The paper analyzes some productivity forecast equations and critical production rate calculation of horizontal wells especially Joshi's equation of predicting productivity and Chaperon's equation of critical production rate calculation used in reservoir engineering. This paper suggests that the effective permeability should be used in calculating horizontal well productivity and points out the error existing in Joshi's equations. It also evaluates and introduces several equations of critical production rate such as Chaperon's equation and corrects the equation. Also, this paper derives two new equations for predicting horizontal well productivity and a general prediction equation of the calculation horizontal well critical production rate applying the Mirror Effect Theory Field. Applications show that the relative error between practical value and prediction value is less than 17% using a new method of prediction and the calculation result is more accurate than that of Joshi's equation. Moreover, the oil and gas fields actual examples was proved and corrected Chaperon's equation and in the derived equation both can be applied to deal with reservoir engineering calculation in the present.


With the increase in the number of horizontal production wells from 30 in 1986 to ten thousands at present, the prediction of horizontal well productivity has become very important. At the beginning of 1980's, F. M. Giger, L.H. Reiss, Renard and Dupuy derived some equations to predict the horizontal well productivity. In 1981, S. D. Joshi re-derived the equation by using complex potential method. Regardless of an item of 1n [h/(2rw)] in the nominator, which is different from that of 1n[b/(2rw)] in Renard's equation, no difference had been made in the accuracy of the results.

In Joshi's equation, he postulated that the fluid flowing could be divided into vertical flowing and horizontal flowing. In fact, these two parts of flows are mutually perpendicular and mutually contained. But in Joshi's equation, no thought had been directed to the repeated calculation, thus the calculation accuracy was influenced.

In this paper, the equation is corrected by using average efficient permeability and as a result the Calculation error is reduced below 58 percent. Also, a new equation derived from mirror image theory, which can be used to predict precisely the horizontal well productivity in a homogeneous formation, is presented here.

In the developing of reservoir with water in horizontal wells, the main concern is the reduction of production because of the water coning. How to control the water coning is a big technological problem which has been facing petroleum engineers for a long time. Many researchers have spent a great deal of effort in studying the calculation method of critical production rate(3),(5) in horizontal wells with water coning and given their equation respectively. However, based on the same production well data, different equation will give different results, which can cause great trouble to the petroleum engineers in the reservoir calculation. In this paper, a new calculation formulation of critical production is introduced on the basis of further discussion of the concept of critical production and the detail analysis of several calculation formulations which are widely used at present.

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