Theories of Arps' Decline Curve Exponent and Loss Ratio, for Saturated Reservoirs

Rate decline curve analysis is an essential tool in predicting reservoir performance and in estimating reservoir properties. In its most basic form, decline curve analysis is to a large extent based on Arps’ empirical models that have little theoretical basis. The use of historical production data to predict future performance is the focus of the empirical approach of decline analysis while the theoretical approach focuses on the derivation of relationships between the empirical model parameters and reservoir rock/fluid properties; thereby establishing a theoretical basis for the empirical models. Such relationships are useful in formulating techniques for reservoir properties estimation using production data. Many previous attempts at establishing relationships between the empirical parameters and the rock/fluid properties have been concerned primarily with the exponential decline of single phase oil reservoirs. A previous attempt to establish the theories of hyperbolic decline of saturated reservoirs (multiphase) have yielded an expression relating the Arps’ decline exponent, to rock/fluid properties. However, the values of exponent computed from the expression are not constant through time, whereas, the empirically-determined exponent b is a constant value. This work utilizes basic concepts of compressibility and mobility to justify the dynamic behaviour of the values obtained from the existing theoretical expression of the previous theory; to prove that the expression, though rigorously derived, is not the theoretical equivalence of the empirical Arps’ b-exponent; and finally, to properly to offer a new logical perspective to the previous theory relating b-exponent to rock and fluid property. Ultimately, this work presents, for the first time, a new consistent theoretical expression for the Arps’ exponent, b. The derivation of the new expression is still founded on the concept of Loss Ratio, as in previous attempts; however, this latest attempt utilizes the cumulative derivative of the Loss Ratio, instead of the instantaneous derivative implied in the previous attempt. The new expression derived in this work have been applied to a number of saturated reservoir models and found to yield values of b-exponent that are constant through time and are equivalent to the empirically-determined b-exponent

Improved Streamline-generating Technique That Uses The Boundary (integral) Element Method

The boundary element method (BEM) has been used to generate streamlines for homogeneous and sectionally homogeneous reservoirs having irregular boundaries. This technique is superior to earlier methods that use \u27image wells\u27 to simulate the reservoir boundary, especially for cases where the reservoir boundary is irregularly shaped. It has wider applicability to different kinds of reservoirs and eliminates the need for trial-and-error solutions. The errors caused by discretization and numerical approximation arise on and adjacent to the boundaries only, therefore the pressures and pressure gradients on which the streamlines are derived can be calculated with very high accuracy in the interior of the reservoir. Thus, the streamlines generated with this method are expected to be more realistic and representative of the actual physical system

The PROM1 mutation p.R373C causes an autosomal dominant bull's eye maculopathy associated with rod, rod-cone, and macular dystrophy.

PURPOSE: To characterize in detail the phenotype of five unrelated families with autosomal dominant bull's eye maculopathy (BEM) due to the R373C mutation in the PROM1 gene. METHODS: Forty-one individuals of five families of Caribbean (family A), British (families B, D, E), and Italian (family C) origin, segregating the R373C mutation in PROM1, were ascertained. Electrophysiological assessment, fundus autofluorescence (FAF) imaging, fundus fluorescein angiography (FFA), and optical coherence tomography (OCT) were performed in available subjects. Mutation screening of PROM1 was performed. RESULTS: The R373C mutant was present heterozygously in all affected patients. The age at onset was variable and ranged between 9 and 58 years, with most of the individuals presenting with reading difficulties. Subjects commonly had a mild to moderate reduction in visual acuity except for members of family C who experienced markedly reduced central vision. The retinal phenotype was characterized by macular dystrophy, with retinal pigment epithelial mottling in younger subjects, progressing to typical BEM over time, with the development of macular atrophy in older patients. In addition, all members of family C had typical features of RP. The electrophysiological findings were variable both within and between families. CONCLUSIONS: Mutations in PROM1 have been described to cause a severe form of autosomal recessive RP in two families of Indian and Pakistani descent. The results of this study have demonstrated that a distinct redundant PROM1 mutation (R373C) can also produce an autosomal dominant, fully penetrant retinopathy, characterized by BEM with little inter- and intrafamilial variability, and retinal dystrophy with variable rod or rod-cone dysfunction and marked intra- and interfamilial variability, ranging from isolated maculopathy without generalized photoreceptor dysfunction to maculopathy associated with very severe rod-cone dysfunction

