understand by the term history matching? [2marks} ii. Name the parameters which can be varied either singly or collectively for history matching optimization [3marks| (ii) With a flow chart only, state the reservoir simulation study process [4maris] » (List the history matching parameters.|4marks} (i) Differentiate between simultaneous solution method and IMPES solution of a reservoir simulator {3marks| (ii) Show the Sow chart of solving the simulation equation using Sivvultaneous solution (4marks). gon? fn es (a)Siate the parta! differential equations for both oil phase and water phase using a fully implicit formulation [4marks} (b) Differentiate between a one dimensional model and a three dimensional model [3arks| (c) List the groups of data generally required in making a simulation Fun [4marks| (¢) State the data sources and their paramsters a8 required by the engineer {Smarks] (¢) Enumerate the parameters which are significant in the model selection [4marts| Question 3 sq —_® What are the mechanisms of history matching?(Smavks) (b) Wiy is IMPIS method sled a Simultaneaus solution method(3marks} (c) Show how the two phases, that is, oil phase and water phase can be solved using matrix system(4marks) (d) What is the objective of an Engineer curing histor’ m>tching?(3marks) (e)Enumerate the bacie processes which are controllable in history matching operation(4marks) (f) On January 20, 2023, | woke up in y . tice seat the ofsery e294 fare are tag hich, + he roaiched, what wou likely cause? @marks) SECTION B 2 lesion 4 a. 1 List two advantages of reservoir simulation, two disadvantages and two abuses of reservoir simulation. (6 marks} ap seme loin asd pes ne following toma [9 mai Figure Grid typeiname | imax Jmax [Kmax_ ‘Applications | Figure T | iC | Figure? i I Figures —— i Cs ©. Given the basic single phase flow equation as equation | below: ” (Geta tt) nx + 2 (6, 28228) ay 4 2 (p,m . q@ em wa Sao) + afm 2 rod pein nc an een a 2D mags tei wd y Hast) agy | " z . as Bt orb bor © ay4 (ex ‘ Question § oO a. A3D slightly compressible fluid transport equation is given as equation 2 4(,5 2 (g, Art 22) ay 4 2 (i, tke d0 = Yeeeide He (Be SEs) ax 5 (Be peas) OY + (Be ape) Ae + ae = “ASSP i. Write the explicit finite-difference approximation to this equation for time level e* ii Weite the implicit fnite-dfference approximation to this equation for time level ¢ (5 marks} bi Identify the type of boundaries shown inthe grid block (Fig 4) (3 marks] ; ii, Fora 1D Single phase flow of slightly compressible oil, we can show that the flow equation for an explicit formulation in block iis: ms of pe (SBC ie (2218) free som, (7 4-7" 5) PR 4 Tm PR ares {00 (eu (AE) (raat ~ (Maan + Tea) E+ Tae] ©) Where the interbloek transmissibility is 4 5 “ake _ This = (Be Bae? 615 & Be = 1.127 1,000 re weet : : t baeow | , P= 6:00 pata Pg Fig.4: [D horizontal reservoir Using a time step of 15 days ( i.e At = 15 days), detersine the pressure distribution in 30 days for the reservoir showa in Figure 4. All blocks have a: wid fo=i5 md, The other properties are B, = BY = 1,0 RBISTB, pi=11 cp, and CSc Opa". fait prOssie 15 OUUY Psa ahd porwaily ~ v.Ld. Arswite Bidets as & wuNeIA witcm d he Fay OF hate [12 marks}, LeQuestion 6 . & The single phase wansmissibiliy of “8 porous medium to gos is given by Tyy(P) = Zettel Te F here Bertier Aas Kes Toes Pye and T ae constants while jj, P,and Z are functions of pressure, Use the combined product and quotient rule to obtain a derivative of the transmissibility with respect to pressure, . Find the expression for production rate from an oil reservoir undergoing simultaneous saturation and pressute changes, Take N = bpehaf t 2) VW; ef, 7 fe URuestion 7 . SM: = fn ~ fe 2 Using Tar Series expo, derive the nie diferenc approxima tor (2° 5. The incompressible flow equation fr a one dimensional homogeneous reservoir model which consist of ix equally spaced grid Blocks in the xirecton i given by 2 (ByAcKg 2%) AX + ude = 0. Develop the tr-diagonal matrix af he incompressible Now eauation if wo production wells placed on grid blocks 2 and $ are producing at arate of due and 1,5 due respectively 2 oO. a v Ce ky - eS Bo: ' ¥ Y ie Sy a ~| & 8 . LF \ 4 TPs