An Attempt to Predict the Time Dependence of Well Deliverability in Gas Condensate Fields

Abstract

Abstract A systematic variation of well deliverability, as reflected from isochronal back-pressure tests performed at regular intervals, has been observed in some gas condensate wells producing at high rates. The same effects have been obtained using a numerical model of gas and condensate flow which takes into account secondary gasoline deposited in the pore space as a result of pressure reduction, and nondarcy flow of gas in the vicinity of the wells. Matching calculated values with previous test results bas been possible, and future predictions have been obtained. An application of this method to the Hassi Er R'Mel gas-condensate field in Algeria is tentatively shown. Introduction Flow capacity of gas wells is generally derived from an analysis of back-pressure tests. The empirical equation q = C(Delta p)n used by Rawlins and Schellhardt can be derived rigorously assuming that steady-state radial flow of a dry gas of constant viscosity and compressibility is established during each flow period of the well tests. Furthermore, when Darcy's law applies in the entire flow region, the theory predicts that the exponent n is equal to 1. In low-permeability reservoirs, it was soon discovered that the time required to reach a stabilized flow often exceeded the duration of the flow periods normally available for testing wells. Consequently, transient gas flow had to be considered instead of the steady-state assumption previously used. This led to the isochronal testing procedure established by Cullender which has largely replaced conventional back-pressure testing. For dry gas fields, this method yields definite values of C and n equivalent to those of the empirical equation. These values should remain constant for each well as long as the permeability of the formation and the characteristics of the gas (viscosity and compressibility) do not change appreciably. This is the case when reservoir pressure remains close to the original value and when the formation near the wellbore remains free of plugging. Under those conditions, stabilized flow potential curves of gas wells can be established from a single sequence of isochronal flow and shut-in periods. An analysis of a pressure build-up following a longer production period provides additional data on the transmissivity (kh/mu) of the reservoir, and eventually on the drainage radius rd of the well, which can be related to the value of C so that future performance of the well can be predicted using the concepts developed by A. Houpeurt. At high How rates, Darcy's law no longer applies in the vicinity of the wellbore, and inertial effects in the high velocity gas flow introduce additional pressure drops. As a consequence, exponent n of the back-pressure tests becomes smaller than 1, and a slight curvature of the log-log plot of Delta p vs q can be predicted When going from very low to high rates of flow (Elenbaas and Katz). The effects of variations of viscosity and compressibility with pressure on the radial flow of dry gas in an infinite reservoir were taken into account by Jenkins and Aronofsky. Numerical solutions of the transient flow of an ideal gas in finite radial reservoirs were presented by Bruce, Peaceman, Rachford and Rice. In the case of gas condensate wells however the presence of gasoline in the pore space as soon as reservoir pressure is reduced below the dewpoint pressure further complicates the interpretation of flow tests so that the prediction of stabilized well performance becomes very difficult. Field observation shows that both C and n derived from isochronal tests vary in time, even when reservoir pressure has not changed appreciably. Such a variation cannot be attributed to any change of the gas characteristics, and must result from the effect of a gasoline saturation on the gas flow. SPEJ P. 113ˆ