Complex Fluids and Hydraulic Fracturing

Nearly 70 years old, hydraulic fracturing is a core technique for stimulating hydrocarbon production in a majority of oil and gas reservoirs. Complex fluids are implemented in nearly every step of the fracturing process, most significantly to generate and sustain fractures and transport and distribute proppant particles during and following fluid injection. An extremely wide range of complex fluids are used: naturally occurring polysaccharide and synthetic polymer solutions, aqueous physical and chemical gels, organic gels, micellar surfactant solutions, emulsions, and foams. These fluids are loaded over a wide range of concentrations with particles of varying sizes and aspect ratios and are subjected to extreme mechanical and environmental conditions. We describe the settings of hydraulic fracturing (framed by geology), fracturing mechanics and physics, and the critical role that non-Newtonian fluid dynamics and complex fluids play in the hydraulic fracturing process

New techniques for estimating properties of saturated reservoirs, using readily-available rate decline data

A recent work presented two techniques for estimating permeability and well drainage radius, for solution-gas drive reservoirs. However, data requirement has placed a limitation on the application of the techniques. Applying the techniques requires readily-available production data – cumulative production and production rate, versus time. In addition to these, it also requires the scarcely-measured average reservoir pressure, P¯ and average oil saturation, So¯¯, versus time. This work presents a practical method for deriving the scarcely-measured data from the readily-available data. This method, based on a new solution methodology to the MBE for solution-gas drive reservoirs, is presented as a sub-routine, added to the procedures of the properties estimation techniques. The methodology is analytically founded on the equality of the LHS (fluid withdrawal terms) and RHS (fluid expansion terms) of the conventional MBE, and the pressure value that upholds the equality. The sub-routine has been applied to two reservoir models and was found to yield excellent estimates of P¯ and So¯ data, exhibiting good agreement with P¯ and So¯ data resulting from simulating the reservoirs. Furthermore, the sub-routine-generated P¯ and So¯ data that have been used in implementing the properties estimation techniques, and the results have compared well both with the results of the techniques× implementation using simulator×s P¯ and So¯ data, and with the true values of these properties

Pressure Transient Analysis of Partially Penetrating Wells in a Naturally Fractured Reservoir

Abstract Often and for many reasons the wellbore does not completely penetrate the entire formation, yielding a unique early-time pressure behaviour. Some of the main reasons for partial penetration, in both fractured and unfractured formations, are to prevent or delay the intrusion of unwanted fluids into the wellbore, i.e., water coning. The transient flow behaviour in these types of completions is different and more complex compared to that of a fully penetrating well. This paper proposes a method for identifying, on the pressure and pressure derivative curves, the unique characteristics of the different flow regimes resulting from these types of completions and to obtain various reservoir parameters, such as vertical and horizontal permeability, fracture properties and various skin factors. Both naturally fractured and unfractured (homogeneous) reservoirs have been investigated. For a naturally fractured formation, the type curves of the pressure and pressure derivative reveal that the combination of partial penetration and dual-porosity effects yields unique finger prints at early and transition periods. These unique characteristics are used to calculate several reservoir parameters, including the storage capacity ratio, interporosity flow coefficient, permeability and pseudoskin. Equations have been developed for calculating the skin for three partial completion cases: top, centre and bottom. The analytical solution was obtained by combining the partially penetrating well model in a homogeneous reservoir with the pseudo-steady model for a naturally fractured reservoir (NFR). The interpretation of pressure tests is performed using the TDS (Tiab's Direct Synthesis) technique for analyzing log-log pressure and pressure derivative plots. The TDS technique uses analytical equations to determine reservoir and well characteristics without using type-curve matching. These characteristics are obtained from unique fingerprints, such as flow regime lines and points of intersection of these lines, which are found on the log-log plot of pressure and pressure derivative. Two numerical examples are included to illustrate the application of the. proposed technique. Introduction Consider a vertical well partially penetrating a naturally fractured reservoir, i.e., only a portion of hydrocarbon-bearing formations is perforated. The naturally fractured reservoir has an infinite radial extent. The Warren and Root(1) model is used in which the matrix blocks are replaced by a system of uniform rectangular parallelepipeds with identical properties. The fractures are assumed to be parallel with the principal axes. FIGURE 1: Different types of partially penetrating vertical wells based on the position in the perforated interval hw. Available in Full Paper The pressure solution is derived using the Laplace transformation and the separation of variables technique as proposed by Bui et al.(2). This solution is expressed as an infinite Fourier-Bessel series in Laplace domain. The theory for a partially penetrating well in a homogenous reservoir developed by Yildiz and Bassiouni(3) is used for comparison purposes. The analytical solution for constant flow rate in Laplace space was inverted into real dimensionless pressure using the Stehfest algorithm(4). Pressure Derivative Behaviour Four types of partial penetration or completion schemes are considered (as shown in Figure 1). A plot of the dimensionless pressure derivative tD * P'D versus tD is shown in Figures 2 and 3. </jats:sec