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

A New Theory for Interpreting Rate Decline Trends in Solution-Gas Drive Reservoirs

A number of attempts have been made to establish the theories of rate decline in solution-gas drive reservoirs with multiphase flow. However, none of these attempts have established a functional link between the empirical and the theoretical domains of decline curve analysis for such reservoirs. The absence of such a link has inhibited the formulation of simple techniques for reservoir properties estimation. The purpose of this work is therefore to establish the missing link. In this work, functional relationships between the empirical bemp and the theoretical bth were derived. The derivation was based on a novel definition of a new parameter known as time-weighted average of the theoretical exponent bth .This new parameter was found to be related to the empirical exponent bemp, thus establishing the link. A reservoir simulator was used to generate sets of production data used in verifying the derived relationships. Results presented in this paper show that the relationships derived herein are valid, even for heterogeneous reservoirs. The work also offered theoretical justifications for the various ranges of bth values, and for the first time, four distinct rate decline regimes in solution-gas drive reservoirs were identified. Sensitivity analyses were performed on the results. The effects of non-Darcy flow on decline parameters were also investigated. Lastly, this work provided a mathematical justification for the existence of the hyperbolic family of curves in decline analysis of solution-gas drive reservoir

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

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