9 Having computed the front positions the corresponding layer flow rates are obtained by combining the two Darcyequations qiki wiAi ID: 392896
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layered reservoir The Dykstra-Parson«s method applies to a non-communicating layered reservoir, which may be represented schematically as follows: Here, each layer has different height ( side: We may now write Darcy«s equations for this layer as: oil equation (ahead of the front) uoi=!ki"!oi#PoiL!xi (1) water equation (behind the front) uwi=!ki"!wi#Pwixi, (2) layer 1: h1!1k1"S1M1 layer 2: h2!2k2"S2M2 layer N: hN!NkN"SNMN P1 P2 L Water injection Oil and water production Soi=Sori L!xi xi "Poi "Pwi Swi=Swiri !!wi=!krwµw"#$%&'i. For an incompressible system, the two velocities are equal, i.e. ui=uoi=uwi. These Darcy !ki!i"Si"Pxi#"wi+L!xi#"oi ]Mi!1(Mi"1). (12) For the special case of , the integration yields the following expression: � ú x i=12Fiú x R2(1!MR)+2MRú x R[](Mi=1) (13) Finally, for the case of Mi=MR=1, the integration yields the following simple expression: � ú x i=ú x RFi(Mi=MR=1) (14) Equation (14) represents the Stiles Method (see Dake page 410), which is similar to the Dykstra-Parson«s Method, except that it assumes that the end point mobility ratio is 1. Now, based on Equation (12), we would like to find the position of the front in layer i at the time when break-through occurs in layer R. Thus, for � ú x R=1 (break-through in layer R) the expression reduces to (similar to Equation 4.59 in the Monograph, except that here qwi=!ki" # wiAi$PL, A disadvantage is that this expression includes pressure drop and a time term. We will