The paper was presented at the SPE/DOE Unconventional Gas Recovery Symposium of the Society of Petroleum Engineers held in Pittsburgh, PA, May 16–18, 1982. The material is subject to correction by the author. Permission to copy is restricted to an abstract of not more than 300 words. Write: 6200 N. Central Expwy., Dallas, TX 75206.

Abstract

Several studies on production decline curves have shown that an exponential or hyperbolic curve adequately fits production decline data for Devonian shale wells. Attempts to characterize the production decline based on open flows, rock pressures, and specific shale production mechanisms have also been made. This paper seeks to provide a genesis of the decline curves with the use of a simple hydrodynamic analogy. Some physical factors critical to well productivity are also examined. physical factors critical to well productivity are also examined

Introduction

Production from Devonian shale wells is generally characterized by low production rates and large production timespans. Wells with continued production rates and large production timespans. Wells with continued production of over 25 years are rather common, and some wells with over 50 production of over 25 years are rather common, and some wells with over 50 years of production are still producing. However, with production rates being relatively low an average well might only produce around 300 MMCF in about 20 years or more. Increasing production rates, on a per well basis, not only adds to gas supplies but also enhances the economic viability of producing more in less time. producing more in less time. It is often desirable to estimate well productivity based on readily measurable variables during the initial stages. Initial open flows and rock pressures might be used, but these do not necessarily signal long-term well performance. This clearly is the case as in some of the observations which appear in Table 1. These observations reveal that productivity may be sensitive to physical factors, other than open flows and rock pressures, which cannot perhaps be measured directly. Given that relatively low open flows and rock pressures do not necessarily imply low productivity, it will be necessary to analyze the generating mechanism of production decline curves for possible clues. Merely graduating production decline data by various curve fits is not in itself sufficient to understand the mechanism. A possible hydrodynamic analogy is used to obtain some insights.

THE HYDRODYNAMIC ANALOGY

A detailed treatment of geological reservoirs is not intended here. Precise reservoir configurations including fracture geometry (shape, size Precise reservoir configurations including fracture geometry (shape, size and spatial orientation), structural, lithologic and other geologic features are not addressed. However, the broad division between the gas-generating shale matrix (lower permeability and porosity) from gas-filled fractures, fissures, sandstones, siltstones and other sources (higher permeability and porosity) is made. Schematically, the total reservoir system is partitioned into domains R 1 and R 2 as shown in Figure 1.Basic attributes of R 1 and R 2 are contained in the set {K, beta, P, V} where K = permeability, beta = porosity, P = pressure, V = volume of gas. It will be assumed that flow takes place, and has taken place over geologic time, from domain R 1 to R 2. Flow to the wellbore is place over geologic time, from domain R 1 to R 2. Flow to the wellbore is from R 2.The hydrodynamic analogy is that of two circular cylinders containing liquid that are interconnected with inlets (sources) and outlets (sinks), as shown in Figure 2.Q 1 is outflow (sink) from R 1 but inflow (source) to R 2; C 1 (capacitance) is uniform cross-sectional area; h 1 (t) is pressure at time t at the boundary, which is proportional to the height of liquid; is resistance to flow at the boundary separating R 1 from and is a measure of the permeability in the region of the boundary. Similar interpretations hold for the R 2 reservoir. A first-order equivalence relationship between pressure-volume (PV) initial conditions in the actual reservoirs with the analog cylinder "reservoirs" could be theoretically established.

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