| The productivity of horizontal and multi-branch horizontal wells shows these wells' ability of liquid supply, and it is one of important contents that must be studied by both horizontal reservoir engineering and production engineering. Because there is a distinct difference in the producing procedure between horizontal and multi-branch horizontal wells and vertical wells, and the wide application of these kinds of wells, it is very significative to further the study of the productivity of these wells.Based on the extended studies of the prediction theory references at home and abroad about single-phase and oil gas two phase driven by solution gas related with horizontal and multi-branch horizontal well and aiming at the productivity prediction problems existing in these kinds of wells, the research on single phase steady and non-steady productivity was carried out and the following results were achieved in the paper.This paper took horizontal wells as 3-D line convergence, deduced velocity potential distribution of a single phase steady state percolation of horizontal wells, gained the potentiometric surface equation, and it is proved that its potentiometric surfaces are a bunch of revolving ellipsoids whose focuses are the two ends of the horizontal well. On the basis of above mentioned theories and aiming at some ordinary kinds of reservoirs, a derivation of the zone pressure distribution of 3-D steady state percolation in these reservoirs was achieved according to potential superposition theory and the productivity prediction formulas of the steady state in ordinary kinds of reservoirs were also established.A more reasonable steady state formula in multi-branch horizontal wells was achieved by using the method of conform transformation and the theory of equivalent percolation resistance. Based on the concept of substitution ratio of horizontal well numbers, a new method of calculating productivity of multi-branch horizontal was found by making use of the productivity appraising results of the vertical wells.A coupling model of reservoir and wellbore flow on the condition of steady state was established which can be used to study the influence on the productivity calculation caused by the wellbore pressure drop, another error model of calculating the productivity of horizontal well with the consideration of wellbore pressure drop was also established, and the sensibility analysis of these factors which influence the calculation of horizontal well under the condition of steady state was carried out.The calculating model of optimizing the length of the well was achieved for thetime according to the coupling model of zone and wellbore flow under the condition of steady stale flow. In this model, economic factor was taken into consideration.According to the flowing characteristics of wellbore inner flow of the horizontal well and the theory of mass balance and momentum balance, a general calculating model, in which the single wellbore pressure drop of well-wall inflow along any slope angle was took into consideration, was achieved with the consideration of pressure drop along the wellbore.A non-steady state flowing coupling model of zone and wellbore flow is achieved in this paper. In this model, oil zone inflow (from the earlier instantaneous flow to following pseudo steady state) was dealt with the integrating method with the consideration of instantaneous point source/convergence solution crossed with time and space.On the basis of the non-linear relationship between solution gas drive reservoir and flowing pressure, this paper suggested that productivity model should be established by the numerical simulation method. The influences on 1PR affected by reservoirs themselves, characteristics of liquid and wells were studied through a lot of simulation examples, and change law about the curvature of IPR varying with reservoir average pressure was also synthetized. The general well dimensionless equation on IPR curve was derived according to the non-linear percolation theory. The newly-deriv...
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