Mathematical modeling of geomechanical behavior of tarmat during the depletion of giant oil reservoir-aquifer systemsReport as inadecuate

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Journal of Petroleum Exploration and Production Technology

, Volume 1, Issue 2–4, pp 71–80

First Online: 28 June 2011Received: 12 April 2011Accepted: 02 June 2011


In this work, deformation and failure behavior of tarmat layers during depletion of a giant reservoir–aquifer system has been studied. Deformation response of the tarmat to increasing pressure differential caused by continuous depletion of reservoir is examined and a mathematical model is developed for the study of this type of composite systems. The geomechanical failure that takes place when the pressure differential reaches a critical value is also evaluated, along with the characterization of the resulting fracture. Plate theory, maximum shear stress failure criterion, conventional well test model, Perkins–Kern–Nordgren PKN and Khristianovic–Geertsma–de Klerk KGD models and flow through fractures models are used. The developed sensitivity analysis proposes the proper protocol to be followed in order to undertake production design in such composite systems. The methodology presented in this paper, ultimately, predicts fracture width and fracture permeability that would be developed in a system with a tarmat layer having a certain thickness and a reservoir being produced at a certain production rate and total depletion time.

KeywordsGeomechanics Tarmat Numerical modeling Giant oil reservoir Aquifer List of symbolsACross-sectional area, L

a, bDimensions of the drainage area considered, L

BFormation volume factor, dimensionless

cCompressibility, Lt-M

DFlexural rigidity coefficient, dimensionless

dx, dy, dzIncremental lengths, L

EModulus of elasticity in tension and compression, m-Lt

GShear modulus, m-Lt

hThickness, L

kAbsolute permeability, L

MBending moment, mL

pPressure, m-Lt

qApplied load, m

qVolumetric flow rate, L-t

rwWellbore radius, L

tTime, t

VShear forces, mL-t

wDisplacement deformation, fracture width, L

x, y, zCoordinate directions

ϕPorosity, dimensionless

μViscosity, m-Lt

λUnit conversion constant 2.637 × 10 in practical field units

γUnit conversion constant 141.2 in practical field units

τShear stress, m-Lt

σStress, m-Lt

νPoisson’s ratio, dimensionless

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Author: Ayse Pamir Cirdi - Turgay Ertekin - Luis F. Ayala H. - Ali H. Dogru


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