In a private blockchain, you don't need "mining" in the same sense as a public blockchain like bitcoin. Instead, the network is protected by the need for distributed consensus (or "mining diversity" as we call it) and no difficult computation is required at all. For more information please see the white paper:
http://www.multichain.com/download/MultiChain-White-Paper.pdf
You can set the required mining diversity when creating a blockchain in its params.dat file:
http://www.multichain.com/developers/blockchain-parameters/
