By Wilson C. Chin PhD

For the practitioner, this quantity is a precious device for predicting reservoir circulation within the best and ecocnomic demeanour attainable, utilizing quantitative equipment instead of anecdotal and superseded equipment. For the coed, this quantity bargains perception no longer lined in different textbooks.Too many techniques in conventional petroleum engineering are in accordance with "ad hoc" and "common feel" equipment that experience no rigorous mathematical foundation. such a lot textbooks facing reservoir engineering don't move into the mandatory mathematical aspect and intensity. This new booklet through Wilson Chin, a revision of 2 past books released via Gulf Publishing, sleek Reservoir circulate and good temporary research and Formation Invasion, integrates rigorous mathematical equipment for simulating and predicting reservoir move either close to and clear of the well.Predicts reservoir circulate to maximise assets, time, and profitsIncludes difficulties and suggestions for studentsPresents mathematical types in an easy-to-understand and easy-to-simulate structure.

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**Extra resources for Quantitative Methods in Reservoir Engineering**

**Example text**

Here, we give a complementary solution to Example 2-5 and consider the flow of a constant density liquid into a fracture held at a constant pressure pf. Thus, the derivative p f ’(ξ) vanishes identically, and Equation 2-15 reduces to +1 f(x) = [PV ∫ {p f ’(ξ)/(ξ-x)}√(1-ξ2 ) d ξ −1 +1 - (1/ loge2) ∫ p f (ξ)/ √(1-ξ2 ) d ξ] /{π2√(1-x2 )}+ H/{π loge2√(1-x2 )} -1 +1 = - (p f/log e2) { ∫ d ξ /√(1-ξ2 )}/{π2√(1-x2 )}+ H/{π loge2√(1-x2 )} -1 = (H - p f )/{πloge2√(1-x2 )} (2-99) Note that the integral of f(x) over (-1,+1) equals (H – pf )/ loge2, a result consistent with Equation 2-113 when C0 = pf and C2 = C4 = 0.

At the same time, the pressure itself is continuous and single-valued through the slit. The logarithmic solution is one of many elementary singularities of Laplace’s equation; others commonly used include doublets, vortexes, source rings, and horseshoe vortexes (Thwaites, 1960). Chapter 2 demonstrates how practical solutions are constructed from distributions or superpositions of logarithms. Another useful singularity is the arc tangent (Yih, 1969). In this chapter, we will explore its usefulness in modeling flows about solid shaly bodies.

Usually, numerical simulators with fully heterogeneous permeabilities and porosities are used; shales, for example, might be modeled by taking “k” or “φ” very small locally. Producing fractures, on the other hand, might be simulated by using rows of discrete wells or point sources. These approaches are sometimes acceptable, but they do not afford the physical insight that precise mathematical modeling provides. One example is the existence of square root velocity singularities at fracture tips; certainly, an awareness of its ramifications only leads to an improved understanding of the 43 44 Quantitative Methods in Reservoir Engineering flow and to more accurate numerical models.