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...ould definitely read Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro Transient analysis mathematics Green's function for solving transient flow problems ...
As discussed in Source function solutions of the diffusion equation, the conventional development of the source function solutions uses the instantaneous point-source solution as the building block with the appropriate integration (superposition) in space and time. In 1973, Gringarten and Ramey introduced the use of the source and Green's function method to the petroleum engineering literature with a more efficient method of developing the source solutions. Specifically, they suggested the use of infinite-plane sources as the building block with Newman's product method. In this page we discuss the use of Green's functions and source functions in solving unsteady-flow problems in reservoirs. Green's function for transient flow in a porous medium is defined as the pressure at M (x, y, z) at time t because of an instantaneous point source of unit strength generated at point M′(x′, y′, z′) at time τ t with the porous medium initially at zero pressure and the boundary of the medium kept at zero pressure or impermeable to flow.
...org/10.2118/28393-PA Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro Solving unsteady flow problems with Green's and source functions Source function sol...
There are many advantages of developing transient flow solutions in the Laplace transform domain. For example, in the Laplace transform domain, Duhamel's theorem provides a convenient means of developing transient flow solutions for variable rate production problems using the solutions for the corresponding constant rate production problem. Applying the Laplace transform converts the convolution integral in Eq. 1 to an algebraic expression, and Duhamel's theorem is given in the Laplace transform domain as The simplicity of the expression given in Eq. 2 explains our interest in obtaining transient-flow solutions in the Laplace transform domain. Another example to explain the convenience of the Laplace domain solutions is for the naturally fractured reservoirs. Common transient flow models of naturally fractured reservoirs lead to the following differential equation in radial coordinates in the Laplace transform domain:  The naturally fractured reservoir function, f (s), is a function of matrix and fracture properties and depends on the model chosen to represent the naturally fractured reservoir. The general solutions for Eqs. 3 and 4 are given, respectively, by This discussion demonstrates that it is possible to derive transient flow solutions for naturally fractured reservoirs by following the same lines as those for the homogeneous reservoirs.
...rg/10.2118/949305-G. Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro Transient analysis mathematics Source function solutions of the diffusion equation ...
Integral transforms are useful in solving differential equations. A special form of the linear integral transforms, known as the Laplace transformation, is particularly useful in the solution of the diffusion equation in transient flow. The following fundamental properties of the Laplace transformation are useful in the solution of common transient flow problems. For the Laplace transform to be useful, the inverse Laplace transformation must be uniquely defined. In this operation, p(t) represents the inverse (transform) of the Laplace domain function, .
...rg/10.2118/10337-MS. Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro PEH:Artificial_Lift_Systems...
Historically health, safety, and environment (HSE) standards have been developed using a prescriptive management approach. A new, and potentially more effective, approach to the development of company HSE standards is to shift towards a more risk-based HSE strategy. The risk-based approach allows resources to be focused towards geographic locations, activities, and services that present higher risk to a company and its customers. Some risk-based HSE approaches involves setting prescribed fundamental controls that apply to all activities and employees at all company sites. While some controls apply without variation, the application of many controls increases proportionally with the assessed risk.
...ould definitely read Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro Single well chemical tracer test Well to well tracer tests PEH:The_Single-Well_Chem...
Even with a properly designed single well chemical tracer (SWCT) test, interpreting the data requires judgment calls, and typically, simulation, to arrive at a final estimation of residual oil. Tomich et al. report one of the earliest SWCT tests, which was performed on a Frio Sandstone reservoir on the Texas Gulf Coast. The results of this test are used here to demonstrate the details of SWCT test interpretation for an ideal situation. The test well in the Tomich et al. report was in a fault block that had been depleted for several years. Because of the natural water drive and high permeability of the sand, the formation was believed to be near true Sor.
...ould definitely read Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro Reservoir management PEH:Reservoir_Management_Programs...
This page provides a reservoir management case study for a steeply dipping sandstone field in which gravity stable miscible gas injection techniques have been implemented. This field was formed by a piercement salt plug that breached a regional fault system. The reservoir is composed of unconsolidated sands that dip away from the salt dome at 65 to 85 . The reservoir is divided into several fault blocks. Within each block, the sand is relatively homogeneous.
...ould definitely read Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro Single well chemical tracer test Designing single well chemical tracer test for resi...
The single-well chemical tracer (SWCT) test is an in-situ method for measuring fluid saturations in reservoirs. The most common use is the assessment of residual oil saturation (Sor) prior to improved oil recovery (IOR) operations (post-waterflooding). The SWCT test for Sor uses only one well and involves the injection and back production of water carrying chemical tracers. A typical target interval for SWCT testing is shown in Figure 1. The candidate well should be completed only to the watered-out zone of interest (zone at Sor).
Although reserves estimates for known accumulations historically have used deterministic calculation procedures, the 1997 SPE/WPC definitions allow either deterministic or probabilistic procedures. Each of these is discussed briefly in the next two sections. Thereafter--except for another section on probabilistic procedures near the end--the chapter will focus on deterministic procedures because they still are more widely used. Both procedures need the same basic data and equations. Deterministic calculations of oil and/or gas initially in place (O/GIP) and reserves are based on best estimates of the true values of pertinent parameters, although it is recognized that there may be considerable uncertainty in such values.
The first SWCT test for Sor was run in the East Texas Field in 1968. Patent rights were issued in 1971. Since then, numerous oil companies have used the SWCT method. More than 400 SWCT tests have been carried out, mainly to measure Sor after waterflooding. The SWCT method has gained considerable recognition over the past few years because of increasing interest in the quantitative measurement of Sor. Some experts consider the SWCT test to be the method of choice because of its demonstrated accuracy and reasonable cost. Figure 1.1b – Reservoir evaluation by material balance with measured Sor. A reliable in-situ measurement of Sor simultaneously defines the target for enhanced oil recovery (EOR) and allows estimation of the potential bypassed (mobile) oil in the field. This moveable oil is the target for infill drilling and/or flood sweep efficiency improvements. Because Sor varies greatly with formation type, oil/water properties, and other variables that are not completely understood (e.g., wettability changes caused by water flood practices), Sor measurements range from 10% to 45%. There is no reliable way to predict Sor with acceptable accuracy for most reservoirs. Furthermore, measuring residual oil is not easy.