Low Field NMR Water Cut Metering
Authors: Wright I.W. , Lastockin D. , Allsopp K. , Evers-Dakers M.E. , Kantzas A. 
Published: March 2010

Abstract
Enhancing oil extraction from oil sands with a hydraulic fracturing techniquehas been widely used in practice. Due to the complexity of the actual process, modelling of hydraulic fracturing is far behind its application. Reproducingthe effects of high pore pressure and high temperature, combined with complexstress changes in the oil sand reservoir, requires a comprehensive numericalmodel which is capable of simulating the fracturing phenomenon. To capture allof these aspects in the problem, three partial differential equations, i.e., equilibrium, flow, and heat transfer, should be solved simultaneously in afully implicit (coupled) manner.
A fully coupled thermo-hydro-mechanical fracture finite element model isdeveloped to incorporate all of the above features. The model is capable ofanalyzing hydraulic fracture problems in axisymmetric or plane strainconditions with any desired boundary conditions, e.g., constant rate of fluidinjection, pressure, temperature, and fluid flow/thermal flux. Fractures can beinitiated either by excessive tensile stress or shear stress. The fractureprocess is simulated using a node-splitting technique. Once a fracture isformed, special fracture elements are introduced to provide in-planetransmissivity of fluid. Effectiveness of the model is evaluated by solvingseveral examples and comparing the numerical results with analytical solutions.The model is also used to simulate large-scale laboratory hydraulic fracturingexperiments.

Introduction
Hydraulic fracturing technique has been a fast growing technology since itsfirst application in 1947. By 1988, more than one million hydraulic fracturingtreatments had been performed(1), and today this technique is one ofthe most important methods in enhancing oil extraction from wells. Hydraulicfracturing in oil and reservoirs plays an even more important role. Due to lowtemperature and low permeability of oil sand deposits and high viscosity ofbitumen, oil is virtually immobile(2). Hence, any attempt for insitu oil extraction should employ one of the following techniques: cyclic steamstimulation, in situ combustion, or hydraulic fracturing.
Despite the fact that hydraulic fracturing technology has advancedsignificantly over the past fifty years, our ability to model the process hasnot changed as rapidly. As a matter of fact, this technique has been sosuccessful that in the past, designing the treatment with a high degree ofprecision was not of any interest. ut as the industry moved towardsapplications of very high volume/rate, and highly engineered and sophisticatedhydraulic fracturing treatments, the demand for more rigorous designs in orderto optimize the procedure have become more important. On the other hand, without a thorough understanding of the physical process and the factors thatare involved, our ability for an optimal design is limited. Modelling fluidflow combined with heat transfer in the reservoir has been used by the industryfor a long time, and the fracturing process was often designed based ontwodimensional closed-form solutions, such as Geertsma-deKlerk(3), or GdK in brief, and Perkins-Kern(4) and Nordgren(5), or PKN.